Merge branch 'master' into abomonation

.travis.yml

@@ -11,6 +11,12 @@ matrix:
   allow_failures:
     - rust: nightly
     - rust: beta
+addons:
+  apt:
+    packages:
+      - gfortran
+      - libblas3gf
+      - liblapack3gf
 script:
     - rustc --version
     - cargo --version
@@ -19,3 +25,8 @@ script:
     - cargo build --verbose --features serde-serialize
     - cargo build --verbose --features abomonation-serialize
     - cargo test --verbose --features "arbitrary serde-serialize abomonation-serialize"
+    - cd nalgebra-lapack; cargo test --verbose
+
+env:
+  matrix:
+    - CARGO_FEATURE_SYSTEM_NETLIB=1 CARGO_FEATURE_EXCLUDE_LAPACKE=1 CARGO_FEATURE_EXCLUDE_CBLAS=1

CHANGELOG.md

@@ -4,20 +4,117 @@ documented here.
 
 This project adheres to [Semantic Versioning](http://semver.org/).
 
-## [0.13.0] - WIP
+
+## [0.13.0]
+
+The **nalgebra-lapack** crate has been updated. This now includes a broad range
+matrix decompositions using LAPACK bindings.
+
+### Breaking semantic change
+  * The implementation of slicing with steps now matches the documentation.
+    Before, step identified the number to add to pass from one column/row index
+    to the next one. This made 0 step invalid. Now (and on the documentation so
+    far), the step is the number of ignored row/columns between each
+    row/column. Thus, a step of 0 means that no row/column is ignored.  For
+    example, a step of, say, 3 on previous versions should now bet set to 2.
+
+### Modified
+  * The trait `Axpy` has been replaced by a metod `.axpy`.
+  * The alias `MatrixNM` is now deprecated. Use `MatrixMN` instead (we
+    reordered M and N to be in alphabetical order).
+  * In-place componentwise multiplication and division
+    `.component_mul_mut(...)` and `.component_div_mut(...)` have bee deprecated
+    for a future renaming. Use `.component_mul_assign(...)` and
+    `.component_div_assign(...)` instead.
+
 ### Added
+  * `alga::general::Real` is now re-exported by nalgebra.
+    elements.)
+  * `::zeros(...)` that creates a matrix filled with zeroes.
+  * `::from_partial_diagonal(...)` that creates a matrix from diagonal elements.
+    The matrix can be rectangular. If not enough elements are provided, the rest
+    of the diagonal is set to 0.
+  * `.conjugate_transpose()` computes the transposed conjugate of a
+    complex matrix.
+  * `.conjugate_transpose_to(...)` computes the transposed conjugate of a
+    complex matrix. The result written into a user-provided matrix.
+  * `.transpose_to(...)` is the same as `.transpose()` but stores the result in
+    the provided matrix.
+  * `.conjugate_transpose_to(...)` is the same as `.conjugate_transpose()` but
+    stores the result in the provided matrix.
+  * Implements `IntoIterator` for `&Matrix`, `&mut Matrix` and `Matrix`.
+  * `.mul_to(...)` multiplies two matrices and stores the result to the given buffer.
+  * `.tr_mul_to(...)` left-multiplies `self.transpose()` to another matrix and stores the result to the given buffer.
+  * `.add_scalar(...)` that adds a scalar to each component of a matrix.
+  * `.add_scalar_mut(...)` that adds in-place a scalar to each component of a matrix.
   * `.kronecker(a, b)` computes the kronecker product (i.e. matrix tensor
     product) of two matrices.
-  * `.set_row(i, row)` sets the i-th row of the matrix.
-  * `.set_column(j, column)` sets the i-th column of the matrix.
+  * `.apply(f)` replaces each component of a matrix with the results of the
+    closure `f` called on each of them.
 
+Pure Rust implementation of some Blas operations:
+
+  * `.iamax()` retuns the index of the maximum value of a vector.
+  * `.axpy(...)` computes `self = a * x + b * self`.
+  * `.gemv(...)` computes `self = alpha * a * x + beta * self` with a matrix and vector `a` and `x`.
+  * `.ger(...)` computes `self = alpha * x^t * y + beta * self` where `x` and `y` are vectors.
+  * `.gemm(...)` computes `self = alpha * a * b + beta * self` where `a` and `b` are matrices.
+  * `.gemv_symm(...)` is the same as `.gemv` except that `self` is assumed symmetric.
+  * `.ger_symm(...)` is the same as `.ger` except that `self` is assumed symmetric.
+
+New slicing methods:
+  * `.rows_range(...)` that retrieves a reference to a range of rows.
+  * `.rows_range_mut(...)` that retrieves a mutable reference to a range of rows.
+  * `.columns_range(...)` that retrieves a reference to a range of columns.
+  * `.columns_range_mut(...)` that retrieves a mutable reference to a range of columns.
+
+Matrix decompositions implemented in pure Rust:
+  * Cholesky, SVD, LU, QR, Hessenberg, Schur, Symmetric eigendecompositions,
+    Bidiagonal, Symmetric tridiagonal
+  * Computation of householder reflectors and givens rotations.
+
+Matrix edition:
+  * `.upper_triangle()` extracts the upper triangle of a matrix, including the diagonal.
+  * `.lower_triangle()` extracts the lower triangle of a matrix, including the diagonal.
+  * `.fill(...)` fills the matrix with a single value.
+  * `.fill_with_identity(...)` fills the matrix with the identity.
+  * `.fill_diagonal(...)` fills the matrix diagonal with a single value.
+  * `.fill_row(...)` fills a selected matrix row with a single value.
+  * `.fill_column(...)` fills a selected matrix column with a single value.
+  * `.set_diagonal(...)` sets the matrix diagonal.
+  * `.set_row(...)` sets a selected row.
+  * `.set_column(...)` sets a selected column.
+  * `.fill_lower_triangle(...)` fills some sub-diagonals bellow the main diagonal with a value.
+  * `.fill_upper_triangle(...)` fills some sub-diagonals above the main diagonal with a value.
+  * `.swap_rows(...)` swaps two rows.
+  * `.swap_columns(...)` swaps two columns.
+
+Column removal:
+  * `.remove_column(...)` removes one column.
+  * `.remove_fixed_columns<D>(...)` removes `D` columns.
+  * `.remove_columns(...)` removes a number of columns known at run-time.
+
+Row removal:
+  * `.remove_row(...)` removes one row.
+  * `.remove_fixed_rows<D>(...)` removes `D` rows.
+  * `.remove_rows(...)` removes a number of rows known at run-time.
+
+Column insertion:
+  * `.insert_column(...)` adds one column at the given position.
+  * `.insert_fixed_columns<D>(...)` adds `D` columns at the given position.
+  * `.insert_columns(...)` adds at the given position a number of columns known at run-time.
+
+Row insertion:
+  * `.insert_row(...)` adds one row at the given position.
+  * `.insert_fixed_rows<D>(...)` adds `D` rows at the given position.
+  * `.insert_rows(...)` adds at the given position a number of rows known at run-time.
 
 ## [0.12.0]
 The main change of this release is the update of the dependency serde to 1.0.
 
 ### Added
- * `.trace()` that computes the trace of a matrix (i.e., the sum of its
-   diagonal elements.)
+ * `.trace()` that computes the trace of a matrix (the sum of its diagonal
+   elements.)
 
 ## [0.11.0]
 The [website](http://nalgebra.org) has been fully rewritten and gives a good

Cargo.toml

@@ -19,19 +19,20 @@ path = "src/lib.rs"
 arbitrary       = [ "quickcheck" ]
 serde-serialize = [ "serde", "serde_derive", "num-complex/serde" ]
 abomonation-serialize = [ "abomonation" ]
+debug = [ ]
 
 [dependencies]
-typenum         = "1.4"
+typenum        = "1.7"
 generic-array  = "0.8"
 rand           = "0.3"
 num-traits     = "0.1"
 num-complex    = "0.1"
 approx         = "0.1"
 alga           = "0.5"
+matrixmultiply = "0.1"
 serde          = { version = "1.0", optional = true }
 serde_derive   = { version = "1.0", optional = true }
 abomonation     = { version = "0.4", optional = true }
-# clippy = "*"
 
 [dependencies.quickcheck]
 optional = true
@@ -39,3 +40,6 @@ version  = "0.4"
 
 [dev-dependencies]
 serde_json = "1.0"
+
+[workspace]
+members = [ "nalgebra-lapack" ]

Makefile

@@ -1,11 +1,11 @@
 all:
-	CARGO_INCREMENTAL=1 cargo build --features "arbitrary serde-serialize"
+	cargo check --features "debug arbitrary serde-serialize"
 
 doc:
-	CARGO_INCREMENTAL=1 cargo doc --no-deps --features "arbitrary serde-serialize"
+	cargo doc --no-deps --features "debug arbitrary serde-serialize"
 
 bench:
 	cargo bench
 
 test:
-	cargo test --features "arbitrary serde-serialize"
+	cargo test --features "debug arbitrary serde-serialize"

README.md

@@ -24,3 +24,13 @@
 <b>Linear algebra library</b>
 <i>for the Rust programming language.</i>
 </p>
+
+-----
+
+<p align = "center">
+  <i>Click this button if you which to donate to support the development of</i> <b>nalgebra</b>:
+</p>
+
+<p align = "center">
+    <a href="https://www.patreon.com/bePatron?u=7111380" ><img src="https://c5.patreon.com/external/logo/become_a_patron_button.png" alt="Become a Patron!" /></a>
+</p>

benches/common/macros.rs

@@ -4,20 +4,12 @@ macro_rules! bench_binop(
     ($name: ident, $t1: ty, $t2: ty, $binop: ident) => {
         #[bench]
         fn $name(bh: &mut Bencher) {
-            const LEN: usize = 1 << 13;
-
             let mut rng = IsaacRng::new_unseeded();
-
-            let elems1: Vec<$t1> = (0usize .. LEN).map(|_| rng.gen::<$t1>()).collect();
-            let elems2: Vec<$t2> = (0usize .. LEN).map(|_| rng.gen::<$t2>()).collect();
-            let mut i = 0;
+            let a = rng.gen::<$t1>();
+            let b = rng.gen::<$t2>();
 
             bh.iter(|| {
-                i = (i + 1) & (LEN - 1);
-
-                unsafe {
-                    test::black_box(elems1.get_unchecked(i).$binop(*elems2.get_unchecked(i)))
-                }
+                a.$binop(b)
             })
         }
     }
@@ -27,43 +19,27 @@ macro_rules! bench_binop_ref(
     ($name: ident, $t1: ty, $t2: ty, $binop: ident) => {
         #[bench]
         fn $name(bh: &mut Bencher) {
-            const LEN: usize = 1 << 13;
-
             let mut rng = IsaacRng::new_unseeded();
-
-            let elems1: Vec<$t1> = (0usize .. LEN).map(|_| rng.gen::<$t1>()).collect();
-            let elems2: Vec<$t2> = (0usize .. LEN).map(|_| rng.gen::<$t2>()).collect();
-            let mut i = 0;
+            let a = rng.gen::<$t1>();
+            let b = rng.gen::<$t2>();
 
             bh.iter(|| {
-                i = (i + 1) & (LEN - 1);
-
-                unsafe {
-                    test::black_box(elems1.get_unchecked(i).$binop(elems2.get_unchecked(i)))
-                }
+                a.$binop(&b)
             })
         }
     }
 );
 
-macro_rules! bench_binop_na(
-    ($name: ident, $t1: ty, $t2: ty, $binop: ident) => {
+macro_rules! bench_binop_fn(
+    ($name: ident, $t1: ty, $t2: ty, $binop: path) => {
         #[bench]
         fn $name(bh: &mut Bencher) {
-            const LEN: usize = 1 << 13;
-
             let mut rng = IsaacRng::new_unseeded();
-
-            let elems1: Vec<$t1> = (0usize .. LEN).map(|_| rng.gen::<$t1>()).collect();
-            let elems2: Vec<$t2> = (0usize .. LEN).map(|_| rng.gen::<$t2>()).collect();
-            let mut i = 0;
+            let a = rng.gen::<$t1>();
+            let b = rng.gen::<$t2>();
 
             bh.iter(|| {
-                i = (i + 1) & (LEN - 1);
-
-                unsafe {
-                    test::black_box(na::$binop(elems1.get_unchecked(i), elems2.get_unchecked(i)))
-                }
+                $binop(&a, &b)
             })
         }
     }

benches/core/matrix.rs

@@ -0,0 +1,192 @@
+use rand::{IsaacRng, Rng};
+use test::{self, Bencher};
+use na::{Vector2, Vector3, Vector4, Matrix2, Matrix3, Matrix4,
+         MatrixN, U10,
+         DMatrix, DVector};
+use std::ops::{Add, Sub, Mul, Div};
+
+#[path="../common/macros.rs"]
+mod macros;
+
+bench_binop!(mat2_mul_m, Matrix2<f32>, Matrix2<f32>, mul);
+bench_binop!(mat3_mul_m, Matrix3<f32>, Matrix3<f32>, mul);
+bench_binop!(mat4_mul_m, Matrix4<f32>, Matrix4<f32>, mul);
+
+bench_binop_ref!(mat2_tr_mul_m, Matrix2<f32>, Matrix2<f32>, tr_mul);
+bench_binop_ref!(mat3_tr_mul_m, Matrix3<f32>, Matrix3<f32>, tr_mul);
+bench_binop_ref!(mat4_tr_mul_m, Matrix4<f32>, Matrix4<f32>, tr_mul);
+
+bench_binop!(mat2_add_m, Matrix2<f32>, Matrix2<f32>, add);
+bench_binop!(mat3_add_m, Matrix3<f32>, Matrix3<f32>, add);
+bench_binop!(mat4_add_m, Matrix4<f32>, Matrix4<f32>, add);
+
+bench_binop!(mat2_sub_m, Matrix2<f32>, Matrix2<f32>, sub);
+bench_binop!(mat3_sub_m, Matrix3<f32>, Matrix3<f32>, sub);
+bench_binop!(mat4_sub_m, Matrix4<f32>, Matrix4<f32>, sub);
+
+bench_binop!(mat2_mul_v, Matrix2<f32>, Vector2<f32>, mul);
+bench_binop!(mat3_mul_v, Matrix3<f32>, Vector3<f32>, mul);
+bench_binop!(mat4_mul_v, Matrix4<f32>, Vector4<f32>, mul);
+
+bench_binop_ref!(mat2_tr_mul_v, Matrix2<f32>, Vector2<f32>, tr_mul);
+bench_binop_ref!(mat3_tr_mul_v, Matrix3<f32>, Vector3<f32>, tr_mul);
+bench_binop_ref!(mat4_tr_mul_v, Matrix4<f32>, Vector4<f32>, tr_mul);
+
+bench_binop!(mat2_mul_s, Matrix2<f32>, f32, mul);
+bench_binop!(mat3_mul_s, Matrix3<f32>, f32, mul);
+bench_binop!(mat4_mul_s, Matrix4<f32>, f32, mul);
+
+bench_binop!(mat2_div_s, Matrix2<f32>, f32, div);
+bench_binop!(mat3_div_s, Matrix3<f32>, f32, div);
+bench_binop!(mat4_div_s, Matrix4<f32>, f32, div);
+
+bench_unop!(mat2_inv, Matrix2<f32>, try_inverse);
+bench_unop!(mat3_inv, Matrix3<f32>, try_inverse);
+bench_unop!(mat4_inv, Matrix4<f32>, try_inverse);
+
+bench_unop!(mat2_transpose, Matrix2<f32>, transpose);
+bench_unop!(mat3_transpose, Matrix3<f32>, transpose);
+bench_unop!(mat4_transpose, Matrix4<f32>, transpose);
+
+#[bench]
+fn mat_div_scalar(b: &mut Bencher) {
+    let a = DMatrix::from_row_slice(1000, 1000, &vec![2.0;1000000]);
+    let n = 42.0;
+
+    b.iter(|| {
+        let mut aa = a.clone();
+        let mut b = aa.slice_mut((0, 0), (1000, 1000));
+        b /= n
+    })
+}
+
+#[bench]
+fn mat100_add_mat100(bench: &mut Bencher) {
+    let a = DMatrix::<f64>::new_random(100, 100);
+    let b = DMatrix::<f64>::new_random(100, 100);
+
+    bench.iter(|| { &a + &b })
+}
+
+#[bench]
+fn mat4_mul_mat4(bench: &mut Bencher) {
+    let a = DMatrix::<f64>::new_random(4, 4);
+    let b = DMatrix::<f64>::new_random(4, 4);
+
+    bench.iter(|| { &a * &b })
+}
+
+#[bench]
+fn mat5_mul_mat5(bench: &mut Bencher) {
+    let a = DMatrix::<f64>::new_random(5, 5);
+    let b = DMatrix::<f64>::new_random(5, 5);
+
+    bench.iter(|| { &a * &b })
+}
+
+#[bench]
+fn mat6_mul_mat6(bench: &mut Bencher) {
+    let a = DMatrix::<f64>::new_random(6, 6);
+    let b = DMatrix::<f64>::new_random(6, 6);
+
+    bench.iter(|| { &a * &b })
+}
+
+#[bench]
+fn mat7_mul_mat7(bench: &mut Bencher) {
+    let a = DMatrix::<f64>::new_random(7, 7);
+    let b = DMatrix::<f64>::new_random(7, 7);
+
+    bench.iter(|| { &a * &b })
+}
+
+#[bench]
+fn mat8_mul_mat8(bench: &mut Bencher) {
+    let a = DMatrix::<f64>::new_random(8, 8);
+    let b = DMatrix::<f64>::new_random(8, 8);
+
+    bench.iter(|| { &a * &b })
+}
+
+#[bench]
+fn mat9_mul_mat9(bench: &mut Bencher) {
+    let a = DMatrix::<f64>::new_random(9, 9);
+    let b = DMatrix::<f64>::new_random(9, 9);
+
+    bench.iter(|| { &a * &b })
+}
+
+#[bench]
+fn mat10_mul_mat10(bench: &mut Bencher) {
+    let a = DMatrix::<f64>::new_random(10, 10);
+    let b = DMatrix::<f64>::new_random(10, 10);
+
+    bench.iter(|| { &a * &b })
+}
+
+#[bench]
+fn mat10_mul_mat10_static(bench: &mut Bencher) {
+    let a = MatrixN::<f64, U10>::new_random();
+    let b = MatrixN::<f64, U10>::new_random();
+
+    bench.iter(|| { &a * &b })
+}
+
+#[bench]
+fn mat100_mul_mat100(bench: &mut Bencher) {
+    let a = DMatrix::<f64>::new_random(100, 100);
+    let b = DMatrix::<f64>::new_random(100, 100);
+
+    bench.iter(|| { &a * &b })
+}
+
+#[bench]
+fn mat500_mul_mat500(bench: &mut Bencher) {
+    let a = DMatrix::<f64>::from_element(500, 500, 5f64);
+    let b = DMatrix::<f64>::from_element(500, 500, 6f64);
+
+    bench.iter(|| { &a * &b })
+}
+
+#[bench]
+fn copy_from(bench: &mut Bencher) {
+    let a = DMatrix::<f64>::new_random(1000, 1000);
+    let mut b = DMatrix::<f64>::new_random(1000, 1000);
+
+    bench.iter(|| {
+        b.copy_from(&a);
+    })
+}
+
+#[bench]
+fn axpy(bench: &mut Bencher) {
+    let x = DVector::<f64>::from_element(100000, 2.0);
+    let mut y = DVector::<f64>::from_element(100000, 3.0);
+    let a = 42.0;
+
+    bench.iter(|| {
+        y.axpy(a, &x, 1.0);
+    })
+}
+
+#[bench]
+fn tr_mul_to(bench: &mut Bencher) {
+    let a = DMatrix::<f64>::new_random(1000, 1000);
+    let b = DVector::<f64>::new_random(1000);
+    let mut c = DVector::from_element(1000, 0.0);
+
+    bench.iter(|| {
+        a.tr_mul_to(&b, &mut c)
+    })
+}
+
+#[bench]
+fn mat_mul_mat(bench: &mut Bencher) {
+    let a = DMatrix::<f64>::new_random(100, 100);
+    let b = DMatrix::<f64>::new_random(100, 100);
+    let mut ab = DMatrix::<f64>::from_element(100, 100, 0.0);
+
+    bench.iter(|| {
+        test::black_box(a.mul_to(&b, &mut ab));
+    })
+}

benches/core/mod.rs

@@ -0,0 +1,2 @@
+mod matrix;
+mod vector;

benches/core/vector.rs

@@ -0,0 +1,128 @@
+use rand::{IsaacRng, Rng};
+use test::{self, Bencher};
+use typenum::U10000;
+use na::{Vector2, Vector3, Vector4, VectorN, DVector};
+use std::ops::{Add, Sub, Mul, Div};
+
+#[path="../common/macros.rs"]
+mod macros;
+
+bench_binop!(vec2_add_v_f32, Vector2<f32>, Vector2<f32>, add);
+bench_binop!(vec3_add_v_f32, Vector3<f32>, Vector3<f32>, add);
+bench_binop!(vec4_add_v_f32, Vector4<f32>, Vector4<f32>, add);
+
+bench_binop!(vec2_add_v_f64, Vector2<f64>, Vector2<f64>, add);
+bench_binop!(vec3_add_v_f64, Vector3<f64>, Vector3<f64>, add);
+bench_binop!(vec4_add_v_f64, Vector4<f64>, Vector4<f64>, add);
+
+bench_binop!(vec2_sub_v, Vector2<f32>, Vector2<f32>, sub);
+bench_binop!(vec3_sub_v, Vector3<f32>, Vector3<f32>, sub);
+bench_binop!(vec4_sub_v, Vector4<f32>, Vector4<f32>, sub);
+
+bench_binop!(vec2_mul_s, Vector2<f32>, f32, mul);
+bench_binop!(vec3_mul_s, Vector3<f32>, f32, mul);
+bench_binop!(vec4_mul_s, Vector4<f32>, f32, mul);
+
+bench_binop!(vec2_div_s, Vector2<f32>, f32, div);
+bench_binop!(vec3_div_s, Vector3<f32>, f32, div);
+bench_binop!(vec4_div_s, Vector4<f32>, f32, div);
+
+bench_binop_ref!(vec2_dot_f32, Vector2<f32>, Vector2<f32>, dot);
+bench_binop_ref!(vec3_dot_f32, Vector3<f32>, Vector3<f32>, dot);
+bench_binop_ref!(vec4_dot_f32, Vector4<f32>, Vector4<f32>, dot);
+
+bench_binop_ref!(vec2_dot_f64, Vector2<f64>, Vector2<f64>, dot);
+bench_binop_ref!(vec3_dot_f64, Vector3<f64>, Vector3<f64>, dot);
+bench_binop_ref!(vec4_dot_f64, Vector4<f64>, Vector4<f64>, dot);
+
+bench_binop_ref!(vec3_cross, Vector3<f32>, Vector3<f32>, cross);
+
+bench_unop!(vec2_norm, Vector2<f32>, norm);
+bench_unop!(vec3_norm, Vector3<f32>, norm);
+bench_unop!(vec4_norm, Vector4<f32>, norm);
+
+bench_unop!(vec2_normalize, Vector2<f32>, normalize);
+bench_unop!(vec3_normalize, Vector3<f32>, normalize);
+bench_unop!(vec4_normalize, Vector4<f32>, normalize);
+
+bench_binop_ref!(vec10000_dot_f64, VectorN<f64, U10000>, VectorN<f64, U10000>, dot);
+bench_binop_ref!(vec10000_dot_f32, VectorN<f32, U10000>, VectorN<f32, U10000>, dot);
+
+#[bench]
+fn vec10000_axpy_f64(bh: &mut Bencher) {
+    let mut rng = IsaacRng::new_unseeded();
+    let mut a = DVector::new_random(10000);
+    let b = DVector::new_random(10000);
+    let n = rng.gen::<f64>();
+
+    bh.iter(|| {
+        a.axpy(n, &b, 1.0)
+    })
+}
+
+#[bench]
+fn vec10000_axpy_beta_f64(bh: &mut Bencher) {
+    let mut rng = IsaacRng::new_unseeded();
+    let mut a = DVector::new_random(10000);
+    let b = DVector::new_random(10000);
+    let n = rng.gen::<f64>();
+    let beta = rng.gen::<f64>();
+
+    bh.iter(|| {
+        a.axpy(n, &b, beta)
+    })
+}
+
+#[bench]
+fn vec10000_axpy_f64_slice(bh: &mut Bencher) {
+    let mut rng = IsaacRng::new_unseeded();
+    let mut a = DVector::new_random(10000);
+    let b = DVector::new_random(10000);
+    let n = rng.gen::<f64>();
+
+    bh.iter(|| {
+        let mut a = a.fixed_rows_mut::<U10000>(0);
+        let b = b.fixed_rows::<U10000>(0);
+
+        a.axpy(n, &b, 1.0)
+    })
+}
+
+#[bench]
+fn vec10000_axpy_f64_static(bh: &mut Bencher) {
+    let mut rng = IsaacRng::new_unseeded();
+    let mut a = VectorN::<f64, U10000>::new_random();
+    let b = VectorN::<f64, U10000>::new_random();
+    let n = rng.gen::<f64>();
+
+    // NOTE: for some reasons, it is much faster if the arument are boxed (Box::new(VectorN...)).
+    bh.iter(|| {
+        a.axpy(n, &b, 1.0)
+    })
+}
+
+
+#[bench]
+fn vec10000_axpy_f32(bh: &mut Bencher) {
+    let mut rng = IsaacRng::new_unseeded();
+    let mut a = DVector::new_random(10000);
+    let b = DVector::new_random(10000);
+    let n = rng.gen::<f32>();
+
+    bh.iter(|| {
+        a.axpy(n, &b, 1.0)
+    })
+}
+
+#[bench]
+fn vec10000_axpy_beta_f32(bh: &mut Bencher) {
+    let mut rng = IsaacRng::new_unseeded();
+    let mut a = DVector::new_random(10000);
+    let b = DVector::new_random(10000);
+    let n = rng.gen::<f32>();
+    let beta = rng.gen::<f32>();
+
+    bh.iter(|| {
+        a.axpy(n, &b, beta)
+    })
+}

benches/geometry/mod.rs

@@ -0,0 +1 @@
+mod quaternion;

benches/geometry/quaternion.rs

@@ -0,0 +1,22 @@
+use rand::{IsaacRng, Rng};
+use test::{self, Bencher};
+use na::{Quaternion, UnitQuaternion, Vector3};
+use std::ops::{Add, Sub, Mul, Div};
+
+#[path="../common/macros.rs"]
+mod macros;
+
+bench_binop!(quaternion_add_q, Quaternion<f32>, Quaternion<f32>, add);
+bench_binop!(quaternion_sub_q, Quaternion<f32>, Quaternion<f32>, sub);
+bench_binop!(quaternion_mul_q, Quaternion<f32>, Quaternion<f32>, mul);
+
+bench_binop!(unit_quaternion_mul_v, UnitQuaternion<f32>, Vector3<f32>, mul);
+
+bench_binop!(quaternion_mul_s, Quaternion<f32>, f32, mul);
+bench_binop!(quaternion_div_s, Quaternion<f32>, f32, div);
+
+bench_unop!(quaternion_inv, Quaternion<f32>, try_inverse);
+bench_unop!(unit_quaternion_inv, UnitQuaternion<f32>, inverse);
+
+// bench_unop_self!(quaternion_conjugate, Quaternion<f32>, conjugate);
+// bench_unop!(quaternion_normalize, Quaternion<f32>, normalize);

benches/lib.rs

@@ -0,0 +1,21 @@
+#![feature(test)]
+#![allow(unused_macros)]
+
+extern crate test;
+extern crate rand;
+extern crate typenum;
+extern crate nalgebra as na;
+
+
+use rand::{Rng, IsaacRng};
+use na::DMatrix;
+
+
+mod core;
+mod linalg;
+mod geometry;
+
+fn reproductible_dmatrix(nrows: usize, ncols: usize) -> DMatrix<f64> {
+    let mut rng = IsaacRng::new_unseeded();
+    DMatrix::<f64>::from_fn(nrows, ncols, |_, _| rng.gen())
+}

benches/linalg/bidiagonal.rs

@@ -0,0 +1,75 @@
+use test::{self, Bencher};
+use na::{Matrix4, DMatrix, Bidiagonal};
+
+#[path="../common/macros.rs"]
+mod macros;
+
+// Without unpack.
+#[bench]
+fn bidiagonalize_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    bh.iter(|| test::black_box(Bidiagonal::new(m.clone())))
+}
+
+#[bench]
+fn bidiagonalize_100x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 500);
+    bh.iter(|| test::black_box(Bidiagonal::new(m.clone())))
+}
+
+#[bench]
+fn bidiagonalize_4x4(bh: &mut Bencher) {
+    let m = Matrix4::<f64>::new_random();
+    bh.iter(|| test::black_box(Bidiagonal::new(m.clone())))
+}
+
+#[bench]
+fn bidiagonalize_500x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 100);
+    bh.iter(|| test::black_box(Bidiagonal::new(m.clone())))
+}
+
+#[bench]
+fn bidiagonalize_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+    bh.iter(|| test::black_box(Bidiagonal::new(m.clone())))
+}
+
+
+// With unpack.
+#[bench]
+fn bidiagonalize_unpack_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    bh.iter(|| {
+        let bidiag = Bidiagonal::new(m.clone());
+        let _ = bidiag.unpack();
+    })
+}
+
+#[bench]
+fn bidiagonalize_unpack_100x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 500);
+    bh.iter(|| {
+        let bidiag = Bidiagonal::new(m.clone());
+        let _ = bidiag.unpack();
+    })
+}
+
+#[bench]
+fn bidiagonalize_unpack_500x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 100);
+    bh.iter(|| {
+        let bidiag = Bidiagonal::new(m.clone());
+        let _ = bidiag.unpack();
+    })
+}
+
+#[bench]
+fn bidiagonalize_unpack_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+    bh.iter(|| {
+        let bidiag = Bidiagonal::new(m.clone());
+        let _ = bidiag.unpack();
+    })
+}
+

benches/linalg/cholesky.rs

@@ -0,0 +1,109 @@
+use test::{self, Bencher};
+use na::{DMatrix, DVector, Cholesky};
+
+#[bench]
+fn cholesky_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    let m = &m * m.transpose();
+
+    bh.iter(|| test::black_box(Cholesky::new(m.clone())))
+}
+
+#[bench]
+fn cholesky_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+    let m = &m * m.transpose();
+
+    bh.iter(|| test::black_box(Cholesky::new(m.clone())))
+}
+
+// With unpack.
+#[bench]
+fn cholesky_decompose_unpack_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    let m = &m * m.transpose();
+
+    bh.iter(|| {
+        let chol = Cholesky::new(m.clone()).unwrap();
+        let _ = chol.unpack();
+    })
+}
+#[bench]
+fn cholesky_decompose_unpack_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+    let m = &m * m.transpose();
+
+    bh.iter(|| {
+        let chol = Cholesky::new(m.clone()).unwrap();
+        let _ = chol.unpack();
+    })
+}
+
+#[bench]
+fn cholesky_solve_10x10(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(10, 10);
+    let m = &m * m.transpose();
+    let v = DVector::<f64>::new_random(10);
+    let chol = Cholesky::new(m.clone()).unwrap();
+
+    bh.iter(|| {
+        let _ = chol.solve(&v);
+    })
+}
+
+#[bench]
+fn cholesky_solve_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    let m = &m * m.transpose();
+    let v = DVector::<f64>::new_random(100);
+    let chol = Cholesky::new(m.clone()).unwrap();
+
+    bh.iter(|| {
+        let _ = chol.solve(&v);
+    })
+}
+
+#[bench]
+fn cholesky_solve_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+    let m = &m * m.transpose();
+    let v = DVector::<f64>::new_random(500);
+    let chol = Cholesky::new(m.clone()).unwrap();
+
+    bh.iter(|| {
+        let _ = chol.solve(&v);
+    })
+}
+
+#[bench]
+fn cholesky_inverse_10x10(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(10, 10);
+    let m = &m * m.transpose();
+    let chol = Cholesky::new(m.clone()).unwrap();
+
+    bh.iter(|| {
+        let _ = chol.inverse();
+    })
+}
+
+#[bench]
+fn cholesky_inverse_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    let m = &m * m.transpose();
+    let chol = Cholesky::new(m.clone()).unwrap();
+
+    bh.iter(|| {
+        let _ = chol.inverse();
+    })
+}
+
+#[bench]
+fn cholesky_inverse_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+    let m = &m * m.transpose();
+    let chol = Cholesky::new(m.clone()).unwrap();
+
+    bh.iter(|| {
+        let _ = chol.inverse();
+    })
+}

benches/linalg/eigen.rs

@@ -0,0 +1,30 @@
+use test::Bencher;
+use na::{DMatrix, Eigen};
+
+#[bench]
+fn eigen_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+
+    bh.iter(|| Eigen::new(m.clone(), 1.0e-7, 0))
+}
+
+#[bench]
+fn eigen_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+
+    bh.iter(|| Eigen::new(m.clone(), 1.0e-7, 0))
+}
+
+#[bench]
+fn eigenvalues_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+
+    bh.iter(|| m.clone().eigenvalues(1.0e-7, 0))
+}
+
+#[bench]
+fn eigenvalues_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+
+    bh.iter(|| m.clone().eigenvalues(1.0e-7, 0))
+}

benches/linalg/full_piv_lu.rs

@@ -0,0 +1,114 @@
+use test::{self, Bencher};
+use na::{DMatrix, DVector, FullPivLU};
+
+// Without unpack.
+#[bench]
+fn full_piv_lu_decompose_10x10(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(10, 10);
+    bh.iter(|| test::black_box(FullPivLU::new(m.clone())))
+}
+
+#[bench]
+fn full_piv_lu_decompose_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    bh.iter(|| test::black_box(FullPivLU::new(m.clone())))
+}
+
+#[bench]
+fn full_piv_lu_decompose_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+    bh.iter(|| test::black_box(FullPivLU::new(m.clone())))
+}
+
+#[bench]
+fn full_piv_lu_solve_10x10(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(10, 10);
+    let lu = FullPivLU::new(m.clone());
+
+    bh.iter(|| {
+        let mut b = DVector::<f64>::from_element(10, 1.0);
+        lu.solve(&mut b);
+    })
+}
+
+#[bench]
+fn full_piv_lu_solve_100x100(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(100, 100);
+    let lu = FullPivLU::new(m.clone());
+
+    bh.iter(|| {
+        let mut b = DVector::<f64>::from_element(100, 1.0);
+        lu.solve(&mut b);
+    })
+}
+
+#[bench]
+fn full_piv_lu_solve_500x500(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(500, 500);
+    let lu = FullPivLU::new(m.clone());
+
+    bh.iter(|| {
+        let mut b = DVector::<f64>::from_element(500, 1.0);
+        lu.solve(&mut b);
+    })
+}
+
+#[bench]
+fn full_piv_lu_inverse_10x10(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(10, 10);
+    let lu = FullPivLU::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(lu.try_inverse())
+    })
+}
+
+#[bench]
+fn full_piv_lu_inverse_100x100(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(100, 100);
+    let lu = FullPivLU::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(lu.try_inverse())
+    })
+}
+
+#[bench]
+fn full_piv_lu_inverse_500x500(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(500, 500);
+    let lu = FullPivLU::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(lu.try_inverse())
+    })
+}
+
+#[bench]
+fn full_piv_lu_determinant_10x10(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(10, 10);
+    let lu = FullPivLU::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(lu.determinant())
+    })
+}
+
+#[bench]
+fn full_piv_lu_determinant_100x100(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(100, 100);
+    let lu = FullPivLU::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(lu.determinant())
+    })
+}
+
+#[bench]
+fn full_piv_lu_determinant_500x500(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(500, 500);
+    let lu = FullPivLU::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(lu.determinant())
+    })
+}

benches/linalg/hessenberg.rs

@@ -0,0 +1,60 @@
+use test::{self, Bencher};
+use na::{Matrix4, DMatrix, Hessenberg};
+
+#[path="../common/macros.rs"]
+mod macros;
+
+// Without unpack.
+#[bench]
+fn hessenberg_decompose_4x4(bh: &mut Bencher) {
+    let m = Matrix4::<f64>::new_random();
+    bh.iter(|| test::black_box(Hessenberg::new(m.clone())))
+}
+
+#[bench]
+fn hessenberg_decompose_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    bh.iter(|| test::black_box(Hessenberg::new(m.clone())))
+}
+
+#[bench]
+fn hessenberg_decompose_200x200(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(200, 200);
+    bh.iter(|| test::black_box(Hessenberg::new(m.clone())))
+}
+
+
+#[bench]
+fn hessenberg_decompose_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+    bh.iter(|| test::black_box(Hessenberg::new(m.clone())))
+}
+
+
+// With unpack.
+#[bench]
+fn hessenberg_decompose_unpack_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    bh.iter(|| {
+        let hess = Hessenberg::new(m.clone());
+        let _ = hess.unpack();
+    })
+}
+
+#[bench]
+fn hessenberg_decompose_unpack_200x200(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(200, 200);
+    bh.iter(|| {
+        let hess = Hessenberg::new(m.clone());
+        let _ = hess.unpack();
+    })
+}
+
+#[bench]
+fn hessenberg_decompose_unpack_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+    bh.iter(|| {
+        let hess = Hessenberg::new(m.clone());
+        let _ = hess.unpack();
+    })
+}

benches/linalg/lu.rs

@@ -0,0 +1,114 @@
+use test::{self, Bencher};
+use na::{DMatrix, DVector, LU};
+
+// Without unpack.
+#[bench]
+fn lu_decompose_10x10(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(10, 10);
+    bh.iter(|| test::black_box(LU::new(m.clone())))
+}
+
+#[bench]
+fn lu_decompose_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    bh.iter(|| test::black_box(LU::new(m.clone())))
+}
+
+#[bench]
+fn lu_decompose_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+    bh.iter(|| test::black_box(LU::new(m.clone())))
+}
+
+#[bench]
+fn lu_solve_10x10(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(10, 10);
+    let lu = LU::new(m.clone());
+
+    bh.iter(|| {
+        let mut b = DVector::<f64>::from_element(10, 1.0);
+        lu.solve(&mut b);
+    })
+}
+
+#[bench]
+fn lu_solve_100x100(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(100, 100);
+    let lu = LU::new(m.clone());
+
+    bh.iter(|| {
+        let mut b = DVector::<f64>::from_element(100, 1.0);
+        lu.solve(&mut b);
+    })
+}
+
+#[bench]
+fn lu_solve_500x500(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(500, 500);
+    let lu = LU::new(m.clone());
+
+    bh.iter(|| {
+        let mut b = DVector::<f64>::from_element(500, 1.0);
+        lu.solve(&mut b);
+    })
+}
+
+#[bench]
+fn lu_inverse_10x10(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(10, 10);
+    let lu = LU::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(lu.try_inverse())
+    })
+}
+
+#[bench]
+fn lu_inverse_100x100(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(100, 100);
+    let lu = LU::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(lu.try_inverse())
+    })
+}
+
+#[bench]
+fn lu_inverse_500x500(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(500, 500);
+    let lu = LU::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(lu.try_inverse())
+    })
+}
+
+#[bench]
+fn lu_determinant_10x10(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(10, 10);
+    let lu = LU::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(lu.determinant())
+    })
+}
+
+#[bench]
+fn lu_determinant_100x100(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(100, 100);
+    let lu = LU::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(lu.determinant())
+    })
+}
+
+#[bench]
+fn lu_determinant_500x500(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(500, 500);
+    let lu = LU::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(lu.determinant())
+    })
+}

benches/linalg/mod.rs

@@ -0,0 +1,11 @@
+mod solve;
+mod cholesky;
+mod qr;
+mod hessenberg;
+mod bidiagonal;
+mod lu;
+mod full_piv_lu;
+mod svd;
+mod schur;
+mod symmetric_eigen;
+// mod eigen;

benches/linalg/qr.rs

@@ -0,0 +1,137 @@
+use test::{self, Bencher};
+use na::{Matrix4, DMatrix, DVector, QR};
+
+#[path="../common/macros.rs"]
+mod macros;
+
+// Without unpack.
+#[bench]
+fn qr_decompose_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    bh.iter(|| test::black_box(QR::new(m.clone())))
+}
+
+#[bench]
+fn qr_decompose_100x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 500);
+    bh.iter(|| test::black_box(QR::new(m.clone())))
+}
+
+#[bench]
+fn qr_decompose_4x4(bh: &mut Bencher) {
+    let m = Matrix4::<f64>::new_random();
+    bh.iter(|| test::black_box(QR::new(m.clone())))
+}
+
+#[bench]
+fn qr_decompose_500x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 100);
+    bh.iter(|| test::black_box(QR::new(m.clone())))
+}
+
+#[bench]
+fn qr_decompose_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+    bh.iter(|| test::black_box(QR::new(m.clone())))
+}
+
+
+// With unpack.
+#[bench]
+fn qr_decompose_unpack_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    bh.iter(|| {
+        let qr = QR::new(m.clone());
+        let _ = qr.unpack();
+    })
+}
+
+#[bench]
+fn qr_decompose_unpack_100x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 500);
+    bh.iter(|| {
+        let qr = QR::new(m.clone());
+        let _ = qr.unpack();
+    })
+}
+
+#[bench]
+fn qr_decompose_unpack_500x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 100);
+    bh.iter(|| {
+        let qr = QR::new(m.clone());
+        let _ = qr.unpack();
+    })
+}
+
+#[bench]
+fn qr_decompose_unpack_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+    bh.iter(|| {
+        let qr = QR::new(m.clone());
+        let _ = qr.unpack();
+    })
+}
+
+#[bench]
+fn qr_solve_10x10(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(10, 10);
+    let qr = QR::new(m.clone());
+
+    bh.iter(|| {
+        let mut b = DVector::<f64>::from_element(10, 1.0);
+        qr.solve(&mut b);
+    })
+}
+
+#[bench]
+fn qr_solve_100x100(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(100, 100);
+    let qr = QR::new(m.clone());
+
+    bh.iter(|| {
+        let mut b = DVector::<f64>::from_element(100, 1.0);
+        qr.solve(&mut b);
+    })
+}
+
+#[bench]
+fn qr_solve_500x500(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(500, 500);
+    let qr = QR::new(m.clone());
+
+    bh.iter(|| {
+        let mut b = DVector::<f64>::from_element(500, 1.0);
+        qr.solve(&mut b);
+    })
+}
+
+#[bench]
+fn qr_inverse_10x10(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(10, 10);
+    let qr = QR::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(qr.try_inverse())
+    })
+}
+
+#[bench]
+fn qr_inverse_100x100(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(100, 100);
+    let qr = QR::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(qr.try_inverse())
+    })
+}
+
+#[bench]
+fn qr_inverse_500x500(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(500, 500);
+    let qr = QR::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(qr.try_inverse())
+    })
+}

benches/linalg/schur.rs

@@ -0,0 +1,51 @@
+use test::{self, Bencher};
+use na::{Matrix4, RealSchur};
+
+#[bench]
+fn schur_decompose_4x4(bh: &mut Bencher) {
+    let m = Matrix4::<f64>::new_random();
+    bh.iter(|| test::black_box(RealSchur::new(m.clone())))
+}
+
+#[bench]
+fn schur_decompose_10x10(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(10, 10);
+    bh.iter(|| test::black_box(RealSchur::new(m.clone())))
+}
+
+
+#[bench]
+fn schur_decompose_100x100(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(100, 100);
+    bh.iter(|| test::black_box(RealSchur::new(m.clone())))
+}
+
+#[bench]
+fn schur_decompose_200x200(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(200, 200);
+    bh.iter(|| test::black_box(RealSchur::new(m.clone())))
+}
+
+#[bench]
+fn eigenvalues_4x4(bh: &mut Bencher) {
+    let m = Matrix4::<f64>::new_random();
+    bh.iter(|| test::black_box(m.complex_eigenvalues()))
+}
+
+#[bench]
+fn eigenvalues_10x10(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(10, 10);
+    bh.iter(|| test::black_box(m.complex_eigenvalues()))
+}
+
+#[bench]
+fn eigenvalues_100x100(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(100, 100);
+    bh.iter(|| test::black_box(m.complex_eigenvalues()))
+}
+
+#[bench]
+fn eigenvalues_200x200(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(200, 200);
+    bh.iter(|| test::black_box(m.complex_eigenvalues()))
+}

benches/linalg/solve.rs

@@ -0,0 +1,82 @@
+use test::Bencher;
+use na::{DMatrix, DVector};
+
+#[bench]
+fn solve_l_triangular_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    let v = DVector::<f64>::new_random(100);
+
+    bh.iter(|| {
+        let _ = m.solve_lower_triangular(&v);
+    })
+}
+
+#[bench]
+fn solve_l_triangular_1000x1000(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(1000, 1000);
+    let v = DVector::<f64>::new_random(1000);
+
+    bh.iter(|| {
+        let _ = m.solve_lower_triangular(&v);
+    })
+}
+
+#[bench]
+fn tr_solve_l_triangular_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    let v = DVector::<f64>::new_random(100);
+
+    bh.iter(|| {
+        let _ = m.tr_solve_lower_triangular(&v);
+    })
+}
+
+#[bench]
+fn tr_solve_l_triangular_1000x1000(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(1000, 1000);
+    let v = DVector::<f64>::new_random(1000);
+
+    bh.iter(|| {
+        let _ = m.tr_solve_lower_triangular(&v);
+    })
+}
+
+#[bench]
+fn solve_u_triangular_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    let v = DVector::<f64>::new_random(100);
+
+    bh.iter(|| {
+        let _ = m.solve_upper_triangular(&v);
+    })
+}
+
+#[bench]
+fn solve_u_triangular_1000x1000(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(1000, 1000);
+    let v = DVector::<f64>::new_random(1000);
+
+    bh.iter(|| {
+        let _ = m.solve_upper_triangular(&v);
+    })
+}
+
+#[bench]
+fn tr_solve_u_triangular_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    let v = DVector::<f64>::new_random(100);
+
+    bh.iter(|| {
+        let _ = m.tr_solve_upper_triangular(&v);
+    })
+}
+
+#[bench]
+fn tr_solve_u_triangular_1000x1000(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(1000, 1000);
+    let v = DVector::<f64>::new_random(1000);
+
+    bh.iter(|| {
+        let _ = m.tr_solve_upper_triangular(&v);
+    })
+}

benches/linalg/svd.rs

@@ -0,0 +1,99 @@
+use test::{self, Bencher};
+use na::{Matrix4, SVD};
+
+#[bench]
+fn svd_decompose_4x4(bh: &mut Bencher) {
+    let m = Matrix4::<f64>::new_random();
+    bh.iter(|| test::black_box(SVD::new(m.clone(), true, true)))
+}
+
+#[bench]
+fn svd_decompose_10x10(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(10, 10);
+    bh.iter(|| test::black_box(SVD::new(m.clone(), true, true)))
+}
+
+#[bench]
+fn svd_decompose_100x100(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(100, 100);
+    bh.iter(|| test::black_box(SVD::new(m.clone(), true, true)))
+}
+
+#[bench]
+fn svd_decompose_200x200(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(200, 200);
+    bh.iter(|| test::black_box(SVD::new(m.clone(), true, true)))
+}
+
+#[bench]
+fn rank_4x4(bh: &mut Bencher) {
+    let m = Matrix4::<f64>::new_random();
+    bh.iter(|| test::black_box(m.rank(1.0e-10)))
+}
+
+#[bench]
+fn rank_10x10(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(10, 10);
+    bh.iter(|| test::black_box(m.rank(1.0e-10)))
+}
+
+#[bench]
+fn rank_100x100(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(100, 100);
+    bh.iter(|| test::black_box(m.rank(1.0e-10)))
+}
+
+#[bench]
+fn rank_200x200(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(200, 200);
+    bh.iter(|| test::black_box(m.rank(1.0e-10)))
+}
+
+#[bench]
+fn singular_values_4x4(bh: &mut Bencher) {
+    let m = Matrix4::<f64>::new_random();
+    bh.iter(|| test::black_box(m.singular_values()))
+}
+
+#[bench]
+fn singular_values_10x10(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(10, 10);
+    bh.iter(|| test::black_box(m.singular_values()))
+}
+
+#[bench]
+fn singular_values_100x100(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(100, 100);
+    bh.iter(|| test::black_box(m.singular_values()))
+}
+
+#[bench]
+fn singular_values_200x200(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(200, 200);
+    bh.iter(|| test::black_box(m.singular_values()))
+}
+
+
+#[bench]
+fn pseudo_inverse_4x4(bh: &mut Bencher) {
+    let m = Matrix4::<f64>::new_random();
+    bh.iter(|| test::black_box(m.clone().pseudo_inverse(1.0e-10)))
+}
+
+#[bench]
+fn pseudo_inverse_10x10(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(10, 10);
+    bh.iter(|| test::black_box(m.clone().pseudo_inverse(1.0e-10)))
+}
+
+#[bench]
+fn pseudo_inverse_100x100(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(100, 100);
+    bh.iter(|| test::black_box(m.clone().pseudo_inverse(1.0e-10)))
+}
+
+#[bench]
+fn pseudo_inverse_200x200(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(200, 200);
+    bh.iter(|| test::black_box(m.clone().pseudo_inverse(1.0e-10)))
+}

benches/linalg/symmetric_eigen.rs

@@ -0,0 +1,27 @@
+use test::{self, Bencher};
+use na::{Matrix4, SymmetricEigen};
+
+#[bench]
+fn symmetric_eigen_decompose_4x4(bh: &mut Bencher) {
+    let m = Matrix4::<f64>::new_random();
+    bh.iter(|| test::black_box(SymmetricEigen::new(m.clone())))
+}
+
+#[bench]
+fn symmetric_eigen_decompose_10x10(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(10, 10);
+    bh.iter(|| test::black_box(SymmetricEigen::new(m.clone())))
+}
+
+
+#[bench]
+fn symmetric_eigen_decompose_100x100(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(100, 100);
+    bh.iter(|| test::black_box(SymmetricEigen::new(m.clone())))
+}
+
+#[bench]
+fn symmetric_eigen_decompose_200x200(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(200, 200);
+    bh.iter(|| test::black_box(SymmetricEigen::new(m.clone())))
+}

benches/matrix.rs

@@ -1,53 +0,0 @@
-#![feature(test)]
-
-extern crate test;
-extern crate rand;
-extern crate nalgebra as na;
-
-use rand::{IsaacRng, Rng};
-use test::Bencher;
-use na::{Vector2, Vector3, Vector4, Matrix2, Matrix3, Matrix4};
-use std::ops::{Add, Sub, Mul, Div};
-
-#[path="common/macros.rs"]
-mod macros;
-
-bench_binop!(_bench_mat2_mul_m, Matrix2<f32>, Matrix2<f32>, mul);
-bench_binop!(_bench_mat3_mul_m, Matrix3<f32>, Matrix3<f32>, mul);
-bench_binop!(_bench_mat4_mul_m, Matrix4<f32>, Matrix4<f32>, mul);
-
-bench_binop_ref!(_bench_mat2_tr_mul_m, Matrix2<f32>, Matrix2<f32>, tr_mul);
-bench_binop_ref!(_bench_mat3_tr_mul_m, Matrix3<f32>, Matrix3<f32>, tr_mul);
-bench_binop_ref!(_bench_mat4_tr_mul_m, Matrix4<f32>, Matrix4<f32>, tr_mul);
-
-bench_binop!(_bench_mat2_add_m, Matrix2<f32>, Matrix2<f32>, add);
-bench_binop!(_bench_mat3_add_m, Matrix3<f32>, Matrix3<f32>, add);
-bench_binop!(_bench_mat4_add_m, Matrix4<f32>, Matrix4<f32>, add);
-
-bench_binop!(_bench_mat2_sub_m, Matrix2<f32>, Matrix2<f32>, sub);
-bench_binop!(_bench_mat3_sub_m, Matrix3<f32>, Matrix3<f32>, sub);
-bench_binop!(_bench_mat4_sub_m, Matrix4<f32>, Matrix4<f32>, sub);
-
-bench_binop!(_bench_mat2_mul_v, Matrix2<f32>, Vector2<f32>, mul);
-bench_binop!(_bench_mat3_mul_v, Matrix3<f32>, Vector3<f32>, mul);
-bench_binop!(_bench_mat4_mul_v, Matrix4<f32>, Vector4<f32>, mul);
-
-bench_binop_ref!(_bench_mat2_tr_mul_v, Matrix2<f32>, Vector2<f32>, tr_mul);
-bench_binop_ref!(_bench_mat3_tr_mul_v, Matrix3<f32>, Vector3<f32>, tr_mul);
-bench_binop_ref!(_bench_mat4_tr_mul_v, Matrix4<f32>, Vector4<f32>, tr_mul);
-
-bench_binop!(_bench_mat2_mul_s, Matrix2<f32>, f32, mul);
-bench_binop!(_bench_mat3_mul_s, Matrix3<f32>, f32, mul);
-bench_binop!(_bench_mat4_mul_s, Matrix4<f32>, f32, mul);
-
-bench_binop!(_bench_mat2_div_s, Matrix2<f32>, f32, div);
-bench_binop!(_bench_mat3_div_s, Matrix3<f32>, f32, div);
-bench_binop!(_bench_mat4_div_s, Matrix4<f32>, f32, div);
-
-bench_unop!(_bench_mat2_inv, Matrix2<f32>, try_inverse);
-bench_unop!(_bench_mat3_inv, Matrix3<f32>, try_inverse);
-bench_unop!(_bench_mat4_inv, Matrix4<f32>, try_inverse);
-
-bench_unop!(_bench_mat2_transpose, Matrix2<f32>, transpose);
-bench_unop!(_bench_mat3_transpose, Matrix3<f32>, transpose);
-bench_unop!(_bench_mat4_transpose, Matrix4<f32>, transpose);

benches/quaternion.rs

@@ -1,28 +0,0 @@
-#![feature(test)]
-
-extern crate test;
-extern crate rand;
-extern crate nalgebra as na;
-
-use rand::{IsaacRng, Rng};
-use test::Bencher;
-use na::{Quaternion, UnitQuaternion, Vector3};
-use std::ops::{Add, Sub, Mul, Div};
-
-#[path="common/macros.rs"]
-mod macros;
-
-bench_binop!(_bench_quaternion_add_q, Quaternion<f32>, Quaternion<f32>, add);
-bench_binop!(_bench_quaternion_sub_q, Quaternion<f32>, Quaternion<f32>, sub);
-bench_binop!(_bench_quaternion_mul_q, Quaternion<f32>, Quaternion<f32>, mul);
-
-bench_binop!(_bench_unit_quaternion_mul_v, UnitQuaternion<f32>, Vector3<f32>, mul);
-
-bench_binop!(_bench_quaternion_mul_s, Quaternion<f32>, f32, mul);
-bench_binop!(_bench_quaternion_div_s, Quaternion<f32>, f32, div);
-
-bench_unop!(_bench_quaternion_inv, Quaternion<f32>, try_inverse);
-bench_unop!(_bench_unit_quaternion_inv, UnitQuaternion<f32>, inverse);
-
-// bench_unop_self!(_bench_quaternion_conjugate, Quaternion<f32>, conjugate);
-// bench_unop!(_bench_quaternion_normalize, Quaternion<f32>, normalize);

benches/vector.rs

@@ -1,43 +0,0 @@
-#![feature(test)]
-
-extern crate test;
-extern crate rand;
-extern crate nalgebra as na;
-
-use rand::{IsaacRng, Rng};
-use test::Bencher;
-use na::{Vector2, Vector3, Vector4};
-use std::ops::{Add, Sub, Mul, Div};
-
-#[path="common/macros.rs"]
-mod macros;
-
-bench_binop!(_bench_vec2_add_v, Vector2<f32>, Vector2<f32>, add);
-bench_binop!(_bench_vec3_add_v, Vector3<f32>, Vector3<f32>, add);
-bench_binop!(_bench_vec4_add_v, Vector4<f32>, Vector4<f32>, add);
-
-bench_binop!(_bench_vec2_sub_v, Vector2<f32>, Vector2<f32>, sub);
-bench_binop!(_bench_vec3_sub_v, Vector3<f32>, Vector3<f32>, sub);
-bench_binop!(_bench_vec4_sub_v, Vector4<f32>, Vector4<f32>, sub);
-
-bench_binop!(_bench_vec2_mul_s, Vector2<f32>, f32, mul);
-bench_binop!(_bench_vec3_mul_s, Vector3<f32>, f32, mul);
-bench_binop!(_bench_vec4_mul_s, Vector4<f32>, f32, mul);
-
-bench_binop!(_bench_vec2_div_s, Vector2<f32>, f32, div);
-bench_binop!(_bench_vec3_div_s, Vector3<f32>, f32, div);
-bench_binop!(_bench_vec4_div_s, Vector4<f32>, f32, div);
-
-bench_binop_ref!(_bench_vec2_dot, Vector2<f32>, Vector2<f32>, dot);
-bench_binop_ref!(_bench_vec3_dot, Vector3<f32>, Vector3<f32>, dot);
-bench_binop_ref!(_bench_vec4_dot, Vector4<f32>, Vector4<f32>, dot);
-
-bench_binop_ref!(_bench_vec3_cross, Vector3<f32>, Vector3<f32>, cross);
-
-bench_unop!(_bench_vec2_norm, Vector2<f32>, norm);
-bench_unop!(_bench_vec3_norm, Vector3<f32>, norm);
-bench_unop!(_bench_vec4_norm, Vector4<f32>, norm);
-
-bench_unop!(_bench_vec2_normalize, Vector2<f32>, normalize);
-bench_unop!(_bench_vec3_normalize, Vector3<f32>, normalize);
-bench_unop!(_bench_vec4_normalize, Vector4<f32>, normalize);

examples/dimensional_genericity.rs

@@ -1,11 +1,10 @@
 extern crate alga;
 extern crate nalgebra as na;
 
-use alga::general::Real;
 use alga::linear::FiniteDimInnerSpace;
-use na::{Unit, ColumnVector, OwnedColumnVector, Vector2, Vector3};
-use na::storage::Storage;
-use na::dimension::{DimName, U1};
+use na::{Real, DefaultAllocator, Unit, VectorN, Vector2, Vector3};
+use na::allocator::Allocator;
+use na::dimension::Dim;
 
 /// Reflects a vector wrt. the hyperplane with normal `plane_normal`.
 fn reflect_wrt_hyperplane_with_algebraic_genericity<V>(plane_normal: &Unit<V>, vector: &V) -> V
@@ -16,12 +15,12 @@ fn reflect_wrt_hyperplane_with_algebraic_genericity<V>(plane_normal: &Unit<V>, v
 
 
 /// Reflects a vector wrt. the hyperplane with normal `plane_normal`.
-fn reflect_wrt_hyperplane_with_structural_genericity<N, D, S>(plane_normal: &Unit<ColumnVector<N, D, S>>,
-                                                               vector:       &ColumnVector<N, D, S>)
-                                                               -> OwnedColumnVector<N, D, S::Alloc>
+fn reflect_wrt_hyperplane_with_dimensional_genericity<N: Real, D: Dim>(plane_normal: &Unit<VectorN<N, D>>,
+                                                                       vector:       &VectorN<N, D>)
+                                                                       -> VectorN<N, D>
     where N: Real,
-          D: DimName,
-          S: Storage<N, D, U1> {
+          D: Dim,
+          DefaultAllocator: Allocator<N, D> {
     let n = plane_normal.as_ref(); // Get the underlying V.
     vector - n * (n.dot(vector) * na::convert(2.0))
 }
@@ -57,8 +56,8 @@ fn main() {
     assert_eq!(reflect_wrt_hyperplane_with_algebraic_genericity(&plane2, &v2).y, -2.0);
     assert_eq!(reflect_wrt_hyperplane_with_algebraic_genericity(&plane3, &v3).y, -2.0);
 
-    assert_eq!(reflect_wrt_hyperplane_with_structural_genericity(&plane2, &v2).y, -2.0);
-    assert_eq!(reflect_wrt_hyperplane_with_structural_genericity(&plane3, &v3).y, -2.0);
+    assert_eq!(reflect_wrt_hyperplane_with_dimensional_genericity(&plane2, &v2).y, -2.0);
+    assert_eq!(reflect_wrt_hyperplane_with_dimensional_genericity(&plane3, &v3).y, -2.0);
 
     // Call each specific implementation depending on the dimension.
     assert_eq!(reflect_wrt_hyperplane2(&plane2, &v2).y, -2.0);

nalgebra-lapack/CHANGELOG.md

@@ -0,0 +1,22 @@
+# Change Log
+
+## [0.4.0] - 2016-09-07
+
+* Made all traits use associated types for their output type parameters. This
+  simplifies usage of the traits and is consistent with the concept of
+  associated types used as output type parameters (not input type parameters) as
+  described in [the associated type
+  RFC](https://github.com/rust-lang/rfcs/blob/master/text/0195-associated-items.md).
+* Implemented `check_info!` macro to check all LAPACK calls.
+* Implemented error handling with [error_chain](https://crates.io/crates/error-chain).
+
+## [0.3.0] - 2016-09-06
+
+* Documentation is hosted at https://docs.rs/nalgebra-lapack/
+* Updated `nalgebra` to 0.10.
+* Rename traits `HasSVD` to `SVD` and `HasEigensystem` to `Eigensystem`.
+* Added `Solve` trait for solving a linear matrix equation.
+* Added `Inverse` for computing the multiplicative inverse of a matrix.
+* Added `Cholesky` for decomposing a positive-definite matrix.
+* The `Eigensystem` and `SVD` traits are now generic over types. The
+  associated types have been removed.

nalgebra-lapack/Cargo.toml

@@ -0,0 +1,40 @@
+[package]
+name    = "nalgebra-lapack"
+version = "0.11.2"
+authors = [ "Sébastien Crozet <developer@crozet.re>", "Andrew Straw <strawman@astraw.com>" ]
+
+description   = "Linear algebra library with transformations and satically-sized or dynamically-sized matrices."
+documentation = "http://nalgebra.org/doc/nalgebra/index.html"
+homepage      = "http://nalgebra.org"
+repository    = "https://github.com/sebcrozet/nalgebra"
+readme        = "README.md"
+keywords      = [ "linear", "algebra", "matrix", "vector" ]
+license       = "BSD-3-Clause"
+
+[features]
+serde-serialize = [ "serde", "serde_derive" ]
+
+# For BLAS/LAPACK
+default    = ["openblas"]
+openblas   = ["lapack/openblas"]
+netlib     = ["lapack/netlib"]
+accelerate = ["lapack/accelerate"]
+
+[dependencies]
+nalgebra      = { version = "0.12", path = ".." }
+num-traits    = "0.1"
+num-complex   = "0.1"
+alga          = "0.5"
+serde         = { version = "0.9", optional = true }
+serde_derive  = { version = "0.9", optional = true }
+# clippy = "*"
+
+[dependencies.lapack]
+version          = "0.11"
+default-features = false
+
+[dev-dependencies]
+nalgebra   = { version = "0.12", path = "..", features = [ "arbitrary" ] }
+quickcheck = "0.4"
+approx     = "0.1"
+rand       = "0.3"

nalgebra-lapack/LICENSE.txt

@@ -0,0 +1,21 @@
+The MIT License (MIT)
+
+Copyright (c) 2015 Andrew D. Straw
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+THE SOFTWARE.

nalgebra-lapack/Makefile

@@ -0,0 +1,11 @@
+all:
+	cargo build
+
+test:
+	cargo test
+
+doc:
+	cargo doc --all --no-deps
+
+bench:
+	cargo bench

nalgebra-lapack/README.md

@@ -0,0 +1,59 @@
+# nalgebra-lapack [![Version][version-img]][version-url] [![Status][status-img]][status-url] [![Doc][doc-img]][doc-url]
+
+Rust library for linear algebra using nalgebra and LAPACK.
+
+## Documentation
+
+Documentation is available [here](https://docs.rs/nalgebra-lapack/).
+
+## License
+
+MIT
+
+## Cargo features to select lapack provider
+
+Like the [lapack crate](https://crates.io/crates/lapack) from which this
+behavior is inherited, nalgebra-lapack uses [cargo
+features](http://doc.crates.io/manifest.html#the-[features]-section) to select
+which lapack provider (or implementation) is used. Command line arguments to
+cargo are the easiest way to do this, and the best provider depends on your
+particular system. In some cases, the providers can be further tuned with
+environment variables.
+
+Below are given examples of how to invoke `cargo build` on two different systems
+using two different providers. The `--no-default-features --features "provider"`
+arguments will be consistent for other `cargo` commands.
+
+### Ubuntu
+
+As tested on Ubuntu 12.04, do this to build the lapack package against
+the system installation of netlib without LAPACKE (note the E) or
+CBLAS:
+
+    sudo apt-get install gfortran libblas3gf liblapack3gf
+    export CARGO_FEATURE_SYSTEM_NETLIB=1
+    export CARGO_FEATURE_EXCLUDE_LAPACKE=1
+    export CARGO_FEATURE_EXCLUDE_CBLAS=1
+
+    export CARGO_FEATURES='--no-default-features --features netlib'
+    cargo build ${CARGO_FEATURES}
+
+### Mac OS X
+
+On Mac OS X, do this to use Apple's Accelerate framework:
+
+    export CARGO_FEATURES='--no-default-features --features accelerate'
+    cargo build ${CARGO_FEATURES}
+
+[version-img]: https://img.shields.io/crates/v/nalgebra-lapack.svg
+[version-url]: https://crates.io/crates/nalgebra-lapack
+[status-img]: https://travis-ci.org/strawlab/nalgebra-lapack.svg?branch=master
+[status-url]: https://travis-ci.org/strawlab/nalgebra-lapack
+[doc-img]: https://docs.rs/nalgebra-lapack/badge.svg
+[doc-url]: https://docs.rs/nalgebra-lapack/
+
+## Contributors
+This integration of LAPACK on nalgebra was
+[initiated](https://github.com/strawlab/nalgebra-lapack) by Andrew Straw. It
+then became officially supported and integrated to the main nalgebra
+repository.

nalgebra-lapack/benches/lib.rs

@@ -0,0 +1,8 @@
+#![feature(test)]
+
+extern crate test;
+extern crate rand;
+extern crate nalgebra as na;
+extern crate nalgebra_lapack as nl;
+
+mod linalg;

nalgebra-lapack/benches/linalg/hessenberg.rs

@@ -0,0 +1,21 @@
+use test::{self, Bencher};
+use na::{DMatrix, Matrix4};
+use nl::Hessenberg;
+
+#[bench]
+fn hessenberg_decompose_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    bh.iter(|| test::black_box(Hessenberg::new(m.clone())))
+}
+
+#[bench]
+fn hessenberg_decompose_4x4(bh: &mut Bencher) {
+    let m = Matrix4::<f64>::new_random();
+    bh.iter(|| test::black_box(Hessenberg::new(m.clone())))
+}
+
+#[bench]
+fn hessenberg_decompose_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+    bh.iter(|| test::black_box(Hessenberg::new(m.clone())))
+}

nalgebra-lapack/benches/linalg/lu.rs

@@ -0,0 +1,34 @@
+use test::{self, Bencher};
+use na::{DMatrix, Matrix4};
+use nl::LU;
+
+
+#[bench]
+fn lu_decompose_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    bh.iter(|| test::black_box(LU::new(m.clone())))
+}
+
+#[bench]
+fn lu_decompose_100x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 500);
+    bh.iter(|| test::black_box(LU::new(m.clone())))
+}
+
+#[bench]
+fn lu_decompose_4x4(bh: &mut Bencher) {
+    let m = Matrix4::<f64>::new_random();
+    bh.iter(|| test::black_box(LU::new(m.clone())))
+}
+
+#[bench]
+fn lu_decompose_500x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 100);
+    bh.iter(|| test::black_box(LU::new(m.clone())))
+}
+
+#[bench]
+fn lu_decompose_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+    bh.iter(|| test::black_box(LU::new(m.clone())))
+}

nalgebra-lapack/benches/linalg/mod.rs

@@ -0,0 +1,3 @@
+mod qr;
+mod lu;
+mod hessenberg;

nalgebra-lapack/benches/linalg/qr.rs

@@ -0,0 +1,33 @@
+use test::{self, Bencher};
+use na::{DMatrix, Matrix4};
+use nl::QR;
+
+#[bench]
+fn qr_decompose_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    bh.iter(|| test::black_box(QR::new(m.clone())))
+}
+
+#[bench]
+fn qr_decompose_100x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 500);
+    bh.iter(|| test::black_box(QR::new(m.clone())))
+}
+
+#[bench]
+fn qr_decompose_4x4(bh: &mut Bencher) {
+    let m = Matrix4::<f64>::new_random();
+    bh.iter(|| test::black_box(QR::new(m.clone())))
+}
+
+#[bench]
+fn qr_decompose_500x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 100);
+    bh.iter(|| test::black_box(QR::new(m.clone())))
+}
+
+#[bench]
+fn qr_decompose_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+    bh.iter(|| test::black_box(QR::new(m.clone())))
+}

nalgebra-lapack/src/cholesky.rs

@@ -0,0 +1,183 @@
+#[cfg(feature = "serde-serialize")]
+use serde;
+
+use num::Zero;
+use num_complex::Complex;
+
+use na::{Scalar, DefaultAllocator, Matrix, MatrixN, MatrixMN};
+use na::dimension::Dim;
+use na::storage::Storage;
+use na::allocator::Allocator;
+
+use lapack::fortran as interface;
+
+/// The cholesky decomposion of a symmetric-definite-positive matrix.
+#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
+#[cfg_attr(feature = "serde-serialize",
+    serde(bound(serialize =
+        "DefaultAllocator: Allocator<N, D>,
+         MatrixN<N, D>: serde::Serialize")))]
+#[cfg_attr(feature = "serde-serialize",
+    serde(bound(deserialize =
+        "DefaultAllocator: Allocator<N, D>,
+         MatrixN<N, D>: serde::Deserialize<'de>")))]
+#[derive(Clone, Debug)]
+pub struct Cholesky<N: Scalar, D: Dim>
+    where DefaultAllocator: Allocator<N, D, D> {
+    l: MatrixN<N, D>
+}
+
+impl<N: Scalar, D: Dim> Copy for Cholesky<N, D>
+    where DefaultAllocator: Allocator<N, D, D>,
+          MatrixN<N, D>: Copy { }
+
+impl<N: CholeskyScalar + Zero, D: Dim> Cholesky<N, D>
+    where DefaultAllocator: Allocator<N, D, D> {
+
+    /// Complutes the cholesky decomposition of the given symmetric-definite-positive square
+    /// matrix.
+    ///
+    /// Only the lower-triangular part of the input matrix is considered.
+    #[inline]
+    pub fn new(mut m: MatrixN<N, D>) -> Option<Self> {
+        // FIXME: check symmetry as well?
+        assert!(m.is_square(), "Unable to compute the cholesky decomposition of a non-square matrix.");
+
+        let uplo     = b'L';
+        let dim      = m.nrows() as i32;
+        let mut info = 0;
+
+        N::xpotrf(uplo, dim, m.as_mut_slice(), dim, &mut info);
+        lapack_check!(info);
+
+        Some(Cholesky { l: m })
+    }
+
+    /// Retrieves the lower-triangular factor of the cholesky decomposition.
+    pub fn unpack(mut self) -> MatrixN<N, D> {
+        self.l.fill_upper_triangle(Zero::zero(), 1);
+        self.l
+    }
+
+    /// Retrieves the lower-triangular factor of che cholesky decomposition, without zeroing-out
+    /// its strict upper-triangular part.
+    ///
+    /// This is an allocation-less version of `self.l()`. The values of the strict upper-triangular
+    /// part are garbage and should be ignored by further computations.
+    pub fn unpack_dirty(self) -> MatrixN<N, D> {
+        self.l
+    }
+
+    /// Retrieves the lower-triangular factor of the cholesky decomposition.
+    pub fn l(&self) -> MatrixN<N, D> {
+        let mut res = self.l.clone();
+        res.fill_upper_triangle(Zero::zero(), 1);
+        res
+    }
+
+    /// Retrieves the lower-triangular factor of the cholesky decomposition, without zeroing-out
+    /// its strict upper-triangular part.
+    ///
+    /// This is an allocation-less version of `self.l()`. The values of the strict upper-triangular
+    /// part are garbage and should be ignored by further computations.
+    pub fn l_dirty(&self) -> &MatrixN<N, D> {
+        &self.l
+    }
+
+    /// Solves the symmetric-definite-positive linear system `self * x = b`, where `x` is the
+    /// unknown to be determined.
+    pub fn solve<R2: Dim, C2: Dim, S2>(&self, b: &Matrix<N, R2, C2, S2>) -> Option<MatrixMN<N, R2, C2>>
+        where S2: Storage<N, R2, C2>,
+              DefaultAllocator: Allocator<N, R2, C2> {
+
+        let mut res = b.clone_owned();
+        if self.solve_mut(&mut res) {
+            Some(res)
+        }
+        else {
+            None
+        }
+    }
+
+    /// Solves in-place the symmetric-definite-positive linear system `self * x = b`, where `x` is
+    /// the unknown to be determined.
+    pub fn solve_mut<R2: Dim, C2: Dim>(&self, b: &mut MatrixMN<N, R2, C2>) -> bool
+        where DefaultAllocator: Allocator<N, R2, C2> {
+
+        let dim = self.l.nrows();
+
+        assert!(b.nrows() == dim, "The number of rows of `b` must be equal to the dimension of the matrix `a`.");
+
+        let nrhs = b.ncols() as i32;
+        let lda  = dim as i32;
+        let ldb  = dim as i32;
+        let mut info = 0;
+
+        N::xpotrs(b'L', dim as i32, nrhs, self.l.as_slice(), lda, b.as_mut_slice(), ldb, &mut info);
+        lapack_test!(info)
+    }
+
+    /// Computes the inverse of the decomposed matrix.
+    pub fn inverse(mut self) -> Option<MatrixN<N, D>> {
+        let dim = self.l.nrows();
+        let mut info = 0;
+
+        N::xpotri(b'L', dim as i32, self.l.as_mut_slice(), dim as i32, &mut info);
+        lapack_check!(info);
+
+        // Copy lower triangle to upper triangle.
+        for i in 0 .. dim {
+            for j in i + 1 .. dim {
+                unsafe { *self.l.get_unchecked_mut(i, j) = *self.l.get_unchecked(j, i) };
+            }
+        }
+
+        Some(self.l)
+    }
+}
+
+
+
+
+/*
+ *
+ * Lapack functions dispatch.
+ *
+ */
+/// Trait implemented by floats (`f32`, `f64`) and complex floats (`Complex<f32>`, `Complex<f64>`)
+/// supported by the cholesky decompotition.
+pub trait CholeskyScalar: Scalar {
+    #[allow(missing_docs)]
+    fn xpotrf(uplo: u8, n: i32, a: &mut [Self], lda: i32, info: &mut i32);
+    #[allow(missing_docs)]
+    fn xpotrs(uplo: u8, n: i32, nrhs: i32, a: &[Self], lda: i32, b: &mut [Self], ldb: i32, info: &mut i32);
+    #[allow(missing_docs)]
+    fn xpotri(uplo: u8, n: i32, a: &mut [Self], lda: i32, info: &mut i32);
+}
+
+macro_rules! cholesky_scalar_impl(
+    ($N: ty, $xpotrf: path, $xpotrs: path, $xpotri: path) => (
+        impl CholeskyScalar for $N {
+            #[inline]
+            fn xpotrf(uplo: u8, n: i32, a: &mut [Self], lda: i32, info: &mut i32) {
+                $xpotrf(uplo, n, a, lda, info)
+            }
+
+            #[inline]
+            fn xpotrs(uplo: u8, n: i32, nrhs: i32, a: &[Self], lda: i32,
+                      b: &mut [Self], ldb: i32, info: &mut i32) {
+                $xpotrs(uplo, n, nrhs, a, lda, b, ldb, info)
+            }
+
+            #[inline]
+            fn xpotri(uplo: u8, n: i32, a: &mut [Self], lda: i32, info: &mut i32) {
+                $xpotri(uplo, n, a, lda, info)
+            }
+        }
+    )
+);
+
+cholesky_scalar_impl!(f32, interface::spotrf, interface::spotrs, interface::spotri);
+cholesky_scalar_impl!(f64, interface::dpotrf, interface::dpotrs, interface::dpotri);
+cholesky_scalar_impl!(Complex<f32>, interface::cpotrf, interface::cpotrs, interface::cpotri);
+cholesky_scalar_impl!(Complex<f64>, interface::zpotrf, interface::zpotrs, interface::zpotri);

nalgebra-lapack/src/eigen.rs

@@ -0,0 +1,253 @@
+#[cfg(feature = "serde-serialize")]
+use serde;
+
+use num::Zero;
+use num_complex::Complex;
+
+use alga::general::Real;
+
+use ::ComplexHelper;
+use na::{Scalar, DefaultAllocator, Matrix, VectorN, MatrixN};
+use na::dimension::{Dim, U1};
+use na::storage::Storage;
+use na::allocator::Allocator;
+
+use lapack::fortran as interface;
+
+/// Eigendecomposition of a real square matrix with real eigenvalues.
+#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
+#[cfg_attr(feature = "serde-serialize",
+    serde(bound(serialize =
+        "DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
+         VectorN<N, D>: serde::Serialize,
+         MatrixN<N, D>: serde::Serialize")))]
+#[cfg_attr(feature = "serde-serialize",
+    serde(bound(deserialize =
+        "DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
+         VectorN<N, D>: serde::Serialize,
+         MatrixN<N, D>: serde::Deserialize<'de>")))]
+#[derive(Clone, Debug)]
+pub struct Eigen<N: Scalar, D: Dim>
+    where DefaultAllocator: Allocator<N, D> +
+                            Allocator<N, D, D> {
+    /// The eigenvalues of the decomposed matrix.
+    pub eigenvalues:       VectorN<N, D>,
+    /// The (right) eigenvectors of the decomposed matrix.
+    pub eigenvectors:      Option<MatrixN<N, D>>,
+    /// The left eigenvectors of the decomposed matrix.
+    pub left_eigenvectors: Option<MatrixN<N, D>>
+}
+
+impl<N: Scalar, D: Dim> Copy for Eigen<N, D>
+    where DefaultAllocator: Allocator<N, D> +
+                            Allocator<N, D, D>,
+          VectorN<N, D>: Copy,
+          MatrixN<N, D>: Copy { }
+
+
+impl<N: EigenScalar + Real, D: Dim> Eigen<N, D>
+    where DefaultAllocator: Allocator<N, D, D> +
+                            Allocator<N, D> {
+    /// Computes the eigenvalues and eigenvectors of the square matrix `m`.
+    ///
+    /// If `eigenvectors` is `false` then, the eigenvectors are not computed explicitly.
+    pub fn new(mut m: MatrixN<N, D>, left_eigenvectors: bool, eigenvectors: bool)
+           -> Option<Eigen<N, D>> {
+
+        assert!(m.is_square(), "Unable to compute the eigenvalue decomposition of a non-square matrix.");
+
+        let ljob = if left_eigenvectors  { b'V' } else { b'N' };
+        let rjob = if eigenvectors { b'V' } else { b'N' };
+
+        let (nrows, ncols) = m.data.shape();
+        let n = nrows.value();
+
+        let lda = n as i32;
+
+        let mut wr = unsafe { Matrix::new_uninitialized_generic(nrows, U1) };
+        // FIXME: Tap into the workspace.
+        let mut wi = unsafe { Matrix::new_uninitialized_generic(nrows, U1) };
+
+
+        let mut info = 0;
+        let mut placeholder1 = [ N::zero() ];
+        let mut placeholder2 = [ N::zero() ];
+
+        let lwork = N::xgeev_work_size(ljob, rjob, n as i32, m.as_mut_slice(), lda,
+                                       wr.as_mut_slice(), wi.as_mut_slice(), &mut placeholder1,
+                                       n as i32, &mut placeholder2, n as i32, &mut info);
+
+        lapack_check!(info);
+
+        let mut work = unsafe { ::uninitialized_vec(lwork as usize) };
+
+        match (left_eigenvectors, eigenvectors) {
+            (true, true) => {
+                let mut vl = unsafe { Matrix::new_uninitialized_generic(nrows, ncols) };
+                let mut vr = unsafe { Matrix::new_uninitialized_generic(nrows, ncols) };
+
+                N::xgeev(ljob, rjob, n as i32, m.as_mut_slice(), lda, wr.as_mut_slice(),
+                    wi.as_mut_slice(), &mut vl.as_mut_slice(), n as i32, &mut vr.as_mut_slice(),
+                    n as i32, &mut work, lwork, &mut info);
+                lapack_check!(info);
+
+                if wi.iter().all(|e| e.is_zero()) {
+                    return Some(Eigen {
+                        eigenvalues: wr, left_eigenvectors: Some(vl), eigenvectors: Some(vr)
+                    })
+                }
+            },
+            (true, false) => {
+                let mut vl = unsafe { Matrix::new_uninitialized_generic(nrows, ncols) };
+
+                N::xgeev(ljob, rjob, n as i32, m.as_mut_slice(), lda, wr.as_mut_slice(),
+                    wi.as_mut_slice(), &mut vl.as_mut_slice(), n as i32, &mut placeholder2,
+                    1 as i32, &mut work, lwork, &mut info);
+                lapack_check!(info);
+
+                if wi.iter().all(|e| e.is_zero()) {
+                    return Some(Eigen {
+                        eigenvalues: wr, left_eigenvectors: Some(vl), eigenvectors: None
+                    });
+                }
+            },
+            (false, true) => {
+                let mut vr = unsafe { Matrix::new_uninitialized_generic(nrows, ncols) };
+
+                N::xgeev(ljob, rjob, n as i32, m.as_mut_slice(), lda, wr.as_mut_slice(),
+                    wi.as_mut_slice(), &mut placeholder1, 1 as i32, &mut vr.as_mut_slice(),
+                    n as i32, &mut work, lwork, &mut info);
+                lapack_check!(info);
+
+                if wi.iter().all(|e| e.is_zero()) {
+                    return Some(Eigen {
+                        eigenvalues: wr, left_eigenvectors: None, eigenvectors: Some(vr)
+                    });
+                }
+            },
+            (false, false) => {
+                N::xgeev(ljob, rjob, n as i32, m.as_mut_slice(), lda, wr.as_mut_slice(),
+                    wi.as_mut_slice(), &mut placeholder1, 1 as i32, &mut placeholder2,
+                    1 as i32, &mut work, lwork, &mut info);
+                lapack_check!(info);
+
+                if wi.iter().all(|e| e.is_zero()) {
+                    return Some(Eigen {
+                        eigenvalues: wr, left_eigenvectors: None, eigenvectors: None
+                    });
+                }
+            }
+        }
+
+        None
+    }
+
+    /// The complex eigenvalues of the given matrix.
+    ///
+    /// Panics if the eigenvalue computation does not converge.
+    pub fn complex_eigenvalues(mut m: MatrixN<N, D>) -> VectorN<Complex<N>, D>
+        where DefaultAllocator: Allocator<Complex<N>, D> {
+        assert!(m.is_square(), "Unable to compute the eigenvalue decomposition of a non-square matrix.");
+
+        let nrows = m.data.shape().0;
+        let n = nrows.value();
+
+        let lda = n as i32;
+
+        let mut wr = unsafe { Matrix::new_uninitialized_generic(nrows, U1) };
+        let mut wi = unsafe { Matrix::new_uninitialized_generic(nrows, U1) };
+
+
+        let mut info = 0;
+        let mut placeholder1 = [ N::zero() ];
+        let mut placeholder2 = [ N::zero() ];
+
+        let lwork = N::xgeev_work_size(b'N', b'N', n as i32, m.as_mut_slice(), lda,
+                                       wr.as_mut_slice(), wi.as_mut_slice(), &mut placeholder1,
+                                       n as i32, &mut placeholder2, n as i32, &mut info);
+
+        lapack_panic!(info);
+
+        let mut work = unsafe { ::uninitialized_vec(lwork as usize) };
+
+        N::xgeev(b'N', b'N', n as i32, m.as_mut_slice(), lda, wr.as_mut_slice(),
+            wi.as_mut_slice(), &mut placeholder1, 1 as i32, &mut placeholder2,
+            1 as i32, &mut work, lwork, &mut info);
+        lapack_panic!(info);
+
+        let mut res = unsafe { Matrix::new_uninitialized_generic(nrows, U1) };
+
+        for i in 0 .. res.len() {
+            res[i] = Complex::new(wr[i], wi[i]);
+        }
+
+        res
+    }
+
+    /// The determinant of the decomposed matrix.
+    #[inline]
+    pub fn determinant(&self) -> N {
+        let mut det = N::one();
+        for e in self.eigenvalues.iter() {
+            det *= *e;
+        }
+
+        det
+    }
+}
+
+
+
+
+
+/*
+ *
+ * Lapack functions dispatch.
+ *
+ */
+/// Trait implemented by scalar type for which Lapack funtion exist to compute the
+/// eigendecomposition.
+pub trait EigenScalar: Scalar {
+    #[allow(missing_docs)]
+    fn xgeev(jobvl: u8, jobvr: u8, n: i32, a: &mut [Self], lda: i32,
+             wr: &mut [Self], wi: &mut [Self],
+             vl: &mut [Self], ldvl: i32, vr: &mut [Self], ldvr: i32,
+             work: &mut [Self], lwork: i32, info: &mut i32);
+    #[allow(missing_docs)]
+    fn xgeev_work_size(jobvl: u8, jobvr: u8, n: i32, a: &mut [Self], lda: i32,
+                       wr: &mut [Self], wi: &mut [Self], vl: &mut [Self], ldvl: i32,
+                       vr: &mut [Self], ldvr: i32, info: &mut i32) -> i32;
+}
+
+macro_rules! real_eigensystem_scalar_impl (
+    ($N: ty, $xgeev: path) => (
+        impl EigenScalar for $N {
+            #[inline]
+            fn xgeev(jobvl: u8, jobvr: u8, n: i32, a: &mut [Self], lda: i32,
+                     wr: &mut [Self], wi: &mut [Self],
+                     vl: &mut [Self], ldvl: i32, vr: &mut [Self], ldvr: i32,
+                     work: &mut [Self], lwork: i32, info: &mut i32) {
+                $xgeev(jobvl, jobvr, n, a, lda, wr, wi, vl, ldvl, vr, ldvr, work, lwork, info)
+            }
+
+
+            #[inline]
+            fn xgeev_work_size(jobvl: u8, jobvr: u8, n: i32, a: &mut [Self], lda: i32,
+                               wr: &mut [Self], wi: &mut [Self], vl: &mut [Self], ldvl: i32,
+                               vr: &mut [Self], ldvr: i32, info: &mut i32) -> i32 {
+                let mut work = [ Zero::zero() ];
+                let lwork = -1 as i32;
+
+                $xgeev(jobvl, jobvr, n, a, lda, wr, wi, vl, ldvl, vr, ldvr, &mut work, lwork, info);
+                ComplexHelper::real_part(work[0]) as i32
+            }
+        }
+    )
+);
+
+real_eigensystem_scalar_impl!(f32, interface::sgeev);
+real_eigensystem_scalar_impl!(f64, interface::dgeev);
+
+//// FIXME: decomposition of complex matrix and matrices with complex eigenvalues.
+// eigensystem_complex_impl!(f32, interface::cgeev);
+// eigensystem_complex_impl!(f64, interface::zgeev);

nalgebra-lapack/src/hessenberg.rs

@@ -0,0 +1,178 @@
+use num::Zero;
+use num_complex::Complex;
+
+use ::ComplexHelper;
+use na::{Scalar, Matrix, DefaultAllocator, VectorN, MatrixN};
+use na::dimension::{DimSub, DimDiff, U1};
+use na::storage::Storage;
+use na::allocator::Allocator;
+
+use lapack::fortran as interface;
+
+
+/// The Hessenberg decomposition of a general matrix.
+#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
+#[cfg_attr(feature = "serde-serialize",
+    serde(bound(serialize =
+        "DefaultAllocator: Allocator<N, D, D> +
+                           Allocator<N, DimDiff<D, U1>>,
+         MatrixN<N, D>: serde::Serialize,
+         VectorN<N, DimDiff<D, U1>>: serde::Serialize")))]
+#[cfg_attr(feature = "serde-serialize",
+    serde(bound(deserialize =
+        "DefaultAllocator: Allocator<N, D, D> +
+                           Allocator<N, DimDiff<D, U1>>,
+         MatrixN<N, D>: serde::Deserialize<'de>,
+         VectorN<N, DimDiff<D, U1>>: serde::Deserialize<'de>")))]
+#[derive(Clone, Debug)]
+pub struct Hessenberg<N: Scalar, D: DimSub<U1>>
+    where DefaultAllocator: Allocator<N, D, D> +
+                            Allocator<N, DimDiff<D, U1>> {
+    h:   MatrixN<N, D>,
+    tau: VectorN<N, DimDiff<D, U1>>
+}
+
+
+impl<N: Scalar, D: DimSub<U1>> Copy for Hessenberg<N, D>
+    where DefaultAllocator: Allocator<N, D, D> +
+                            Allocator<N, DimDiff<D, U1>>,
+          MatrixN<N, D>: Copy,
+          VectorN<N, DimDiff<D, U1>>: Copy { }
+
+impl<N: HessenbergScalar + Zero, D: DimSub<U1>> Hessenberg<N, D>
+        where DefaultAllocator: Allocator<N, D, D> +
+                                Allocator<N, DimDiff<D, U1>> {
+    /// Computes the hessenberg decomposition of the matrix `m`.
+    pub fn new(mut m: MatrixN<N, D>) -> Hessenberg<N, D> {
+        let nrows = m.data.shape().0;
+        let n     = nrows.value() as i32;
+
+        assert!(m.is_square(), "Unable to compute the hessenberg decomposition of a non-square matrix.");
+        assert!(!m.is_empty(), "Unable to compute the hessenberg decomposition of an empty matrix.");
+
+        let mut tau = unsafe { Matrix::new_uninitialized_generic(nrows.sub(U1), U1) };
+
+        let mut info  = 0;
+        let lwork = N::xgehrd_work_size(n, 1, n, m.as_mut_slice(), n, tau.as_mut_slice(), &mut info);
+        let mut work = unsafe { ::uninitialized_vec(lwork as usize) };
+
+        lapack_panic!(info);
+
+        N::xgehrd(n, 1, n, m.as_mut_slice(), n, tau.as_mut_slice(), &mut work, lwork, &mut info);
+        lapack_panic!(info);
+
+        Hessenberg { h: m, tau: tau }
+    }
+
+    /// Computes the hessenberg matrix of this decomposition.
+    #[inline]
+    pub fn h(&self) -> MatrixN<N, D> {
+        let mut h = self.h.clone_owned();
+        h.fill_lower_triangle(N::zero(), 2);
+
+        h
+    }
+}
+
+impl<N: HessenbergReal + Zero, D: DimSub<U1>> Hessenberg<N, D>
+        where DefaultAllocator: Allocator<N, D, D> +
+                                Allocator<N, DimDiff<D, U1>> {
+    /// Computes the matrices `(Q, H)` of this decomposition.
+    #[inline]
+    pub fn unpack(self) -> (MatrixN<N, D>, MatrixN<N, D>) {
+        (self.q(), self.h())
+    }
+
+    /// Computes the unitary matrix `Q` of this decomposition.
+    #[inline]
+    pub fn q(&self) -> MatrixN<N, D> {
+        let n = self.h.nrows() as i32;
+        let mut q = self.h.clone_owned();
+        let mut info  = 0;
+
+        let lwork = N::xorghr_work_size(n, 1, n, q.as_mut_slice(), n, self.tau.as_slice(), &mut info);
+        let mut work = vec![ N::zero(); lwork as usize ];
+
+        N::xorghr(n, 1, n, q.as_mut_slice(), n, self.tau.as_slice(), &mut work, lwork, &mut info);
+
+        q
+    }
+}
+
+
+
+
+/*
+ *
+ * Lapack functions dispatch.
+ *
+ */
+pub trait HessenbergScalar: Scalar {
+    fn xgehrd(n: i32, ilo: i32, ihi: i32, a: &mut [Self], lda: i32, 
+              tau: &mut [Self], work: &mut [Self], lwork: i32, info: &mut i32);
+    fn xgehrd_work_size(n: i32, ilo: i32, ihi: i32, a: &mut [Self], lda: i32, 
+                        tau: &mut [Self], info: &mut i32) -> i32;
+}
+
+/// Trait implemented by scalars for which Lapack implements the hessenberg decomposition.
+pub trait HessenbergReal: HessenbergScalar {
+    #[allow(missing_docs)]
+    fn xorghr(n: i32, ilo: i32, ihi: i32, a: &mut [Self], lda: i32, tau: &[Self],
+              work: &mut [Self], lwork: i32, info: &mut i32);
+    #[allow(missing_docs)]
+    fn xorghr_work_size(n: i32, ilo: i32, ihi: i32, a: &mut [Self], lda: i32,
+                        tau: &[Self], info: &mut i32) -> i32;
+}
+
+macro_rules! hessenberg_scalar_impl(
+    ($N: ty, $xgehrd: path) => (
+        impl HessenbergScalar for $N {
+            #[inline]
+            fn xgehrd(n: i32, ilo: i32, ihi: i32, a: &mut [Self], lda: i32, 
+                      tau: &mut [Self], work: &mut [Self], lwork: i32, info: &mut i32) {
+                $xgehrd(n, ilo, ihi, a, lda, tau, work, lwork, info)
+            }
+
+            #[inline]
+            fn xgehrd_work_size(n: i32, ilo: i32, ihi: i32, a: &mut [Self], lda: i32, 
+                                tau: &mut [Self], info: &mut i32) -> i32 {
+                let mut work = [ Zero::zero() ];
+                let lwork = -1 as i32;
+
+                $xgehrd(n, ilo, ihi, a, lda, tau, &mut work, lwork, info);
+                ComplexHelper::real_part(work[0]) as i32
+            }
+        }
+    )
+);
+
+macro_rules! hessenberg_real_impl(
+    ($N: ty, $xorghr: path) => (
+        impl HessenbergReal for $N {
+            #[inline]
+            fn xorghr(n: i32, ilo: i32, ihi: i32, a: &mut [Self], lda: i32, tau: &[Self],
+                      work: &mut [Self], lwork: i32, info: &mut i32) {
+                $xorghr(n, ilo, ihi, a, lda, tau, work, lwork, info)
+            }
+
+            #[inline]
+            fn xorghr_work_size(n: i32, ilo: i32, ihi: i32, a: &mut [Self], lda: i32,
+                                tau: &[Self], info: &mut i32) -> i32 {
+                let mut work = [ Zero::zero() ];
+                let lwork = -1 as i32;
+
+                $xorghr(n, ilo, ihi, a, lda, tau, &mut work, lwork, info);
+                ComplexHelper::real_part(work[0]) as i32
+            }
+        }
+    )
+);
+
+hessenberg_scalar_impl!(f32, interface::sgehrd);
+hessenberg_scalar_impl!(f64, interface::dgehrd);
+hessenberg_scalar_impl!(Complex<f32>, interface::cgehrd);
+hessenberg_scalar_impl!(Complex<f64>, interface::zgehrd);
+
+hessenberg_real_impl!(f32, interface::sorghr);
+hessenberg_real_impl!(f64, interface::dorghr);
+

nalgebra-lapack/src/lapack_check.rs

@@ -0,0 +1,27 @@
+#![macro_use]
+
+macro_rules! lapack_check(
+    ($info: expr) => (
+        // FIXME: return a richer error.
+        if $info != 0 {
+            return None;
+        }
+        // if $info < 0 {
+        //     return Err(Error::from(ErrorKind::LapackIllegalArgument(-$info)));
+        // } else if $info > 0 {
+        //     return Err(Error::from(ErrorKind::LapackFailure($info)));
+        // }
+    );
+);
+
+macro_rules! lapack_panic(
+    ($info: expr) => (
+        assert!($info == 0, "Lapack error.");
+    );
+);
+
+macro_rules! lapack_test(
+    ($info: expr) => (
+        $info == 0
+    );
+);

nalgebra-lapack/src/lib.rs

@@ -0,0 +1,148 @@
+//! # nalgebra-lapack
+//! 
+//! Rust library for linear algebra using nalgebra and LAPACK.
+//! 
+//! ## Documentation
+//! 
+//! Documentation is available [here](https://docs.rs/nalgebra-lapack/).
+//! 
+//! ## License
+//! 
+//! MIT
+//! 
+//! ## Cargo features to select lapack provider
+//! 
+//! Like the [lapack crate](https://crates.io/crates/lapack) from which this
+//! behavior is inherited, nalgebra-lapack uses [cargo
+//! features](http://doc.crates.io/manifest.html#the-[features]-section) to select
+//! which lapack provider (or implementation) is used. Command line arguments to
+//! cargo are the easiest way to do this, and the best provider depends on your
+//! particular system. In some cases, the providers can be further tuned with
+//! environment variables.
+//! 
+//! Below are given examples of how to invoke `cargo build` on two different systems
+//! using two different providers. The `--no-default-features --features "provider"`
+//! arguments will be consistent for other `cargo` commands.
+//! 
+//! ### Ubuntu
+//! 
+//! As tested on Ubuntu 12.04, do this to build the lapack package against
+//! the system installation of netlib without LAPACKE (note the E) or
+//! CBLAS:
+//! 
+//! ```.ignore
+//! sudo apt-get install gfortran libblas3gf liblapack3gf
+//! export CARGO_FEATURE_SYSTEM_NETLIB=1
+//! export CARGO_FEATURE_EXCLUDE_LAPACKE=1
+//! export CARGO_FEATURE_EXCLUDE_CBLAS=1
+//! 
+//! export CARGO_FEATURES='--no-default-features --features netlib'
+//! cargo build ${CARGO_FEATURES}
+//! ```
+//! 
+//! ### Mac OS X
+//! 
+//! On Mac OS X, do this to use Apple's Accelerate framework:
+//! 
+//! ```.ignore
+//! export CARGO_FEATURES='--no-default-features --features accelerate'
+//! cargo build ${CARGO_FEATURES}
+//! ```
+//! 
+//! [version-img]: https://img.shields.io/crates/v/nalgebra-lapack.svg
+//! [version-url]: https://crates.io/crates/nalgebra-lapack
+//! [status-img]: https://travis-ci.org/strawlab/nalgebra-lapack.svg?branch=master
+//! [status-url]: https://travis-ci.org/strawlab/nalgebra-lapack
+//! [doc-img]: https://docs.rs/nalgebra-lapack/badge.svg
+//! [doc-url]: https://docs.rs/nalgebra-lapack/
+//! 
+//! ## Contributors
+//! This integration of LAPACK on nalgebra was
+//! [initiated](https://github.com/strawlab/nalgebra-lapack) by Andrew Straw. It
+//! then became officially supported and integrated to the main nalgebra
+//! repository.
+
+#![deny(non_camel_case_types)]
+#![deny(unused_parens)]
+#![deny(non_upper_case_globals)]
+#![deny(unused_qualifications)]
+#![deny(unused_results)]
+#![deny(missing_docs)]
+#![doc(html_root_url = "http://nalgebra.org/rustdoc")]
+
+extern crate num_traits as num;
+extern crate num_complex;
+extern crate lapack;
+extern crate alga;
+extern crate nalgebra as na;
+
+mod lapack_check;
+mod svd;
+mod eigen;
+mod symmetric_eigen;
+mod cholesky;
+mod lu;
+mod qr;
+mod hessenberg;
+mod schur;
+
+use num_complex::Complex;
+
+pub use self::svd::SVD;
+pub use self::cholesky::{Cholesky, CholeskyScalar};
+pub use self::lu::{LU, LUScalar};
+pub use self::eigen::Eigen;
+pub use self::symmetric_eigen::SymmetricEigen;
+pub use self::qr::QR;
+pub use self::hessenberg::Hessenberg;
+pub use self::schur::RealSchur;
+
+
+trait ComplexHelper {
+    type RealPart;
+
+    fn real_part(self) -> Self::RealPart;
+}
+
+impl ComplexHelper for f32 {
+    type RealPart = f32;
+
+    #[inline]
+    fn real_part(self) -> Self::RealPart {
+        self
+    }
+}
+
+impl ComplexHelper for f64 {
+    type RealPart = f64;
+
+    #[inline]
+    fn real_part(self) -> Self::RealPart {
+        self
+    }
+}
+
+impl ComplexHelper for Complex<f32> {
+    type RealPart = f32;
+
+    #[inline]
+    fn real_part(self) -> Self::RealPart {
+        self.re
+    }
+}
+
+impl ComplexHelper for Complex<f64> {
+    type RealPart = f64;
+
+    #[inline]
+    fn real_part(self) -> Self::RealPart {
+        self.re
+    }
+}
+
+unsafe fn uninitialized_vec<T: Copy>(n: usize) -> Vec<T> {
+    let mut res = Vec::new();
+    res.reserve_exact(n);
+    res.set_len(n);
+    res
+}

nalgebra-lapack/src/lu.rs

@@ -0,0 +1,320 @@
+use num::{Zero, One};
+use num_complex::Complex;
+
+use ::ComplexHelper;
+use na::{Scalar, DefaultAllocator, Matrix, MatrixMN, MatrixN, VectorN};
+use na::dimension::{Dim, DimMin, DimMinimum, U1};
+use na::storage::Storage;
+use na::allocator::Allocator;
+
+use lapack::fortran as interface;
+
+/// LU decomposition with partial pivoting.
+///
+/// This decomposes a matrix `M` with m rows and n columns into three parts:
+/// * `L` which is a `m × min(m, n)` lower-triangular matrix.
+/// * `U` which is a `min(m, n) × n` upper-triangular matrix.
+/// * `P` which is a `m * m` permutation matrix.
+///
+/// Those are such that `M == P * L * U`.
+#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
+#[cfg_attr(feature = "serde-serialize",
+    serde(bound(serialize =
+        "DefaultAllocator: Allocator<N, R, C> +
+                           Allocator<i32, DimMinimum<R, C>>,
+         MatrixMN<N, R, C>: serde::Serialize,
+         PermutationSequence<DimMinimum<R, C>>: serde::Serialize")))]
+#[cfg_attr(feature = "serde-serialize",
+    serde(bound(deserialize =
+        "DefaultAllocator: Allocator<N, R, C> +
+                           Allocator<i32, DimMinimum<R, C>>,
+         MatrixMN<N, R, C>: serde::Deserialize<'de>,
+         PermutationSequence<DimMinimum<R, C>>: serde::Deserialize<'de>")))]
+#[derive(Clone, Debug)]
+pub struct LU<N: Scalar, R: DimMin<C>, C: Dim>
+    where DefaultAllocator: Allocator<i32, DimMinimum<R, C>> +
+                            Allocator<N, R, C> {
+    lu: MatrixMN<N, R, C>,
+    p:  VectorN<i32, DimMinimum<R, C>>
+}
+
+impl<N: Scalar, R: DimMin<C>, C: Dim> Copy for LU<N, R, C>
+    where DefaultAllocator: Allocator<N, R, C> +
+                            Allocator<i32, DimMinimum<R, C>>,
+          MatrixMN<N, R, C>: Copy,
+          VectorN<i32, DimMinimum<R, C>>: Copy { }
+
+impl<N: LUScalar, R: Dim, C: Dim> LU<N, R, C>
+    where N: Zero + One,
+          R: DimMin<C>,
+          DefaultAllocator: Allocator<N, R, C> +
+                            Allocator<N, R, R> +
+                            Allocator<N, R, DimMinimum<R, C>> +
+                            Allocator<N, DimMinimum<R, C>, C> +
+                            Allocator<i32, DimMinimum<R, C>> {
+
+    /// Computes the LU decomposition with partial (row) pivoting of `matrix`.
+    pub fn new(mut m: MatrixMN<N, R, C>) -> Self {
+        let (nrows, ncols)  = m.data.shape();
+        let min_nrows_ncols = nrows.min(ncols);
+        let nrows           = nrows.value() as i32;
+        let ncols           = ncols.value() as i32;
+
+        let mut ipiv: VectorN<i32, _> = Matrix::zeros_generic(min_nrows_ncols, U1);
+
+        let mut info = 0;
+
+        N::xgetrf(nrows, ncols, m.as_mut_slice(), nrows, ipiv.as_mut_slice(), &mut info);
+        lapack_panic!(info);
+
+        LU { lu: m, p: ipiv }
+    }
+
+    /// Gets the lower-triangular matrix part of the decomposition.
+    #[inline]
+    pub fn l(&self) -> MatrixMN<N, R, DimMinimum<R, C>> {
+        let (nrows, ncols) = self.lu.data.shape();
+        let mut res = self.lu.columns_generic(0, nrows.min(ncols)).into_owned();
+
+        res.fill_upper_triangle(Zero::zero(), 1);
+        res.fill_diagonal(One::one());
+
+        res
+    }
+
+    /// Gets the upper-triangular matrix part of the decomposition.
+    #[inline]
+    pub fn u(&self) -> MatrixMN<N, DimMinimum<R, C>, C> {
+        let (nrows, ncols) = self.lu.data.shape();
+        let mut res = self.lu.rows_generic(0, nrows.min(ncols)).into_owned();
+
+        res.fill_lower_triangle(Zero::zero(), 1);
+
+        res
+    }
+
+    /// Gets the row permutation matrix of this decomposition.
+    ///
+    /// Computing the permutation matrix explicitly is costly and usually not necessary.
+    /// To permute rows of a matrix or vector, use the method `self.permute(...)` instead.
+    #[inline]
+    pub fn p(&self) -> MatrixN<N, R> {
+        let (dim, _) = self.lu.data.shape();
+        let mut id = Matrix::identity_generic(dim, dim);
+        self.permute(&mut id);
+
+        id
+    }
+
+    // FIXME: when we support resizing a matrix, we could add unwrap_u/unwrap_l that would
+    // re-use the memory from the internal matrix!
+
+    /// Gets the LAPACK permutation indices.
+    #[inline]
+    pub fn permutation_indices(&self) -> &VectorN<i32, DimMinimum<R, C>> {
+        &self.p
+    }
+
+    /// Applies the permutation matrix to a given matrix or vector in-place.
+    #[inline]
+    pub fn permute<C2: Dim>(&self, rhs: &mut MatrixMN<N, R, C2>)
+        where DefaultAllocator: Allocator<N, R, C2> {
+
+        let (nrows, ncols) = rhs.shape();
+
+        N::xlaswp(ncols as i32, rhs.as_mut_slice(), nrows as i32,
+                  1, self.p.len() as i32, self.p.as_slice(), -1);
+    }
+
+    fn generic_solve_mut<R2: Dim, C2: Dim>(&self, trans: u8, b: &mut MatrixMN<N, R2, C2>) -> bool
+        where DefaultAllocator: Allocator<N, R2, C2> +
+                                Allocator<i32, R2> {
+
+        let dim = self.lu.nrows();
+
+        assert!(self.lu.is_square(), "Unable to solve a set of under/over-determined equations.");
+        assert!(b.nrows() == dim, "The number of rows of `b` must be equal to the dimension of the matrix `a`.");
+
+        let nrhs = b.ncols() as i32;
+        let lda  = dim as i32;
+        let ldb  = dim as i32;
+        let mut info = 0;
+
+        N::xgetrs(trans, dim as i32, nrhs, self.lu.as_slice(), lda, self.p.as_slice(),
+                  b.as_mut_slice(), ldb, &mut info);
+        lapack_test!(info)
+    }
+
+    /// Solves the linear system `self * x = b`, where `x` is the unknown to be determined.
+    pub fn solve<R2: Dim, C2: Dim, S2>(&self, b: &Matrix<N, R2, C2, S2>) -> Option<MatrixMN<N, R2, C2>>
+        where S2: Storage<N, R2, C2>,
+              DefaultAllocator: Allocator<N, R2, C2> +
+                                Allocator<i32, R2> {
+
+        let mut res = b.clone_owned();
+        if self.generic_solve_mut(b'N', &mut res) {
+            Some(res)
+        }
+        else {
+            None
+        }
+    }
+
+    /// Solves the linear system `self.transpose() * x = b`, where `x` is the unknown to be
+    /// determined.
+    pub fn solve_transpose<R2: Dim, C2: Dim, S2>(&self, b: &Matrix<N, R2, C2, S2>)
+        -> Option<MatrixMN<N, R2, C2>>
+        where S2: Storage<N, R2, C2>,
+              DefaultAllocator: Allocator<N, R2, C2> +
+                                Allocator<i32, R2> {
+
+        let mut res = b.clone_owned();
+        if self.generic_solve_mut(b'T', &mut res) {
+            Some(res)
+        }
+        else {
+            None
+        }
+    }
+
+    /// Solves the linear system `self.conjugate_transpose() * x = b`, where `x` is the unknown to
+    /// be determined.
+    pub fn solve_conjugate_transpose<R2: Dim, C2: Dim, S2>(&self, b: &Matrix<N, R2, C2, S2>)
+        -> Option<MatrixMN<N, R2, C2>>
+        where S2: Storage<N, R2, C2>,
+              DefaultAllocator: Allocator<N, R2, C2> +
+                                Allocator<i32, R2> {
+
+        let mut res = b.clone_owned();
+        if self.generic_solve_mut(b'T', &mut res) {
+            Some(res)
+        }
+        else {
+            None
+        }
+    }
+
+    /// Solves in-place the linear system `self * x = b`, where `x` is the unknown to be determined.
+    ///
+    /// Retuns `false` if no solution was found (the decomposed matrix is singular).
+    pub fn solve_mut<R2: Dim, C2: Dim>(&self, b: &mut MatrixMN<N, R2, C2>) -> bool
+        where DefaultAllocator: Allocator<N, R2, C2> +
+                                Allocator<i32, R2> {
+
+        self.generic_solve_mut(b'N', b)
+    }
+
+    /// Solves in-place the linear system `self.transpose() * x = b`, where `x` is the unknown to be
+    /// determined.
+    ///
+    /// Retuns `false` if no solution was found (the decomposed matrix is singular).
+    pub fn solve_transpose_mut<R2: Dim, C2: Dim>(&self, b: &mut MatrixMN<N, R2, C2>) -> bool
+        where DefaultAllocator: Allocator<N, R2, C2> +
+                                Allocator<i32, R2> {
+
+        self.generic_solve_mut(b'T', b)
+    }
+
+    /// Solves in-place the linear system `self.conjugate_transpose() * x = b`, where `x` is the unknown to
+    /// be determined.
+    ///
+    /// Retuns `false` if no solution was found (the decomposed matrix is singular).
+    pub fn solve_conjugate_transpose_mut<R2: Dim, C2: Dim>(&self, b: &mut MatrixMN<N, R2, C2>) -> bool
+        where DefaultAllocator: Allocator<N, R2, C2> +
+                                Allocator<i32, R2> {
+
+        self.generic_solve_mut(b'T', b)
+    }
+}
+
+impl<N: LUScalar, D: Dim> LU<N, D, D>
+    where N: Zero + One,
+          D: DimMin<D, Output = D>,
+          DefaultAllocator: Allocator<N, D, D> +
+                            Allocator<i32, D> {
+    /// Computes the inverse of the decomposed matrix.
+    pub fn inverse(mut self) -> Option<MatrixN<N, D>> {
+        let dim = self.lu.nrows() as i32;
+        let mut info = 0;
+        let lwork = N::xgetri_work_size(dim, self.lu.as_mut_slice(),
+                                        dim, self.p.as_mut_slice(),
+                                        &mut info);
+        lapack_check!(info);
+
+        let mut work = unsafe { ::uninitialized_vec(lwork as usize) };
+
+        N::xgetri(dim, self.lu.as_mut_slice(), dim, self.p.as_mut_slice(),
+                  &mut work, lwork, &mut info);
+        lapack_check!(info);
+
+        Some(self.lu)
+    }
+}
+
+
+
+
+/*
+ *
+ * Lapack functions dispatch.
+ *
+ */
+/// Trait implemented by scalars for which Lapack implements the LU decomposition.
+pub trait LUScalar: Scalar {
+    #[allow(missing_docs)]
+    fn xgetrf(m: i32, n: i32, a: &mut [Self], lda: i32, ipiv: &mut [i32], info: &mut i32);
+    #[allow(missing_docs)]
+    fn xlaswp(n: i32, a: &mut [Self], lda: i32, k1: i32, k2: i32, ipiv: &[i32], incx: i32);
+    #[allow(missing_docs)]
+    fn xgetrs(trans: u8, n: i32, nrhs: i32, a: &[Self], lda: i32, ipiv: &[i32],
+              b: &mut [Self], ldb: i32, info: &mut i32);
+    #[allow(missing_docs)]
+    fn xgetri(n: i32, a: &mut [Self], lda: i32, ipiv: &[i32],
+              work: &mut [Self], lwork: i32, info: &mut i32);
+    #[allow(missing_docs)]
+    fn xgetri_work_size(n: i32, a: &mut [Self], lda: i32, ipiv: &[i32], info: &mut i32) -> i32;
+}
+
+
+macro_rules! lup_scalar_impl(
+    ($N: ty, $xgetrf: path, $xlaswp: path, $xgetrs: path, $xgetri: path) => (
+        impl LUScalar for $N {
+            #[inline]
+            fn xgetrf(m: i32, n: i32, a: &mut [Self], lda: i32, ipiv: &mut [i32], info: &mut i32) {
+                $xgetrf(m, n, a, lda, ipiv, info)
+            }
+
+            #[inline]
+            fn xlaswp(n: i32, a: &mut [Self], lda: i32, k1: i32, k2: i32, ipiv: &[i32], incx: i32) {
+                $xlaswp(n, a, lda, k1, k2, ipiv, incx)
+            }
+
+            #[inline]
+            fn xgetrs(trans: u8, n: i32, nrhs: i32, a: &[Self], lda: i32, ipiv: &[i32],
+                      b: &mut [Self], ldb: i32, info: &mut i32) {
+                $xgetrs(trans, n, nrhs, a, lda, ipiv, b, ldb, info)
+            }
+
+            #[inline]
+            fn xgetri(n: i32, a: &mut [Self], lda: i32, ipiv: &[i32],
+                      work: &mut [Self], lwork: i32, info: &mut i32) {
+                $xgetri(n, a, lda, ipiv, work, lwork, info)
+            }
+
+            #[inline]
+            fn xgetri_work_size(n: i32, a: &mut [Self], lda: i32, ipiv: &[i32], info: &mut i32) -> i32 {
+                let mut work = [ Zero::zero() ];
+                let lwork = -1 as i32;
+
+                $xgetri(n, a, lda, ipiv, &mut work, lwork, info);
+                ComplexHelper::real_part(work[0]) as i32
+            }
+        }
+    )
+);
+
+
+lup_scalar_impl!(f32, interface::sgetrf, interface::slaswp, interface::sgetrs, interface::sgetri);
+lup_scalar_impl!(f64, interface::dgetrf, interface::dlaswp, interface::dgetrs, interface::dgetri);
+lup_scalar_impl!(Complex<f32>, interface::cgetrf, interface::claswp, interface::cgetrs, interface::cgetri);
+lup_scalar_impl!(Complex<f64>, interface::zgetrf, interface::zlaswp, interface::zgetrs, interface::zgetri);

nalgebra-lapack/src/qr.rs

@@ -0,0 +1,200 @@
+#[cfg(feature = "serde-serialize")]
+use serde;
+
+use num_complex::Complex;
+use num::Zero;
+
+use ::ComplexHelper;
+use na::{Scalar, DefaultAllocator, Matrix, VectorN, MatrixMN};
+use na::dimension::{Dim, DimMin, DimMinimum, U1};
+use na::storage::Storage;
+use na::allocator::Allocator;
+
+use lapack::fortran as interface;
+
+
+/// The QR decomposition of a general matrix.
+#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
+#[cfg_attr(feature = "serde-serialize",
+    serde(bound(serialize =
+        "DefaultAllocator: Allocator<N, R, C> +
+                           Allocator<N, DimMinimum<R, C>>,
+         MatrixMN<N, R, C>: serde::Serialize,
+         VectorN<N, DimMinimum<R, C>>: serde::Serialize")))]
+#[cfg_attr(feature = "serde-serialize",
+    serde(bound(deserialize =
+        "DefaultAllocator: Allocator<N, R, C> +
+                           Allocator<N, DimMinimum<R, C>>,
+         MatrixMN<N, R, C>: serde::Deserialize<'de>,
+         VectorN<N, DimMinimum<R, C>>: serde::Deserialize<'de>")))]
+#[derive(Clone, Debug)]
+pub struct QR<N: Scalar, R: DimMin<C>, C: Dim>
+    where DefaultAllocator: Allocator<N, R, C> +
+                            Allocator<N, DimMinimum<R, C>> {
+    qr:  MatrixMN<N, R, C>,
+    tau: VectorN<N, DimMinimum<R, C>>
+}
+
+impl<N: Scalar, R: DimMin<C>, C: Dim> Copy for QR<N, R, C>
+    where DefaultAllocator: Allocator<N, R, C> +
+                            Allocator<N, DimMinimum<R, C>>,
+          MatrixMN<N, R, C>: Copy,
+          VectorN<N, DimMinimum<R, C>>: Copy { }
+
+impl<N: QRScalar + Zero, R: DimMin<C>, C: Dim> QR<N, R, C>
+    where DefaultAllocator: Allocator<N, R, C> +
+                            Allocator<N, R, DimMinimum<R, C>> +
+                            Allocator<N, DimMinimum<R, C>, C> +
+                            Allocator<N, DimMinimum<R, C>> {
+    /// Computes the QR decomposition of the matrix `m`.
+    pub fn new(mut m: MatrixMN<N, R, C>) -> QR<N, R, C> {
+        let (nrows, ncols) = m.data.shape();
+
+        let mut info  = 0;
+        let mut tau = unsafe { Matrix::new_uninitialized_generic(nrows.min(ncols), U1) };
+
+        if nrows.value() == 0 || ncols.value() == 0 {
+            return QR { qr: m, tau: tau };
+        }
+
+        let lwork = N::xgeqrf_work_size(nrows.value() as i32, ncols.value() as i32,
+                                        m.as_mut_slice(), nrows.value() as i32,
+                                        tau.as_mut_slice(), &mut info);
+
+        let mut work = unsafe { ::uninitialized_vec(lwork as usize) };
+
+        N::xgeqrf(nrows.value() as i32, ncols.value() as i32, m.as_mut_slice(),
+                  nrows.value() as i32, tau.as_mut_slice(), &mut work, lwork, &mut info);
+
+        QR { qr: m, tau: tau }
+    }
+
+    /// Retrieves the upper trapezoidal submatrix `R` of this decomposition.
+    #[inline]
+    pub fn r(&self) -> MatrixMN<N, DimMinimum<R, C>, C> {
+        let (nrows, ncols) = self.qr.data.shape();
+        self.qr.rows_generic(0, nrows.min(ncols)).upper_triangle()
+    }
+}
+
+impl<N: QRReal + Zero, R: DimMin<C>, C: Dim> QR<N, R, C>
+    where DefaultAllocator: Allocator<N, R, C> +
+                            Allocator<N, R, DimMinimum<R, C>> +
+                            Allocator<N, DimMinimum<R, C>, C> +
+                            Allocator<N, DimMinimum<R, C>> {
+    /// Retrieves the matrices `(Q, R)` of this decompositions.
+    pub fn unpack(self) -> (MatrixMN<N, R, DimMinimum<R, C>>, MatrixMN<N, DimMinimum<R, C>, C>) {
+        (self.q(), self.r())
+    }
+
+
+    /// Computes the orthogonal matrix `Q` of this decomposition.
+    #[inline]
+    pub fn q(&self) -> MatrixMN<N, R, DimMinimum<R, C>> {
+        let (nrows, ncols)  = self.qr.data.shape();
+        let min_nrows_ncols = nrows.min(ncols);
+
+        if min_nrows_ncols.value() == 0 {
+            return MatrixMN::from_element_generic(nrows, min_nrows_ncols, N::zero());
+        }
+
+        let mut q = self.qr.generic_slice((0, 0), (nrows, min_nrows_ncols)).into_owned();
+
+        let mut info  = 0;
+        let nrows = nrows.value() as i32;
+
+        let lwork = N::xorgqr_work_size(nrows, min_nrows_ncols.value() as i32,
+                                        self.tau.len() as i32, q.as_mut_slice(), nrows,
+                                        self.tau.as_slice(), &mut info);
+
+        let mut work = vec![ N::zero(); lwork as usize ];
+
+        N::xorgqr(nrows, min_nrows_ncols.value() as i32, self.tau.len() as i32, q.as_mut_slice(),
+                  nrows, self.tau.as_slice(), &mut work, lwork, &mut info);
+
+        q
+    }
+}
+
+
+
+
+
+/*
+ *
+ * Lapack functions dispatch.
+ *
+ */
+/// Trait implemented by scalar types for which Lapack funtion exist to compute the
+/// QR decomposition.
+pub trait QRScalar: Scalar {
+    fn xgeqrf(m: i32, n: i32, a: &mut [Self], lda: i32, tau: &mut [Self],
+              work: &mut [Self], lwork: i32, info: &mut i32);
+
+    fn xgeqrf_work_size(m: i32, n: i32, a: &mut [Self], lda: i32,
+                        tau: &mut [Self], info: &mut i32) -> i32;
+}
+
+/// Trait implemented by reals for which Lapack funtion exist to compute the
+/// QR decomposition.
+pub trait QRReal: QRScalar {
+    #[allow(missing_docs)]
+    fn xorgqr(m: i32, n: i32, k: i32, a: &mut [Self], lda: i32, tau: &[Self], work: &mut [Self],
+              lwork: i32, info: &mut i32);
+
+    #[allow(missing_docs)]
+    fn xorgqr_work_size(m: i32, n: i32, k: i32, a: &mut [Self], lda: i32,
+                        tau: &[Self], info: &mut i32) -> i32;
+}
+
+macro_rules! qr_scalar_impl(
+    ($N: ty, $xgeqrf: path) => (
+        impl QRScalar for $N {
+            #[inline]
+            fn xgeqrf(m: i32, n: i32, a: &mut [Self], lda: i32, tau: &mut [Self],
+                      work: &mut [Self], lwork: i32, info: &mut i32) {
+                $xgeqrf(m, n, a, lda, tau, work, lwork, info)
+            }
+
+            #[inline]
+            fn xgeqrf_work_size(m: i32, n: i32, a: &mut [Self], lda: i32, tau: &mut [Self],
+                                info: &mut i32) -> i32 {
+                let mut work = [ Zero::zero() ];
+                let lwork = -1 as i32;
+
+                $xgeqrf(m, n, a, lda, tau, &mut work, lwork, info);
+                ComplexHelper::real_part(work[0]) as i32
+            }
+        }
+    )
+);
+
+macro_rules! qr_real_impl(
+    ($N: ty, $xorgqr: path) => (
+        impl QRReal for $N {
+            #[inline]
+            fn xorgqr(m: i32, n: i32, k: i32, a: &mut [Self], lda: i32, tau: &[Self],
+                      work: &mut [Self], lwork: i32, info: &mut i32) {
+                $xorgqr(m, n, k, a, lda, tau, work, lwork, info)
+            }
+
+            #[inline]
+            fn xorgqr_work_size(m: i32, n: i32, k: i32, a: &mut [Self], lda: i32, tau: &[Self],
+                                info: &mut i32) -> i32 {
+                let mut work = [ Zero::zero() ];
+                let lwork = -1 as i32;
+
+                $xorgqr(m, n, k, a, lda, tau, &mut work, lwork, info);
+                ComplexHelper::real_part(work[0]) as i32
+            }
+        }
+    )
+);
+
+qr_scalar_impl!(f32, interface::sgeqrf);
+qr_scalar_impl!(f64, interface::dgeqrf);
+qr_scalar_impl!(Complex<f32>, interface::cgeqrf);
+qr_scalar_impl!(Complex<f64>, interface::zgeqrf);
+
+qr_real_impl!(f32, interface::sorgqr);
+qr_real_impl!(f64, interface::dorgqr);

nalgebra-lapack/src/schur.rs

@@ -0,0 +1,214 @@
+#[cfg(feature = "serde-serialize")]
+use serde;
+
+use num::Zero;
+use num_complex::Complex;
+
+use alga::general::Real;
+
+use ::ComplexHelper;
+use na::{Scalar, DefaultAllocator, Matrix, VectorN, MatrixN};
+use na::dimension::{Dim, U1};
+use na::storage::Storage;
+use na::allocator::Allocator;
+
+use lapack::fortran as interface;
+
+/// Eigendecomposition of a real square matrix with real eigenvalues.
+#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
+#[cfg_attr(feature = "serde-serialize",
+    serde(bound(serialize =
+        "DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
+         VectorN<N, D>: serde::Serialize,
+         MatrixN<N, D>: serde::Serialize")))]
+#[cfg_attr(feature = "serde-serialize",
+    serde(bound(deserialize =
+        "DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
+         VectorN<N, D>: serde::Serialize,
+         MatrixN<N, D>: serde::Deserialize<'de>")))]
+#[derive(Clone, Debug)]
+pub struct RealSchur<N: Scalar, D: Dim>
+    where DefaultAllocator: Allocator<N, D> +
+                            Allocator<N, D, D> {
+
+    re: VectorN<N, D>,
+    im: VectorN<N, D>,
+    t:  MatrixN<N, D>,
+    q:  MatrixN<N, D>
+}
+
+impl<N: Scalar, D: Dim> Copy for RealSchur<N, D>
+    where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
+                            MatrixN<N, D>: Copy,
+                            VectorN<N, D>: Copy { }
+
+
+impl<N: RealSchurScalar + Real, D: Dim> RealSchur<N, D>
+    where DefaultAllocator: Allocator<N, D, D> +
+                            Allocator<N, D> {
+    /// Computes the eigenvalues and real Schur foorm of the matrix `m`.
+    ///
+    /// Panics if the method did not converge.
+    pub fn new(m: MatrixN<N, D>) -> Self {
+        Self::try_new(m).expect("RealSchur decomposition: convergence failed.")
+    }
+
+    /// Computes the eigenvalues and real Schur foorm of the matrix `m`.
+    ///
+    /// Returns `None` if the method did not converge.
+    pub fn try_new(mut m: MatrixN<N, D>) -> Option<Self> {
+        assert!(m.is_square(), "Unable to compute the eigenvalue decomposition of a non-square matrix.");
+
+        let (nrows, ncols) = m.data.shape();
+        let n = nrows.value();
+
+        let lda = n as i32;
+
+        let mut info = 0;
+
+        let mut wr = unsafe { Matrix::new_uninitialized_generic(nrows, U1) };
+        let mut wi = unsafe { Matrix::new_uninitialized_generic(nrows, U1) };
+        let mut q  = unsafe { Matrix::new_uninitialized_generic(nrows, ncols) };
+        // Placeholders:
+        let mut bwork  = [ 0i32 ];
+        let mut unused = 0;
+
+        let lwork = N::xgees_work_size(b'V', b'N', n as i32, m.as_mut_slice(), lda, &mut unused,
+                        wr.as_mut_slice(), wi.as_mut_slice(), q.as_mut_slice(), n as i32,
+                        &mut bwork, &mut info);
+        lapack_check!(info);
+
+        let mut work = unsafe { ::uninitialized_vec(lwork as usize) };
+
+        N::xgees(b'V', b'N', n as i32, m.as_mut_slice(), lda, &mut unused,
+                 wr.as_mut_slice(), wi.as_mut_slice(), q.as_mut_slice(),
+                 n as i32, &mut work, lwork, &mut bwork, &mut info);
+        lapack_check!(info);
+
+        Some(RealSchur { re: wr, im: wi, t: m, q: q })
+    }
+
+    /// Retrieves the unitary matrix `Q` and the upper-quasitriangular matrix `T` such that the
+    /// decomposed matrix equals `Q * T * Q.transpose()`.
+    pub fn unpack(self) -> (MatrixN<N, D>, MatrixN<N, D>) {
+        (self.q, self.t)
+    }
+
+    /// Computes the real eigenvalues of the decomposed matrix.
+    ///
+    /// Return `None` if some eigenvalues are complex.
+    pub fn eigenvalues(&self) -> Option<VectorN<N, D>> {
+        if self.im.iter().all(|e| e.is_zero()) {
+            Some(self.re.clone())
+        }
+        else {
+            None
+        }
+    }
+
+    /// Computes the complex eigenvalues of the decomposed matrix.
+    pub fn complex_eigenvalues(&self) -> VectorN<Complex<N>, D>
+        where DefaultAllocator: Allocator<Complex<N>, D> {
+
+        let mut out = unsafe { VectorN::new_uninitialized_generic(self.t.data.shape().0, U1) };
+
+        for i in 0 .. out.len() {
+            out[i] = Complex::new(self.re[i], self.im[i])
+        }
+
+        out
+    }
+}
+
+
+/*
+ *
+ * Lapack functions dispatch.
+ *
+ */
+/// Trait implemented by scalars for which Lapack implements the Real Schur decomposition.
+pub trait RealSchurScalar: Scalar {
+    #[allow(missing_docs)]
+    fn xgees(jobvs:  u8, 
+             sort:   u8, 
+             // select: ???
+             n:      i32, 
+             a:      &mut [Self], 
+             lda:    i32, 
+             sdim:   &mut i32, 
+             wr:     &mut [Self], 
+             wi:     &mut [Self], 
+             vs:     &mut [Self], 
+             ldvs:   i32, 
+             work:   &mut [Self], 
+             lwork:  i32, 
+             bwork:  &mut [i32], 
+             info:   &mut i32);
+
+    #[allow(missing_docs)]
+    fn xgees_work_size(jobvs:  u8, 
+                       sort:   u8, 
+                       // select: ???
+                       n:      i32, 
+                       a:      &mut [Self], 
+                       lda:    i32, 
+                       sdim:   &mut i32, 
+                       wr:     &mut [Self], 
+                       wi:     &mut [Self], 
+                       vs:     &mut [Self], 
+                       ldvs:   i32, 
+                       bwork:  &mut [i32], 
+                       info:   &mut i32)
+                       -> i32;
+}
+
+macro_rules! real_eigensystem_scalar_impl (
+    ($N: ty, $xgees: path) => (
+        impl RealSchurScalar for $N {
+            #[inline]
+            fn xgees(jobvs:  u8, 
+                     sort:   u8, 
+                     // select: ???
+                     n:      i32, 
+                     a:      &mut [$N], 
+                     lda:    i32, 
+                     sdim:   &mut i32, 
+                     wr:     &mut [$N], 
+                     wi:     &mut [$N], 
+                     vs:     &mut [$N], 
+                     ldvs:   i32, 
+                     work:   &mut [$N], 
+                     lwork:  i32, 
+                     bwork:  &mut [i32], 
+                     info:   &mut i32) {
+                $xgees(jobvs, sort, None, n, a, lda, sdim, wr, wi, vs, ldvs, work, lwork, bwork, info);
+            }
+
+
+            #[inline]
+            fn xgees_work_size(jobvs:  u8, 
+                               sort:   u8, 
+                               // select: ???
+                               n:      i32, 
+                               a:      &mut [$N], 
+                               lda:    i32, 
+                               sdim:   &mut i32, 
+                               wr:     &mut [$N], 
+                               wi:     &mut [$N], 
+                               vs:     &mut [$N], 
+                               ldvs:   i32, 
+                               bwork:  &mut [i32], 
+                               info:   &mut i32)
+                               -> i32 {
+                let mut work = [ Zero::zero() ];
+                let lwork    = -1 as i32;
+
+                $xgees(jobvs, sort, None, n, a, lda, sdim, wr, wi, vs, ldvs, &mut work, lwork, bwork, info);
+                ComplexHelper::real_part(work[0]) as i32
+            }
+        }
+    )
+);
+
+real_eigensystem_scalar_impl!(f32, interface::sgees);
+real_eigensystem_scalar_impl!(f64, interface::dgees);

nalgebra-lapack/src/svd.rs

@@ -0,0 +1,279 @@
+#[cfg(feature = "serde-serialize")]
+use serde;
+
+use std::cmp;
+use num::Signed;
+
+use na::{Scalar, Matrix, VectorN, MatrixN, MatrixMN,
+         DefaultAllocator};
+use na::dimension::{Dim, DimMin, DimMinimum, U1};
+use na::storage::Storage;
+use na::allocator::Allocator;
+
+use lapack::fortran as interface;
+
+
+/// The SVD decomposition of a general matrix.
+#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
+#[cfg_attr(feature = "serde-serialize",
+    serde(bound(serialize =
+        "DefaultAllocator: Allocator<N, DimMinimum<R, C>> +
+                           Allocator<N, R, R> +
+                           Allocator<N, C, C>,
+         MatrixN<N, R>: serde::Serialize,
+         MatrixN<N, C>: serde::Serialize,
+         VectorN<N, DimMinimum<R, C>>: serde::Serialize")))]
+#[cfg_attr(feature = "serde-serialize",
+    serde(bound(serialize =
+        "DefaultAllocator: Allocator<N, DimMinimum<R, C>> +
+                           Allocator<N, R, R> +
+                           Allocator<N, C, C>,
+         MatrixN<N, R>: serde::Deserialize<'de>,
+         MatrixN<N, C>: serde::Deserialize<'de>,
+         VectorN<N, DimMinimum<R, C>>: serde::Deserialize<'de>")))]
+#[derive(Clone, Debug)]
+pub struct SVD<N: Scalar, R: DimMin<C>, C: Dim>
+    where DefaultAllocator: Allocator<N, R, R>                 +
+                            Allocator<N, DimMinimum<R, C>> +
+                            Allocator<N, C, C> {
+    /// The left-singular vectors `U` of this SVD.
+    pub u:  MatrixN<N, R>, // FIXME: should be MatrixMN<N, R, DimMinimum<R, C>>
+    /// The right-singular vectors `V^t` of this SVD.
+    pub vt: MatrixN<N, C>, // FIXME: should be MatrixMN<N, DimMinimum<R, C>, C>
+    /// The singular values of this SVD.
+    pub singular_values: VectorN<N, DimMinimum<R, C>>
+}
+
+impl<N: Scalar, R: DimMin<C>, C: Dim> Copy for SVD<N, R, C>
+    where DefaultAllocator: Allocator<N, C, C> +
+                            Allocator<N, R, R> +
+                            Allocator<N, DimMinimum<R, C>>,
+          MatrixMN<N, R, R>: Copy,
+          MatrixMN<N, C, C>: Copy,
+          VectorN<N, DimMinimum<R, C>>: Copy { }
+
+/// Trait implemented by floats (`f32`, `f64`) and complex floats (`Complex<f32>`, `Complex<f64>`)
+/// supported by the Singular Value Decompotition.
+pub trait SVDScalar<R: DimMin<C>, C: Dim>: Scalar
+    where DefaultAllocator: Allocator<Self, R, R>                 +
+                            Allocator<Self, R, C>                 +
+                            Allocator<Self, DimMinimum<R, C>> +
+                            Allocator<Self, C, C> {
+    /// Computes the SVD decomposition of `m`.
+    fn compute(m: MatrixMN<Self, R, C>) -> Option<SVD<Self, R, C>>;
+}
+
+impl<N: SVDScalar<R, C>, R: DimMin<C>, C: Dim> SVD<N, R, C>
+    where DefaultAllocator: Allocator<N, R, R>             +
+                            Allocator<N, R, C>             +
+                            Allocator<N, DimMinimum<R, C>> +
+                            Allocator<N, C, C> {
+    /// Computes the Singular Value Decomposition of `matrix`.
+    pub fn new(m: MatrixMN<N, R, C>) -> Option<Self> {
+        N::compute(m)
+    }
+}
+
+macro_rules! svd_impl(
+    ($t: ty, $lapack_func: path) => (
+        impl<R: Dim, C: Dim> SVDScalar<R, C> for $t
+                where R: DimMin<C>,
+                      DefaultAllocator: Allocator<$t, R, C> +
+                                        Allocator<$t, R, R> +
+                                        Allocator<$t, C, C> +
+                                        Allocator<$t, DimMinimum<R, C>> {
+
+            fn compute(mut m: MatrixMN<$t, R, C>) -> Option<SVD<$t, R, C>> {
+                let (nrows, ncols) = m.data.shape();
+
+                if nrows.value() == 0 || ncols.value() == 0 {
+                    return None;
+                }
+
+                let job = b'A';
+
+                let lda = nrows.value() as i32;
+
+                let mut u  = unsafe { Matrix::new_uninitialized_generic(nrows, nrows) };
+                let mut s  = unsafe { Matrix::new_uninitialized_generic(nrows.min(ncols), U1) };
+                let mut vt = unsafe { Matrix::new_uninitialized_generic(ncols, ncols) };
+
+                let ldu  = nrows.value();
+                let ldvt = ncols.value();
+
+                let mut work  = [ 0.0 ];
+                let mut lwork = -1 as i32;
+                let mut info  = 0;
+                let mut iwork = unsafe { ::uninitialized_vec(8 * cmp::min(nrows.value(), ncols.value())) };
+
+                $lapack_func(job, nrows.value() as i32, ncols.value() as i32, m.as_mut_slice(),
+                    lda, &mut s.as_mut_slice(), u.as_mut_slice(), ldu as i32, vt.as_mut_slice(),
+                    ldvt as i32, &mut work, lwork, &mut iwork, &mut info);
+                lapack_check!(info);
+
+                lwork = work[0] as i32;
+                let mut work = unsafe { ::uninitialized_vec(lwork as usize) };
+
+                $lapack_func(job, nrows.value() as i32, ncols.value() as i32, m.as_mut_slice(),
+                    lda, &mut s.as_mut_slice(), u.as_mut_slice(), ldu as i32, vt.as_mut_slice(),
+                    ldvt as i32, &mut work, lwork, &mut iwork, &mut info);
+                lapack_check!(info);
+
+                Some(SVD { u: u, singular_values: s, vt: vt })
+            }
+        }
+
+        impl<R: DimMin<C>, C: Dim> SVD<$t, R, C>
+            // FIXME: All those bounds…
+            where DefaultAllocator: Allocator<$t, R, C>                 +
+                                    Allocator<$t, C, R>                 +
+                                    Allocator<$t, U1, R>                +
+                                    Allocator<$t, U1, C>                +
+                                    Allocator<$t, R, R>                 +
+                                    Allocator<$t, DimMinimum<R, C>> +
+                                    Allocator<$t, DimMinimum<R, C>, R>  +
+                                    Allocator<$t, DimMinimum<R, C>, C>  +
+                                    Allocator<$t, R, DimMinimum<R, C>>  +
+                                    Allocator<$t, C, C> {
+            /// Reconstructs the matrix from its decomposition.
+            ///
+            /// Useful if some components (e.g. some singular values) of this decomposition have
+            /// been manually changed by the user.
+            #[inline]
+            pub fn recompose(self) -> MatrixMN<$t, R, C> {
+                let nrows           = self.u.data.shape().0;
+                let ncols           = self.vt.data.shape().1;
+                let min_nrows_ncols = nrows.min(ncols);
+
+                let mut res: MatrixMN<_, R, C> = Matrix::zeros_generic(nrows, ncols);
+
+                {
+                    let mut sres = res.generic_slice_mut((0, 0), (min_nrows_ncols, ncols));
+                    sres.copy_from(&self.vt.rows_generic(0, min_nrows_ncols));
+
+                    for i in 0 .. min_nrows_ncols.value() {
+                        let eigval  = self.singular_values[i];
+                        let mut row = sres.row_mut(i);
+                        row *= eigval;
+                    }
+                }
+
+                self.u * res
+            }
+
+            /// Computes the pseudo-inverse of the decomposed matrix.
+            ///
+            /// All singular value bellow epsilon will be set to zero instead of being inverted.
+            #[inline]
+            pub fn pseudo_inverse(&self, epsilon: $t) -> MatrixMN<$t, C, R> {
+                let nrows           = self.u.data.shape().0;
+                let ncols           = self.vt.data.shape().1;
+                let min_nrows_ncols = nrows.min(ncols);
+
+                let mut res: MatrixMN<_, C, R> = Matrix::zeros_generic(ncols, nrows);
+
+                {
+                    let mut sres = res.generic_slice_mut((0, 0), (min_nrows_ncols, nrows));
+                    self.u.columns_generic(0, min_nrows_ncols).transpose_to(&mut sres);
+
+                    for i in 0 .. min_nrows_ncols.value() {
+                        let eigval  = self.singular_values[i];
+                        let mut row = sres.row_mut(i);
+
+                        if eigval.abs() > epsilon {
+                            row /= eigval
+                        }
+                        else {
+                            row.fill(0.0);
+                        }
+                    }
+                }
+
+                self.vt.tr_mul(&res)
+            }
+
+            /// The rank of the decomposed matrix.
+            ///
+            /// This is the number of singular values that are not too small (i.e. greater than
+            /// the given `epsilon`).
+            #[inline]
+            pub fn rank(&self, epsilon: $t) -> usize {
+                let mut i = 0;
+
+                for e in self.singular_values.as_slice().iter() {
+                    if e.abs() > epsilon {
+                        i += 1;
+                    }
+                }
+
+                i
+            }
+
+            // FIXME: add methods to retrieve the null-space and column-space? (Respectively
+            // corresponding to the zero and non-zero singular values).
+        }
+    );
+);
+
+/*
+macro_rules! svd_complex_impl(
+    ($name: ident, $t: ty, $lapack_func: path) => (
+        impl SVDScalar for Complex<$t> {
+            fn compute<R: Dim, C: Dim, S>(mut m: Matrix<$t, R, C, S>) -> Option<SVD<$t, R, C, S::Alloc>>
+            Option<(MatrixN<Complex<$t>, R, S::Alloc>,
+                    VectorN<$t, DimMinimum<R, C>, S::Alloc>,
+                    MatrixN<Complex<$t>, C, S::Alloc>)>
+            where R: DimMin<C>,
+                  S: ContiguousStorage<Complex<$t>, R, C>,
+                  S::Alloc: OwnedAllocator<Complex<$t>, R, C, S> +
+                            Allocator<Complex<$t>, R, R>         +
+                            Allocator<Complex<$t>, C, C>         +
+                            Allocator<$t, DimMinimum<R, C>> {
+            let (nrows, ncols) = m.data.shape();
+
+            if nrows.value() == 0 || ncols.value() == 0 {
+                return None;
+            }
+
+            let jobu  = b'A';
+            let jobvt = b'A';
+
+            let lda = nrows.value() as i32;
+            let min_nrows_ncols = nrows.min(ncols);
+
+
+            let mut u  = unsafe { Matrix::new_uninitialized_generic(nrows, nrows) };
+            let mut s  = unsafe { Matrix::new_uninitialized_generic(min_nrows_ncols, U1) };
+            let mut vt = unsafe { Matrix::new_uninitialized_generic(ncols, ncols) };
+
+            let ldu  = nrows.value();
+            let ldvt = ncols.value();
+
+            let mut work  = [ Complex::new(0.0, 0.0) ];
+            let mut lwork = -1 as i32;
+            let mut rwork = vec![ 0.0; (5 * min_nrows_ncols.value()) ];
+            let mut info  = 0;
+
+            $lapack_func(jobu, jobvt, nrows.value() as i32, ncols.value() as i32, m.as_mut_slice(),
+                lda, s.as_mut_slice(), u.as_mut_slice(), ldu as i32, vt.as_mut_slice(),
+                ldvt as i32, &mut work, lwork, &mut rwork, &mut info);
+            lapack_check!(info);
+
+            lwork = work[0].re as i32;
+            let mut work = vec![Complex::new(0.0, 0.0); lwork as usize];
+
+            $lapack_func(jobu, jobvt, nrows.value() as i32, ncols.value() as i32, m.as_mut_slice(),
+                lda, s.as_mut_slice(), u.as_mut_slice(), ldu as i32, vt.as_mut_slice(),
+                ldvt as i32, &mut work, lwork, &mut rwork, &mut info);
+            lapack_check!(info);
+
+            Some((u, s, vt))
+        }
+    );
+);
+*/
+
+svd_impl!(f32, interface::sgesdd);
+svd_impl!(f64, interface::dgesdd);
+// svd_complex_impl!(lapack_svd_complex_f32, f32, interface::cgesvd);
+// svd_complex_impl!(lapack_svd_complex_f64, f64, interface::zgesvd);

nalgebra-lapack/src/symmetric_eigen.rs

@@ -0,0 +1,176 @@
+#[cfg(feature = "serde-serialize")]
+use serde;
+
+use num::Zero;
+use std::ops::MulAssign;
+
+use alga::general::Real;
+
+use ::ComplexHelper;
+use na::{Scalar, DefaultAllocator, Matrix, VectorN, MatrixN};
+use na::dimension::{Dim, U1};
+use na::storage::Storage;
+use na::allocator::Allocator;
+
+use lapack::fortran as interface;
+
+/// Eigendecomposition of a real square symmetric matrix with real eigenvalues.
+#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
+#[cfg_attr(feature = "serde-serialize",
+    serde(bound(serialize =
+        "DefaultAllocator: Allocator<N, D, D> +
+                           Allocator<N, D>,
+         VectorN<N, D>: serde::Serialize,
+         MatrixN<N, D>: serde::Serialize")))]
+#[cfg_attr(feature = "serde-serialize",
+    serde(bound(deserialize =
+        "DefaultAllocator: Allocator<N, D, D> +
+                           Allocator<N, D>,
+         VectorN<N, D>: serde::Deserialize<'de>,
+         MatrixN<N, D>: serde::Deserialize<'de>")))]
+#[derive(Clone, Debug)]
+pub struct SymmetricEigen<N: Scalar, D: Dim>
+    where DefaultAllocator: Allocator<N, D> +
+    Allocator<N, D, D> {
+    /// The eigenvectors of the decomposed matrix.
+    pub eigenvectors: MatrixN<N, D>,
+
+    /// The unsorted eigenvalues of the decomposed matrix.
+    pub eigenvalues:  VectorN<N, D>,
+}
+
+
+impl<N: Scalar, D: Dim> Copy for SymmetricEigen<N, D>
+    where DefaultAllocator: Allocator<N, D, D> +
+                            Allocator<N, D>,
+          MatrixN<N, D>: Copy,
+          VectorN<N, D>: Copy { }
+
+impl<N: SymmetricEigenScalar + Real, D: Dim> SymmetricEigen<N, D>
+    where DefaultAllocator: Allocator<N, D, D> +
+                            Allocator<N, D> {
+
+    /// Computes the eigenvalues and eigenvectors of the symmetric matrix `m`.
+    ///
+    /// Only the lower-triangular part of `m` is read. If `eigenvectors` is `false` then, the
+    /// eigenvectors are not computed explicitly. Panics if the method did not converge.
+    pub fn new(m: MatrixN<N, D>) -> Self {
+        let (vals, vecs) = Self::do_decompose(m, true).expect("SymmetricEigen: convergence failure.");
+        SymmetricEigen { eigenvalues: vals, eigenvectors: vecs.unwrap() }
+    }
+
+    /// Computes the eigenvalues and eigenvectors of the symmetric matrix `m`.
+    ///
+    /// Only the lower-triangular part of `m` is read. If `eigenvectors` is `false` then, the
+    /// eigenvectors are not computed explicitly. Returns `None` if the method did not converge.
+    pub fn try_new(m: MatrixN<N, D>) -> Option<Self> {
+        Self::do_decompose(m, true).map(|(vals, vecs)| {
+            SymmetricEigen { eigenvalues: vals, eigenvectors: vecs.unwrap() }
+        })
+    }
+
+    fn do_decompose(mut m: MatrixN<N, D>, eigenvectors: bool) -> Option<(VectorN<N, D>, Option<MatrixN<N, D>>)> {
+        assert!(m.is_square(), "Unable to compute the eigenvalue decomposition of a non-square matrix.");
+
+        let jobz = if eigenvectors { b'V' } else { b'N' };
+
+        let nrows = m.data.shape().0;
+        let n = nrows.value();
+
+        let lda = n as i32;
+
+        let mut values = unsafe { Matrix::new_uninitialized_generic(nrows, U1) };
+        let mut info = 0;
+
+        let lwork = N::xsyev_work_size(jobz, b'L', n as i32, m.as_mut_slice(), lda, &mut info);
+        lapack_check!(info);
+
+        let mut work = unsafe { ::uninitialized_vec(lwork as usize) };
+
+        N::xsyev(jobz, b'L', n as i32, m.as_mut_slice(), lda, values.as_mut_slice(), &mut work, lwork, &mut info);
+        lapack_check!(info);
+
+        let vectors = if eigenvectors { Some(m) } else { None };
+        Some((values, vectors))
+    }
+
+    /// Computes only the eigenvalues of the input matrix.
+    ///
+    /// Panics if the method does not converge.
+    pub fn eigenvalues(m: MatrixN<N, D>) -> VectorN<N, D> {
+        Self::do_decompose(m, false).expect("SymmetricEigen eigenvalues: convergence failure.").0
+    }
+
+    /// Computes only the eigenvalues of the input matrix.
+    ///
+    /// Returns `None` if the method does not converge.
+    pub fn try_eigenvalues(m: MatrixN<N, D>) -> Option<VectorN<N, D>> {
+        Self::do_decompose(m, false).map(|res| res.0)
+    }
+
+    /// The determinant of the decomposed matrix.
+    #[inline]
+    pub fn determinant(&self) -> N {
+        let mut det = N::one();
+        for e in self.eigenvalues.iter() {
+            det *= *e;
+        }
+
+        det
+    }
+
+    /// Rebuild the original matrix.
+    ///
+    /// This is useful if some of the eigenvalues have been manually modified.
+    pub fn recompose(&self) -> MatrixN<N, D> {
+        let mut u_t = self.eigenvectors.clone();
+        for i in 0 .. self.eigenvalues.len() {
+            let val = self.eigenvalues[i];
+            u_t.column_mut(i).mul_assign(val);
+        }
+        u_t.transpose_mut();
+        &self.eigenvectors * u_t
+    }
+}
+
+
+/*
+ *
+ * Lapack functions dispatch.
+ *
+ */
+/// Trait implemented by scalars for which Lapack implements the eigendecomposition of symmetric
+/// real matrices.
+pub trait SymmetricEigenScalar: Scalar {
+    #[allow(missing_docs)]
+    fn xsyev(jobz: u8, uplo: u8, n: i32, a: &mut [Self], lda: i32, w: &mut [Self], work: &mut [Self],
+             lwork: i32, info: &mut i32);
+    #[allow(missing_docs)]
+    fn xsyev_work_size(jobz: u8, uplo: u8, n: i32, a: &mut [Self], lda: i32, info: &mut i32) -> i32;
+}
+
+macro_rules! real_eigensystem_scalar_impl (
+    ($N: ty, $xsyev: path) => (
+        impl SymmetricEigenScalar for $N {
+            #[inline]
+            fn xsyev(jobz: u8, uplo: u8, n: i32, a: &mut [Self], lda: i32, w: &mut [Self], work: &mut [Self],
+                     lwork: i32, info: &mut i32) {
+                $xsyev(jobz, uplo, n, a, lda, w, work, lwork, info)
+            }
+
+
+            #[inline]
+            fn xsyev_work_size(jobz: u8, uplo: u8, n: i32, a: &mut [Self], lda: i32, info: &mut i32) -> i32 {
+                let mut work = [ Zero::zero() ];
+                let mut w    = [ Zero::zero() ];
+                let lwork    = -1 as i32;
+
+                $xsyev(jobz, uplo, n, a, lda, &mut w, &mut work, lwork, info);
+                ComplexHelper::real_part(work[0]) as i32
+            }
+        }
+    )
+);
+
+real_eigensystem_scalar_impl!(f32, interface::ssyev);
+real_eigensystem_scalar_impl!(f64, interface::dsyev);

nalgebra-lapack/tests/lib.rs

@@ -0,0 +1,9 @@
+#[macro_use]
+extern crate quickcheck;
+#[macro_use]
+extern crate approx;
+extern crate nalgebra as na;
+extern crate nalgebra_lapack as nl;
+
+
+mod linalg;

nalgebra-lapack/tests/linalg/cholesky.rs

@@ -0,0 +1,101 @@
+use std::cmp;
+
+use nl::Cholesky;
+use na::{DMatrix, DVector, Vector4, Matrix3, Matrix4x3, Matrix4};
+
+quickcheck!{
+    fn cholesky(m: DMatrix<f64>) -> bool {
+        if m.len() != 0 {
+            let m = &m * m.transpose();
+            if let Some(chol) = Cholesky::new(m.clone()) {
+                let l = chol.unpack();
+                let reconstructed_m = &l * l.transpose();
+
+                return relative_eq!(reconstructed_m, m, epsilon = 1.0e-7)
+            }
+        }
+        return true
+    }
+
+    fn cholesky_static(m: Matrix3<f64>) -> bool {
+        let m = &m * m.transpose();
+        if let Some(chol) = Cholesky::new(m) {
+            let l = chol.unpack();
+            let reconstructed_m = &l * l.transpose();
+
+            relative_eq!(reconstructed_m, m, epsilon = 1.0e-7)
+        }
+        else {
+            false
+        }
+    }
+
+    fn cholesky_solve(n: usize, nb: usize) -> bool {
+        if n != 0 {
+            let n  = cmp::min(n, 15);  // To avoid slowing down the test too much.
+            let nb = cmp::min(nb, 15); // To avoid slowing down the test too much.
+            let m  = DMatrix::<f64>::new_random(n, n);
+            let m   = &m * m.transpose();
+
+            if let Some(chol) = Cholesky::new(m.clone()) {
+                let b1 = DVector::new_random(n);
+                let b2 = DMatrix::new_random(n, nb);
+
+                let sol1 = chol.solve(&b1).unwrap();
+                let sol2 = chol.solve(&b2).unwrap();
+
+                return relative_eq!(&m * sol1, b1, epsilon = 1.0e-6) &&
+                       relative_eq!(&m * sol2, b2, epsilon = 1.0e-6)
+            }
+        }
+
+        return true;
+    }
+
+    fn cholesky_solve_static(m: Matrix4<f64>) -> bool {
+        let m = &m * m.transpose();
+        match Cholesky::new(m) {
+            Some(chol) => {
+                let b1 = Vector4::new_random();
+                let b2 = Matrix4x3::new_random();
+
+                let sol1 = chol.solve(&b1).unwrap();
+                let sol2 = chol.solve(&b2).unwrap();
+
+                relative_eq!(m * sol1, b1, epsilon = 1.0e-7) &&
+                relative_eq!(m * sol2, b2, epsilon = 1.0e-7)
+            },
+            None => true
+        }
+    }
+
+    fn cholesky_inverse(n: usize) -> bool {
+        if n != 0 {
+            let n = cmp::min(n, 15); // To avoid slowing down the test too much.
+            let m = DMatrix::<f64>::new_random(n, n);
+            let m = &m * m.transpose();
+
+            if let Some(m1) = Cholesky::new(m.clone()).unwrap().inverse() {
+                let id1 = &m  * &m1;
+                let id2 = &m1 * &m;
+
+                return id1.is_identity(1.0e-6) && id2.is_identity(1.0e-6);
+            }
+        }
+
+        return true;
+    }
+
+    fn cholesky_inverse_static(m: Matrix4<f64>) -> bool {
+        let m = m * m.transpose();
+        match Cholesky::new(m.clone()).unwrap().inverse() {
+            Some(m1) => {
+                let id1 = &m  * &m1;
+                let id2 = &m1 * &m;
+
+                id1.is_identity(1.0e-5) && id2.is_identity(1.0e-5)
+            },
+            None => true
+        }
+    }
+}

nalgebra-lapack/tests/linalg/hessenberg.rs

@@ -0,0 +1,38 @@
+use std::cmp;
+
+use nl::Hessenberg;
+use na::{DMatrix, Matrix4};
+
+quickcheck!{
+    fn hessenberg(n: usize) -> bool {
+        if n != 0 {
+            let n = cmp::min(n, 25);
+            let m = DMatrix::<f64>::new_random(n, n);
+
+            match Hessenberg::new(m.clone()) {
+                Some(hess) => {
+                    let h = hess.h();
+                    let p = hess.p();
+
+                    relative_eq!(m, &p * h * p.transpose(), epsilon = 1.0e-7)
+                },
+                None => true
+            }
+        }
+        else {
+            true
+        }
+    }
+
+    fn hessenberg_static(m: Matrix4<f64>) -> bool {
+        match Hessenberg::new(m) {
+            Some(hess) => {
+                let h = hess.h();
+                let p = hess.p();
+
+                relative_eq!(m, p * h * p.transpose(), epsilon = 1.0e-7)
+            },
+            None => true
+        }
+    }
+}

nalgebra-lapack/tests/linalg/lu.rs

@@ -0,0 +1,107 @@
+use std::cmp;
+
+use nl::LU;
+use na::{DMatrix, DVector, Matrix4, Matrix4x3, Matrix3x4, Vector4};
+
+quickcheck!{
+    fn lup(m: DMatrix<f64>) -> bool {
+        if m.len() != 0 {
+            let lup = LU::new(m.clone());
+            let l = lup.l();
+            let u = lup.u();
+            let mut computed1 = &l * &u;
+            lup.permute(&mut computed1);
+
+            let computed2 = lup.p() * l * u;
+
+            relative_eq!(computed1, m, epsilon = 1.0e-7) &&
+            relative_eq!(computed2, m, epsilon = 1.0e-7)
+        }
+        else {
+            true
+        }
+    }
+
+    fn lu_static(m: Matrix3x4<f64>) -> bool {
+        let lup = LU::new(m);
+        let l = lup.l();
+        let u = lup.u();
+        let mut computed1 = l * u;
+        lup.permute(&mut computed1);
+
+        let computed2 = lup.p() * l * u;
+
+        relative_eq!(computed1, m, epsilon = 1.0e-7) &&
+        relative_eq!(computed2, m, epsilon = 1.0e-7)
+    }
+
+    fn lu_solve(n: usize, nb: usize) -> bool {
+        if n != 0 {
+            let n  = cmp::min(n, 25);  // To avoid slowing down the test too much.
+            let nb = cmp::min(nb, 25); // To avoid slowing down the test too much.
+            let m  = DMatrix::<f64>::new_random(n, n);
+
+            let lup = LU::new(m.clone());
+            let b1 = DVector::new_random(n);
+            let b2 = DMatrix::new_random(n, nb);
+
+            let sol1 = lup.solve(&b1).unwrap();
+            let sol2 = lup.solve(&b2).unwrap();
+
+            let tr_sol1 = lup.solve_transpose(&b1).unwrap();
+            let tr_sol2 = lup.solve_transpose(&b2).unwrap();
+
+            relative_eq!(&m * sol1, b1, epsilon = 1.0e-7) &&
+            relative_eq!(&m * sol2, b2, epsilon = 1.0e-7) &&
+            relative_eq!(m.transpose() * tr_sol1, b1, epsilon = 1.0e-7) &&
+            relative_eq!(m.transpose() * tr_sol2, b2, epsilon = 1.0e-7)
+        }
+        else {
+            true
+        }
+    }
+
+    fn lu_solve_static(m: Matrix4<f64>) -> bool {
+        let lup = LU::new(m);
+        let b1 = Vector4::new_random();
+        let b2 = Matrix4x3::new_random();
+
+        let sol1 = lup.solve(&b1).unwrap();
+        let sol2 = lup.solve(&b2).unwrap();
+        let tr_sol1 = lup.solve_transpose(&b1).unwrap();
+        let tr_sol2 = lup.solve_transpose(&b2).unwrap();
+
+        relative_eq!(m * sol1, b1, epsilon = 1.0e-7) &&
+        relative_eq!(m * sol2, b2, epsilon = 1.0e-7) &&
+        relative_eq!(m.transpose() * tr_sol1, b1, epsilon = 1.0e-7) &&
+        relative_eq!(m.transpose() * tr_sol2, b2, epsilon = 1.0e-7)
+    }
+
+    fn lu_inverse(n: usize) -> bool {
+        if n != 0 {
+            let n = cmp::min(n, 25); // To avoid slowing down the test too much.
+            let m = DMatrix::<f64>::new_random(n, n);
+
+            if let Some(m1) = LU::new(m.clone()).inverse() {
+                let id1 = &m  * &m1;
+                let id2 = &m1 * &m;
+
+                return id1.is_identity(1.0e-7) && id2.is_identity(1.0e-7);
+            }
+        }
+
+        return true;
+    }
+
+    fn lu_inverse_static(m: Matrix4<f64>) -> bool {
+        match LU::new(m.clone()).inverse() {
+            Some(m1) => {
+                let id1 = &m  * &m1;
+                let id2 = &m1 * &m;
+
+                id1.is_identity(1.0e-5) && id2.is_identity(1.0e-5)
+            },
+            None => true
+        }
+    }
+}

nalgebra-lapack/tests/linalg/mod.rs

@@ -0,0 +1,7 @@
+mod real_eigensystem;
+mod symmetric_eigen;
+mod cholesky;
+mod lu;
+mod qr;
+mod svd;
+mod real_schur;

nalgebra-lapack/tests/linalg/qr.rs

@@ -0,0 +1,20 @@
+use nl::QR;
+use na::{DMatrix, Matrix4x3};
+
+quickcheck!{
+    fn qr(m: DMatrix<f64>) -> bool {
+        let qr = QR::new(m.clone());
+        let q  = qr.q();
+        let r  = qr.r();
+
+        relative_eq!(m, q * r, epsilon = 1.0e-7)
+    }
+
+    fn qr_static(m: Matrix4x3<f64>) -> bool {
+        let qr = QR::new(m);
+        let q  = qr.q();
+        let r  = qr.r();
+
+        relative_eq!(m, q * r, epsilon = 1.0e-7)
+    }
+}

nalgebra-lapack/tests/linalg/real_eigensystem.rs

@@ -0,0 +1,48 @@
+use std::cmp;
+
+use nl::Eigen;
+use na::{DMatrix, Matrix4};
+
+quickcheck!{
+    fn eigensystem(n: usize) -> bool {
+        if n != 0 {
+            let n = cmp::min(n, 25);
+            let m = DMatrix::<f64>::new_random(n, n);
+
+            match Eigen::new(m.clone(), true, true) {
+                Some(eig) => {
+                    let eigvals                = DMatrix::from_diagonal(&eig.eigenvalues);
+                    let transformed_eigvectors = &m * eig.eigenvectors.as_ref().unwrap();
+                    let scaled_eigvectors      = eig.eigenvectors.as_ref().unwrap() * &eigvals;
+
+                    let transformed_left_eigvectors = m.transpose() * eig.left_eigenvectors.as_ref().unwrap();
+                    let scaled_left_eigvectors      = eig.left_eigenvectors.as_ref().unwrap() * &eigvals;
+
+                    relative_eq!(transformed_eigvectors, scaled_eigvectors, epsilon = 1.0e-7) &&
+                    relative_eq!(transformed_left_eigvectors, scaled_left_eigvectors, epsilon = 1.0e-7)
+                },
+                None => true
+            }
+        }
+        else {
+            true
+        }
+    }
+
+    fn eigensystem_static(m: Matrix4<f64>) -> bool {
+        match Eigen::new(m, true, true) {
+            Some(eig) => {
+                let eigvals                = Matrix4::from_diagonal(&eig.eigenvalues);
+                let transformed_eigvectors = m * eig.eigenvectors.unwrap();
+                let scaled_eigvectors      = eig.eigenvectors.unwrap() * eigvals;
+
+                let transformed_left_eigvectors = m.transpose() * eig.left_eigenvectors.unwrap();
+                let scaled_left_eigvectors      = eig.left_eigenvectors.unwrap() * eigvals;
+
+                relative_eq!(transformed_eigvectors, scaled_eigvectors, epsilon = 1.0e-7) &&
+                relative_eq!(transformed_left_eigvectors, scaled_left_eigvectors, epsilon = 1.0e-7)
+            },
+            None => true
+        }
+    }
+}

nalgebra-lapack/tests/linalg/real_schur.rs

@@ -0,0 +1,21 @@
+use std::cmp;
+use nl::RealSchur;
+use na::{DMatrix, Matrix4};
+
+quickcheck! {
+    fn schur(n: usize) -> bool {
+        let n = cmp::max(1, cmp::min(n, 10));
+        let m = DMatrix::<f64>::new_random(n, n);
+
+        let (vecs, vals) = RealSchur::new(m.clone()).unpack();
+
+        relative_eq!(&vecs * vals * vecs.transpose(), m, epsilon = 1.0e-7)
+    }
+
+    fn schur_static(m: Matrix4<f64>) -> bool {
+        let (vecs, vals) = RealSchur::new(m.clone()).unpack();
+
+        relative_eq!(vecs * vals * vecs.transpose(), m, epsilon = 1.0e-7)
+    }
+}
+

nalgebra-lapack/tests/linalg/svd.rs

@@ -0,0 +1,57 @@
+use nl::SVD;
+use na::{DMatrix, Matrix3x4};
+
+quickcheck!{
+    fn svd(m: DMatrix<f64>) -> bool {
+        if m.nrows() != 0 && m.ncols() != 0 {
+            let svd = SVD::new(m.clone()).unwrap();
+            let sm  = DMatrix::from_partial_diagonal(m.nrows(), m.ncols(), svd.singular_values.as_slice());
+
+            let reconstructed_m = &svd.u * sm * &svd.vt;
+            let reconstructed_m2 = svd.recompose();
+
+            relative_eq!(reconstructed_m, m, epsilon = 1.0e-7) &&
+            relative_eq!(reconstructed_m2, reconstructed_m, epsilon = 1.0e-7)
+        }
+        else {
+            true
+        }
+    }
+
+    fn svd_static(m: Matrix3x4<f64>) -> bool {
+        let svd = SVD::new(m).unwrap();
+        let sm  = Matrix3x4::from_partial_diagonal(svd.singular_values.as_slice());
+
+        let reconstructed_m  = &svd.u * &sm * &svd.vt;
+        let reconstructed_m2 = svd.recompose();
+
+        relative_eq!(reconstructed_m, m, epsilon = 1.0e-7) &&
+        relative_eq!(reconstructed_m2, m, epsilon = 1.0e-7)
+    }
+
+    fn pseudo_inverse(m: DMatrix<f64>) -> bool {
+        if m.nrows() == 0 || m.ncols() == 0 {
+            return true;
+        }
+
+        let svd = SVD::new(m.clone()).unwrap();
+        let im  = svd.pseudo_inverse(1.0e-7);
+
+        if m.nrows() <= m.ncols() {
+            return (&m * &im).is_identity(1.0e-7)
+        }
+
+        if m.nrows() >= m.ncols() {
+            return (im * m).is_identity(1.0e-7)
+        }
+
+        return true;
+    }
+
+    fn pseudo_inverse_static(m: Matrix3x4<f64>) -> bool {
+        let svd = SVD::new(m).unwrap();
+        let im  = svd.pseudo_inverse(1.0e-7);
+
+        (m * im).is_identity(1.0e-7)
+    }
+}

nalgebra-lapack/tests/linalg/symmetric_eigen.rs

@@ -0,0 +1,20 @@
+use std::cmp;
+
+use nl::SymmetricEigen;
+use na::{DMatrix, Matrix4};
+
+quickcheck!{
+    fn symmetric_eigen(n: usize) -> bool {
+        let n = cmp::max(1, cmp::min(n, 10));
+        let m = DMatrix::<f64>::new_random(n, n);
+        let eig = SymmetricEigen::new(m.clone());
+        let recomp = eig.recompose();
+        relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5)
+    }
+
+    fn symmetric_eigen_static(m: Matrix4<f64>) -> bool {
+        let eig = SymmetricEigen::new(m);
+        let recomp = eig.recompose();
+        relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5)
+    }
+}

src/core/alias.rs

@@ -1,7 +1,7 @@
 use core::Matrix;
 use core::dimension::{Dynamic, U1, U2, U3, U4, U5, U6};
-use core::matrix_array::MatrixArray;
 use core::matrix_vec::MatrixVec;
+use core::storage::Owned;
 
 /*
  *
@@ -10,14 +10,18 @@ use core::matrix_vec::MatrixVec;
  *
  *
  */
-/// A dynamically sized column-major matrix.
-pub type DMatrix<N> = Matrix<N, Dynamic, Dynamic, MatrixVec<N, Dynamic, Dynamic>>;
+/// A staticaly sized column-major matrix with `R` rows and `C` columns.
+#[deprecated(note = "This matrix name contains a typo. Use MatrixMN instead.")]
+pub type MatrixNM<N, R, C> = Matrix<N, R, C, Owned<N, R, C>>;
 
 /// A staticaly sized column-major matrix with `R` rows and `C` columns.
-pub type MatrixNM<N, R, C> = Matrix<N, R, C, MatrixArray<N, R, C>>;
+pub type MatrixMN<N, R, C> = Matrix<N, R, C, Owned<N, R, C>>;
 
 /// A staticaly sized column-major square matrix with `D` rows and columns.
-pub type MatrixN<N, D> = MatrixNM<N, D, D>;
+pub type MatrixN<N, D> = MatrixMN<N, D, D>;
+
+/// A dynamically sized column-major matrix.
+pub type DMatrix<N> = MatrixN<N, Dynamic>;
 
 /// A stack-allocated, column-major, 1x1 square matrix.
 pub type Matrix1<N> = MatrixN<N, U1>;
@@ -33,75 +37,75 @@ pub type Matrix5<N> = MatrixN<N, U5>;
 pub type Matrix6<N> = MatrixN<N, U6>;
 
 /// A stack-allocated, column-major, 1x2 square matrix.
-pub type Matrix1x2<N> = MatrixNM<N, U1, U2>;
+pub type Matrix1x2<N> = MatrixMN<N, U1, U2>;
 /// A stack-allocated, column-major, 1x3 square matrix.
-pub type Matrix1x3<N> = MatrixNM<N, U1, U3>;
+pub type Matrix1x3<N> = MatrixMN<N, U1, U3>;
 /// A stack-allocated, column-major, 1x4 square matrix.
-pub type Matrix1x4<N> = MatrixNM<N, U1, U4>;
+pub type Matrix1x4<N> = MatrixMN<N, U1, U4>;
 /// A stack-allocated, column-major, 1x5 square matrix.
-pub type Matrix1x5<N> = MatrixNM<N, U1, U5>;
+pub type Matrix1x5<N> = MatrixMN<N, U1, U5>;
 /// A stack-allocated, column-major, 1x6 square matrix.
-pub type Matrix1x6<N> = MatrixNM<N, U1, U6>;
+pub type Matrix1x6<N> = MatrixMN<N, U1, U6>;
 
 /// A stack-allocated, column-major, 2x3 square matrix.
-pub type Matrix2x3<N> = MatrixNM<N, U2, U3>;
+pub type Matrix2x3<N> = MatrixMN<N, U2, U3>;
 /// A stack-allocated, column-major, 2x4 square matrix.
-pub type Matrix2x4<N> = MatrixNM<N, U2, U4>;
+pub type Matrix2x4<N> = MatrixMN<N, U2, U4>;
 /// A stack-allocated, column-major, 2x5 square matrix.
-pub type Matrix2x5<N> = MatrixNM<N, U2, U5>;
+pub type Matrix2x5<N> = MatrixMN<N, U2, U5>;
 /// A stack-allocated, column-major, 2x6 square matrix.
-pub type Matrix2x6<N> = MatrixNM<N, U2, U6>;
+pub type Matrix2x6<N> = MatrixMN<N, U2, U6>;
 
 /// A stack-allocated, column-major, 3x4 square matrix.
-pub type Matrix3x4<N> = MatrixNM<N, U3, U4>;
+pub type Matrix3x4<N> = MatrixMN<N, U3, U4>;
 /// A stack-allocated, column-major, 3x5 square matrix.
-pub type Matrix3x5<N> = MatrixNM<N, U3, U5>;
+pub type Matrix3x5<N> = MatrixMN<N, U3, U5>;
 /// A stack-allocated, column-major, 3x6 square matrix.
-pub type Matrix3x6<N> = MatrixNM<N, U3, U6>;
+pub type Matrix3x6<N> = MatrixMN<N, U3, U6>;
 
 /// A stack-allocated, column-major, 4x5 square matrix.
-pub type Matrix4x5<N> = MatrixNM<N, U4, U5>;
+pub type Matrix4x5<N> = MatrixMN<N, U4, U5>;
 /// A stack-allocated, column-major, 4x6 square matrix.
-pub type Matrix4x6<N> = MatrixNM<N, U4, U6>;
+pub type Matrix4x6<N> = MatrixMN<N, U4, U6>;
 
 /// A stack-allocated, column-major, 5x6 square matrix.
-pub type Matrix5x6<N> = MatrixNM<N, U5, U6>;
+pub type Matrix5x6<N> = MatrixMN<N, U5, U6>;
 
 
 /// A stack-allocated, column-major, 2x1 square matrix.
-pub type Matrix2x1<N> = MatrixNM<N, U2, U1>;
+pub type Matrix2x1<N> = MatrixMN<N, U2, U1>;
 /// A stack-allocated, column-major, 3x1 square matrix.
-pub type Matrix3x1<N> = MatrixNM<N, U3, U1>;
+pub type Matrix3x1<N> = MatrixMN<N, U3, U1>;
 /// A stack-allocated, column-major, 4x1 square matrix.
-pub type Matrix4x1<N> = MatrixNM<N, U4, U1>;
+pub type Matrix4x1<N> = MatrixMN<N, U4, U1>;
 /// A stack-allocated, column-major, 5x1 square matrix.
-pub type Matrix5x1<N> = MatrixNM<N, U5, U1>;
+pub type Matrix5x1<N> = MatrixMN<N, U5, U1>;
 /// A stack-allocated, column-major, 6x1 square matrix.
-pub type Matrix6x1<N> = MatrixNM<N, U6, U1>;
+pub type Matrix6x1<N> = MatrixMN<N, U6, U1>;
 
 /// A stack-allocated, column-major, 3x2 square matrix.
-pub type Matrix3x2<N> = MatrixNM<N, U3, U2>;
+pub type Matrix3x2<N> = MatrixMN<N, U3, U2>;
 /// A stack-allocated, column-major, 4x2 square matrix.
-pub type Matrix4x2<N> = MatrixNM<N, U4, U2>;
+pub type Matrix4x2<N> = MatrixMN<N, U4, U2>;
 /// A stack-allocated, column-major, 5x2 square matrix.
-pub type Matrix5x2<N> = MatrixNM<N, U5, U2>;
+pub type Matrix5x2<N> = MatrixMN<N, U5, U2>;
 /// A stack-allocated, column-major, 6x2 square matrix.
-pub type Matrix6x2<N> = MatrixNM<N, U6, U2>;
+pub type Matrix6x2<N> = MatrixMN<N, U6, U2>;
 
 /// A stack-allocated, column-major, 4x3 square matrix.
-pub type Matrix4x3<N> = MatrixNM<N, U4, U3>;
+pub type Matrix4x3<N> = MatrixMN<N, U4, U3>;
 /// A stack-allocated, column-major, 5x3 square matrix.
-pub type Matrix5x3<N> = MatrixNM<N, U5, U3>;
+pub type Matrix5x3<N> = MatrixMN<N, U5, U3>;
 /// A stack-allocated, column-major, 6x3 square matrix.
-pub type Matrix6x3<N> = MatrixNM<N, U6, U3>;
+pub type Matrix6x3<N> = MatrixMN<N, U6, U3>;
 
 /// A stack-allocated, column-major, 5x4 square matrix.
-pub type Matrix5x4<N> = MatrixNM<N, U5, U4>;
+pub type Matrix5x4<N> = MatrixMN<N, U5, U4>;
 /// A stack-allocated, column-major, 6x4 square matrix.
-pub type Matrix6x4<N> = MatrixNM<N, U6, U4>;
+pub type Matrix6x4<N> = MatrixMN<N, U6, U4>;
 
 /// A stack-allocated, column-major, 6x5 square matrix.
-pub type Matrix6x5<N> = MatrixNM<N, U6, U5>;
+pub type Matrix6x5<N> = MatrixMN<N, U6, U5>;
 
 
 /*
@@ -115,7 +119,7 @@ pub type Matrix6x5<N> = MatrixNM<N, U6, U5>;
 pub type DVector<N> = Matrix<N, Dynamic, U1, MatrixVec<N, Dynamic, U1>>;
 
 /// A statically sized D-dimensional column vector.
-pub type VectorN<N, D> = MatrixNM<N, D, U1>;
+pub type VectorN<N, D> = MatrixMN<N, D, U1>;
 
 /// A stack-allocated, 1-dimensional column vector.
 pub type Vector1<N> = VectorN<N, U1>;
@@ -142,7 +146,7 @@ pub type Vector6<N> = VectorN<N, U6>;
 pub type RowDVector<N> = Matrix<N, U1, Dynamic, MatrixVec<N, U1, Dynamic>>;
 
 /// A statically sized D-dimensional row vector.
-pub type RowVectorN<N, D> = MatrixNM<N, U1, D>;
+pub type RowVectorN<N, D> = MatrixMN<N, U1, D>;
 
 /// A stack-allocated, 1-dimensional row vector.
 pub type RowVector1<N> = RowVectorN<N, U1>;

src/core/allocator.rs

@@ -2,10 +2,10 @@
 
 use std::any::Any;
 
-use core::Scalar;
+use core::{DefaultAllocator, Scalar};
 use core::constraint::{SameNumberOfRows, SameNumberOfColumns, ShapeConstraint};
 use core::dimension::{Dim, U1};
-use core::storage::{Storage, OwnedStorage};
+use core::storage::ContiguousStorageMut;
 
 /// A matrix allocator of a memory buffer that may contain `R::to_usize() * C::to_usize()`
 /// elements of type `N`.
@@ -16,9 +16,9 @@ use core::storage::{Storage, OwnedStorage};
 ///
 /// Every allocator must be both static and dynamic. Though not all implementations may share the
 /// same `Buffer` type.
-pub trait Allocator<N: Scalar, R: Dim, C: Dim>: Any + Sized {
+pub trait Allocator<N: Scalar, R: Dim, C: Dim = U1>: Any + Sized {
     /// The type of buffer this allocator can instanciate.
-    type Buffer: OwnedStorage<N, R, C, Alloc = Self>;
+    type Buffer: ContiguousStorageMut<N, R, C> + Clone;
 
     /// Allocates a buffer with the given number of rows and columns without initializing its content.
     unsafe fn allocate_uninitialized(nrows: R, ncols: C) -> Self::Buffer;
@@ -27,15 +27,20 @@ pub trait Allocator<N: Scalar, R: Dim, C: Dim>: Any + Sized {
     fn allocate_from_iterator<I: IntoIterator<Item = N>>(nrows: R, ncols: C, iter: I) -> Self::Buffer;
 }
 
-/// A matrix data allocator dedicated to the given owned matrix storage.
-pub trait OwnedAllocator<N: Scalar, R: Dim, C: Dim, S: OwnedStorage<N, R, C, Alloc = Self>>:
-    Allocator<N, R, C, Buffer = S> {
-}
-
-impl<N, R, C, T, S> OwnedAllocator<N, R, C, S> for T
-    where N: Scalar, R: Dim, C: Dim,
-          T: Allocator<N, R, C, Buffer = S>,
-          S: OwnedStorage<N, R, C, Alloc = T> {
+/// A matrix reallocator. Changes the size of the memory buffer that initially contains (RFrom ×
+/// CFrom) elements to a smaller or larger size (RTo, CTo).
+pub trait Reallocator<N: Scalar, RFrom: Dim, CFrom: Dim, RTo: Dim, CTo: Dim>:
+    Allocator<N, RFrom, CFrom> + Allocator<N, RTo, CTo> {
+    /// Reallocates a buffer of shape `(RTo, CTo)`, possibly reusing a previously allocated buffer
+    /// `buf`. Data stored by `buf` are linearly copied to the output:
+    ///
+    /// * The copy is performed as if both were just arrays (without a matrix structure).
+    /// * If `buf` is larger than the output size, then extra elements of `buf` are truncated.
+    /// * If `buf` is smaller than the output size, then extra elements of the output are left
+    /// uninitialized.
+    unsafe fn reallocate_copy(nrows: RTo, ncols: CTo,
+                              buf: <Self as Allocator<N, RFrom, CFrom>>::Buffer)
+                              -> <Self as Allocator<N, RTo, CTo>>::Buffer;
 }
 
 /// The number of rows of the result of a componentwise operation on two matrices.
@@ -45,45 +50,36 @@ pub type SameShapeR<R1, R2> = <ShapeConstraint as SameNumberOfRows<R1, R2>>::Rep
 pub type SameShapeC<C1, C2> = <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative;
 
 // FIXME: Bad name.
-/// Restricts the given number of rows and columns to be respectively the same. Can only be used
-/// when `Self = SA::Alloc`.
-pub trait SameShapeAllocator<N, R1, C1, R2, C2, SA>:
+/// Restricts the given number of rows and columns to be respectively the same.
+pub trait SameShapeAllocator<N, R1, C1, R2, C2>:
         Allocator<N, R1, C1> +
         Allocator<N, SameShapeR<R1, R2>, SameShapeC<C1, C2>>
     where R1: Dim, R2: Dim, C1: Dim, C2: Dim,
           N: Scalar,
-          SA: Storage<N, R1, C1, Alloc = Self>,
           ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
 }
 
-impl<N, R1, R2, C1, C2, SA> SameShapeAllocator<N, R1, C1, R2, C2, SA> for SA::Alloc
+impl<N, R1, R2, C1, C2> SameShapeAllocator<N, R1, C1, R2, C2> for DefaultAllocator
     where R1: Dim, R2: Dim, C1: Dim, C2: Dim,
           N: Scalar,
-          SA: Storage<N, R1, C1>,
-          SA::Alloc:
-            Allocator<N, R1, C1> +
-            Allocator<N, SameShapeR<R1, R2>, SameShapeC<C1, C2>>,
+          DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, SameShapeR<R1, R2>, SameShapeC<C1, C2>>,
           ShapeConstraint:  SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
 }
 
 // XXX: Bad name.
-/// Restricts the given number of rows to be equal. Can only be used when `Self = SA::Alloc`.
-pub trait SameShapeColumnVectorAllocator<N, R1, R2, SA>:
-        Allocator<N, R1, U1> +
-        Allocator<N, SameShapeR<R1, R2>, U1> +
-        SameShapeAllocator<N, R1, U1, R2, U1, SA>
+/// Restricts the given number of rows to be equal.
+pub trait SameShapeVectorAllocator<N, R1, R2>:
+        Allocator<N, R1> +
+        Allocator<N, SameShapeR<R1, R2>> +
+        SameShapeAllocator<N, R1, U1, R2, U1>
     where R1: Dim, R2: Dim,
           N: Scalar,
-          SA: Storage<N, R1, U1, Alloc = Self>,
           ShapeConstraint: SameNumberOfRows<R1, R2> {
 }
 
-impl<N, R1, R2, SA> SameShapeColumnVectorAllocator<N, R1, R2, SA> for SA::Alloc
+impl<N, R1, R2> SameShapeVectorAllocator<N, R1, R2> for DefaultAllocator
     where R1: Dim, R2: Dim,
           N: Scalar,
-          SA: Storage<N, R1, U1>,
-          SA::Alloc:
-            Allocator<N, R1, U1> +
-            Allocator<N, SameShapeR<R1, R2>, U1>,
+          DefaultAllocator: Allocator<N, R1, U1> + Allocator<N, SameShapeR<R1, R2>>,
           ShapeConstraint:  SameNumberOfRows<R1, R2> {
 }

src/core/blas.rs

@@ -0,0 +1,458 @@
+use std::mem;
+use num::{Zero, One, Signed};
+use matrixmultiply;
+use alga::general::{ClosedMul, ClosedAdd};
+
+use core::{Scalar, Matrix, Vector};
+use core::dimension::{Dim, U1, U2, U3, U4, Dynamic};
+use core::constraint::{ShapeConstraint, SameNumberOfRows, SameNumberOfColumns, AreMultipliable, DimEq};
+use core::storage::{Storage, StorageMut};
+
+
+
+impl<N: Scalar + PartialOrd + Signed, D: Dim, S: Storage<N, D>> Vector<N, D, S> {
+    /// Computes the index of the vector component with the largest absolute value.
+    #[inline]
+    pub fn iamax(&self) -> usize {
+        assert!(!self.is_empty(), "The input vector must not be empty.");
+
+        let mut the_max = unsafe { self.vget_unchecked(0).abs() };
+        let mut the_i   = 0;
+
+        for i in 1 .. self.nrows() {
+            let val = unsafe { self.vget_unchecked(i).abs() };
+
+            if val > the_max {
+                the_max = val;
+                the_i   = i;
+            }
+        }
+
+        the_i
+    }
+}
+
+impl<N: Scalar + PartialOrd + Signed, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
+    /// Computes the index of the matrix component with the largest absolute value.
+    #[inline]
+    pub fn iamax_full(&self) -> (usize, usize) {
+        assert!(!self.is_empty(), "The input matrix must not be empty.");
+
+        let mut the_max = unsafe { self.get_unchecked(0, 0).abs() };
+        let mut the_ij  = (0, 0);
+
+        for j in 0 .. self.ncols() {
+            for i in 0 .. self.nrows() {
+                let val = unsafe { self.get_unchecked(i, j).abs() };
+
+                if val > the_max {
+                    the_max = val;
+                    the_ij  = (i, j);
+                }
+            }
+        }
+
+        the_ij
+    }
+}
+
+impl<N, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S>
+    where N: Scalar + Zero + ClosedAdd + ClosedMul {
+    /// The dot product between two matrices (seen as vectors).
+    ///
+    /// Note that this is **not** the matrix multiplication as in, e.g., numpy. For matrix
+    /// multiplication, use one of: `.gemm`, `mul_to`, `.mul`, `*`.
+    #[inline]
+    pub fn dot<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<N, R2, C2, SB>) -> N
+        where SB: Storage<N, R2, C2>,
+              ShapeConstraint: DimEq<R, R2> + DimEq<C, C2> {
+        assert!(self.nrows() == rhs.nrows(), "Dot product dimensions mismatch.");
+
+
+        // So we do some special cases for common fixed-size vectors of dimension lower than 8
+        // because the `for` loop bellow won't be very efficient on those.
+        if (R::is::<U2>() || R2::is::<U2>()) &&
+           (C::is::<U1>() || C2::is::<U1>()) {
+            unsafe {
+                let a = *self.get_unchecked(0, 0) * *rhs.get_unchecked(0, 0);
+                let b = *self.get_unchecked(1, 0) * *rhs.get_unchecked(1, 0);
+
+                return a + b;
+            }
+        }
+        if (R::is::<U3>() || R2::is::<U3>()) &&
+           (C::is::<U1>() || C2::is::<U1>()) {
+            unsafe {
+                let a = *self.get_unchecked(0, 0) * *rhs.get_unchecked(0, 0);
+                let b = *self.get_unchecked(1, 0) * *rhs.get_unchecked(1, 0);
+                let c = *self.get_unchecked(2, 0) * *rhs.get_unchecked(2, 0);
+
+                return a + b + c;
+            }
+        }
+        if (R::is::<U4>() || R2::is::<U4>()) &&
+           (C::is::<U1>() || C2::is::<U1>()) {
+            unsafe {
+                let mut a = *self.get_unchecked(0, 0) * *rhs.get_unchecked(0, 0);
+                let mut b = *self.get_unchecked(1, 0) * *rhs.get_unchecked(1, 0);
+                let c = *self.get_unchecked(2, 0) * *rhs.get_unchecked(2, 0);
+                let d = *self.get_unchecked(3, 0) * *rhs.get_unchecked(3, 0);
+
+                a += c;
+                b += d;
+
+                return a + b;
+            }
+        }
+
+
+        // All this is inspired from the "unrolled version" discussed in:
+        // http://blog.theincredibleholk.org/blog/2012/12/10/optimizing-dot-product/
+        //
+        // And this comment from bluss:
+        // https://users.rust-lang.org/t/how-to-zip-two-slices-efficiently/2048/12
+        let mut res = N::zero();
+
+        // We have to define them outside of the loop (and not inside at first assignment)
+        // otherwize vectorization won't kick in for some reason.
+        let mut acc0;
+        let mut acc1;
+        let mut acc2;
+        let mut acc3;
+        let mut acc4;
+        let mut acc5;
+        let mut acc6;
+        let mut acc7;
+
+        for j in 0 .. self.ncols() {
+            let mut i = 0;
+
+            acc0 = N::zero();
+            acc1 = N::zero();
+            acc2 = N::zero();
+            acc3 = N::zero();
+            acc4 = N::zero();
+            acc5 = N::zero();
+            acc6 = N::zero();
+            acc7 = N::zero();
+
+            while self.nrows() - i >= 8 {
+                acc0 += unsafe { *self.get_unchecked(i + 0, j) * *rhs.get_unchecked(i + 0, j) };
+                acc1 += unsafe { *self.get_unchecked(i + 1, j) * *rhs.get_unchecked(i + 1, j) };
+                acc2 += unsafe { *self.get_unchecked(i + 2, j) * *rhs.get_unchecked(i + 2, j) };
+                acc3 += unsafe { *self.get_unchecked(i + 3, j) * *rhs.get_unchecked(i + 3, j) };
+                acc4 += unsafe { *self.get_unchecked(i + 4, j) * *rhs.get_unchecked(i + 4, j) };
+                acc5 += unsafe { *self.get_unchecked(i + 5, j) * *rhs.get_unchecked(i + 5, j) };
+                acc6 += unsafe { *self.get_unchecked(i + 6, j) * *rhs.get_unchecked(i + 6, j) };
+                acc7 += unsafe { *self.get_unchecked(i + 7, j) * *rhs.get_unchecked(i + 7, j) };
+                i += 8;
+            }
+
+            res += acc0 + acc4;
+            res += acc1 + acc5;
+            res += acc2 + acc6;
+            res += acc3 + acc7;
+
+            for k in i .. self.nrows() {
+                res += unsafe { *self.get_unchecked(k, j) * *rhs.get_unchecked(k, j) }
+            }
+        }
+
+        res
+    }
+
+    /// The dot product between the transpose of `self` and `rhs`.
+    #[inline]
+    pub fn tr_dot<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<N, R2, C2, SB>) -> N
+        where SB: Storage<N, R2, C2>,
+              ShapeConstraint: DimEq<C, R2> + DimEq<R, C2> {
+        let (nrows, ncols) = self.shape();
+        assert!((ncols, nrows) == rhs.shape(), "Transposed dot product dimension mismatch.");
+
+        let mut res = N::zero();
+
+        for j in 0 .. self.nrows() {
+            for i in 0 .. self.ncols() {
+                res += unsafe { *self.get_unchecked(j, i) * *rhs.get_unchecked(i, j) }
+            }
+        }
+
+        res
+    }
+}
+
+fn array_axpy<N>(y: &mut [N], a: N, x: &[N], beta: N, stride1: usize, stride2: usize, len: usize)
+    where N: Scalar + Zero + ClosedAdd + ClosedMul {
+    for i in 0 .. len {
+        unsafe {
+            let y = y.get_unchecked_mut(i * stride1);
+            *y = a * *x.get_unchecked(i * stride2) + beta * *y;
+        }
+    }
+}
+
+fn array_ax<N>(y: &mut [N], a: N, x: &[N], stride1: usize, stride2: usize, len: usize)
+    where N: Scalar + Zero + ClosedAdd + ClosedMul {
+    for i in 0 .. len {
+        unsafe {
+            *y.get_unchecked_mut(i * stride1) = a * *x.get_unchecked(i * stride2);
+        }
+    }
+}
+
+impl<N, D: Dim, S> Vector<N, D, S>
+    where N: Scalar + Zero + ClosedAdd + ClosedMul,
+          S: StorageMut<N, D> {
+    /// Computes `self = a * x + b * self`.
+    ///
+    /// If be is zero, `self` is never read from.
+    #[inline]
+    pub fn axpy<D2: Dim, SB>(&mut self, a: N, x: &Vector<N, D2, SB>, b: N)
+        where SB: Storage<N, D2>,
+              ShapeConstraint: DimEq<D, D2> {
+
+        assert_eq!(self.nrows(), x.nrows(), "Axpy: mismatched vector shapes.");
+
+        let rstride1 = self.strides().0;
+        let rstride2 = x.strides().0;
+
+        let y = self.data.as_mut_slice();
+        let x = x.data.as_slice();
+
+        if !b.is_zero() {
+            array_axpy(y, a, x, b, rstride1, rstride2, x.len());
+        }
+        else {
+            array_ax(y, a, x, rstride1, rstride2, x.len());
+        }
+    }
+
+    /// Computes `self = alpha * a * x + beta * self`, where `a` is a matrix, `x` a vector, and
+    /// `alpha, beta` two scalars.
+    ///
+    /// If `beta` is zero, `self` is never read.
+    #[inline]
+    pub fn gemv<R2: Dim, C2: Dim, D3: Dim, SB, SC>(&mut self,
+                                                   alpha: N,
+                                                   a:     &Matrix<N, R2, C2, SB>,
+                                                   x:     &Vector<N, D3, SC>,
+                                                   beta:  N)
+        where N:  One,
+              SB: Storage<N, R2, C2>,
+              SC: Storage<N, D3>,
+              ShapeConstraint: DimEq<D, R2> +
+                               AreMultipliable<R2, C2, D3, U1> {
+        let dim1 = self.nrows();
+        let (nrows2, ncols2) = a.shape();
+        let dim3 = x.nrows();
+
+        assert!(ncols2 == dim3 && dim1 == nrows2, "Gemv: dimensions mismatch.");
+
+        if ncols2 == 0 {
+            return;
+        }
+
+        // FIXME: avoid bound checks.
+        let col2 = a.column(0);
+        let val  = unsafe { *x.vget_unchecked(0) };
+        self.axpy(alpha * val, &col2, beta);
+
+        for j in 1 .. ncols2 {
+            let col2 = a.column(j);
+            let val  = unsafe { *x.vget_unchecked(j) };
+
+            self.axpy(alpha * val, &col2, N::one());
+        }
+    }
+
+    /// Computes `self = alpha * a * x + beta * self`, where `a` is a **symmetric** matrix, `x` a
+    /// vector, and `alpha, beta` two scalars.
+    ///
+    /// If `beta` is zero, `self` is never read. If `self` is read, only its lower-triangular part
+    /// (including the diagonal) is actually read.
+    #[inline]
+    pub fn gemv_symm<D2: Dim, D3: Dim, SB, SC>(&mut self,
+                                               alpha: N,
+                                               a:     &Matrix<N, D2, D2, SB>,
+                                               x:     &Vector<N, D3, SC>,
+                                               beta:  N)
+        where N:  One,
+              SB: Storage<N, D2, D2>,
+              SC: Storage<N, D3>,
+              ShapeConstraint: DimEq<D, D2> +
+                               AreMultipliable<D2, D2, D3, U1> {
+        let dim1 = self.nrows();
+        let dim2 = a.nrows();
+        let dim3 = x.nrows();
+
+        assert!(a.is_square(), "Syetric gemv: the input matrix must be square.");
+        assert!(dim2 == dim3 && dim1 == dim2, "Symmetric gemv: dimensions mismatch.");
+
+        if dim2 == 0 {
+            return;
+        }
+
+        // FIXME: avoid bound checks.
+        let col2 = a.column(0);
+        let val  = unsafe { *x.vget_unchecked(0) };
+        self.axpy(alpha * val, &col2, beta);
+        self[0] += alpha * x.rows_range(1 ..).dot(&a.slice_range(1 .., 0));
+
+        for j in 1 .. dim2 {
+            let col2 = a.column(j);
+            let dot  = x.rows_range(j ..).dot(&col2.rows_range(j ..));
+
+            let val;
+            unsafe {
+                val = *x.vget_unchecked(j);
+                *self.vget_unchecked_mut(j) += alpha * dot;
+            }
+            self.rows_range_mut(j + 1 ..).axpy(alpha * val, &col2.rows_range(j + 1 ..), N::one());
+        }
+    }
+}
+
+impl<N, R1: Dim, C1: Dim, S: StorageMut<N, R1, C1>> Matrix<N, R1, C1, S>
+    where N: Scalar + Zero + ClosedAdd + ClosedMul {
+
+    /// Computes `self = alpha * x * y.transpose() + beta * self`.
+    ///
+    /// If `beta` is zero, `self` is never read.
+    #[inline]
+    pub fn ger<D2: Dim, D3: Dim, SB, SC>(&mut self, alpha: N, x: &Vector<N, D2, SB>, y: &Vector<N, D3, SC>, beta: N)
+        where N: One,
+              SB: Storage<N, D2>,
+              SC: Storage<N, D3>,
+              ShapeConstraint: DimEq<R1, D2> + DimEq<C1, D3> {
+        let (nrows1, ncols1) = self.shape();
+        let dim2 = x.nrows();
+        let dim3 = y.nrows();
+
+        assert!(nrows1 == dim2 && ncols1 == dim3, "ger: dimensions mismatch.");
+
+        for j in 0 .. ncols1 {
+            // FIXME: avoid bound checks.
+            let val = unsafe { *y.vget_unchecked(j) };
+            self.column_mut(j).axpy(alpha * val, x, beta);
+        }
+    }
+
+    /// Computes `self = alpha * a * b + beta * self`, where `a, b, self` are matrices.
+    /// `alpha` and `beta` are scalar.
+    ///
+    /// If `beta` is zero, `self` is never read.
+    #[inline]
+    pub fn gemm<R2: Dim, C2: Dim, R3: Dim, C3: Dim, SB, SC>(&mut self,
+                                                            alpha: N,
+                                                            a: &Matrix<N, R2, C2, SB>,
+                                                            b: &Matrix<N, R3, C3, SC>,
+                                                            beta: N)
+        where N:  One,
+              SB: Storage<N, R2, C2>,
+              SC: Storage<N, R3, C3>,
+              ShapeConstraint: SameNumberOfRows<R1, R2>    +
+                               SameNumberOfColumns<C1, C3> +
+                               AreMultipliable<R2, C2, R3, C3> {
+       let (nrows1, ncols1) = self.shape();
+       let (nrows2, ncols2) = a.shape();
+       let (nrows3, ncols3) = b.shape();
+
+       assert_eq!(ncols2, nrows3, "gemm: dimensions mismatch for multiplication.");
+       assert_eq!((nrows1, ncols1), (nrows2, ncols3), "gemm: dimensions mismatch for addition.");
+
+       // We assume large matrices will be Dynamic but small matrices static.
+       // We could use matrixmultiply for large statically-sized matrices but the performance
+       // threshold to activate it would be different from SMALL_DIM because our code optimizes
+       // better for statically-sized matrices.
+       let is_dynamic = R1::is::<Dynamic>() || C1::is::<Dynamic>() ||
+                        R2::is::<Dynamic>() || C2::is::<Dynamic>() ||
+                        R3::is::<Dynamic>() || C3::is::<Dynamic>();
+       // Thershold determined ampirically.
+       const SMALL_DIM: usize = 5;
+
+       if is_dynamic &&
+          nrows1 > SMALL_DIM && ncols1 > SMALL_DIM &&
+          nrows2 > SMALL_DIM && ncols2 > SMALL_DIM {
+           if N::is::<f32>() {
+               let (rsa, csa) = a.strides();
+               let (rsb, csb) = b.strides();
+               let (rsc, csc) = self.strides();
+
+               unsafe {
+                   matrixmultiply::sgemm(
+                       nrows2,
+                       ncols2,
+                       ncols3,
+                       mem::transmute_copy(&alpha),
+                       a.data.ptr() as *const f32,
+                       rsa as isize, csa as isize,
+                       b.data.ptr() as *const f32,
+                       rsb as isize, csb as isize,
+                       mem::transmute_copy(&beta),
+                       self.data.ptr_mut() as *mut f32,
+                       rsc as isize, csc as isize);
+               }
+           }
+           else if N::is::<f64>() {
+               let (rsa, csa) = a.strides();
+               let (rsb, csb) = b.strides();
+               let (rsc, csc) = self.strides();
+
+               unsafe {
+                   matrixmultiply::dgemm(
+                       nrows2,
+                       ncols2,
+                       ncols3,
+                       mem::transmute_copy(&alpha),
+                       a.data.ptr() as *const f64,
+                       rsa as isize, csa as isize,
+                       b.data.ptr() as *const f64,
+                       rsb as isize, csb as isize,
+                       mem::transmute_copy(&beta),
+                       self.data.ptr_mut() as *mut f64,
+                       rsc as isize, csc as isize);
+               }
+           }
+       }
+       else {
+           for j1 in 0 .. ncols1 {
+               // FIXME: avoid bound checks.
+               self.column_mut(j1).gemv(alpha, a, &b.column(j1), beta);
+           }
+       }
+    }
+}
+
+
+impl<N, R1: Dim, C1: Dim, S: StorageMut<N, R1, C1>> Matrix<N, R1, C1, S>
+    where N: Scalar + Zero + ClosedAdd + ClosedMul {
+    /// Computes `self = alpha * x * y.transpose() + beta * self`, where `self` is a **symmetric**
+    /// matrix.
+    ///
+    /// If `beta` is zero, `self` is never read. The result is symmetric. Only the lower-triangular
+    /// (including the diagonal) part of `self` is read/written.
+    #[inline]
+    pub fn ger_symm<D2: Dim, D3: Dim, SB, SC>(&mut self,
+                                              alpha: N,
+                                              x:     &Vector<N, D2, SB>,
+                                              y:     &Vector<N, D3, SC>,
+                                              beta:  N)
+        where N: One,
+              SB: Storage<N, D2>,
+              SC: Storage<N, D3>,
+              ShapeConstraint: DimEq<R1, D2> + DimEq<C1, D3> {
+        let dim1 = self.nrows();
+        let dim2 = x.nrows();
+        let dim3 = y.nrows();
+
+        assert!(self.is_square(), "Symmetric ger: the input matrix must be square.");
+        assert!(dim1 == dim2 && dim1 == dim3, "ger: dimensions mismatch.");
+
+        for j in 0 .. dim1 {
+            // FIXME: avoid bound checks.
+            let val = unsafe { *y.vget_unchecked(j) };
+            let subdim = Dynamic::new(dim1 - j);
+            self.generic_slice_mut((j, j), (subdim, U1)).axpy(alpha * val, &x.rows_range(j ..), beta);
+        }
+    }
+}

src/core/cg.rs

@@ -7,20 +7,20 @@
 
 use num::One;
 
-use core::{Scalar, SquareMatrix, OwnedSquareMatrix, ColumnVector, Unit};
-use core::dimension::{DimName, DimNameSub, DimNameDiff, U1, U2, U3, U4};
-use core::storage::{Storage, StorageMut, OwnedStorage};
-use core::allocator::{Allocator, OwnedAllocator};
-use geometry::{PointBase, OrthographicBase, PerspectiveBase, IsometryBase, OwnedRotation, OwnedPoint};
+use core::{DefaultAllocator, Scalar, SquareMatrix, Vector, Unit,
+           VectorN, MatrixN, Vector3, Matrix3, Matrix4};
+use core::dimension::{DimName, DimNameSub, DimNameDiff, U1};
+use core::storage::{Storage, StorageMut};
+use core::allocator::Allocator;
+use geometry::{Point, Isometry, Point3, Rotation2, Rotation3, Orthographic3, Perspective3, IsometryMatrix3};
 
 use alga::general::{Real, Field};
 use alga::linear::Transformation;
 
 
-impl<N, D: DimName, S> SquareMatrix<N, D, S>
+impl<N, D: DimName> MatrixN<N, D>
     where N: Scalar + Field,
-          S: OwnedStorage<N, D, D>,
-          S::Alloc: OwnedAllocator<N, D, D, S> {
+          DefaultAllocator: Allocator<N, D, D> {
     /// Creates a new homogeneous matrix that applies the same scaling factor on each dimension.
     #[inline]
     pub fn new_scaling(scaling: N) -> Self {
@@ -32,9 +32,9 @@ impl<N, D: DimName, S> SquareMatrix<N, D, S>
 
     /// Creates a new homogeneous matrix that applies a distinct scaling factor for each dimension.
     #[inline]
-    pub fn new_nonuniform_scaling<SB>(scaling: &ColumnVector<N, DimNameDiff<D, U1>, SB>) -> Self
+    pub fn new_nonuniform_scaling<SB>(scaling: &Vector<N, DimNameDiff<D, U1>, SB>) -> Self
         where D:  DimNameSub<U1>,
-              SB: Storage<N, DimNameDiff<D, U1>, U1> {
+              SB: Storage<N, DimNameDiff<D, U1>> {
         let mut res = Self::one();
         for i in 0 .. scaling.len() {
             res[(i, i)] = scaling[i];
@@ -45,10 +45,9 @@ impl<N, D: DimName, S> SquareMatrix<N, D, S>
 
     /// Creates a new homogeneous matrix that applies a pure translation.
     #[inline]
-    pub fn new_translation<SB>(translation: &ColumnVector<N, DimNameDiff<D, U1>, SB>) -> Self
+    pub fn new_translation<SB>(translation: &Vector<N, DimNameDiff<D, U1>, SB>) -> Self
         where D:  DimNameSub<U1>,
-              SB: Storage<N, DimNameDiff<D, U1>, U1>,
-              S::Alloc: Allocator<N, DimNameDiff<D, U1>, U1> {
+              SB: Storage<N, DimNameDiff<D, U1>> {
         let mut res = Self::one();
         res.fixed_slice_mut::<DimNameDiff<D, U1>, U1>(0, D::dim() - 1).copy_from(translation);
 
@@ -56,44 +55,30 @@ impl<N, D: DimName, S> SquareMatrix<N, D, S>
     }
 }
 
-impl<N, S> SquareMatrix<N, U3, S>
-    where N: Real,
-          S: OwnedStorage<N, U3, U3>,
-          S::Alloc: OwnedAllocator<N, U3, U3, S> {
+impl<N: Real> Matrix3<N> {
     /// Builds a 2 dimensional homogeneous rotation matrix from an angle in radian.
     #[inline]
-    pub fn new_rotation(angle: N) -> Self
-        where S::Alloc: Allocator<N, U2, U2> {
-        OwnedRotation::<N, U2, S::Alloc>::new(angle).to_homogeneous()
+    pub fn new_rotation(angle: N) -> Self {
+        Rotation2::new(angle).to_homogeneous()
     }
 }
 
-impl<N, S> SquareMatrix<N, U4, S>
-    where N: Real,
-          S: OwnedStorage<N, U4, U4>,
-          S::Alloc: OwnedAllocator<N, U4, U4, S> {
-
+impl<N: Real> Matrix4<N> {
     /// Builds a 3D homogeneous rotation matrix from an axis and an angle (multiplied together).
     /// 
     /// Returns the identity matrix if the given argument is zero.
     #[inline]
-    pub fn new_rotation<SB>(axisangle: ColumnVector<N, U3, SB>) -> Self
-        where SB: Storage<N, U3, U1>,
-              S::Alloc: Allocator<N, U3, U3> {
-        OwnedRotation::<N, U3, S::Alloc>::new(axisangle).to_homogeneous()
+    pub fn new_rotation(axisangle: Vector3<N>) -> Self {
+        Rotation3::new(axisangle).to_homogeneous()
     }
 
     /// Builds a 3D homogeneous rotation matrix from an axis and an angle (multiplied together).
     /// 
     /// Returns the identity matrix if the given argument is zero.
     #[inline]
-    pub fn new_rotation_wrt_point<SB>(axisangle: ColumnVector<N, U3, SB>, pt: OwnedPoint<N, U3, S::Alloc>) -> Self
-        where SB: Storage<N, U3, U1>,
-              S::Alloc: Allocator<N, U3, U3> +
-                        Allocator<N, U3, U1> +
-                        Allocator<N, U1, U3> {
-        let rot = OwnedRotation::<N, U3, S::Alloc>::from_scaled_axis(axisangle);
-        IsometryBase::rotation_wrt_point(rot, pt).to_homogeneous()
+    pub fn new_rotation_wrt_point(axisangle: Vector3<N>, pt: Point3<N>) -> Self {
+        let rot = Rotation3::from_scaled_axis(axisangle);
+        Isometry::rotation_wrt_point(rot, pt).to_homogeneous()
     }
 
     /// Builds a 3D homogeneous rotation matrix from an axis and an angle (multiplied together).
@@ -101,37 +86,32 @@ impl<N, S> SquareMatrix<N, U4, S>
     /// Returns the identity matrix if the given argument is zero.
     /// This is identical to `Self::new_rotation`.
     #[inline]
-    pub fn from_scaled_axis<SB>(axisangle: ColumnVector<N, U3, SB>) -> Self
-        where SB: Storage<N, U3, U1>,
-              S::Alloc: Allocator<N, U3, U3> {
-        OwnedRotation::<N, U3, S::Alloc>::from_scaled_axis(axisangle).to_homogeneous()
+    pub fn from_scaled_axis(axisangle: Vector3<N>) -> Self {
+        Rotation3::from_scaled_axis(axisangle).to_homogeneous()
     }
 
     /// Creates a new rotation from Euler angles.
     ///
     /// The primitive rotations are applied in order: 1 roll − 2 pitch − 3 yaw.
-    pub fn from_euler_angles(roll: N, pitch: N, yaw: N) -> Self
-        where S::Alloc: Allocator<N, U3, U3> {
-        OwnedRotation::<N, U3, S::Alloc>::from_euler_angles(roll, pitch, yaw).to_homogeneous()
+    pub fn from_euler_angles(roll: N, pitch: N, yaw: N) -> Self {
+        Rotation3::from_euler_angles(roll, pitch, yaw).to_homogeneous()
     }
 
     /// Builds a 3D homogeneous rotation matrix from an axis and a rotation angle.
-    pub fn from_axis_angle<SB>(axis: &Unit<ColumnVector<N, U3, SB>>, angle: N) -> Self
-        where SB: Storage<N, U3, U1>,
-              S::Alloc: Allocator<N, U3, U3> {
-        OwnedRotation::<N, U3, S::Alloc>::from_axis_angle(axis, angle).to_homogeneous()
+    pub fn from_axis_angle(axis: &Unit<Vector3<N>>, angle: N) -> Self {
+        Rotation3::from_axis_angle(axis, angle).to_homogeneous()
     }
 
     /// Creates a new homogeneous matrix for an orthographic projection.
     #[inline]
     pub fn new_orthographic(left: N, right: N, bottom: N, top: N, znear: N, zfar: N) -> Self {
-        OrthographicBase::new(left, right, bottom, top, znear, zfar).unwrap()
+        Orthographic3::new(left, right, bottom, top, znear, zfar).unwrap()
     }
 
     /// Creates a new homogeneous matrix for a perspective projection.
     #[inline]
     pub fn new_perspective(aspect: N, fovy: N, znear: N, zfar: N) -> Self {
-        PerspectiveBase::new(aspect, fovy, znear, zfar).unwrap()
+        Perspective3::new(aspect, fovy, znear, zfar).unwrap()
     }
 
     /// Creates an isometry that corresponds to the local frame of an observer standing at the
@@ -140,57 +120,30 @@ impl<N, S> SquareMatrix<N, U4, S>
     /// It maps the view direction `target - eye` to the positive `z` axis and the origin to the
     /// `eye`.
     #[inline]
-    pub fn new_observer_frame<SB>(eye:    &PointBase<N, U3, SB>,
-                                  target: &PointBase<N, U3, SB>,
-                                  up:     &ColumnVector<N, U3, SB>)
-                                  -> Self
-        where SB: OwnedStorage<N, U3, U1, Alloc = S::Alloc>,
-              SB::Alloc: OwnedAllocator<N, U3, U1, SB> +
-                         Allocator<N, U1, U3> +
-                         Allocator<N, U3, U3> {
-        IsometryBase::<N, U3, SB, OwnedRotation<N, U3, SB::Alloc>>
-                    ::new_observer_frame(eye, target, up).to_homogeneous()
+    pub fn new_observer_frame(eye: &Point3<N>, target: &Point3<N>, up: &Vector3<N>) -> Self {
+        IsometryMatrix3::new_observer_frame(eye, target, up).to_homogeneous()
     }
 
     /// Builds a right-handed look-at view matrix.
     #[inline]
-    pub fn look_at_rh<SB>(eye:    &PointBase<N, U3, SB>,
-                          target: &PointBase<N, U3, SB>,
-                          up:     &ColumnVector<N, U3, SB>)
-                          -> Self
-        where SB: OwnedStorage<N, U3, U1, Alloc = S::Alloc>,
-              SB::Alloc: OwnedAllocator<N, U3, U1, SB> +
-                         Allocator<N, U1, U3> +
-                         Allocator<N, U3, U3> {
-        IsometryBase::<N, U3, SB, OwnedRotation<N, U3, SB::Alloc>>
-                    ::look_at_rh(eye, target, up).to_homogeneous()
+    pub fn look_at_rh(eye: &Point3<N>, target: &Point3<N>, up: &Vector3<N>) -> Self {
+        IsometryMatrix3::look_at_rh(eye, target, up).to_homogeneous()
     }
 
     /// Builds a left-handed look-at view matrix.
     #[inline]
-    pub fn look_at_lh<SB>(eye:    &PointBase<N, U3, SB>,
-                          target: &PointBase<N, U3, SB>,
-                          up:     &ColumnVector<N, U3, SB>)
-                          -> Self
-        where SB: OwnedStorage<N, U3, U1, Alloc = S::Alloc>,
-              SB::Alloc: OwnedAllocator<N, U3, U1, SB> +
-                         Allocator<N, U1, U3> +
-                         Allocator<N, U3, U3> {
-        IsometryBase::<N, U3, SB, OwnedRotation<N, U3, SB::Alloc>>
-                    ::look_at_lh(eye, target, up).to_homogeneous()
+    pub fn look_at_lh(eye: &Point3<N>, target: &Point3<N>, up: &Vector3<N>) -> Self {
+        IsometryMatrix3::look_at_lh(eye, target, up).to_homogeneous()
     }
 }
 
 
-impl<N, D: DimName, S> SquareMatrix<N, D, S>
-    where N: Scalar + Field,
-          S: Storage<N, D, D> {
-
+impl<N: Scalar + Field, D: DimName, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
     /// Computes the transformation equal to `self` followed by an uniform scaling factor.
     #[inline]
-    pub fn append_scaling(&self, scaling: N) -> OwnedSquareMatrix<N, D, S::Alloc>
+    pub fn append_scaling(&self, scaling: N) -> MatrixN<N, D>
         where D: DimNameSub<U1>,
-              S::Alloc: Allocator<N, DimNameDiff<D, U1>, D> {
+              DefaultAllocator: Allocator<N, D, D> {
         let mut res = self.clone_owned();
         res.append_scaling_mut(scaling);
         res
@@ -198,9 +151,9 @@ impl<N, D: DimName, S> SquareMatrix<N, D, S>
 
     /// Computes the transformation equal to an uniform scaling factor followed by `self`.
     #[inline]
-    pub fn prepend_scaling(&self, scaling: N) -> OwnedSquareMatrix<N, D, S::Alloc>
+    pub fn prepend_scaling(&self, scaling: N) -> MatrixN<N, D>
         where D: DimNameSub<U1>,
-              S::Alloc: Allocator<N, D, DimNameDiff<D, U1>> {
+              DefaultAllocator: Allocator<N, D, D> {
         let mut res = self.clone_owned();
         res.prepend_scaling_mut(scaling);
         res
@@ -208,11 +161,10 @@ impl<N, D: DimName, S> SquareMatrix<N, D, S>
 
     /// Computes the transformation equal to `self` followed by a non-uniform scaling factor.
     #[inline]
-    pub fn append_nonuniform_scaling<SB>(&self, scaling: &ColumnVector<N, DimNameDiff<D, U1>, SB>)
-        -> OwnedSquareMatrix<N, D, S::Alloc>
+    pub fn append_nonuniform_scaling<SB>(&self, scaling: &Vector<N, DimNameDiff<D, U1>, SB>) -> MatrixN<N, D>
         where D: DimNameSub<U1>,
-              SB: Storage<N, DimNameDiff<D, U1>, U1>,
-              S::Alloc: Allocator<N, U1, D> {
+              SB: Storage<N, DimNameDiff<D, U1>>,
+              DefaultAllocator: Allocator<N, D, D> {
         let mut res = self.clone_owned();
         res.append_nonuniform_scaling_mut(scaling);
         res
@@ -220,11 +172,10 @@ impl<N, D: DimName, S> SquareMatrix<N, D, S>
 
     /// Computes the transformation equal to a non-uniform scaling factor followed by `self`.
     #[inline]
-    pub fn prepend_nonuniform_scaling<SB>(&self, scaling: &ColumnVector<N, DimNameDiff<D, U1>, SB>)
-        -> OwnedSquareMatrix<N, D, S::Alloc>
+    pub fn prepend_nonuniform_scaling<SB>(&self, scaling: &Vector<N, DimNameDiff<D, U1>, SB>) -> MatrixN<N, D>
         where D: DimNameSub<U1>,
-              SB: Storage<N, DimNameDiff<D, U1>, U1>,
-              S::Alloc: Allocator<N, D, U1> {
+              SB: Storage<N, DimNameDiff<D, U1>>,
+              DefaultAllocator: Allocator<N, D, D> {
         let mut res = self.clone_owned();
         res.prepend_nonuniform_scaling_mut(scaling);
         res
@@ -232,11 +183,10 @@ impl<N, D: DimName, S> SquareMatrix<N, D, S>
 
     /// Computes the transformation equal to `self` followed by a translation.
     #[inline]
-    pub fn append_translation<SB>(&self, shift: &ColumnVector<N, DimNameDiff<D, U1>, SB>)
-        -> OwnedSquareMatrix<N, D, S::Alloc>
+    pub fn append_translation<SB>(&self, shift: &Vector<N, DimNameDiff<D, U1>, SB>) -> MatrixN<N, D>
         where D: DimNameSub<U1>,
-              SB: Storage<N, DimNameDiff<D, U1>, U1>,
-              S::Alloc: Allocator<N, DimNameDiff<D, U1>, U1> {
+              SB: Storage<N, DimNameDiff<D, U1>>,
+              DefaultAllocator: Allocator<N, D, D> {
         let mut res = self.clone_owned();
         res.append_translation_mut(shift);
         res
@@ -244,28 +194,23 @@ impl<N, D: DimName, S> SquareMatrix<N, D, S>
 
     /// Computes the transformation equal to a translation followed by `self`.
     #[inline]
-    pub fn prepend_translation<SB>(&self, shift: &ColumnVector<N, DimNameDiff<D, U1>, SB>)
-        -> OwnedSquareMatrix<N, D, S::Alloc>
+    pub fn prepend_translation<SB>(&self, shift: &Vector<N, DimNameDiff<D, U1>, SB>) -> MatrixN<N, D>
         where D: DimNameSub<U1>,
-              SB: Storage<N, DimNameDiff<D, U1>, U1>,
-              S::Alloc: Allocator<N, DimNameDiff<D, U1>, U1> +
-                        Allocator<N, DimNameDiff<D, U1>, DimNameDiff<D, U1>> +
-                        Allocator<N, U1, DimNameDiff<D, U1>> {
+              SB: Storage<N, DimNameDiff<D, U1>>,
+              DefaultAllocator: Allocator<N, D, D> +
+                                Allocator<N, DimNameDiff<D, U1>> {
         let mut res = self.clone_owned();
         res.prepend_translation_mut(shift);
         res
     }
 }
 
-impl<N, D: DimName, S> SquareMatrix<N, D, S>
-    where N: Scalar + Field,
-          S: StorageMut<N, D, D> {
+impl<N: Scalar + Field, D: DimName, S: StorageMut<N, D, D>> SquareMatrix<N, D, S> {
 
     /// Computes in-place the transformation equal to `self` followed by an uniform scaling factor.
     #[inline]
     pub fn append_scaling_mut(&mut self, scaling: N)
-        where D: DimNameSub<U1>,
-              S::Alloc: Allocator<N, DimNameDiff<D, U1>, D> {
+        where D: DimNameSub<U1> {
         let mut to_scale = self.fixed_rows_mut::<DimNameDiff<D, U1>>(0);
         to_scale *= scaling;
     }
@@ -273,18 +218,16 @@ impl<N, D: DimName, S> SquareMatrix<N, D, S>
     /// Computes in-place the transformation equal to an uniform scaling factor followed by `self`.
     #[inline]
     pub fn prepend_scaling_mut(&mut self, scaling: N)
-        where D: DimNameSub<U1>,
-              S::Alloc: Allocator<N, D, DimNameDiff<D, U1>> {
+        where D: DimNameSub<U1> {
         let mut to_scale = self.fixed_columns_mut::<DimNameDiff<D, U1>>(0);
         to_scale *= scaling;
     }
 
     /// Computes in-place the transformation equal to `self` followed by a non-uniform scaling factor.
     #[inline]
-    pub fn append_nonuniform_scaling_mut<SB>(&mut self, scaling: &ColumnVector<N, DimNameDiff<D, U1>, SB>)
+    pub fn append_nonuniform_scaling_mut<SB>(&mut self, scaling: &Vector<N, DimNameDiff<D, U1>, SB>)
         where D:  DimNameSub<U1>,
-              SB: Storage<N, DimNameDiff<D, U1>, U1>,
-              S::Alloc: Allocator<N, U1, D> {
+              SB: Storage<N, DimNameDiff<D, U1>> {
         for i in 0 .. scaling.len() {
             let mut to_scale = self.fixed_rows_mut::<U1>(i);
             to_scale *= scaling[i];
@@ -293,10 +236,9 @@ impl<N, D: DimName, S> SquareMatrix<N, D, S>
 
     /// Computes in-place the transformation equal to a non-uniform scaling factor followed by `self`.
     #[inline]
-    pub fn prepend_nonuniform_scaling_mut<SB>(&mut self, scaling: &ColumnVector<N, DimNameDiff<D, U1>, SB>)
+    pub fn prepend_nonuniform_scaling_mut<SB>(&mut self, scaling: &Vector<N, DimNameDiff<D, U1>, SB>)
         where D:  DimNameSub<U1>,
-              SB: Storage<N, DimNameDiff<D, U1>, U1>,
-              S::Alloc: Allocator<N, D, U1> {
+              SB: Storage<N, DimNameDiff<D, U1>> {
         for i in 0 .. scaling.len() {
             let mut to_scale = self.fixed_columns_mut::<U1>(i);
             to_scale *= scaling[i];
@@ -305,10 +247,9 @@ impl<N, D: DimName, S> SquareMatrix<N, D, S>
 
     /// Computes the transformation equal to `self` followed by a translation.
     #[inline]
-    pub fn append_translation_mut<SB>(&mut self, shift: &ColumnVector<N, DimNameDiff<D, U1>, SB>)
+    pub fn append_translation_mut<SB>(&mut self, shift: &Vector<N, DimNameDiff<D, U1>, SB>)
         where D: DimNameSub<U1>,
-              SB: Storage<N, DimNameDiff<D, U1>, U1>,
-              S::Alloc: Allocator<N, DimNameDiff<D, U1>, U1> {
+              SB: Storage<N, DimNameDiff<D, U1>> {
         for i in 0 .. D::dim() {
             for j in 0 .. D::dim() - 1 {
                 self[(j, i)] += shift[j] * self[(D::dim() - 1, i)];
@@ -318,12 +259,10 @@ impl<N, D: DimName, S> SquareMatrix<N, D, S>
 
     /// Computes the transformation equal to a translation followed by `self`.
     #[inline]
-    pub fn prepend_translation_mut<SB>(&mut self, shift: &ColumnVector<N, DimNameDiff<D, U1>, SB>)
+    pub fn prepend_translation_mut<SB>(&mut self, shift: &Vector<N, DimNameDiff<D, U1>, SB>)
         where D: DimNameSub<U1>,
-              SB: Storage<N, DimNameDiff<D, U1>, U1>,
-              S::Alloc: Allocator<N, DimNameDiff<D, U1>, U1> +
-                        Allocator<N, DimNameDiff<D, U1>, DimNameDiff<D, U1>> +
-                        Allocator<N, U1, DimNameDiff<D, U1>> {
+              SB: Storage<N, DimNameDiff<D, U1>>,
+              DefaultAllocator: Allocator<N, DimNameDiff<D, U1>> {
         let scale = self.fixed_slice::<U1, DimNameDiff<D, U1>>(D::dim() - 1, 0).tr_dot(&shift);
         let post_translation = self.fixed_slice::<DimNameDiff<D, U1>, DimNameDiff<D, U1>>(0, 0) * shift;
 
@@ -335,19 +274,12 @@ impl<N, D: DimName, S> SquareMatrix<N, D, S>
 }
 
 
-impl<N, D, SA, SB> Transformation<PointBase<N, DimNameDiff<D, U1>, SB>> for SquareMatrix<N, D, SA>
-    where N:  Real,
-          D:  DimNameSub<U1>,
-          SA: OwnedStorage<N, D, D>,
-          SB: OwnedStorage<N, DimNameDiff<D, U1>, U1, Alloc = SA::Alloc>,
-          SA::Alloc: OwnedAllocator<N, D, D, SA> +
-                     Allocator<N, DimNameDiff<D, U1>, DimNameDiff<D, U1>> +
-                     Allocator<N, DimNameDiff<D, U1>, U1> +
-                     Allocator<N, U1, DimNameDiff<D, U1>>,
-          SB::Alloc: OwnedAllocator<N, DimNameDiff<D, U1>, U1, SB> {
+impl<N: Real, D: DimNameSub<U1>> Transformation<Point<N, DimNameDiff<D, U1>>> for MatrixN<N, D>
+    where DefaultAllocator: Allocator<N, D, D> +
+                            Allocator<N, DimNameDiff<D, U1>> +
+                            Allocator<N, DimNameDiff<D, U1>, DimNameDiff<D, U1>> {
     #[inline]
-    fn transform_vector(&self, v: &ColumnVector<N, DimNameDiff<D, U1>, SB>)
-        -> ColumnVector<N, DimNameDiff<D, U1>, SB> {
+    fn transform_vector(&self, v: &VectorN<N, DimNameDiff<D, U1>>) -> VectorN<N, DimNameDiff<D, U1>> {
         let transform  = self.fixed_slice::<DimNameDiff<D, U1>, DimNameDiff<D, U1>>(0, 0);
         let normalizer = self.fixed_slice::<U1, DimNameDiff<D, U1>>(D::dim() - 1, 0);
         let n = normalizer.tr_dot(&v);
@@ -360,8 +292,7 @@ impl<N, D, SA, SB> Transformation<PointBase<N, DimNameDiff<D, U1>, SB>> for Squa
     }
 
     #[inline]
-    fn transform_point(&self, pt: &PointBase<N, DimNameDiff<D, U1>, SB>)
-        -> PointBase<N, DimNameDiff<D, U1>, SB> {
+    fn transform_point(&self, pt: &Point<N, DimNameDiff<D, U1>>) -> Point<N, DimNameDiff<D, U1>> {
         let transform   = self.fixed_slice::<DimNameDiff<D, U1>, DimNameDiff<D, U1>>(0, 0);
         let translation = self.fixed_slice::<DimNameDiff<D, U1>, U1>(0, D::dim() - 1);
         let normalizer  = self.fixed_slice::<U1, DimNameDiff<D, U1>>(D::dim() - 1, 0);

src/core/componentwise.rs

@@ -4,21 +4,22 @@ use num::Signed;
 
 use alga::general::{ClosedMul, ClosedDiv};
 
-use core::{Scalar, Matrix, OwnedMatrix, MatrixSum};
+use core::{DefaultAllocator, Scalar, Matrix, MatrixMN, MatrixSum};
 use core::dimension::Dim;
 use core::storage::{Storage, StorageMut};
-use core::allocator::SameShapeAllocator;
+use core::allocator::{Allocator, SameShapeAllocator};
 use core::constraint::{ShapeConstraint, SameNumberOfRows, SameNumberOfColumns};
 
 
 /// The type of the result of a matrix componentwise operation.
-pub type MatrixComponentOp<N, R1, C1, R2, C2, SA> = MatrixSum<N, R1, C1, R2, C2, SA>;
+pub type MatrixComponentOp<N, R1, C1, R2, C2> = MatrixSum<N, R1, C1, R2, C2>;
 
 impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /// Computes the componentwise absolute value.
     #[inline]
-    pub fn abs(&self) -> OwnedMatrix<N, R, C, S::Alloc>
-        where N: Signed {
+    pub fn abs(&self) -> MatrixMN<N, R, C>
+        where N: Signed,
+              DefaultAllocator: Allocator<N, R, C> {
         let mut res = self.clone_owned();
 
         for e in res.iter_mut() {
@@ -32,48 +33,72 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
 }
 
 macro_rules! component_binop_impl(
-    ($($binop: ident, $binop_mut: ident, $Trait: ident . $binop_assign: ident, $desc:expr, $desc_mut:expr);* $(;)*) => {$(
-        impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
+    ($($binop: ident, $binop_mut: ident, $binop_assign: ident, $Trait: ident . $op_assign: ident, $desc:expr, $desc_mut:expr);* $(;)*) => {$(
+        impl<N: Scalar, R1: Dim, C1: Dim, SA: Storage<N, R1, C1>> Matrix<N, R1, C1, SA> {
             #[doc = $desc]
             #[inline]
-            pub fn $binop<R2, C2, SB>(&self, rhs: &Matrix<N, R2, C2, SB>) -> MatrixComponentOp<N, R, C, R2, C2, S>
+            pub fn $binop<R2, C2, SB>(&self, rhs: &Matrix<N, R2, C2, SB>) -> MatrixComponentOp<N, R1, C1, R2, C2>
                 where N: $Trait,
                       R2: Dim, C2: Dim,
                       SB: Storage<N, R2, C2>,
-                      S::Alloc: SameShapeAllocator<N, R, C, R2, C2, S>,
-                      ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2> {
+                      DefaultAllocator: SameShapeAllocator<N, R1, C1, R2, C2>,
+                      ShapeConstraint:  SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
         
+                assert_eq!(self.shape(), rhs.shape(), "Componentwise mul/div: mismatched matrix dimensions.");
                 let mut res = self.clone_owned_sum();
 
-                for (res, rhs) in res.iter_mut().zip(rhs.iter()) {
-                    res.$binop_assign(*rhs);
+                for j in 0 .. res.ncols() {
+                    for i in 0 .. res.nrows() {
+                        unsafe {
+                            res.get_unchecked_mut(i, j).$op_assign(*rhs.get_unchecked(i, j));
+                        }
+                    }
                 }
 
                 res
             }
         }
 
-        impl<N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
+        impl<N: Scalar, R1: Dim, C1: Dim, SA: StorageMut<N, R1, C1>> Matrix<N, R1, C1, SA> {
             #[doc = $desc_mut]
             #[inline]
+            pub fn $binop_assign<R2, C2, SB>(&mut self, rhs: &Matrix<N, R2, C2, SB>)
+                where N: $Trait,
+                      R2: Dim,
+                      C2: Dim,
+                      SB: Storage<N, R2, C2>,
+                      ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
+
+                assert_eq!(self.shape(), rhs.shape(), "Componentwise mul/div: mismatched matrix dimensions.");
+
+                for j in 0 .. self.ncols() {
+                    for i in 0 .. self.nrows() {
+                        unsafe {
+                            self.get_unchecked_mut(i, j).$op_assign(*rhs.get_unchecked(i, j));
+                        }
+                    }
+                }
+            }
+
+            #[doc = $desc_mut]
+            #[inline]
+            #[deprecated(note = "This is renamed using the `_assign` sufix instead of the `_mut` suffix.")]
             pub fn $binop_mut<R2, C2, SB>(&mut self, rhs: &Matrix<N, R2, C2, SB>)
                 where N: $Trait,
                       R2: Dim,
                       C2: Dim,
                       SB: Storage<N, R2, C2>,
-                      ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2> {
-                for (me, rhs) in self.iter_mut().zip(rhs.iter()) {
-                    me.$binop_assign(*rhs);
-                }
+                      ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
+                self.$binop_assign(rhs)
             }
         }
     )*}
 );
 
 component_binop_impl!(
-    component_mul, component_mul_mut, ClosedMul.mul_assign,
+    component_mul, component_mul_mut, component_mul_assign, ClosedMul.mul_assign,
     "Componentwise matrix multiplication.", "Mutable, componentwise matrix multiplication.";
-    component_div, component_div_mut, ClosedDiv.div_assign,
+    component_div, component_div_mut, component_div_assign, ClosedDiv.div_assign,
     "Componentwise matrix division.", "Mutable, componentwise matrix division.";
     // FIXME: add other operators like bitshift, etc. ?
 );

src/core/constraint.rs

@@ -6,8 +6,7 @@ use core::dimension::{Dim, DimName, Dynamic};
 pub struct ShapeConstraint;
 
 /// Constraints `C1` and `R2` to be equivalent.
-pub trait AreMultipliable<R1: Dim, C1: Dim,
-                          R2: Dim, C2: Dim> {
+pub trait AreMultipliable<R1: Dim, C1: Dim, R2: Dim, C2: Dim>: DimEq<C1, R2> {
 }
 
 
@@ -15,11 +14,30 @@ impl<R1: Dim, C1: Dim, R2: Dim, C2: Dim> AreMultipliable<R1, C1, R2, C2> for Sha
 where ShapeConstraint: DimEq<C1, R2> {
 }
 
+/// Constraints `D1` and `D2` to be equivalent.
+pub trait DimEq<D1: Dim, D2: Dim> {
+    /// This is either equal to `D1` or `D2`, always choosing the one (if any) which is a type-level
+    /// constant.
+    type Representative: Dim;
+}
+
+impl<D: Dim> DimEq<D, D> for ShapeConstraint {
+    type Representative = D;
+}
+
+impl<D: DimName> DimEq<D, Dynamic> for ShapeConstraint {
+    type Representative = D;
+}
+
+impl<D: DimName> DimEq<Dynamic, D> for ShapeConstraint {
+    type Representative = D;
+}
+
 macro_rules! equality_trait_decl(
     ($($doc: expr, $Trait: ident),* $(,)*) => {$(
         // XXX: we can't do something like `DimEq<D1> for D2` because we would require a blancket impl…
         #[doc = $doc]
-        pub trait $Trait<D1: Dim, D2: Dim> {
+        pub trait $Trait<D1: Dim, D2: Dim>: DimEq<D1, D2> + DimEq<D2, D1> {
             /// This is either equal to `D1` or `D2`, always choosing the one (if any) which is a type-level
             /// constant.
             type Representative: Dim;
@@ -40,9 +58,6 @@ macro_rules! equality_trait_decl(
 );
 
 equality_trait_decl!(
-    "Constraints `D1` and `D2` to be equivalent.",
-    DimEq,
-
     "Constraints `D1` and `D2` to be equivalent. \
      They are both assumed to be the number of \
      rows of a matrix.",

src/core/construction.rs

@@ -1,5 +1,7 @@
 #[cfg(feature = "arbitrary")]
 use quickcheck::{Arbitrary, Gen};
+#[cfg(feature = "arbitrary")]
+use core::storage::Owned;
 
 use std::iter;
 use num::{Zero, One, Bounded};
@@ -8,38 +10,44 @@ use typenum::{self, Cmp, Greater};
 
 use alga::general::{ClosedAdd, ClosedMul};
 
-use core::{Scalar, Matrix, SquareMatrix, ColumnVector, Unit};
+use core::{DefaultAllocator, Scalar, Matrix, Vector, Unit, MatrixMN, MatrixN, VectorN};
 use core::dimension::{Dim, DimName, Dynamic, U1, U2, U3, U4, U5, U6};
-use core::allocator::{Allocator, OwnedAllocator};
-use core::storage::{Storage, OwnedStorage};
+use core::allocator::Allocator;
+use core::storage::Storage;
 
 /*
  *
  * Generic constructors.
  *
  */
-impl<N: Scalar, R: Dim, C: Dim, S: OwnedStorage<N, R, C>> Matrix<N, R, C, S>
-    // XXX: needed because of a compiler bug. See the rust compiler issue #26026.
-    where S::Alloc: OwnedAllocator<N, R, C, S> {
+impl<N: Scalar, R: Dim, C: Dim> MatrixMN<N, R, C>
+    where DefaultAllocator: Allocator<N, R, C> {
     /// Creates a new uninitialized matrix. If the matrix has a compile-time dimension, this panics
     /// if `nrows != R::to_usize()` or `ncols != C::to_usize()`.
     #[inline]
-    pub unsafe fn new_uninitialized_generic(nrows: R, ncols: C) -> Matrix<N, R, C, S> {
-        Matrix::from_data(S::Alloc::allocate_uninitialized(nrows, ncols))
+    pub unsafe fn new_uninitialized_generic(nrows: R, ncols: C) -> Self {
+        Self::from_data(DefaultAllocator::allocate_uninitialized(nrows, ncols))
     }
 
     /// Creates a matrix with all its elements set to `elem`.
     #[inline]
-    pub fn from_element_generic(nrows: R, ncols: C, elem: N) -> Matrix<N, R, C, S> {
+    pub fn from_element_generic(nrows: R, ncols: C, elem: N) -> Self {
         let len = nrows.value() * ncols.value();
-        Matrix::from_iterator_generic(nrows, ncols, iter::repeat(elem).take(len))
+        Self::from_iterator_generic(nrows, ncols, iter::repeat(elem).take(len))
+    }
+
+    /// Creates a matrix with all its elements set to 0.
+    #[inline]
+    pub fn zeros_generic(nrows: R, ncols: C) -> Self
+        where N: Zero {
+        Self::from_element_generic(nrows, ncols, N::zero())
     }
 
     /// Creates a matrix with all its elements filled by an iterator.
     #[inline]
-    pub fn from_iterator_generic<I>(nrows: R, ncols: C, iter: I) -> Matrix<N, R, C, S>
+    pub fn from_iterator_generic<I>(nrows: R, ncols: C, iter: I) -> Self
         where I: IntoIterator<Item = N> {
-        Matrix::from_data(S::Alloc::allocate_from_iterator(nrows, ncols, iter))
+        Self::from_data(DefaultAllocator::allocate_from_iterator(nrows, ncols, iter))
     }
 
     /// Creates a matrix with its elements filled with the components provided by a slice in
@@ -48,7 +56,7 @@ impl<N: Scalar, R: Dim, C: Dim, S: OwnedStorage<N, R, C>> Matrix<N, R, C, S>
     /// The order of elements in the slice must follow the usual mathematic writing, i.e.,
     /// row-by-row.
     #[inline]
-    pub fn from_row_slice_generic(nrows: R, ncols: C, slice: &[N]) -> Matrix<N, R, C, S> {
+    pub fn from_row_slice_generic(nrows: R, ncols: C, slice: &[N]) -> Self {
         assert!(slice.len() == nrows.value() * ncols.value(),
                 "Matrix init. error: the slice did not contain the right number of elements.");
 
@@ -69,14 +77,14 @@ impl<N: Scalar, R: Dim, C: Dim, S: OwnedStorage<N, R, C>> Matrix<N, R, C, S>
     /// Creates a matrix with its elements filled with the components provided by a slice. The
     /// components must have the same layout as the matrix data storage (i.e. row-major or column-major).
     #[inline]
-    pub fn from_column_slice_generic(nrows: R, ncols: C, slice: &[N]) -> Matrix<N, R, C, S> {
-        Matrix::from_iterator_generic(nrows, ncols, slice.iter().cloned())
+    pub fn from_column_slice_generic(nrows: R, ncols: C, slice: &[N]) -> Self {
+        Self::from_iterator_generic(nrows, ncols, slice.iter().cloned())
     }
 
     /// Creates a matrix filled with the results of a function applied to each of its component
     /// coordinates.
     #[inline]
-    pub fn from_fn_generic<F>(nrows: R, ncols: C, mut f: F) -> Matrix<N, R, C, S>
+    pub fn from_fn_generic<F>(nrows: R, ncols: C, mut f: F) -> Self
         where F: FnMut(usize, usize) -> N {
         let mut res = unsafe { Self::new_uninitialized_generic(nrows, ncols) };
 
@@ -94,7 +102,7 @@ impl<N: Scalar, R: Dim, C: Dim, S: OwnedStorage<N, R, C>> Matrix<N, R, C, S>
     /// If the matrix is not square, the largest square submatrix starting at index `(0, 0)` is set
     /// to the identity matrix. All other entries are set to zero.
     #[inline]
-    pub fn identity_generic(nrows: R, ncols: C) -> Matrix<N, R, C, S>
+    pub fn identity_generic(nrows: R, ncols: C) -> Self
         where N: Zero + One {
         Self::from_diagonal_element_generic(nrows, ncols, N::one())
     }
@@ -104,10 +112,9 @@ impl<N: Scalar, R: Dim, C: Dim, S: OwnedStorage<N, R, C>> Matrix<N, R, C, S>
     /// If the matrix is not square, the largest square submatrix starting at index `(0, 0)` is set
     /// to the identity matrix. All other entries are set to zero.
     #[inline]
-    pub fn from_diagonal_element_generic(nrows: R, ncols: C, elt: N) -> Matrix<N, R, C, S>
+    pub fn from_diagonal_element_generic(nrows: R, ncols: C, elt: N) -> Self
         where N: Zero + One {
-        let mut res = unsafe { Self::new_uninitialized_generic(nrows, ncols) };
-        res.fill(N::zero());
+        let mut res = Self::zeros_generic(nrows, ncols);
 
         for i in 0 .. ::min(nrows.value(), ncols.value()) {
             unsafe { *res.get_unchecked_mut(i, i) = elt }
@@ -116,12 +123,29 @@ impl<N: Scalar, R: Dim, C: Dim, S: OwnedStorage<N, R, C>> Matrix<N, R, C, S>
         res
     }
 
+    /// Creates a new matrix that may be rectangular. The first `elts.len()` diagonal elements are
+    /// filled with the content of `elts`. Others are set to 0.
+    ///
+    /// Panics if `elts.len()` is larger than the minimum among `nrows` and `ncols`.
+    #[inline]
+    pub fn from_partial_diagonal_generic(nrows: R, ncols: C, elts: &[N]) -> Self
+        where N: Zero {
+        let mut res = Self::zeros_generic(nrows, ncols);
+        assert!(elts.len() <= ::min(nrows.value(), ncols.value()), "Too many diagonal elements provided.");
+
+        for (i, elt) in elts.iter().enumerate() {
+            unsafe { *res.get_unchecked_mut(i, i) = *elt }
+        }
+
+        res
+    }
+
     /// Builds a new matrix from its rows.
     ///
     /// Panics if not enough rows are provided (for statically-sized matrices), or if all rows do
     /// not have the same dimensions.
     #[inline]
-    pub fn from_rows<SB>(rows: &[Matrix<N, U1, C, SB>]) -> Matrix<N, R, C, S>
+    pub fn from_rows<SB>(rows: &[Matrix<N, U1, C, SB>]) -> Self
         where SB: Storage<N, U1, C> {
 
         assert!(rows.len() > 0, "At least one row must be given.");
@@ -144,8 +168,8 @@ impl<N: Scalar, R: Dim, C: Dim, S: OwnedStorage<N, R, C>> Matrix<N, R, C, S>
     /// Panics if not enough columns are provided (for statically-sized matrices), or if all
     /// columns do not have the same dimensions.
     #[inline]
-    pub fn from_columns<SB>(columns: &[ColumnVector<N, R, SB>]) -> Matrix<N, R, C, S>
-        where SB: Storage<N, R, U1> {
+    pub fn from_columns<SB>(columns: &[Vector<N, R, SB>]) -> Self
+        where SB: Storage<N, R> {
 
         assert!(columns.len() > 0, "At least one column must be given.");
         let ncols = C::try_to_usize().unwrap_or(columns.len());
@@ -160,31 +184,27 @@ impl<N: Scalar, R: Dim, C: Dim, S: OwnedStorage<N, R, C>> Matrix<N, R, C, S>
         // FIXME: optimize that.
         Self::from_fn_generic(R::from_usize(nrows), C::from_usize(ncols), |i, j| columns[j][i])
     }
-}
 
-impl<N, R: Dim, C: Dim, S> Matrix<N, R, C, S>
-    where N: Scalar + Rand,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
     /// Creates a matrix filled with random values.
     #[inline]
-    pub fn new_random_generic(nrows: R, ncols: C) -> Matrix<N, R, C, S> {
-        Matrix::from_fn_generic(nrows, ncols, |_, _| rand::random())
+    pub fn new_random_generic(nrows: R, ncols: C) -> Self
+        where N: Rand {
+        Self::from_fn_generic(nrows, ncols, |_, _| rand::random())
     }
 }
 
-impl<N, D: Dim, S> SquareMatrix<N, D, S>
-    where N: Scalar + Zero,
-          S: OwnedStorage<N, D, D>,
-          S::Alloc: OwnedAllocator<N, D, D, S> {
+impl<N, D: Dim> MatrixN<N, D>
+    where N: Scalar,
+          DefaultAllocator: Allocator<N, D, D> {
     /// Creates a square matrix with its diagonal set to `diag` and all other entries set to 0.
     #[inline]
-    pub fn from_diagonal<SB: Storage<N, D, U1>>(diag: &ColumnVector<N, D, SB>) -> Self {
+    pub fn from_diagonal<SB: Storage<N, D>>(diag: &Vector<N, D, SB>) -> Self
+        where N: Zero {
         let (dim, _) = diag.data.shape();
-        let mut res = Self::from_element_generic(dim, dim, N::zero());
+        let mut res = Self::zeros_generic(dim, dim);
 
         for i in 0 .. diag.len() {
-            unsafe { *res.get_unchecked_mut(i, i) = *diag.get_unchecked(i, 0); }
+            unsafe { *res.get_unchecked_mut(i, i) = *diag.vget_unchecked(i); }
         }
 
         res
@@ -199,25 +219,31 @@ impl<N, D: Dim, S> SquareMatrix<N, D, S>
  */
 macro_rules! impl_constructors(
     ($($Dims: ty),*; $(=> $DimIdent: ident: $DimBound: ident),*; $($gargs: expr),*; $($args: ident),*) => {
-        impl<N: Scalar, $($DimIdent: $DimBound, )* S> Matrix<N $(, $Dims)*, S>
-            where S: OwnedStorage<N $(, $Dims)*>,
-                  S::Alloc: OwnedAllocator<N $(, $Dims)*, S> {
+        impl<N: Scalar, $($DimIdent: $DimBound, )*> MatrixMN<N $(, $Dims)*>
+            where DefaultAllocator: Allocator<N $(, $Dims)*> {
 
             /// Creates a new uninitialized matrix.
             #[inline]
-            pub unsafe fn new_uninitialized($($args: usize),*) -> Matrix<N $(, $Dims)*, S> {
+            pub unsafe fn new_uninitialized($($args: usize),*) -> Self {
                 Self::new_uninitialized_generic($($gargs),*)
             }
 
             /// Creates a matrix with all its elements set to `elem`.
             #[inline]
-            pub fn from_element($($args: usize,)* elem: N) -> Matrix<N $(, $Dims)*, S> {
+            pub fn from_element($($args: usize,)* elem: N) -> Self {
                 Self::from_element_generic($($gargs, )* elem)
             }
 
+            /// Creates a matrix with all its elements set to `0`.
+            #[inline]
+            pub fn zeros($($args: usize),*) -> Self
+                where N: Zero {
+                Self::zeros_generic($($gargs),*)
+            }
+
             /// Creates a matrix with all its elements filled by an iterator.
             #[inline]
-            pub fn from_iterator<I>($($args: usize,)* iter: I) -> Matrix<N $(, $Dims)*, S>
+            pub fn from_iterator<I>($($args: usize,)* iter: I) -> Self
                 where I: IntoIterator<Item = N> {
                 Self::from_iterator_generic($($gargs, )* iter)
             }
@@ -228,14 +254,14 @@ macro_rules! impl_constructors(
             /// The order of elements in the slice must follow the usual mathematic writing, i.e.,
             /// row-by-row.
             #[inline]
-            pub fn from_row_slice($($args: usize,)* slice: &[N]) -> Matrix<N $(, $Dims)*, S> {
+            pub fn from_row_slice($($args: usize,)* slice: &[N]) -> Self {
                 Self::from_row_slice_generic($($gargs, )* slice)
             }
 
             /// Creates a matrix with its elements filled with the components provided by a slice
             /// in column-major order.
             #[inline]
-            pub fn from_column_slice($($args: usize,)* slice: &[N]) -> Matrix<N $(, $Dims)*, S> {
+            pub fn from_column_slice($($args: usize,)* slice: &[N]) -> Self {
                 Self::from_column_slice_generic($($gargs, )* slice)
             }
 
@@ -243,7 +269,7 @@ macro_rules! impl_constructors(
             /// component coordinates.
             // FIXME: don't take a dimension of the matrix is statically sized.
             #[inline]
-            pub fn from_fn<F>($($args: usize,)* f: F) -> Matrix<N $(, $Dims)*, S>
+            pub fn from_fn<F>($($args: usize,)* f: F) -> Self
                 where F: FnMut(usize, usize) -> N {
                 Self::from_fn_generic($($gargs, )* f)
             }
@@ -252,7 +278,7 @@ macro_rules! impl_constructors(
             /// submatrix (starting at the first row and column) is set to the identity while all
             /// other entries are set to zero.
             #[inline]
-            pub fn identity($($args: usize,)*) -> Matrix<N $(, $Dims)*, S>
+            pub fn identity($($args: usize,)*) -> Self
                 where N: Zero + One {
                 Self::identity_generic($($gargs),* )
             }
@@ -260,19 +286,28 @@ macro_rules! impl_constructors(
             /// Creates a matrix filled with its diagonal filled with `elt` and all other
             /// components set to zero.
             #[inline]
-            pub fn from_diagonal_element($($args: usize,)* elt: N) -> Matrix<N $(, $Dims)*, S>
+            pub fn from_diagonal_element($($args: usize,)* elt: N) -> Self
                 where N: Zero + One {
                 Self::from_diagonal_element_generic($($gargs, )* elt)
             }
+
+            /// Creates a new matrix that may be rectangular. The first `elts.len()` diagonal
+            /// elements are filled with the content of `elts`. Others are set to 0.
+            ///
+            /// Panics if `elts.len()` is larger than the minimum among `nrows` and `ncols`.
+            #[inline]
+            pub fn from_partial_diagonal($($args: usize,)* elts: &[N]) -> Self
+                where N: Zero {
+                Self::from_partial_diagonal_generic($($gargs, )* elts)
+            }
         }
 
-        impl<N: Scalar + Rand, $($DimIdent: $DimBound, )* S> Matrix<N $(, $Dims)*, S>
-            where S: OwnedStorage<N $(, $Dims)*>,
-                  S::Alloc: OwnedAllocator<N $(, $Dims)*, S> {
+        impl<N: Scalar + Rand, $($DimIdent: $DimBound, )*> MatrixMN<N $(, $Dims)*>
+            where DefaultAllocator: Allocator<N $(, $Dims)*> {
 
             /// Creates a matrix filled with random values.
             #[inline]
-            pub fn new_random($($args: usize),*) -> Matrix<N $(, $Dims)*, S> {
+            pub fn new_random($($args: usize),*) -> Self {
                 Self::new_random_generic($($gargs),*)
             }
         }
@@ -305,10 +340,9 @@ impl_constructors!(Dynamic, Dynamic;
  * Zero, One, Rand traits.
  *
  */
-impl<N, R: DimName, C: DimName, S> Zero for Matrix<N, R, C, S>
+impl<N, R: DimName, C: DimName> Zero for MatrixMN<N, R, C>
     where N: Scalar + Zero + ClosedAdd,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+          DefaultAllocator: Allocator<N, R, C> {
     #[inline]
     fn zero() -> Self {
         Self::from_element(N::zero())
@@ -320,20 +354,18 @@ impl<N, R: DimName, C: DimName, S> Zero for Matrix<N, R, C, S>
     }
 }
 
-impl<N, D: DimName, S> One for Matrix<N, D, D, S>
+impl<N, D: DimName> One for MatrixN<N, D>
     where N: Scalar + Zero + One + ClosedMul + ClosedAdd,
-          S: OwnedStorage<N, D, D>,
-          S::Alloc: OwnedAllocator<N, D, D, S> {
+          DefaultAllocator: Allocator<N, D, D> {
     #[inline]
     fn one() -> Self {
         Self::identity()
     }
 }
 
-impl<N, R: DimName, C: DimName, S> Bounded for Matrix<N, R, C, S>
+impl<N, R: DimName, C: DimName> Bounded for MatrixMN<N, R, C>
     where N: Scalar + Bounded,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+          DefaultAllocator: Allocator<N, R, C> {
     #[inline]
     fn max_value() -> Self {
         Self::from_element(N::max_value())
@@ -345,9 +377,8 @@ impl<N, R: DimName, C: DimName, S> Bounded for Matrix<N, R, C, S>
     }
 }
 
-impl<N: Scalar + Rand, R: Dim, C: Dim, S> Rand for Matrix<N, R, C, S>
-    where S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+impl<N: Scalar + Rand, R: Dim, C: Dim> Rand for MatrixMN<N, R, C>
+    where DefaultAllocator: Allocator<N, R, C> {
     #[inline]
     fn rand<G: Rng>(rng: &mut G) -> Self {
         let nrows = R::try_to_usize().unwrap_or(rng.gen_range(0, 10));
@@ -359,11 +390,11 @@ impl<N: Scalar + Rand, R: Dim, C: Dim, S> Rand for Matrix<N, R, C, S>
 
 
 #[cfg(feature = "arbitrary")]
-impl<N, R, C, S> Arbitrary for Matrix<N, R, C, S>
+impl<N, R, C> Arbitrary for MatrixMN<N, R, C>
     where R: Dim, C: Dim,
           N: Scalar + Arbitrary + Send,
-          S: OwnedStorage<N, R, C> + Send,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+          DefaultAllocator: Allocator<N, R, C>,
+          Owned<N, R, C>: Clone + Send {
     #[inline]
     fn arbitrary<G: Gen>(g: &mut G) -> Self {
         let nrows = R::try_to_usize().unwrap_or(g.gen_range(0, 10));
@@ -381,13 +412,12 @@ impl<N, R, C, S> Arbitrary for Matrix<N, R, C, S>
  */
 macro_rules! componentwise_constructors_impl(
     ($($R: ty, $C: ty, $($args: ident:($irow: expr,$icol: expr)),*);* $(;)*) => {$(
-        impl<N, S> Matrix<N, $R, $C, S>
+        impl<N> MatrixMN<N, $R, $C>
             where N: Scalar,
-                  S: OwnedStorage<N, $R, $C>,
-                  S::Alloc: OwnedAllocator<N, $R, $C, S> {
+                  DefaultAllocator: Allocator<N, $R, $C> {
             /// Initializes this matrix from its components.
             #[inline]
-            pub fn new($($args: N),*) -> Matrix<N, $R, $C, S> {
+            pub fn new($($args: N),*) -> Self {
                 unsafe {
                     let mut res = Self::new_uninitialized();
                     $( *res.get_unchecked_mut($irow, $icol) = $args; )*
@@ -549,16 +579,15 @@ componentwise_constructors_impl!(
  * Axis constructors.
  *
  */
-impl<N, R: DimName, S> ColumnVector<N, R, S>
+impl<N, R: DimName> VectorN<N, R>
 where N: Scalar + Zero + One,
-      S: OwnedStorage<N, R, U1>,
-      S::Alloc: OwnedAllocator<N, R, U1, S> {
+      DefaultAllocator: Allocator<N, R> {
     /// The column vector with a 1 as its first component, and zero elsewhere.
     #[inline]
     pub fn x() -> Self
       where R::Value: Cmp<typenum::U0, Output = Greater> {
-        let mut res = Self::from_element(N::zero());
-        unsafe { *res.get_unchecked_mut(0, 0) = N::one(); }
+        let mut res = Self::zeros();
+        unsafe { *res.vget_unchecked_mut(0) = N::one(); }
 
         res
     }
@@ -567,8 +596,8 @@ where N: Scalar + Zero + One,
     #[inline]
     pub fn y() -> Self
       where R::Value: Cmp<typenum::U1, Output = Greater> {
-        let mut res = Self::from_element(N::zero());
-        unsafe { *res.get_unchecked_mut(1, 0) = N::one(); }
+        let mut res = Self::zeros();
+        unsafe { *res.vget_unchecked_mut(1) = N::one(); }
 
         res
     }
@@ -577,8 +606,8 @@ where N: Scalar + Zero + One,
     #[inline]
     pub fn z() -> Self
       where R::Value: Cmp<typenum::U2, Output = Greater> {
-        let mut res = Self::from_element(N::zero());
-        unsafe { *res.get_unchecked_mut(2, 0) = N::one(); }
+        let mut res = Self::zeros();
+        unsafe { *res.vget_unchecked_mut(2) = N::one(); }
 
         res
     }
@@ -587,8 +616,8 @@ where N: Scalar + Zero + One,
     #[inline]
     pub fn w() -> Self
       where R::Value: Cmp<typenum::U3, Output = Greater> {
-        let mut res = Self::from_element(N::zero());
-        unsafe { *res.get_unchecked_mut(3, 0) = N::one(); }
+        let mut res = Self::zeros();
+        unsafe { *res.vget_unchecked_mut(3) = N::one(); }
 
         res
     }
@@ -597,8 +626,8 @@ where N: Scalar + Zero + One,
     #[inline]
     pub fn a() -> Self
       where R::Value: Cmp<typenum::U4, Output = Greater> {
-        let mut res = Self::from_element(N::zero());
-        unsafe { *res.get_unchecked_mut(4, 0) = N::one(); }
+        let mut res = Self::zeros();
+        unsafe { *res.vget_unchecked_mut(4) = N::one(); }
 
         res
     }
@@ -607,8 +636,8 @@ where N: Scalar + Zero + One,
     #[inline]
     pub fn b() -> Self
       where R::Value: Cmp<typenum::U5, Output = Greater> {
-        let mut res = Self::from_element(N::zero());
-        unsafe { *res.get_unchecked_mut(5, 0) = N::one(); }
+        let mut res = Self::zeros();
+        unsafe { *res.vget_unchecked_mut(5) = N::one(); }
 
         res
     }

src/core/conversion.rs

@@ -3,37 +3,35 @@ use std::mem;
 use std::convert::{From, Into, AsRef, AsMut};
 use alga::general::{SubsetOf, SupersetOf};
 
-use core::{Scalar, Matrix};
+use core::{DefaultAllocator, Scalar, Matrix, MatrixMN};
 use core::dimension::{Dim,
     U1,  U2,  U3,  U4,
     U5,  U6,  U7,  U8,
     U9,  U10, U11, U12,
     U13, U14, U15, U16
 };
-use core::constraint::{ShapeConstraint, SameNumberOfRows, SameNumberOfColumns};
-use core::storage::{Storage, StorageMut, OwnedStorage};
 use core::iter::{MatrixIter, MatrixIterMut};
-use core::allocator::{OwnedAllocator, SameShapeAllocator};
+use core::constraint::{ShapeConstraint, SameNumberOfRows, SameNumberOfColumns};
+use core::storage::{ContiguousStorage, ContiguousStorageMut, Storage, StorageMut};
+use core::allocator::{Allocator, SameShapeAllocator};
 
 
 // FIXME: too bad this won't work allo slice conversions.
-impl<N1, N2, R1, C1, R2, C2, SA, SB> SubsetOf<Matrix<N2, R2, C2, SB>> for Matrix<N1, R1, C1, SA>
+impl<N1, N2, R1, C1, R2, C2> SubsetOf<MatrixMN<N2, R2, C2>> for MatrixMN<N1, R1, C1>
     where R1: Dim, C1: Dim, R2: Dim, C2: Dim,
           N1: Scalar,
           N2: Scalar + SupersetOf<N1>,
-          SA: OwnedStorage<N1, R1, C1>,
-          SB: OwnedStorage<N2, R2, C2>,
-          SB::Alloc: OwnedAllocator<N2, R2, C2, SB>,
-          SA::Alloc: OwnedAllocator<N1, R1, C1, SA> +
-                     SameShapeAllocator<N1, R1, C1, R2, C2, SA>,
+          DefaultAllocator: Allocator<N2, R2, C2> +
+                            Allocator<N1, R1, C1> +
+                            SameShapeAllocator<N1, R1, C1, R2, C2>,
           ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
     #[inline]
-    fn to_superset(&self) -> Matrix<N2, R2, C2, SB> {
+    fn to_superset(&self) -> MatrixMN<N2, R2, C2> {
         let (nrows, ncols) = self.shape();
         let nrows2 = R2::from_usize(nrows);
         let ncols2 = C2::from_usize(ncols);
 
-        let mut res = unsafe { Matrix::<N2, R2, C2, SB>::new_uninitialized_generic(nrows2, ncols2) };
+        let mut res = unsafe { MatrixMN::<N2, R2, C2>::new_uninitialized_generic(nrows2, ncols2) };
         for i in 0 .. nrows {
             for j in 0 .. ncols {
                 unsafe {
@@ -46,12 +44,12 @@ impl<N1, N2, R1, C1, R2, C2, SA, SB> SubsetOf<Matrix<N2, R2, C2, SB>> for Matrix
     }
 
     #[inline]
-    fn is_in_subset(m: &Matrix<N2, R2, C2, SB>) -> bool {
+    fn is_in_subset(m: &MatrixMN<N2, R2, C2>) -> bool {
         m.iter().all(|e| e.is_in_subset())
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(m: &Matrix<N2, R2, C2, SB>) -> Self {
+    unsafe fn from_superset_unchecked(m: &MatrixMN<N2, R2, C2>) -> Self {
         let (nrows2, ncols2) = m.shape();
         let nrows = R1::from_usize(nrows2);
         let ncols = C1::from_usize(ncols2);
@@ -90,10 +88,9 @@ impl<'a, N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> IntoIterator for &'a
 
 macro_rules! impl_from_into_asref_1D(
     ($(($NRows: ident, $NCols: ident) => $SZ: expr);* $(;)*) => {$(
-        impl<N, S> From<[N; $SZ]> for Matrix<N, $NRows, $NCols, S>
+        impl<N> From<[N; $SZ]> for MatrixMN<N, $NRows, $NCols>
         where N: Scalar,
-              S: OwnedStorage<N, $NRows, $NCols>,
-              S::Alloc: OwnedAllocator<N, $NRows, $NCols, S> {
+              DefaultAllocator: Allocator<N, $NRows, $NCols> {
             #[inline]
             fn from(arr: [N; $SZ]) -> Self {
                 unsafe {
@@ -107,8 +104,7 @@ macro_rules! impl_from_into_asref_1D(
 
         impl<N, S> Into<[N; $SZ]> for Matrix<N, $NRows, $NCols, S>
         where N: Scalar,
-              S: OwnedStorage<N, $NRows, $NCols>,
-              S::Alloc: OwnedAllocator<N, $NRows, $NCols, S> {
+              S: ContiguousStorage<N, $NRows, $NCols> {
             #[inline]
             fn into(self) -> [N; $SZ] {
                 unsafe {
@@ -122,8 +118,7 @@ macro_rules! impl_from_into_asref_1D(
 
         impl<N, S> AsRef<[N; $SZ]> for Matrix<N, $NRows, $NCols, S>
         where N: Scalar,
-              S: OwnedStorage<N, $NRows, $NCols>,
-              S::Alloc: OwnedAllocator<N, $NRows, $NCols, S> {
+              S: ContiguousStorage<N, $NRows, $NCols> {
             #[inline]
             fn as_ref(&self) -> &[N; $SZ] {
                 unsafe {
@@ -134,8 +129,7 @@ macro_rules! impl_from_into_asref_1D(
 
         impl<N, S> AsMut<[N; $SZ]> for Matrix<N, $NRows, $NCols, S>
         where N: Scalar,
-              S: OwnedStorage<N, $NRows, $NCols>,
-              S::Alloc: OwnedAllocator<N, $NRows, $NCols, S> {
+              S: ContiguousStorageMut<N, $NRows, $NCols> {
             #[inline]
             fn as_mut(&mut self) -> &mut [N; $SZ] {
                 unsafe {
@@ -165,10 +159,8 @@ impl_from_into_asref_1D!(
 
 macro_rules! impl_from_into_asref_2D(
     ($(($NRows: ty, $NCols: ty) => ($SZRows: expr, $SZCols: expr));* $(;)*) => {$(
-        impl<N, S> From<[[N; $SZRows]; $SZCols]> for Matrix<N, $NRows, $NCols, S>
-        where N: Scalar,
-              S: OwnedStorage<N, $NRows, $NCols>,
-              S::Alloc: OwnedAllocator<N, $NRows, $NCols, S> {
+        impl<N: Scalar> From<[[N; $SZRows]; $SZCols]> for MatrixMN<N, $NRows, $NCols>
+        where DefaultAllocator: Allocator<N, $NRows, $NCols> {
             #[inline]
             fn from(arr: [[N; $SZRows]; $SZCols]) -> Self {
                 unsafe {
@@ -180,10 +172,8 @@ macro_rules! impl_from_into_asref_2D(
             }
         }
 
-        impl<N, S> Into<[[N; $SZRows]; $SZCols]> for Matrix<N, $NRows, $NCols, S>
-        where N: Scalar,
-              S: OwnedStorage<N, $NRows, $NCols>,
-              S::Alloc: OwnedAllocator<N, $NRows, $NCols, S> {
+        impl<N: Scalar, S> Into<[[N; $SZRows]; $SZCols]> for Matrix<N, $NRows, $NCols, S>
+        where S: ContiguousStorage<N, $NRows, $NCols> {
             #[inline]
             fn into(self) -> [[N; $SZRows]; $SZCols] {
                 unsafe {
@@ -195,10 +185,8 @@ macro_rules! impl_from_into_asref_2D(
             }
         }
 
-        impl<N, S> AsRef<[[N; $SZRows]; $SZCols]> for Matrix<N, $NRows, $NCols, S>
-        where N: Scalar,
-              S: OwnedStorage<N, $NRows, $NCols>,
-              S::Alloc: OwnedAllocator<N, $NRows, $NCols, S> {
+        impl<N: Scalar, S> AsRef<[[N; $SZRows]; $SZCols]> for Matrix<N, $NRows, $NCols, S>
+        where S: ContiguousStorage<N, $NRows, $NCols> {
             #[inline]
             fn as_ref(&self) -> &[[N; $SZRows]; $SZCols] {
                 unsafe {
@@ -207,10 +195,8 @@ macro_rules! impl_from_into_asref_2D(
             }
         }
 
-        impl<N, S> AsMut<[[N; $SZRows]; $SZCols]> for Matrix<N, $NRows, $NCols, S>
-        where N: Scalar,
-              S: OwnedStorage<N, $NRows, $NCols>,
-              S::Alloc: OwnedAllocator<N, $NRows, $NCols, S> {
+        impl<N: Scalar, S> AsMut<[[N; $SZRows]; $SZCols]> for Matrix<N, $NRows, $NCols, S>
+        where S: ContiguousStorageMut<N, $NRows, $NCols> {
             #[inline]
             fn as_mut(&mut self) -> &mut [[N; $SZRows]; $SZCols] {
                 unsafe {
@@ -222,7 +208,7 @@ macro_rules! impl_from_into_asref_2D(
 );
 
 
-// Implement for matrices with shape 2x2 .. 4x4.
+// Implement for matrices with shape 2x2 .. 6x6.
 impl_from_into_asref_2D!(
     (U2, U2) => (2, 2); (U2, U3) => (2, 3); (U2, U4) => (2, 4); (U2, U5) => (2, 5); (U2, U6) => (2, 6);
     (U3, U2) => (3, 2); (U3, U3) => (3, 3); (U3, U4) => (3, 4); (U3, U5) => (3, 5); (U3, U6) => (3, 6);

src/core/coordinates.rs

@@ -9,8 +9,7 @@ use std::ops::{Deref, DerefMut};
 
 use core::{Scalar, Matrix};
 use core::dimension::{U1, U2, U3, U4, U5, U6};
-use core::storage::OwnedStorage;
-use core::allocator::OwnedAllocator;
+use core::storage::{ContiguousStorage, ContiguousStorageMut};
 
 /*
  *
@@ -35,22 +34,20 @@ macro_rules! coords_impl(
 macro_rules! deref_impl(
     ($R: ty, $C: ty; $Target: ident) => {
         impl<N: Scalar, S> Deref for Matrix<N, $R, $C, S>
-            where S: OwnedStorage<N, $R, $C>,
-                  S::Alloc: OwnedAllocator<N, $R, $C, S> {
+            where S: ContiguousStorage<N, $R, $C> {
             type Target = $Target<N>;
 
             #[inline]
             fn deref(&self) -> &Self::Target {
-                unsafe { mem::transmute(self) }
+                unsafe { mem::transmute(self.data.ptr()) }
             }
         }
 
         impl<N: Scalar, S> DerefMut for Matrix<N, $R, $C, S>
-            where S: OwnedStorage<N, $R, $C>,
-                  S::Alloc: OwnedAllocator<N, $R, $C, S> {
+            where S: ContiguousStorageMut<N, $R, $C> {
             #[inline]
             fn deref_mut(&mut self) -> &mut Self::Target {
-                unsafe { mem::transmute(self) }
+                unsafe { mem::transmute(self.data.ptr_mut()) }
             }
         }
     }

src/core/decompositions.rs

@@ -1,373 +0,0 @@
-use std::cmp;
-
-use alga::general::Real;
-use core::{SquareMatrix, OwnedSquareMatrix, ColumnVector, OwnedColumnVector};
-use dimension::{Dim, Dynamic, U1};
-use storage::{Storage, OwnedStorage};
-use allocator::{Allocator, OwnedAllocator};
-
-
-
-impl<N, D: Dim, S> SquareMatrix<N, D, S>
-    where N: Real,
-          S: OwnedStorage<N, D, D>,
-          S::Alloc: OwnedAllocator<N, D, D, S> {
-    /// Get the householder matrix corresponding to a reflexion to the hyperplane
-    /// defined by `vector`. It can be a reflexion contained in a subspace.
-    ///
-    /// # Arguments
-    /// * `dimension` - the dimension of the space the resulting matrix operates in
-    /// * `start` - the starting dimension of the subspace of the reflexion
-    /// * `vector` - the vector defining the reflection.
-    pub fn new_householder_generic<SB, D2>(dimension: D, start: usize, vector: &ColumnVector<N, D2, SB>)
-        -> OwnedSquareMatrix<N, D, S::Alloc>
-        where D2: Dim,
-              SB: Storage<N, D2, U1> {
-        let mut qk = Self::identity_generic(dimension, dimension);
-        let subdim = vector.shape().0;
-
-        let stop = subdim + start;
-
-        assert!(dimension.value() >= stop, "Householder matrix creation: subspace dimension index out of bounds.");
-
-        for j in start .. stop {
-            for i in start .. stop {
-                unsafe {
-                    let vv   = *vector.get_unchecked(i - start, 0) * *vector.get_unchecked(j - start, 0);
-                    let qkij = *qk.get_unchecked(i, j);
-                    *qk.get_unchecked_mut(i, j) = qkij - vv - vv;
-                }
-            }
-        }
-
-        qk
-    }
-}
-
-
-impl<N: Real, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
-    /// QR decomposition using Householder reflections.
-    pub fn qr(self) -> (OwnedSquareMatrix<N, D, S::Alloc>, OwnedSquareMatrix<N, D, S::Alloc>)
-        where S::Alloc: Allocator<N, Dynamic, U1> +
-                        Allocator<N, D, U1> {
-
-        let (nrows, ncols) = self.data.shape();
-
-        // XXX: too restrictive.
-        assert!(nrows.value() >= ncols.value(), "");
-
-        let mut q = OwnedSquareMatrix::<N, D, S::Alloc>::identity_generic(nrows, ncols);
-        let mut r = self.into_owned();
-
-        // Temporary buffer that contains a column.
-        let mut col = unsafe {
-            OwnedColumnVector::<N, D, S::Alloc>::new_uninitialized_generic(nrows, U1)
-        };
-
-        for ite in 0 .. cmp::min(nrows.value() - 1, ncols.value()) {
-            let subdim = Dynamic::new(nrows.value() - ite);
-            let mut v  = col.rows_mut(0, subdim.value());
-            v.copy_from(&r.generic_slice((ite, ite), (subdim, U1)));
-
-            let alpha =
-                if unsafe { *v.get_unchecked(ite, 0) } >= ::zero() {
-                    -v.norm()
-                }
-                else {
-                    v.norm()
-                };
-
-            unsafe {
-                let x = *v.get_unchecked(0, 0);
-                *v.get_unchecked_mut(0, 0) = x - alpha;
-            }
-
-            if !v.normalize_mut().is_zero() {
-                let mut qk = OwnedSquareMatrix::<N, D, S::Alloc>::new_householder_generic(nrows, ite, &v);
-                r = &qk * r;
-
-                // FIXME: add a method `q.mul_tr(qk) := q * qk.transpose` ?
-                qk.transpose_mut();
-                q = q * qk;
-            }
-        }
-
-        (q, r)
-    }
-
-    /// Eigendecomposition of a square symmetric matrix.
-    pub fn eig(&self, eps: N, niter: usize)
-               -> (OwnedSquareMatrix<N, D, S::Alloc>, OwnedColumnVector<N, D, S::Alloc>)
-        where S::Alloc: Allocator<N, D, U1> +
-                        Allocator<N, Dynamic, U1> {
-
-        assert!(self.is_square(),
-                "Unable to compute the eigenvectors and eigenvalues of a non-square matrix.");
-
-        let dim = self.data.shape().0;
-
-        let (mut eigenvectors, mut eigenvalues) = self.hessenberg();
-
-        if dim.value() == 1 {
-            return (eigenvectors, eigenvalues.diagonal());
-        }
-
-        // Allocate arrays for Givens rotation components
-        let mut c = unsafe { OwnedColumnVector::<N, D, S::Alloc>::new_uninitialized_generic(dim, U1) };
-        let mut s = unsafe { OwnedColumnVector::<N, D, S::Alloc>::new_uninitialized_generic(dim, U1) };
-
-        let mut iter = 0;
-        let mut curdim = dim.value() - 1;
-
-        for _ in 0 .. dim.value() {
-
-            let mut stop = false;
-
-            while !stop && iter < niter {
-
-                let lambda;
-
-                unsafe {
-                    let a = *eigenvalues.get_unchecked(curdim - 1, curdim - 1);
-                    let b = *eigenvalues.get_unchecked(curdim - 1, curdim);
-                    let c = *eigenvalues.get_unchecked(curdim, curdim - 1);
-                    let d = *eigenvalues.get_unchecked(curdim, curdim);
-
-                    let trace = a + d;
-                    let determinant = a * d - b * c;
-
-                    let constquarter: N = ::convert(0.25f64);
-                    let consthalf:    N = ::convert(0.5f64);
-
-                    let e = (constquarter * trace * trace - determinant).sqrt();
-
-                    let lambda1 = consthalf * trace + e;
-                    let lambda2 = consthalf * trace - e;
-
-                    if (lambda1 - d).abs() < (lambda2 - d).abs() {
-                        lambda = lambda1;
-                    }
-                    else {
-                        lambda = lambda2;
-                    }
-
-                }
-
-                // Shift matrix
-                for k in 0 .. curdim + 1 {
-                    unsafe {
-                        let a = *eigenvalues.get_unchecked(k, k);
-                        *eigenvalues.get_unchecked_mut(k, k) = a - lambda;
-                    }
-                }
-
-
-                // Givens rotation from left
-                for k in 0 .. curdim {
-                    let x_i = unsafe { *eigenvalues.get_unchecked(k, k) };
-                    let x_j = unsafe { *eigenvalues.get_unchecked(k + 1, k) };
-
-                    let ctmp;
-                    let stmp;
-
-                    if x_j.abs() < eps {
-                        ctmp = N::one();
-                        stmp = N::zero();
-                    }
-                    else if x_i.abs() < eps {
-                        ctmp = N::zero();
-                        stmp = -N::one();
-                    }
-                    else {
-                        let r = x_i.hypot(x_j);
-                        ctmp = x_i / r;
-                        stmp = -x_j / r;
-                    }
-
-                    c[k] = ctmp;
-                    s[k] = stmp;
-
-                    for j in k .. (curdim + 1) {
-                        unsafe {
-                            let a = *eigenvalues.get_unchecked(k, j);
-                            let b = *eigenvalues.get_unchecked(k + 1, j);
-
-                            *eigenvalues.get_unchecked_mut(k, j)     = ctmp * a - stmp * b;
-                            *eigenvalues.get_unchecked_mut(k + 1, j) = stmp * a + ctmp * b;
-                        }
-
-                    }
-                }
-
-                // Givens rotation from right applied to eigenvalues
-                for k in 0 .. curdim {
-                    for i in 0 .. (k + 2) {
-                        unsafe {
-                            let a = *eigenvalues.get_unchecked(i, k);
-                            let b = *eigenvalues.get_unchecked(i, k + 1);
-
-                            *eigenvalues.get_unchecked_mut(i, k)     = c[k] * a - s[k] * b;
-                            *eigenvalues.get_unchecked_mut(i, k + 1) = s[k] * a + c[k] * b;
-                        }
-                    }
-                }
-
-
-                // Shift back
-                for k in 0 .. curdim + 1 {
-                    unsafe {
-                        let a = *eigenvalues.get_unchecked(k, k);
-                        *eigenvalues.get_unchecked_mut(k, k) = a + lambda;
-                    }
-                }
-
-
-                // Givens rotation from right applied to eigenvectors
-                for k in 0 .. curdim {
-                    for i in 0 .. dim.value() {
-
-                        unsafe {
-                            let a = *eigenvectors.get_unchecked(i, k);
-                            let b = *eigenvectors.get_unchecked(i, k + 1);
-
-                            *eigenvectors.get_unchecked_mut(i, k)     = c[k] * a - s[k] * b;
-                            *eigenvectors.get_unchecked_mut(i, k + 1) = s[k] * a + c[k] * b;
-                        }
-                    }
-                }
-
-                iter = iter + 1;
-                stop = true;
-
-                for j in 0 .. curdim {
-                    // Check last row.
-                    if unsafe { *eigenvalues.get_unchecked(curdim, j) }.abs() >= eps {
-                        stop = false;
-                        break;
-                    }
-
-                    // Check last column.
-                    if unsafe { *eigenvalues.get_unchecked(j, curdim) }.abs() >= eps {
-                        stop = false;
-                        break;
-                    }
-                }
-            }
-
-
-            if stop {
-                if curdim > 1 {
-                    curdim = curdim - 1;
-                }
-                else {
-                    break;
-                }
-            }
-        }
-
-        (eigenvectors, eigenvalues.diagonal())
-    }
-
-    /// Cholesky decomposition G of a square symmetric positive definite matrix A, such that A = G * G^T
-    ///
-    /// Matrix symmetricness is not checked. Returns `None` if `self` is not definite positive.
-    #[inline]
-    pub fn cholesky(&self) -> Result<OwnedSquareMatrix<N, D, S::Alloc>, &'static str> {
-        let out = self.transpose();
-
-        if !out.relative_eq(self, N::default_epsilon(), N::default_max_relative()) {
-            return Err("Cholesky: Input matrix is not symmetric");
-        }
-
-        self.do_cholesky(out)
-    }
-
-    /// Cholesky decomposition G of a square symmetric positive definite matrix A, such that A = G * G^T
-    #[inline]
-    pub fn cholesky_unchecked(&self) -> Result<OwnedSquareMatrix<N, D, S::Alloc>, &'static str> {
-        let out = self.transpose();
-        self.do_cholesky(out)
-    }
-
-    #[inline(always)]
-    fn do_cholesky(&self, mut out: OwnedSquareMatrix<N, D, S::Alloc>)
-                   -> Result<OwnedSquareMatrix<N, D, S::Alloc>, &'static str> {
-        assert!(self.is_square(), "The input matrix must be square.");
-
-        for i in 0 .. out.nrows() {
-            for j in 0 .. (i + 1) {
-
-                let mut sum = out[(i, j)];
-
-                for k in 0 .. j {
-                    sum = sum - out[(i, k)] * out[(j, k)];
-                }
-
-                if i > j {
-                    out[(i, j)] = sum / out[(j, j)];
-                }
-                else if sum > N::zero() {
-                    out[(i, i)] = sum.sqrt();
-                }
-                else {
-                    return Err("Cholesky: Input matrix is not positive definite to machine precision.");
-                }
-            }
-        }
-
-        for i in 0 .. out.nrows() {
-            for j in i + 1 .. out.ncols() {
-                out[(i, j)] = N::zero();
-            }
-        }
-
-        Ok(out)
-    }
-
-    /// Hessenberg
-    /// Returns the matrix `self` in Hessenberg form and the corresponding similarity transformation
-    ///
-    /// # Returns
-    /// The tuple (`q`, `h`) that `q * h * q^T = self`
-    pub fn hessenberg(&self) -> (OwnedSquareMatrix<N, D, S::Alloc>, OwnedSquareMatrix<N, D, S::Alloc>)
-        where S::Alloc: Allocator<N, D, U1> + Allocator<N, Dynamic, U1> {
-
-        let (nrows, ncols) = self.data.shape();
-        let mut h = self.clone_owned();
-
-        let mut q = OwnedSquareMatrix::<N, D, S::Alloc>::identity_generic(nrows, ncols);
-
-        if ncols.value() <= 2 {
-            return (q, h);
-        }
-
-        // Temporary buffer that contains a column.
-        let mut col = unsafe {
-            OwnedColumnVector::<N, D, S::Alloc>::new_uninitialized_generic(nrows, U1)
-        };
-
-        for ite in 0 .. (ncols.value() - 2) {
-            let subdim = Dynamic::new(nrows.value() - (ite + 1));
-            let mut v = col.rows_mut(0, subdim.value());
-            v.copy_from(&h.generic_slice((ite + 1, ite), (subdim, U1)));
-
-            let alpha = v.norm();
-
-            unsafe {
-                let x = *v.get_unchecked(0, 0);
-                *v.get_unchecked_mut(0, 0) = x - alpha;
-            }
-
-            if !v.normalize_mut().is_zero() {
-                // XXX: we output the householder matrix to a pre-allocated matrix instead of
-                // return a value to `p`. This would avoid allocation at each iteration.
-                let p = OwnedSquareMatrix::<N, D, S::Alloc>::new_householder_generic(nrows, ite + 1, &v);
-
-                q = q * &p;
-                h = &p * h * p;
-            }
-        }
-
-        (q, h)
-    }
-}

src/core/default_allocator.rs

@@ -4,6 +4,8 @@
 //! heap-allocated buffers for matrices with at least one dimension unknown at compile-time.
 
 use std::mem;
+use std::ptr;
+use std::cmp;
 use std::ops::Mul;
 
 use typenum::Prod;
@@ -11,7 +13,8 @@ use generic_array::ArrayLength;
 
 use core::Scalar;
 use core::dimension::{Dim, DimName, Dynamic};
-use core::allocator::Allocator;
+use core::allocator::{Allocator, Reallocator};
+use core::storage::{Storage, StorageMut};
 use core::matrix_array::MatrixArray;
 use core::matrix_vec::MatrixVec;
 
@@ -107,3 +110,110 @@ impl<N: Scalar, R: DimName> Allocator<N, R, Dynamic> for DefaultAllocator {
         MatrixVec::new(nrows, ncols, res)
     }
 }
+
+/*
+ *
+ * Reallocator.
+ *
+ */
+// Anything -> Static × Static
+impl<N: Scalar, RFrom, CFrom, RTo, CTo> Reallocator<N, RFrom, CFrom, RTo, CTo> for DefaultAllocator
+    where RFrom: Dim,
+          CFrom: Dim,
+          RTo:   DimName,
+          CTo:   DimName,
+          Self: Allocator<N, RFrom, CFrom>,
+          RTo::Value: Mul<CTo::Value>,
+          Prod<RTo::Value, CTo::Value>: ArrayLength<N> {
+
+    #[inline]
+    unsafe fn reallocate_copy(rto: RTo, cto: CTo, buf: <Self as Allocator<N, RFrom, CFrom>>::Buffer) -> MatrixArray<N, RTo, CTo> {
+        let mut res = <Self as Allocator<N, RTo, CTo>>::allocate_uninitialized(rto, cto);
+
+        let (rfrom, cfrom) = buf.shape();
+
+        let len_from = rfrom.value() * cfrom.value();
+        let len_to   = rto.value()   * cto.value();
+        ptr::copy_nonoverlapping(buf.ptr(), res.ptr_mut(), cmp::min(len_from, len_to));
+
+        res
+    }
+}
+
+
+// Static × Static -> Dynamic × Any
+impl<N: Scalar, RFrom, CFrom, CTo> Reallocator<N, RFrom, CFrom, Dynamic, CTo> for DefaultAllocator
+    where RFrom: DimName,
+          CFrom: DimName,
+          CTo:   Dim,
+          RFrom::Value: Mul<CFrom::Value>,
+          Prod<RFrom::Value, CFrom::Value>: ArrayLength<N> {
+
+    #[inline]
+    unsafe fn reallocate_copy(rto: Dynamic, cto: CTo, buf: MatrixArray<N, RFrom, CFrom>) -> MatrixVec<N, Dynamic, CTo> {
+        let mut res = <Self as Allocator<N, Dynamic, CTo>>::allocate_uninitialized(rto, cto);
+
+        let (rfrom, cfrom) = buf.shape();
+
+        let len_from = rfrom.value() * cfrom.value();
+        let len_to   = rto.value()   * cto.value();
+        ptr::copy_nonoverlapping(buf.ptr(), res.ptr_mut(), cmp::min(len_from, len_to));
+
+        res
+    }
+}
+
+// Static × Static -> Static × Dynamic
+impl<N: Scalar, RFrom, CFrom, RTo> Reallocator<N, RFrom, CFrom, RTo, Dynamic> for DefaultAllocator
+    where RFrom: DimName,
+          CFrom: DimName,
+          RTo:   DimName,
+          RFrom::Value: Mul<CFrom::Value>,
+          Prod<RFrom::Value, CFrom::Value>: ArrayLength<N> {
+
+    #[inline]
+    unsafe fn reallocate_copy(rto: RTo, cto: Dynamic, buf: MatrixArray<N, RFrom, CFrom>) -> MatrixVec<N, RTo, Dynamic> {
+        let mut res = <Self as Allocator<N, RTo, Dynamic>>::allocate_uninitialized(rto, cto);
+
+        let (rfrom, cfrom) = buf.shape();
+
+        let len_from = rfrom.value() * cfrom.value();
+        let len_to   = rto.value()   * cto.value();
+        ptr::copy_nonoverlapping(buf.ptr(), res.ptr_mut(), cmp::min(len_from, len_to));
+
+        res
+    }
+}
+
+// All conversion from a dynamic buffer to a dynamic buffer.
+impl<N: Scalar, CFrom: Dim, CTo: Dim> Reallocator<N, Dynamic, CFrom, Dynamic, CTo> for DefaultAllocator {
+    #[inline]
+    unsafe fn reallocate_copy(rto: Dynamic, cto: CTo, buf: MatrixVec<N, Dynamic, CFrom>) -> MatrixVec<N, Dynamic, CTo> {
+        let new_buf = buf.resize(rto.value() * cto.value());
+        MatrixVec::new(rto, cto, new_buf)
+    }
+}
+
+impl<N: Scalar, CFrom: Dim, RTo: DimName> Reallocator<N, Dynamic, CFrom, RTo, Dynamic> for DefaultAllocator {
+    #[inline]
+    unsafe fn reallocate_copy(rto: RTo, cto: Dynamic, buf: MatrixVec<N, Dynamic, CFrom>) -> MatrixVec<N, RTo, Dynamic> {
+        let new_buf = buf.resize(rto.value() * cto.value());
+        MatrixVec::new(rto, cto, new_buf)
+    }
+}
+
+impl<N: Scalar, RFrom: DimName, CTo: Dim> Reallocator<N, RFrom, Dynamic, Dynamic, CTo> for DefaultAllocator {
+    #[inline]
+    unsafe fn reallocate_copy(rto: Dynamic, cto: CTo, buf: MatrixVec<N, RFrom, Dynamic>) -> MatrixVec<N, Dynamic, CTo> {
+        let new_buf = buf.resize(rto.value() * cto.value());
+        MatrixVec::new(rto, cto, new_buf)
+    }
+}
+
+impl<N: Scalar, RFrom: DimName, RTo: DimName> Reallocator<N, RFrom, Dynamic, RTo, Dynamic> for DefaultAllocator {
+    #[inline]
+    unsafe fn reallocate_copy(rto: RTo, cto: Dynamic, buf: MatrixVec<N, RFrom, Dynamic>) -> MatrixVec<N, RTo, Dynamic> {
+        let new_buf = buf.resize(rto.value() * cto.value());
+        MatrixVec::new(rto, cto, new_buf)
+    }
+}

src/core/dimension.rs

@@ -3,9 +3,11 @@
 //! Traits and tags for identifying the dimension of all algebraic entities.
 
 use std::fmt::Debug;
-use std::any::Any;
+use std::any::{TypeId, Any};
+use std::cmp;
 use std::ops::{Add, Sub, Mul, Div};
-use typenum::{self, Unsigned, UInt, B1, Bit, UTerm, Sum, Prod, Diff, Quot};
+use typenum::{self, Unsigned, UInt, B1, Bit, UTerm, Sum, Prod, Diff, Quot,
+              Min, Minimum, Max, Maximum};
 
 #[cfg(feature = "serde-serialize")]
 use serde::{Serialize, Serializer, Deserialize, Deserializer};
@@ -55,6 +57,11 @@ impl IsNotStaticOne for Dynamic { }
 /// Trait implemented by any type that can be used as a dimension. This includes type-level
 /// integers and `Dynamic` (for dimensions not known at compile-time).
 pub trait Dim: Any + Debug + Copy + PartialEq + Send {
+    #[inline(always)]
+    fn is<D: Dim>() -> bool {
+        TypeId::of::<Self>() == TypeId::of::<D>()
+    }
+
     /// Gets the compile-time value of `Self`. Returns `None` if it is not known, i.e., if `Self =
     /// Dynamic`.
     fn try_to_usize() -> Option<usize>;
@@ -85,6 +92,24 @@ impl Dim for Dynamic {
     }
 }
 
+impl Add<usize> for Dynamic {
+    type Output = Dynamic;
+
+    #[inline]
+    fn add(self, rhs: usize) -> Dynamic {
+        Dynamic::new(self.value + rhs)
+    }
+}
+
+impl Sub<usize> for Dynamic {
+    type Output = Dynamic;
+
+    #[inline]
+    fn sub(self, rhs: usize) -> Dynamic {
+        Dynamic::new(self.value - rhs)
+    }
+}
+
 /*
  *
  * Operations.
@@ -93,7 +118,7 @@ impl Dim for Dynamic {
 
 macro_rules! dim_ops(
     ($($DimOp:    ident, $DimNameOp: ident,
-       $Op:       ident, $op: ident,
+       $Op:       ident, $op: ident, $op_path: path,
        $DimResOp: ident, $DimNameResOp: ident,
        $ResOp: ident);* $(;)*) => {$(
         pub type $DimResOp<D1, D2> = <D1 as $DimOp<D2>>::Output;
@@ -120,7 +145,7 @@ macro_rules! dim_ops(
 
             #[inline]
             fn $op(self, other: D) -> Dynamic {
-                Dynamic::new(self.value.$op(other.value()))
+                Dynamic::new($op_path(self.value, other.value()))
             }
         }
 
@@ -129,7 +154,7 @@ macro_rules! dim_ops(
 
             #[inline]
             fn $op(self, other: Dynamic) -> Dynamic {
-                Dynamic::new(self.value().$op(other.value))
+                Dynamic::new($op_path(self.value(), other.value))
             }
         }
 
@@ -155,10 +180,12 @@ macro_rules! dim_ops(
 );
 
 dim_ops!(
-    DimAdd, DimNameAdd, Add, add, DimSum,  DimNameSum,  Sum;
-    DimMul, DimNameMul, Mul, mul, DimProd, DimNameProd, Prod;
-    DimSub, DimNameSub, Sub, sub, DimDiff, DimNameDiff, Diff;
-    DimDiv, DimNameDiv, Div, div, DimQuot, DimNameQuot, Quot;
+    DimAdd, DimNameAdd, Add, add, Add::add, DimSum,     DimNameSum,     Sum;
+    DimMul, DimNameMul, Mul, mul, Mul::mul, DimProd,    DimNameProd,    Prod;
+    DimSub, DimNameSub, Sub, sub, Sub::sub, DimDiff,    DimNameDiff,    Diff;
+    DimDiv, DimNameDiv, Div, div, Div::div, DimQuot,    DimNameQuot,    Quot;
+    DimMin, DimNameMin, Min, min, cmp::min, DimMinimum, DimNameNimimum, Minimum;
+    DimMax, DimNameMax, Max, max, cmp::max, DimMaximum, DimNameMaximum, Maximum;
 );
 
 

src/core/edition.rs

@@ -0,0 +1,565 @@
+use num::{Zero, One};
+use std::cmp;
+use std::ptr;
+
+use core::{DefaultAllocator, Scalar, Matrix, DMatrix, MatrixMN, Vector, RowVector};
+use core::dimension::{Dim, DimName, DimSub, DimDiff, DimAdd, DimSum, DimMin, DimMinimum, U1, Dynamic};
+use core::constraint::{ShapeConstraint, DimEq, SameNumberOfColumns, SameNumberOfRows};
+use core::allocator::{Allocator, Reallocator};
+use core::storage::{Storage, StorageMut};
+
+impl<N: Scalar + Zero, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
+    /// Extracts the upper triangular part of this matrix (including the diagonal).
+    #[inline]
+    pub fn upper_triangle(&self) -> MatrixMN<N, R, C>
+        where DefaultAllocator: Allocator<N, R, C> {
+        let mut res = self.clone_owned();
+        res.fill_lower_triangle(N::zero(), 1);
+
+        res
+    }
+
+    /// Extracts the upper triangular part of this matrix (including the diagonal).
+    #[inline]
+    pub fn lower_triangle(&self) -> MatrixMN<N, R, C>
+        where DefaultAllocator: Allocator<N, R, C> {
+        let mut res = self.clone_owned();
+        res.fill_upper_triangle(N::zero(), 1);
+
+        res
+    }
+}
+
+impl<N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
+    /// Sets all the elements of this matrix to `val`.
+    #[inline]
+    pub fn fill(&mut self, val: N) {
+        for e in self.iter_mut() {
+            *e = val
+        }
+    }
+
+    /// Fills `self` with the identity matrix.
+    #[inline]
+    pub fn fill_with_identity(&mut self)
+        where N: Zero + One {
+        self.fill(N::zero());
+        self.fill_diagonal(N::one());
+    }
+
+    /// Sets all the diagonal elements of this matrix to `val`.
+    #[inline]
+    pub fn fill_diagonal(&mut self, val: N) {
+        let (nrows, ncols) = self.shape();
+        let n = cmp::min(nrows, ncols);
+
+        for i in 0 .. n {
+            unsafe { *self.get_unchecked_mut(i, i) = val }
+        }
+    }
+
+    /// Sets all the elements of the selected row to `val`.
+    #[inline]
+    pub fn fill_row(&mut self, i: usize, val: N) {
+        assert!(i < self.nrows(), "Row index out of bounds.");
+        for j in 0 .. self.ncols() {
+            unsafe { *self.get_unchecked_mut(i, j) = val }
+        }
+    }
+
+    /// Sets all the elements of the selected column to `val`.
+    #[inline]
+    pub fn fill_column(&mut self, j: usize, val: N) {
+        assert!(j < self.ncols(), "Row index out of bounds.");
+        for i in 0 .. self.nrows() {
+            unsafe { *self.get_unchecked_mut(i, j) = val }
+        }
+    }
+
+    /// Fills the diagonal of this matrix with the content of the given vector.
+    #[inline]
+    pub fn set_diagonal<R2: Dim, S2>(&mut self, diag: &Vector<N, R2, S2>)
+        where R:  DimMin<C>,
+              S2: Storage<N, R2>,
+              ShapeConstraint: DimEq<DimMinimum<R, C>, R2> {
+        let (nrows, ncols)  = self.shape();
+        let min_nrows_ncols = cmp::min(nrows, ncols);
+        assert_eq!(diag.len(), min_nrows_ncols, "Mismatched dimensions.");
+
+        for i in 0 .. min_nrows_ncols {
+            unsafe { *self.get_unchecked_mut(i, i) = *diag.vget_unchecked(i) }
+        }
+    }
+
+    /// Fills the selected row of this matrix with the content of the given vector.
+    #[inline]
+    pub fn set_row<C2: Dim, S2>(&mut self, i: usize, row: &RowVector<N, C2, S2>)
+        where S2: Storage<N, U1, C2>,
+              ShapeConstraint: SameNumberOfColumns<C, C2> {
+        self.row_mut(i).copy_from(row);
+    }
+
+    /// Fills the selected column of this matrix with the content of the given vector.
+    #[inline]
+    pub fn set_column<R2: Dim, S2>(&mut self, i: usize, column: &Vector<N, R2, S2>)
+        where S2: Storage<N, R2, U1>,
+              ShapeConstraint: SameNumberOfRows<R, R2> {
+        self.column_mut(i).copy_from(column);
+    }
+
+    /// Sets all the elements of the lower-triangular part of this matrix to `val`.
+    ///
+    /// The parameter `shift` allows some subdiagonals to be left untouched:
+    /// * If `shift = 0` then the diagonal is overwritten as well.
+    /// * If `shift = 1` then the diagonal is left untouched.
+    /// * If `shift > 1`, then the diagonal and the first `shift - 1` subdiagonals are left
+    /// untouched.
+    #[inline]
+    pub fn fill_lower_triangle(&mut self, val: N, shift: usize) {
+        for j in 0 .. self.ncols() {
+            for i in (j + shift) .. self.nrows() {
+                unsafe { *self.get_unchecked_mut(i, j) = val }
+            }
+        }
+    }
+
+    /// Sets all the elements of the lower-triangular part of this matrix to `val`.
+    ///
+    /// The parameter `shift` allows some superdiagonals to be left untouched:
+    /// * If `shift = 0` then the diagonal is overwritten as well.
+    /// * If `shift = 1` then the diagonal is left untouched.
+    /// * If `shift > 1`, then the diagonal and the first `shift - 1` superdiagonals are left
+    /// untouched.
+    #[inline]
+    pub fn fill_upper_triangle(&mut self, val: N, shift: usize) {
+        for j in shift .. self.ncols() {
+            // FIXME: is there a more efficient way to avoid the min ?
+            // (necessary for rectangular matrices)
+            for i in 0 .. cmp::min(j + 1 - shift, self.nrows()) {
+                unsafe { *self.get_unchecked_mut(i, j) = val }
+            }
+        }
+    }
+
+    /// Swaps two rows in-place.
+    #[inline]
+    pub fn swap_rows(&mut self, irow1: usize, irow2: usize) {
+        assert!(irow1 < self.nrows() && irow2 < self.nrows());
+
+        if irow1 != irow2 {
+            // FIXME: optimize that.
+            for i in 0 .. self.ncols() {
+                unsafe { self.swap_unchecked((irow1, i), (irow2, i)) }
+            }
+        }
+        // Otherwise do nothing.
+    }
+
+    /// Swaps two columns in-place.
+    #[inline]
+    pub fn swap_columns(&mut self, icol1: usize, icol2: usize) {
+        assert!(icol1 < self.ncols() && icol2 < self.ncols());
+
+        if icol1 != icol2 {
+            // FIXME: optimize that.
+            for i in 0 .. self.nrows() {
+                unsafe { self.swap_unchecked((i, icol1), (i, icol2)) }
+            }
+        }
+        // Otherwise do nothing.
+    }
+}
+
+impl<N: Scalar, D: Dim, S: StorageMut<N, D, D>> Matrix<N, D, D, S> {
+    /// Copies the upper-triangle of this matrix to its lower-triangular part.
+    ///
+    /// This makes the matrix symmetric. Panics if the matrix is not square.
+    pub fn fill_lower_triangle_with_upper_triangle(&mut self) {
+        assert!(self.is_square(), "The input matrix should be square.");
+
+        let dim = self.nrows();
+        for j in 0 .. dim {
+            for i in j + 1 .. dim {
+                unsafe {
+                    *self.get_unchecked_mut(i, j) = *self.get_unchecked(j, i);
+                }
+            }
+        }
+    }
+
+    /// Copies the upper-triangle of this matrix to its upper-triangular part.
+    ///
+    /// This makes the matrix symmetric. Panics if the matrix is not square.
+    pub fn fill_upper_triangle_with_lower_triangle(&mut self) {
+        assert!(self.is_square(), "The input matrix should be square.");
+
+        for j in 1 .. self.ncols() {
+            for i in 0 .. j {
+                unsafe {
+                    *self.get_unchecked_mut(i, j) = *self.get_unchecked(j, i);
+                }
+            }
+        }
+    }
+}
+
+/*
+ *
+ * FIXME: specialize all the following for slices.
+ *
+ */
+impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
+    /*
+     *
+     * Column removal.
+     *
+     */
+    /// Removes the `i`-th column from this matrix.
+    #[inline]
+    pub fn remove_column(self, i: usize) -> MatrixMN<N, R, DimDiff<C, U1>>
+        where C: DimSub<U1>,
+              DefaultAllocator: Reallocator<N, R, C, R, DimDiff<C, U1>> {
+        self.remove_fixed_columns::<U1>(i)
+    }
+
+    /// Removes `D::dim()` consecutive columns from this matrix, starting with the `i`-th
+    /// (included).
+    #[inline]
+    pub fn remove_fixed_columns<D>(self, i: usize) -> MatrixMN<N, R, DimDiff<C, D>>
+        where D: DimName,
+              C: DimSub<D>,
+              DefaultAllocator: Reallocator<N, R, C, R, DimDiff<C, D>> {
+
+        self.remove_columns_generic(i, D::name())
+    }
+
+    /// Removes `n` consecutive columns from this matrix, starting with the `i`-th (included).
+    #[inline]
+    pub fn remove_columns(self, i: usize, n: usize) -> MatrixMN<N, R, Dynamic>
+        where C: DimSub<Dynamic, Output = Dynamic>,
+              DefaultAllocator: Reallocator<N, R, C, R, Dynamic> {
+
+        self.remove_columns_generic(i, Dynamic::new(n))
+    }
+
+    /// Removes `nremove.value()` columns from this matrix, starting with the `i`-th (included).
+    ///
+    /// This is the generic implementation of `.remove_columns(...)` and
+    /// `.remove_fixed_columns(...)` which have nicer API interfaces.
+    #[inline]
+    pub fn remove_columns_generic<D>(self, i: usize, nremove: D) -> MatrixMN<N, R, DimDiff<C, D>>
+        where D: Dim,
+              C: DimSub<D>,
+              DefaultAllocator: Reallocator<N, R, C, R, DimDiff<C, D>> {
+
+        let mut m = self.into_owned();
+        let (nrows, ncols) = m.data.shape();
+        assert!(i + nremove.value() <= ncols.value(), "Column index out of range.");
+
+        if nremove.value() != 0 && i + nremove.value() < ncols.value() {
+            // The first `deleted_i * nrows` are left untouched.
+            let copied_value_start = i + nremove.value();
+
+            unsafe {
+                let ptr_in  = m.data.ptr().offset((copied_value_start * nrows.value()) as isize);
+                let ptr_out = m.data.ptr_mut().offset((i * nrows.value()) as isize);
+
+                ptr::copy(ptr_in, ptr_out, (ncols.value() - copied_value_start) * nrows.value());
+            }
+        }
+
+        unsafe {
+            Matrix::from_data(DefaultAllocator::reallocate_copy(nrows, ncols.sub(nremove), m.data))
+        }
+    }
+
+
+    /*
+     *
+     * Row removal.
+     *
+     */
+    /// Removes the `i`-th row from this matrix.
+    #[inline]
+    pub fn remove_row(self, i: usize) -> MatrixMN<N, DimDiff<R, U1>, C>
+        where R: DimSub<U1>,
+              DefaultAllocator: Reallocator<N, R, C, DimDiff<R, U1>, C> {
+        self.remove_fixed_rows::<U1>(i)
+    }
+
+    /// Removes `D::dim()` consecutive rows from this matrix, starting with the `i`-th (included).
+    #[inline]
+    pub fn remove_fixed_rows<D>(self, i: usize) -> MatrixMN<N, DimDiff<R, D>, C>
+        where D: DimName,
+              R: DimSub<D>,
+              DefaultAllocator: Reallocator<N, R, C, DimDiff<R, D>, C> {
+
+        self.remove_rows_generic(i, D::name())
+    }
+
+    /// Removes `n` consecutive rows from this matrix, starting with the `i`-th (included).
+    #[inline]
+    pub fn remove_rows(self, i: usize, n: usize) -> MatrixMN<N, Dynamic, C>
+        where R: DimSub<Dynamic, Output = Dynamic>,
+              DefaultAllocator: Reallocator<N, R, C, Dynamic, C> {
+
+        self.remove_rows_generic(i, Dynamic::new(n))
+    }
+
+    /// Removes `nremove.value()` rows from this matrix, starting with the `i`-th (included).
+    ///
+    /// This is the generic implementation of `.remove_rows(...)` and `.remove_fixed_rows(...)`
+    /// which have nicer API interfaces.
+    #[inline]
+    pub fn remove_rows_generic<D>(self, i: usize, nremove: D) -> MatrixMN<N, DimDiff<R, D>, C>
+        where D: Dim,
+              R: DimSub<D>,
+              DefaultAllocator: Reallocator<N, R, C, DimDiff<R, D>, C> {
+        let mut m = self.into_owned();
+        let (nrows, ncols) = m.data.shape();
+        assert!(i + nremove.value() <= nrows.value(), "Row index out of range.");
+
+        if nremove.value() != 0 {
+            unsafe {
+                compress_rows(&mut m.data.as_mut_slice(), nrows.value(), ncols.value(), i, nremove.value());
+            }
+        }
+
+        unsafe {
+            Matrix::from_data(DefaultAllocator::reallocate_copy(nrows.sub(nremove), ncols, m.data))
+        }
+    }
+
+    /*
+     *
+     * Columns insertion.
+     *
+     */
+    /// Inserts a column filled with `val` at the `i-th` position.
+    #[inline]
+    pub fn insert_column(self, i: usize, val: N) -> MatrixMN<N, R, DimSum<C, U1>>
+        where C: DimAdd<U1>,
+              DefaultAllocator: Reallocator<N, R, C, R, DimSum<C, U1>> {
+        self.insert_fixed_columns::<U1>(i, val)
+    }
+
+    /// Inserts `D::dim()` columns filled with `val` starting at the `i-th` position.
+    #[inline]
+    pub fn insert_fixed_columns<D>(self, i: usize, val: N) -> MatrixMN<N, R, DimSum<C, D>>
+        where D: DimName,
+              C: DimAdd<D>,
+              DefaultAllocator: Reallocator<N, R, C, R, DimSum<C, D>> {
+        let mut res = unsafe { self.insert_columns_generic_uninitialized(i, D::name()) };
+        res.fixed_columns_mut::<D>(i).fill(val);
+        res
+    }
+
+    /// Inserts `n` columns filled with `val` starting at the `i-th` position.
+    #[inline]
+    pub fn insert_columns(self, i: usize, n: usize, val: N) -> MatrixMN<N, R, Dynamic>
+        where C: DimAdd<Dynamic, Output = Dynamic>,
+              DefaultAllocator: Reallocator<N, R, C, R, Dynamic> {
+        let mut res = unsafe { self.insert_columns_generic_uninitialized(i, Dynamic::new(n)) };
+        res.columns_mut(i, n).fill(val);
+        res
+    }
+
+    /// Inserts `ninsert.value()` columns starting at the `i-th` place of this matrix.
+    ///
+    /// The added column values are not initialized.
+    #[inline]
+    pub unsafe fn insert_columns_generic_uninitialized<D>(self, i: usize, ninsert: D)
+        -> MatrixMN<N, R, DimSum<C, D>>
+        where D: Dim,
+              C: DimAdd<D>,
+              DefaultAllocator: Reallocator<N, R, C, R, DimSum<C, D>> {
+
+        let m = self.into_owned();
+        let (nrows, ncols) = m.data.shape();
+        let mut res = Matrix::from_data(DefaultAllocator::reallocate_copy(nrows, ncols.add(ninsert), m.data));
+
+        assert!(i <= ncols.value(), "Column insertion index out of range.");
+
+        if ninsert.value() != 0 && i != ncols.value() {
+            let ptr_in  = res.data.ptr().offset((i * nrows.value()) as isize);
+            let ptr_out = res.data.ptr_mut().offset(((i + ninsert.value()) * nrows.value()) as isize);
+
+            ptr::copy(ptr_in, ptr_out, (ncols.value() - i) * nrows.value())
+        }
+
+        res
+    }
+
+    /*
+     *
+     * Rows insertion.
+     *
+     */
+    /// Inserts a row filled with `val` at the `i-th` position.
+    #[inline]
+    pub fn insert_row(self, i: usize, val: N) -> MatrixMN<N, DimSum<R, U1>, C>
+        where R: DimAdd<U1>,
+              DefaultAllocator: Reallocator<N, R, C, DimSum<R, U1>, C> {
+        self.insert_fixed_rows::<U1>(i, val)
+    }
+
+    /// Inserts `D::dim()` rows filled with `val` starting at the `i-th` position.
+    #[inline]
+    pub fn insert_fixed_rows<D>(self, i: usize, val: N) -> MatrixMN<N, DimSum<R, D>, C>
+        where D: DimName,
+              R: DimAdd<D>,
+              DefaultAllocator: Reallocator<N, R, C, DimSum<R, D>, C> {
+        let mut res = unsafe { self.insert_rows_generic_uninitialized(i, D::name()) };
+        res.fixed_rows_mut::<D>(i).fill(val);
+        res
+    }
+
+    /// Inserts `n` rows filled with `val` starting at the `i-th` position.
+    #[inline]
+    pub fn insert_rows(self, i: usize, n: usize, val: N) -> MatrixMN<N, Dynamic, C>
+        where R: DimAdd<Dynamic, Output = Dynamic>,
+              DefaultAllocator: Reallocator<N, R, C, Dynamic, C> {
+        let mut res = unsafe { self.insert_rows_generic_uninitialized(i, Dynamic::new(n)) };
+        res.rows_mut(i, n).fill(val);
+        res
+    }
+
+    /// Inserts `ninsert.value()` rows at the `i-th` place of this matrix.
+    ///
+    /// The added rows values are not initialized.
+    /// This is the generic implementation of `.insert_rows(...)` and
+    /// `.insert_fixed_rows(...)` which have nicer API interfaces.
+    #[inline]
+    pub unsafe fn insert_rows_generic_uninitialized<D>(self, i: usize, ninsert: D)
+        -> MatrixMN<N, DimSum<R, D>, C>
+        where D: Dim,
+              R: DimAdd<D>,
+              DefaultAllocator: Reallocator<N, R, C, DimSum<R, D>, C> {
+
+        let m = self.into_owned();
+        let (nrows, ncols) = m.data.shape();
+        let mut res = Matrix::from_data(DefaultAllocator::reallocate_copy(nrows.add(ninsert), ncols, m.data));
+
+        assert!(i <= nrows.value(), "Row insertion index out of range.");
+
+        if ninsert.value() != 0 {
+            extend_rows(&mut res.data.as_mut_slice(), nrows.value(), ncols.value(), i, ninsert.value());
+        }
+
+        res
+    }
+
+    /*
+     *
+     * Resizing.
+     *
+     */
+
+    /// Resizes this matrix so that it contains `new_nrows` rows and `new_ncols` columns.
+    ///
+    /// The values are copied such that `self[(i, j)] == result[(i, j)]`. If the result has more
+    /// rows and/or columns than `self`, then the extra rows or columns are filled with `val`.
+    pub fn resize(self, new_nrows: usize, new_ncols: usize, val: N) -> DMatrix<N>
+        where DefaultAllocator: Reallocator<N, R, C, Dynamic, Dynamic> {
+
+        self.resize_generic(Dynamic::new(new_nrows), Dynamic::new(new_ncols), val)
+    }
+
+    /// Resizes this matrix so that it contains `R2::value()` rows and `C2::value()` columns.
+    ///
+    /// The values are copied such that `self[(i, j)] == result[(i, j)]`. If the result has more
+    /// rows and/or columns than `self`, then the extra rows or columns are filled with `val`.
+    pub fn fixed_resize<R2: DimName, C2: DimName>(self, val: N) -> MatrixMN<N, R2, C2>
+        where DefaultAllocator: Reallocator<N, R, C, R2, C2> {
+
+        self.resize_generic(R2::name(), C2::name(), val)
+    }
+
+    /// Resizes `self` such that it has dimensions `new_nrows × now_ncols`.
+    ///
+    /// The values are copied such that `self[(i, j)] == result[(i, j)]`. If the result has more
+    /// rows and/or columns than `self`, then the extra rows or columns are filled with `val`.
+    #[inline]
+    pub fn resize_generic<R2: Dim, C2: Dim>(self, new_nrows: R2, new_ncols: C2, val: N) -> MatrixMN<N, R2, C2>
+        where DefaultAllocator: Reallocator<N, R, C, R2, C2> {
+
+        let (nrows, ncols) = self.shape();
+        let mut data = self.data.into_owned();
+
+        if new_nrows.value() == nrows {
+            let res = unsafe { DefaultAllocator::reallocate_copy(new_nrows, new_ncols, data) };
+
+            Matrix::from_data(res)
+        }
+        else {
+            let mut res;
+
+            unsafe {
+                if new_nrows.value() < nrows {
+                    compress_rows(&mut data.as_mut_slice(), nrows, ncols, new_nrows.value(), nrows - new_nrows.value());
+                    res = Matrix::from_data(DefaultAllocator::reallocate_copy(new_nrows, new_ncols, data));
+                }
+                else {
+                    res = Matrix::from_data(DefaultAllocator::reallocate_copy(new_nrows, new_ncols, data));
+                    extend_rows(&mut res.data.as_mut_slice(), nrows, ncols, nrows, new_nrows.value() - nrows);
+                }
+            }
+
+            if new_ncols.value() > ncols {
+                res.columns_range_mut(ncols ..).fill(val);
+            }
+
+            if new_nrows.value() > nrows {
+                res.slice_range_mut(nrows .., .. cmp::min(ncols, new_ncols.value())).fill(val);
+            }
+
+            res
+        }
+    }
+}
+
+
+unsafe fn compress_rows<N: Scalar>(data: &mut [N], nrows: usize, ncols: usize, i: usize, nremove: usize) {
+    let new_nrows = nrows - nremove;
+    let ptr_in    = data.as_ptr();
+    let ptr_out   = data.as_mut_ptr();
+
+    let mut curr_i = i;
+
+    for k in 0 .. ncols - 1 {
+        ptr::copy(ptr_in.offset((curr_i + (k + 1) * nremove) as isize),
+                  ptr_out.offset(curr_i as isize),
+                  new_nrows);
+
+        curr_i += new_nrows;
+    }
+
+    // Deal with the last column from which less values have to be copied.
+    let remaining_len = nrows - i - nremove;
+    ptr::copy(ptr_in.offset((nrows * ncols - remaining_len) as isize),
+              ptr_out.offset(curr_i as isize),
+              remaining_len);
+}
+
+
+unsafe fn extend_rows<N: Scalar>(data: &mut [N], nrows: usize, ncols: usize, i: usize, ninsert: usize) {
+    let new_nrows = nrows + ninsert;
+    let ptr_in    = data.as_ptr();
+    let ptr_out   = data.as_mut_ptr();
+
+    let remaining_len = nrows - i;
+    let mut curr_i = new_nrows * ncols - remaining_len;
+
+    // Deal with the last column from which less values have to be copied.
+    ptr::copy(ptr_in.offset((nrows * ncols - remaining_len) as isize),
+              ptr_out.offset(curr_i as isize),
+              remaining_len);
+
+    for k in (0 .. ncols - 1).rev() {
+        curr_i -= new_nrows;
+
+        ptr::copy(ptr_in.offset((k * nrows + i) as isize),
+                  ptr_out.offset(curr_i as isize),
+                  nrows);
+    }
+}

src/core/inverse.rs

@@ -1,203 +0,0 @@
-use approx::ApproxEq;
-
-use alga::general::Field;
-
-use core::{Scalar, Matrix, SquareMatrix, OwnedSquareMatrix};
-use core::dimension::Dim;
-use core::storage::{Storage, StorageMut};
-
-
-impl<N, D: Dim, S> SquareMatrix<N, D, S>
-    where N: Scalar + Field + ApproxEq,
-          S: Storage<N, D, D> {
-    /// Attempts to invert this matrix.
-    #[inline]
-    pub fn try_inverse(self) -> Option<OwnedSquareMatrix<N, D, S::Alloc>> {
-        let mut res = self.into_owned();
-
-        if res.shape().0 <= 3 {
-            if res.try_inverse_mut() {
-                Some(res)
-            }
-            else {
-                None
-            }
-        }
-        else {
-            gauss_jordan_inverse(res)
-        }
-    }
-}
-
-
-impl<N, D: Dim, S> SquareMatrix<N, D, S>
-    where N: Scalar + Field + ApproxEq,
-          S: StorageMut<N, D, D> {
-    /// Attempts to invert this matrix in-place. Returns `false` and leaves `self` untouched if
-    /// inversion fails.
-    #[inline]
-    pub fn try_inverse_mut(&mut self) -> bool {
-        assert!(self.is_square(), "Unable to invert a non-square matrix.");
-
-        let dim = self.shape().0;
-
-        unsafe {
-            match dim {
-                0 => true,
-                1 => {
-                    let determinant = self.get_unchecked(0, 0).clone();
-                    if determinant == N::zero() {
-                        false
-                    }
-                    else {
-                        *self.get_unchecked_mut(0, 0) = N::one() / determinant;
-                        true
-                    }
-                },
-                2 => {
-                    let determinant = self.determinant();
-
-                    if determinant == N::zero() {
-                        false
-                    }
-                    else {
-                        let m11 = *self.get_unchecked(0, 0); let m12 = *self.get_unchecked(0, 1);
-                        let m21 = *self.get_unchecked(1, 0); let m22 = *self.get_unchecked(1, 1);
-
-                        *self.get_unchecked_mut(0, 0) =  m22 / determinant;
-                        *self.get_unchecked_mut(0, 1) = -m12 / determinant;
-
-                        *self.get_unchecked_mut(1, 0) = -m21 / determinant;
-                        *self.get_unchecked_mut(1, 1) =  m11 / determinant;
-
-                        true
-                    }
-                },
-                3 => {
-                    let m11 = *self.get_unchecked(0, 0);
-                    let m12 = *self.get_unchecked(0, 1);
-                    let m13 = *self.get_unchecked(0, 2);
-
-                    let m21 = *self.get_unchecked(1, 0);
-                    let m22 = *self.get_unchecked(1, 1);
-                    let m23 = *self.get_unchecked(1, 2);
-
-                    let m31 = *self.get_unchecked(2, 0);
-                    let m32 = *self.get_unchecked(2, 1);
-                    let m33 = *self.get_unchecked(2, 2);
-
-
-                    let minor_m12_m23 = m22 * m33 - m32 * m23;
-                    let minor_m11_m23 = m21 * m33 - m31 * m23;
-                    let minor_m11_m22 = m21 * m32 - m31 * m22;
-
-                    let determinant = m11 * minor_m12_m23 -
-                                      m12 * minor_m11_m23 +
-                                      m13 * minor_m11_m22;
-
-                    if determinant == N::zero() {
-                        false
-                    }
-                    else {
-                        *self.get_unchecked_mut(0, 0) = minor_m12_m23 / determinant;
-                        *self.get_unchecked_mut(0, 1) = (m13 * m32 - m33 * m12) / determinant;
-                        *self.get_unchecked_mut(0, 2) = (m12 * m23 - m22 * m13) / determinant;
-
-                        *self.get_unchecked_mut(1, 0) = -minor_m11_m23 / determinant;
-                        *self.get_unchecked_mut(1, 1) = (m11 * m33 - m31 * m13) / determinant;
-                        *self.get_unchecked_mut(1, 2) = (m13 * m21 - m23 * m11) / determinant;
-
-                        *self.get_unchecked_mut(2, 0) = minor_m11_m22  / determinant;
-                        *self.get_unchecked_mut(2, 1) = (m12 * m31 - m32 * m11) / determinant;
-                        *self.get_unchecked_mut(2, 2) = (m11 * m22 - m21 * m12) / determinant;
-
-                        true
-                    }
-                },
-                _ => {
-                    let oself = self.clone_owned();
-                    if let Some(res) = gauss_jordan_inverse(oself) {
-                        self.copy_from(&res);
-                        true
-                    }
-                    else {
-                        false
-                    }
-                }
-            }
-        }
-    }
-}
-
-
-/// Inverts the given matrix using Gauss-Jordan Ellimitation.
-fn gauss_jordan_inverse<N, D, S>(mut matrix: SquareMatrix<N, D, S>) -> Option<OwnedSquareMatrix<N, D, S::Alloc>>
-    where D: Dim,
-          N: Scalar + Field + ApproxEq,
-          S: StorageMut<N, D, D> {
-
-    assert!(matrix.is_square(), "Unable to invert a non-square matrix.");
-    let dim = matrix.data.shape().0;
-    let mut res: OwnedSquareMatrix<N, D, S::Alloc> = Matrix::identity_generic(dim, dim);
-    let dim = dim.value();
-
-    unsafe {
-        for k in 0 .. dim {
-            // Search a non-zero value on the k-th column.
-            // FIXME: would it be worth it to spend some more time searching for the
-            // max instead?
-
-            let mut n0 = k; // index of a non-zero entry.
-
-            while n0 != dim {
-                if !matrix.get_unchecked(n0, k).is_zero() {
-                    break;
-                }
-
-                n0 += 1;
-            }
-
-            if n0 == dim {
-                return None
-            }
-
-            // Swap pivot line.
-            if n0 != k {
-                for j in 0 .. dim {
-                    matrix.swap_unchecked((n0, j), (k, j));
-                    res.swap_unchecked((n0, j), (k, j));
-                }
-            }
-
-            let pivot = *matrix.get_unchecked(k, k);
-
-            for j in k .. dim {
-                let selfval = *matrix.get_unchecked(k, j) / pivot;
-                *matrix.get_unchecked_mut(k, j) = selfval;
-            }
-
-            for j in 0 .. dim {
-                let resval = *res.get_unchecked(k, j) / pivot;
-                *res.get_unchecked_mut(k, j) = resval;
-            }
-
-            for l in 0 .. dim {
-                if l != k {
-                    let normalizer = *matrix.get_unchecked(l, k);
-
-                    for j in k .. dim {
-                        let selfval = *matrix.get_unchecked(l, j) - *matrix.get_unchecked(k, j) * normalizer;
-                        *matrix.get_unchecked_mut(l, j) = selfval;
-                    }
-
-                    for j in 0 .. dim {
-                        let resval  = *res.get_unchecked(l, j) - *res.get_unchecked(k, j) * normalizer;
-                        *res.get_unchecked_mut(l, j) = resval;
-                    }
-                }
-            }
-        }
-
-        Some(res)
-    }
-}

src/core/iter.rs

@@ -81,6 +81,13 @@ macro_rules! iterator {
                 self.size_hint().0
             }
         }
+
+        impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + $Storage<N, R, C>> ExactSizeIterator for $Name<'a, N, R, C, S> {
+            #[inline]
+            fn len(&self) -> usize {
+                self.size
+            }
+        }
     }
 }
 

src/core/matrix_alga.rs

@@ -7,42 +7,39 @@ use alga::general::{AbstractMagma, AbstractGroupAbelian, AbstractGroup, Abstract
                     ClosedAdd, ClosedNeg, ClosedMul};
 use alga::linear::{VectorSpace, NormedSpace, InnerSpace, FiniteDimVectorSpace, FiniteDimInnerSpace};
 
-use core::{Scalar, Matrix, SquareMatrix};
+use core::{DefaultAllocator, Scalar, MatrixMN, MatrixN};
 use core::dimension::{Dim, DimName};
-use core::storage::OwnedStorage;
-use core::allocator::OwnedAllocator;
+use core::storage::{Storage, StorageMut};
+use core::allocator::Allocator;
 
 /*
  *
  * Additive structures.
  *
  */
-impl<N, R: DimName, C: DimName, S> Identity<Additive> for Matrix<N, R, C, S>
+impl<N, R: DimName, C: DimName> Identity<Additive> for MatrixMN<N, R, C>
     where N: Scalar + Zero,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+          DefaultAllocator: Allocator<N, R, C> {
     #[inline]
     fn identity() -> Self {
         Self::from_element(N::zero())
     }
 }
 
-impl<N, R: DimName, C: DimName, S> AbstractMagma<Additive> for Matrix<N, R, C, S>
+impl<N, R: DimName, C: DimName> AbstractMagma<Additive> for MatrixMN<N, R, C>
     where N: Scalar + ClosedAdd,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+          DefaultAllocator: Allocator<N, R, C> {
     #[inline]
     fn operate(&self, other: &Self) -> Self {
         self + other
     }
 }
 
-impl<N, R: DimName, C: DimName, S> Inverse<Additive> for Matrix<N, R, C, S>
+impl<N, R: DimName, C: DimName> Inverse<Additive> for MatrixMN<N, R, C>
     where N: Scalar + ClosedNeg,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+          DefaultAllocator: Allocator<N, R, C> {
     #[inline]
-    fn inverse(&self) -> Matrix<N, R, C, S> {
+    fn inverse(&self) -> MatrixMN<N, R, C> {
         -self
     }
 
@@ -54,10 +51,9 @@ impl<N, R: DimName, C: DimName, S> Inverse<Additive> for Matrix<N, R, C, S>
 
 macro_rules! inherit_additive_structure(
     ($($marker: ident<$operator: ident> $(+ $bounds: ident)*),* $(,)*) => {$(
-        impl<N, R: DimName, C: DimName, S> $marker<$operator> for Matrix<N, R, C, S>
+        impl<N, R: DimName, C: DimName> $marker<$operator> for MatrixMN<N, R, C>
             where N: Scalar + $marker<$operator> $(+ $bounds)*,
-                  S: OwnedStorage<N, R, C>,
-                  S::Alloc: OwnedAllocator<N, R, C, S> { }
+                  DefaultAllocator: Allocator<N, R, C> { }
     )*}
 );
 
@@ -70,10 +66,9 @@ inherit_additive_structure!(
     AbstractGroupAbelian<Additive> + Zero + ClosedAdd + ClosedNeg
 );
 
-impl<N, R: DimName, C: DimName, S> AbstractModule for Matrix<N, R, C, S>
+impl<N, R: DimName, C: DimName> AbstractModule for MatrixMN<N, R, C>
     where N: Scalar + RingCommutative,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+          DefaultAllocator: Allocator<N, R, C> {
     type AbstractRing = N;
 
     #[inline]
@@ -82,24 +77,21 @@ impl<N, R: DimName, C: DimName, S> AbstractModule for Matrix<N, R, C, S>
     }
 }
 
-impl<N, R: DimName, C: DimName, S> Module for Matrix<N, R, C, S>
+impl<N, R: DimName, C: DimName> Module for MatrixMN<N, R, C>
     where N: Scalar + RingCommutative,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+          DefaultAllocator: Allocator<N, R, C> {
     type Ring = N;
 }
 
-impl<N, R: DimName, C: DimName, S> VectorSpace for Matrix<N, R, C, S>
+impl<N, R: DimName, C: DimName> VectorSpace for MatrixMN<N, R, C>
     where N: Scalar + Field,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+          DefaultAllocator: Allocator<N, R, C> {
     type Field = N;
 }
 
-impl<N, R: DimName, C: DimName, S> FiniteDimVectorSpace for Matrix<N, R, C, S>
+impl<N, R: DimName, C: DimName> FiniteDimVectorSpace for MatrixMN<N, R, C>
     where N: Scalar + Field,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+          DefaultAllocator: Allocator<N, R, C> {
     #[inline]
     fn dimension() -> usize {
         R::dim() * C::dim()
@@ -131,10 +123,8 @@ impl<N, R: DimName, C: DimName, S> FiniteDimVectorSpace for Matrix<N, R, C, S>
     }
 }
 
-impl<N, R: DimName, C: DimName, S> NormedSpace for Matrix<N, R, C, S>
-    where N: Real,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+impl<N: Real, R: DimName, C: DimName> NormedSpace for MatrixMN<N, R, C>
+    where DefaultAllocator: Allocator<N, R, C> {
     #[inline]
     fn norm_squared(&self) -> N {
         self.norm_squared()
@@ -166,10 +156,8 @@ impl<N, R: DimName, C: DimName, S> NormedSpace for Matrix<N, R, C, S>
     }
 }
 
-impl<N, R: DimName, C: DimName, S> InnerSpace for Matrix<N, R, C, S>
-    where N: Real,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+impl<N: Real, R: DimName, C: DimName> InnerSpace for MatrixMN<N, R, C>
+    where DefaultAllocator: Allocator<N, R, C> {
     type Real = N;
 
     #[inline]
@@ -187,12 +175,10 @@ impl<N, R: DimName, C: DimName, S> InnerSpace for Matrix<N, R, C, S>
 // In particular:
 //   − use `x()` instead of `::canonical_basis_element`
 //   − use `::new(x, y, z)` instead of `::from_slice`
-impl<N, R: DimName, C: DimName, S> FiniteDimInnerSpace for Matrix<N, R, C, S>
-    where N: Real,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+impl<N: Real, R: DimName, C: DimName> FiniteDimInnerSpace for MatrixMN<N, R, C>
+    where DefaultAllocator: Allocator<N, R, C> {
     #[inline]
-    fn orthonormalize(vs: &mut [Matrix<N, R, C, S>]) -> usize {
+    fn orthonormalize(vs: &mut [MatrixMN<N, R, C>]) -> usize {
         let mut nbasis_elements = 0;
 
         for i in 0 .. vs.len() {
@@ -229,7 +215,7 @@ impl<N, R: DimName, C: DimName, S> FiniteDimInnerSpace for Matrix<N, R, C, S>
         match Self::dimension() {
             1 => {
                 if vs.len() == 0 {
-                    f(&Self::canonical_basis_element(0));
+                    let _ = f(&Self::canonical_basis_element(0));
                 }
             },
             2 => {
@@ -241,7 +227,7 @@ impl<N, R: DimName, C: DimName, S> FiniteDimInnerSpace for Matrix<N, R, C, S>
                     let v = &vs[0];
                     let res = Self::from_column_slice(&[-v[1], v[0]]);
 
-                    f(&res.normalize());
+                    let _ = f(&res.normalize());
                 }
 
                 // Otherwise, nothing.
@@ -266,11 +252,11 @@ impl<N, R: DimName, C: DimName, S> FiniteDimInnerSpace for Matrix<N, R, C, S>
                     let _ = a.normalize_mut();
 
                     if f(&a.cross(v)) {
-                        f(&a);
+                        let _ = f(&a);
                     }
                 }
                 else if vs.len() == 2 {
-                    f(&vs[0].cross(&vs[1]).normalize());
+                    let _ = f(&vs[0].cross(&vs[1]).normalize());
                 }
             },
             _ => {
@@ -307,20 +293,18 @@ impl<N, R: DimName, C: DimName, S> FiniteDimInnerSpace for Matrix<N, R, C, S>
  *
  *
  */
-impl<N, D: DimName, S> Identity<Multiplicative> for SquareMatrix<N, D, S>
+impl<N, D: DimName> Identity<Multiplicative> for MatrixN<N, D>
     where N: Scalar + Zero + One,
-          S: OwnedStorage<N, D, D>,
-          S::Alloc: OwnedAllocator<N, D, D, S> {
+          DefaultAllocator: Allocator<N, D, D> {
     #[inline]
     fn identity() -> Self {
         Self::identity()
     }
 }
 
-impl<N, D: DimName, S> AbstractMagma<Multiplicative> for SquareMatrix<N, D, S>
-    where N: Scalar + Zero + ClosedAdd + ClosedMul,
-          S: OwnedStorage<N, D, D>,
-          S::Alloc: OwnedAllocator<N, D, D, S> {
+impl<N, D: DimName> AbstractMagma<Multiplicative> for MatrixN<N, D>
+    where N: Scalar + Zero + One + ClosedAdd + ClosedMul,
+          DefaultAllocator: Allocator<N, D, D> {
     #[inline]
     fn operate(&self, other: &Self) -> Self {
         self * other
@@ -329,10 +313,9 @@ impl<N, D: DimName, S> AbstractMagma<Multiplicative> for SquareMatrix<N, D, S>
 
 macro_rules! impl_multiplicative_structure(
     ($($marker: ident<$operator: ident> $(+ $bounds: ident)*),* $(,)*) => {$(
-        impl<N, D: DimName, S> $marker<$operator> for SquareMatrix<N, D, S>
-            where N: Scalar + Zero + ClosedAdd + ClosedMul + $marker<$operator> $(+ $bounds)*,
-                  S: OwnedStorage<N, D, D>,
-                  S::Alloc: OwnedAllocator<N, D, D, S> { }
+        impl<N, D: DimName> $marker<$operator> for MatrixN<N, D>
+            where N: Scalar + Zero + One + ClosedAdd + ClosedMul + $marker<$operator> $(+ $bounds)*,
+                  DefaultAllocator: Allocator<N, D, D> { }
     )*}
 );
 
@@ -341,421 +324,24 @@ impl_multiplicative_structure!(
     AbstractMonoid<Multiplicative> + One
 );
 
-// // FIXME: Field too strong?
-// impl<N, S> Matrix for Matrix<N, S>
-//     where N: Scalar + Field,
-//           S: Storage<N> {
-//     type Field     = N;
-//     type Row       = OwnedMatrix<N, Static<U1>, S::C, S::Alloc>;
-//     type Column    = OwnedMatrix<N, S::R, Static<U1>, S::Alloc>;
-//     type Transpose = OwnedMatrix<N, S::C, S::R, S::Alloc>;
-
-//     #[inline]
-//     fn nrows(&self) -> usize {
-//         self.shape().0
-//     }
-
-//     #[inline]
-//     fn ncolumns(&self) -> usize {
-//         self.shape().1
-//     }
-
-//     #[inline]
-//     fn row(&self, row: usize) -> Self::Row {
-//         let mut res: Self::Row = ::zero();
-
-//         for (column, e) in res.iter_mut().enumerate() {
-//             *e = self[(row, column)];
-//         }
-
-//         res
-//     }
-
-//     #[inline]
-//     fn column(&self, column: usize) -> Self::Column {
-//         let mut res: Self::Column = ::zero();
-
-//         for (row, e) in res.iter_mut().enumerate() {
-//             *e = self[(row, column)];
-//         }
-
-//         res
-//     }
-
-//     #[inline]
-//     unsafe fn get_unchecked(&self, i: usize, j: usize) -> Self::Field {
-//         self.get_unchecked(i, j)
-//     }
-
-//     #[inline]
-//     fn transpose(&self) -> Self::Transpose {
-//         self.transpose()
-//     }
-// }
-
-// impl<N, S> MatrixMut for Matrix<N, S>
-//     where N: Scalar + Field,
-//           S: StorageMut<N> {
-//     #[inline]
-//     fn set_row_mut(&mut self, irow: usize, row: &Self::Row) {
-//         assert!(irow < self.shape().0, "Row index out of bounds.");
-
-//         for (icol, e) in row.iter().enumerate() {
-//             unsafe { self.set_unchecked(irow, icol, *e) }
-//         }
-//     }
-
-//     #[inline]
-//     fn set_column_mut(&mut self, icol: usize, col: &Self::Column) {
-//         assert!(icol < self.shape().1, "Column index out of bounds.");
-//         for (irow, e) in col.iter().enumerate() {
-//             unsafe { self.set_unchecked(irow, icol, *e) }
-//         }
-//     }
-
-//     #[inline]
-//     unsafe fn set_unchecked(&mut self, i: usize, j: usize, val: Self::Field) {
-//         *self.get_unchecked_mut(i, j) = val
-//     }
-// }
-
-// // FIXME: Real is needed here only for invertibility...
-// impl<N: Real> SquareMatrixMut for $t<N> {
-//     #[inline]
-//     fn from_diagonal(diag: &Self::Coordinates) -> Self {
-//         let mut res: $t<N> = ::zero();
-//         res.set_diagonal_mut(diag);
-//         res
-//     }
-
-//     #[inline]
-//     fn set_diagonal_mut(&mut self, diag: &Self::Coordinates) {
-//         for (i, e) in diag.iter().enumerate() {
-//             unsafe { self.set_unchecked(i, i, *e) }
-//         }
-//     }
-// }
-
-
-
-// Specializations depending on the dimension.
-// matrix_group_approx_impl!(common: $t, 1, $vector, $($compN),+);
-
-// // FIXME: Real is needed here only for invertibility...
-// impl<N: Real> SquareMatrix for $t<N> {
-//     type Vector = $vector<N>;
-
-//     #[inline]
-//     fn diagonal(&self) -> Self::Coordinates {
-//         $vector::new(self.m11)
-//     }
-
-//     #[inline]
-//     fn determinant(&self) -> Self::Field {
-//         self.m11
-//     }
-
-//     #[inline]
-//     fn try_inverse(&self) -> Option<Self> {
-//         let mut res = *self;
-//         if res.try_inverse_mut() {
-//             Some(res)
-//         }
-//         else {
-//             None
-//         }
-//     }
-
-//     #[inline]
-//     fn try_inverse_mut(&mut self) -> bool {
-//         if relative_eq!(&self.m11, &::zero()) {
-//             false
-//         }
-//         else {
-//             self.m11 = ::one::<N>() / ::determinant(self);
-
-//             true
-//         }
-//     }
-
-//     #[inline]
-//     fn transpose_mut(&mut self) {
-//         // no-op
-//     }
-// }
-
-//  ident, 2, $vector: ident, $($compN: ident),+) => {
-// matrix_group_approx_impl!(common: $t, 2, $vector, $($compN),+);
-
-// // FIXME: Real is needed only for inversion here.
-// impl<N: Real> SquareMatrix for $t<N> {
-//     type Vector = $vector<N>;
-
-//     #[inline]
-//     fn diagonal(&self) -> Self::Coordinates {
-//         $vector::new(self.m11, self.m22)
-//     }
-
-//     #[inline]
-//     fn determinant(&self) -> Self::Field {
-//         self.m11 * self.m22 - self.m21 * self.m12
-//     }
-
-//     #[inline]
-//     fn try_inverse(&self) -> Option<Self> {
-//         let mut res = *self;
-//         if res.try_inverse_mut() {
-//             Some(res)
-//         }
-//         else {
-//             None
-//         }
-//     }
-
-//     #[inline]
-//     fn try_inverse_mut(&mut self) -> bool {
-//         let determinant = ::determinant(self);
-
-//         if relative_eq!(&determinant, &::zero()) {
-//             false
-//         }
-//         else {
-//             *self = Matrix2::new(
-//                 self.m22 / determinant , -self.m12 / determinant,
-//                 -self.m21 / determinant, self.m11 / determinant);
-
-//             true
-//         }
-//     }
-
-//     #[inline]
-//     fn transpose_mut(&mut self) {
-//         mem::swap(&mut self.m12, &mut self.m21)
-//     }
-// }
-
-//  ident, 3, $vector: ident, $($compN: ident),+) => {
-// matrix_group_approx_impl!(common: $t, 3, $vector, $($compN),+);
-
-// // FIXME: Real is needed only for inversion here.
-// impl<N: Real> SquareMatrix for $t<N> {
-//     type Vector = $vector<N>;
-
-//     #[inline]
-//     fn diagonal(&self) -> Self::Coordinates {
-//         $vector::new(self.m11, self.m22, self.m33)
-//     }
-
-//     #[inline]
-//     fn determinant(&self) -> Self::Field {
-//         let minor_m12_m23 = self.m22 * self.m33 - self.m32 * self.m23;
-//         let minor_m11_m23 = self.m21 * self.m33 - self.m31 * self.m23;
-//         let minor_m11_m22 = self.m21 * self.m32 - self.m31 * self.m22;
-
-//         self.m11 * minor_m12_m23 - self.m12 * minor_m11_m23 + self.m13 * minor_m11_m22
-//     }
-
-//     #[inline]
-//     fn try_inverse(&self) -> Option<Self> {
-//         let mut res = *self;
-//         if res.try_inverse_mut() {
-//             Some(res)
-//         }
-//         else {
-//             None
-//         }
-//     }
-
-//     #[inline]
-//     fn try_inverse_mut(&mut self) -> bool {
-//         let minor_m12_m23 = self.m22 * self.m33 - self.m32 * self.m23;
-//         let minor_m11_m23 = self.m21 * self.m33 - self.m31 * self.m23;
-//         let minor_m11_m22 = self.m21 * self.m32 - self.m31 * self.m22;
-
-//         let determinant = self.m11 * minor_m12_m23 -
-//                           self.m12 * minor_m11_m23 +
-//                           self.m13 * minor_m11_m22;
-
-//         if relative_eq!(&determinant, &::zero()) {
-//             false
-//         }
-//         else {
-//             *self = Matrix3::new(
-//                 (minor_m12_m23 / determinant),
-//                 ((self.m13 * self.m32 - self.m33 * self.m12) / determinant),
-//                 ((self.m12 * self.m23 - self.m22 * self.m13) / determinant),
-
-//                 (-minor_m11_m23 / determinant),
-//                 ((self.m11 * self.m33 - self.m31 * self.m13) / determinant),
-//                 ((self.m13 * self.m21 - self.m23 * self.m11) / determinant),
-
-//                 (minor_m11_m22  / determinant),
-//                 ((self.m12 * self.m31 - self.m32 * self.m11) / determinant),
-//                 ((self.m11 * self.m22 - self.m21 * self.m12) / determinant)
-//                 );
-
-//             true
-//         }
-//     }
-
-//     #[inline]
-//     fn transpose_mut(&mut self) {
-//         mem::swap(&mut self.m12, &mut self.m21);
-//         mem::swap(&mut self.m13, &mut self.m31);
-//         mem::swap(&mut self.m23, &mut self.m32);
-//     }
-// }
-
-//  ident, $dimension: expr, $vector: ident, $($compN: ident),+) => {
-// matrix_group_approx_impl!(common: $t, $dimension, $vector, $($compN),+);
-
-// // FIXME: Real is needed only for inversion here.
-// impl<N: Real> SquareMatrix for $t<N> {
-//     type Vector = $vector<N>;
-
-//     #[inline]
-//     fn diagonal(&self) -> Self::Coordinates {
-//         let mut diagonal: $vector<N> = ::zero();
-
-//         for i in 0 .. $dimension {
-//             unsafe { diagonal.unsafe_set(i, self.get_unchecked(i, i)) }
-//         }
-
-//         diagonal
-//     }
-
-//     #[inline]
-//     fn determinant(&self) -> Self::Field {
-//         // FIXME: extremely naive implementation.
-//         let mut det = ::zero();
-
-//         for icol in 0 .. $dimension {
-//             let e = unsafe { self.unsafe_at((0, icol)) };
-
-//             if e != ::zero() {
-//                 let minor_mat = self.delete_row_column(0, icol);
-//                 let minor     = minor_mat.determinant();
-
-//                 if icol % 2 == 0 {
-//                     det += minor;
-//                 }
-//                 else {
-//                     det -= minor;
-//                 }
-//             }
-//         }
-
-//         det
-//     }
-
-//     #[inline]
-//     fn try_inverse(&self) -> Option<Self> {
-//         let mut res = *self;
-//         if res.try_inverse_mut() {
-//             Some(res)
-//         }
-//         else {
-//             None
-//         }
-//     }
-
-//     #[inline]
-//     fn try_inverse_mut(&mut self) -> bool {
-//         let mut res: $t<N> = ::one();
-
-//         // Inversion using Gauss-Jordan elimination
-//         for k in 0 .. $dimension {
-//             // search a non-zero value on the k-th column
-//             // FIXME: would it be worth it to spend some more time searching for the
-//             // max instead?
-
-//             let mut n0 = k; // index of a non-zero entry
-
-//             while n0 != $dimension {
-//                 if self[(n0, k)] != ::zero() {
-//                     break;
-//                 }
-
-//                 n0 = n0 + 1;
-//             }
-
-//             if n0 == $dimension {
-//                 return false
-//             }
-
-//             // swap pivot line
-//             if n0 != k {
-//                 for j in 0 .. $dimension {
-//                     self.swap((n0, j), (k, j));
-//                     res.swap((n0, j), (k, j));
-//                 }
-//             }
-
-//             let pivot = self[(k, k)];
-
-//             for j in k .. $dimension {
-//                 let selfval = self[(k, j)] / pivot;
-//                 self[(k, j)] = selfval;
-//             }
-
-//             for j in 0 .. $dimension {
-//                 let resval = res[(k, j)] / pivot;
-//                 res[(k, j)] = resval;
-//             }
-
-//             for l in 0 .. $dimension {
-//                 if l != k {
-//                     let normalizer = self[(l, k)];
-
-//                     for j in k .. $dimension {
-//                         let selfval = self[(l, j)] - self[(k, j)] * normalizer;
-//                         self[(l, j)] = selfval;
-//                     }
-
-//                     for j in 0 .. $dimension {
-//                         let resval  = res[(l, j)] - res[(k, j)] * normalizer;
-//                         res[(l, j)] = resval;
-//                     }
-//                 }
-//             }
-//         }
-
-//         *self = res;
-
-//         true
-//     }
-
-//     #[inline]
-//     fn transpose_mut(&mut self) {
-//         for i in 1 .. $dimension {
-//             for j in 0 .. i {
-//                 self.swap((i, j), (j, i))
-//             }
-//         }
-//     }
-
-
-
 
 /*
  *
  * Ordering
  *
  */
-impl<N, R: Dim, C: Dim, S> MeetSemilattice for Matrix<N, R, C, S>
+impl<N, R: Dim, C: Dim> MeetSemilattice for MatrixMN<N, R, C>
     where N: Scalar + MeetSemilattice,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+          DefaultAllocator: Allocator<N, R, C> {
     #[inline]
     fn meet(&self, other: &Self) -> Self {
         self.zip_map(other, |a, b| a.meet(&b))
     }
 }
 
-impl<N, R: Dim, C: Dim, S> JoinSemilattice for Matrix<N, R, C, S>
+impl<N, R: Dim, C: Dim> JoinSemilattice for MatrixMN<N, R, C>
     where N: Scalar + JoinSemilattice,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+          DefaultAllocator: Allocator<N, R, C> {
     #[inline]
     fn join(&self, other: &Self) -> Self {
         self.zip_map(other, |a, b| a.join(&b))
@@ -763,10 +349,9 @@ impl<N, R: Dim, C: Dim, S> JoinSemilattice for Matrix<N, R, C, S>
 }
 
 
-impl<N, R: Dim, C: Dim, S> Lattice for Matrix<N, R, C, S>
+impl<N, R: Dim, C: Dim> Lattice for MatrixMN<N, R, C>
     where N: Scalar + Lattice,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+          DefaultAllocator: Allocator<N, R, C> {
     #[inline]
     fn meet_join(&self, other: &Self) -> (Self, Self) {
         let shape = self.data.shape();

src/core/matrix_array.rs

@@ -21,7 +21,7 @@ use generic_array::{ArrayLength, GenericArray};
 
 use core::Scalar;
 use core::dimension::{DimName, U1};
-use core::storage::{Storage, StorageMut, Owned, OwnedStorage};
+use core::storage::{Storage, StorageMut, Owned, ContiguousStorage, ContiguousStorageMut};
 use core::allocator::Allocator;
 use core::default_allocator::DefaultAllocator;
 
@@ -139,22 +139,10 @@ unsafe impl<N, R, C> Storage<N, R, C> for MatrixArray<N, R, C>
           R: DimName,
           C: DimName,
           R::Value: Mul<C::Value>,
-          Prod<R::Value, C::Value>: ArrayLength<N> {
+          Prod<R::Value, C::Value>: ArrayLength<N>,
+          DefaultAllocator: Allocator<N, R, C, Buffer = Self> {
     type RStride = U1;
     type CStride = R;
-    type Alloc   = DefaultAllocator;
-
-    #[inline]
-    fn into_owned(self) -> Owned<N, R, C, Self::Alloc> {
-        self
-    }
-
-    #[inline]
-    fn clone_owned(&self) -> Owned<N, R, C, Self::Alloc> {
-        let it = self.iter().cloned();
-
-        Self::Alloc::allocate_from_iterator(self.shape().0, self.shape().1, it)
-    }
 
     #[inline]
     fn ptr(&self) -> *const N {
@@ -170,30 +158,44 @@ unsafe impl<N, R, C> Storage<N, R, C> for MatrixArray<N, R, C>
     fn strides(&self) -> (Self::RStride, Self::CStride) {
         (Self::RStride::name(), Self::CStride::name())
     }
+
+    #[inline]
+    fn is_contiguous(&self) -> bool {
+        true
+    }
+
+    #[inline]
+    fn into_owned(self) -> Owned<N, R, C>
+        where DefaultAllocator: Allocator<N, R, C> {
+        self
+    }
+
+    #[inline]
+    fn clone_owned(&self) -> Owned<N, R, C>
+        where DefaultAllocator: Allocator<N, R, C> {
+        let it = self.iter().cloned();
+
+        DefaultAllocator::allocate_from_iterator(self.shape().0, self.shape().1, it)
+    }
+
+    #[inline]
+    fn as_slice(&self) -> &[N] {
+        &self[..]
+    }
 }
 
+
 unsafe impl<N, R, C> StorageMut<N, R, C> for MatrixArray<N, R, C>
     where N: Scalar,
           R: DimName,
           C: DimName,
           R::Value: Mul<C::Value>,
-          Prod<R::Value, C::Value>: ArrayLength<N> {
+          Prod<R::Value, C::Value>: ArrayLength<N>,
+          DefaultAllocator: Allocator<N, R, C, Buffer = Self> {
     #[inline]
     fn ptr_mut(&mut self) -> *mut N {
         self[..].as_mut_ptr()
     }
-}
-
-unsafe impl<N, R, C> OwnedStorage<N, R, C> for MatrixArray<N, R, C>
-    where N: Scalar,
-          R: DimName,
-          C: DimName,
-          R::Value: Mul<C::Value>,
-          Prod<R::Value, C::Value>: ArrayLength<N> {
-    #[inline]
-    fn as_slice(&self) -> &[N] {
-        &self[..]
-    }
 
     #[inline]
     fn as_mut_slice(&mut self) -> &mut [N] {
@@ -201,6 +203,24 @@ unsafe impl<N, R, C> OwnedStorage<N, R, C> for MatrixArray<N, R, C>
     }
 }
 
+unsafe impl<N, R, C> ContiguousStorage<N, R, C> for MatrixArray<N, R, C>
+    where N: Scalar,
+          R: DimName,
+          C: DimName,
+          R::Value: Mul<C::Value>,
+          Prod<R::Value, C::Value>: ArrayLength<N>,
+          DefaultAllocator: Allocator<N, R, C, Buffer = Self> {
+}
+
+unsafe impl<N, R, C> ContiguousStorageMut<N, R, C> for MatrixArray<N, R, C>
+    where N: Scalar,
+          R: DimName,
+          C: DimName,
+          R::Value: Mul<C::Value>,
+          Prod<R::Value, C::Value>: ArrayLength<N>,
+          DefaultAllocator: Allocator<N, R, C, Buffer = Self> {
+}
+
 
 /*
  *

src/core/matrix_slice.rs

@@ -1,28 +1,31 @@
 use std::marker::PhantomData;
+use std::ops::{Range, RangeFrom, RangeTo, RangeFull};
+use std::slice;
 
 use core::{Scalar, Matrix};
-use core::dimension::{Dim, DimName, Dynamic, DimMul, DimProd, U1};
+use core::dimension::{Dim, DimName, Dynamic, U1};
 use core::iter::MatrixIter;
 use core::storage::{Storage, StorageMut, Owned};
 use core::allocator::Allocator;
+use core::default_allocator::DefaultAllocator;
 
 macro_rules! slice_storage_impl(
     ($doc: expr; $Storage: ident as $SRef: ty; $T: ident.$get_addr: ident ($Ptr: ty as $Ref: ty)) => {
         #[doc = $doc]
-        pub struct $T<'a, N: Scalar, R: Dim, C: Dim, RStride: Dim, CStride: Dim, Alloc> {
+        #[derive(Debug)]
+        pub struct $T<'a, N: Scalar, R: Dim, C: Dim, RStride: Dim, CStride: Dim> {
             ptr:       $Ptr,
             shape:     (R, C),
             strides:   (RStride, CStride),
-            _phantoms: PhantomData<($Ref, Alloc)>,
+            _phantoms: PhantomData<$Ref>,
         }
 
-        // Dynamic and () are arbitrary. It's just to be able to call the constructors with
-        // `Slice::`
-        impl<'a, N: Scalar, R: Dim, C: Dim> $T<'a, N, R, C, Dynamic, Dynamic, ()> {
+        // Dynamic is arbitrary. It's just to be able to call the constructors with `Slice::`
+        impl<'a, N: Scalar, R: Dim, C: Dim> $T<'a, N, R, C, Dynamic, Dynamic> {
             /// Create a new matrix slice without bound checking.
             #[inline]
             pub unsafe fn new_unchecked<RStor, CStor, S>(storage: $SRef, start: (usize, usize), shape: (R, C))
-                -> $T<'a, N, R, C, S::RStride, S::CStride, S::Alloc>
+                -> $T<'a, N, R, C, S::RStride, S::CStride>
                 where RStor: Dim,
                       CStor: Dim,
                       S:     $Storage<N, RStor, CStor> {
@@ -37,17 +40,29 @@ macro_rules! slice_storage_impl(
                                                                                         start:   (usize, usize),
                                                                                         shape:   (R, C),
                                                                                         strides: (RStride, CStride))
-                -> $T<'a, N, R, C, RStride, CStride, S::Alloc>
+                -> $T<'a, N, R, C, RStride, CStride>
                 where RStor: Dim,
                       CStor: Dim,
                       S: $Storage<N, RStor, CStor>,
                       RStride: Dim,
                       CStride: Dim {
 
+                $T::from_raw_parts(storage.$get_addr(start.0, start.1), shape, strides)
+            }
+
+            /// Create a new matrix slice without bound checking and from a raw pointer.
+            #[inline]
+            pub unsafe fn from_raw_parts<RStride, CStride>(ptr:     $Ptr,
+                                                           shape:   (R, C),
+                                                           strides: (RStride, CStride))
+                -> $T<'a, N, R, C, RStride, CStride>
+                where RStride: Dim,
+                      CStride: Dim {
+
                 $T {
-                    ptr:       storage.$get_addr(start.0, start.1),
+                    ptr:       ptr,
                     shape:     shape,
-                    strides:   (strides.0, strides.1),
+                    strides:   strides,
                     _phantoms: PhantomData
                 }
             }
@@ -65,11 +80,11 @@ slice_storage_impl!("A mutable matrix data storage for mutable matrix slice. Onl
 );
 
 
-impl<'a, N: Scalar, R: Dim, C: Dim, RStride: Dim, CStride: Dim, Alloc> Copy
-for SliceStorage<'a, N, R, C, RStride, CStride, Alloc> { }
+impl<'a, N: Scalar, R: Dim, C: Dim, RStride: Dim, CStride: Dim> Copy
+for SliceStorage<'a, N, R, C, RStride, CStride> { }
 
-impl<'a, N: Scalar, R: Dim, C: Dim, RStride: Dim, CStride: Dim, Alloc> Clone
-for SliceStorage<'a, N, R, C, RStride, CStride, Alloc> {
+impl<'a, N: Scalar, R: Dim, C: Dim, RStride: Dim, CStride: Dim> Clone
+for SliceStorage<'a, N, R, C, RStride, CStride> {
     #[inline]
     fn clone(&self) -> Self {
         SliceStorage {
@@ -83,26 +98,11 @@ for SliceStorage<'a, N, R, C, RStride, CStride, Alloc> {
 
 macro_rules! storage_impl(
     ($($T: ident),* $(,)*) => {$(
-        unsafe impl<'a, N, R: Dim, C: Dim, RStride: Dim, CStride: Dim, Alloc> Storage<N, R, C>
-            for $T<'a, N, R, C, RStride, CStride, Alloc>
-            where N:     Scalar,
-                  Alloc: Allocator<N, R, C> {
+        unsafe impl<'a, N: Scalar, R: Dim, C: Dim, RStride: Dim, CStride: Dim> Storage<N, R, C>
+            for $T<'a, N, R, C, RStride, CStride> {
 
             type RStride = RStride;
             type CStride = CStride;
-            type Alloc   = Alloc;
-
-            #[inline]
-            fn into_owned(self) -> Owned<N, R, C, Self::Alloc> {
-                self.clone_owned()
-            }
-
-            #[inline]
-            fn clone_owned(&self) -> Owned<N, R, C, Self::Alloc> {
-                let (nrows, ncols) = self.shape();
-                let it = MatrixIter::new(self).cloned();
-                Alloc::allocate_from_iterator(nrows, ncols, it)
-            }
 
             #[inline]
             fn ptr(&self) -> *const N {
@@ -118,20 +118,74 @@ macro_rules! storage_impl(
             fn strides(&self) -> (Self::RStride, Self::CStride) {
                 self.strides
             }
+
+            #[inline]
+            fn is_contiguous(&self) -> bool {
+                // Common cases that can be deduced at compile-time even if one of the dimensions
+                // is Dynamic.
+                if (RStride::is::<U1>() && C::is::<U1>()) || // Column vector.
+                   (CStride::is::<U1>() && R::is::<U1>()) {  // Row vector.
+                    true
+                }
+                else {
+                    let (nrows, _)     = self.shape();
+                    let (srows, scols) = self.strides();
+
+                    srows.value() == 1 && scols.value() == nrows.value()
+                }
+            }
+
+
+
+            #[inline]
+            fn into_owned(self) -> Owned<N, R, C>
+                where DefaultAllocator: Allocator<N, R, C> {
+                self.clone_owned()
+            }
+
+            #[inline]
+            fn clone_owned(&self) -> Owned<N, R, C>
+                where DefaultAllocator: Allocator<N, R, C> {
+                let (nrows, ncols) = self.shape();
+                let it = MatrixIter::new(self).cloned();
+                DefaultAllocator::allocate_from_iterator(nrows, ncols, it)
+            }
+
+            #[inline]
+            fn as_slice(&self) -> &[N] {
+                let (nrows, ncols) = self.shape();
+                if nrows.value() != 0 && ncols.value() != 0 {
+                    let sz = self.linear_index(nrows.value() - 1, ncols.value() - 1);
+                    unsafe { slice::from_raw_parts(self.ptr, sz + 1) }
+                }
+                else {
+                    unsafe { slice::from_raw_parts(self.ptr, 0) }
+                }
+            }
         }
     )*}
 );
 
 storage_impl!(SliceStorage, SliceStorageMut);
 
-unsafe impl<'a, N, R: Dim, C: Dim, RStride: Dim, CStride: Dim, Alloc> StorageMut<N, R, C>
-    for SliceStorageMut<'a, N, R, C, RStride, CStride, Alloc>
-    where N: Scalar,
-          Alloc: Allocator<N, R, C> {
+unsafe impl<'a, N: Scalar, R: Dim, C: Dim, RStride: Dim, CStride: Dim> StorageMut<N, R, C>
+    for SliceStorageMut<'a, N, R, C, RStride, CStride> {
     #[inline]
     fn ptr_mut(&mut self) -> *mut N {
         self.ptr
     }
+
+    #[inline]
+    fn as_mut_slice(&mut self) -> &mut [N] {
+        let (nrows, ncols) = self.shape();
+        if nrows.value() != 0 && ncols.value() != 0 {
+            let sz = self.linear_index(nrows.value() - 1, ncols.value() - 1);
+            unsafe { slice::from_raw_parts_mut(self.ptr, sz + 1) }
+        }
+        else {
+            unsafe { slice::from_raw_parts_mut(self.ptr, 0) }
+        }
+    }
 }
 
 
@@ -139,35 +193,45 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     #[inline]
     fn assert_slice_index(&self, start: (usize, usize), shape: (usize, usize), steps: (usize, usize)) {
         let my_shape = self.shape();
-        assert!(start.0 + (shape.0 - 1) * steps.0 <= my_shape.0, "Matrix slicing out of bounds.");
-        assert!(start.1 + (shape.1 - 1) * steps.1 <= my_shape.1, "Matrix slicing out of bounds.");
+        // NOTE: we don't do any subtraction to avoid underflow for zero-sized matrices.
+        //
+        // Terms that would have been negative are moved to the other side of the inequality
+        // instead.
+        assert!(start.0 + (steps.0 + 1) * shape.0 <= my_shape.0 + steps.0, "Matrix slicing out of bounds.");
+        assert!(start.1 + (steps.1 + 1) * shape.1 <= my_shape.1 + steps.1, "Matrix slicing out of bounds.");
     }
 }
 
 
 macro_rules! matrix_slice_impl(
-    ($me: ident: $Me: ty, $MatrixSlice: ident, $SliceStorage: ident, $Storage: ident, $data: expr;
+    ($me: ident: $Me: ty, $MatrixSlice: ident, $SliceStorage: ident, $Storage: ident.$get_addr: ident (), $data: expr;
      $row: ident,
+     $row_part: ident,
      $rows: ident,
      $rows_with_step: ident,
      $fixed_rows: ident,
      $fixed_rows_with_step: ident,
      $rows_generic: ident,
+     $rows_generic_with_step: ident,
      $column: ident,
+     $column_part: ident,
      $columns: ident,
      $columns_with_step: ident,
      $fixed_columns: ident,
      $fixed_columns_with_step: ident,
      $columns_generic: ident,
+     $columns_generic_with_step: ident,
      $slice: ident,
      $slice_with_steps: ident,
      $fixed_slice: ident,
      $fixed_slice_with_steps: ident,
      $generic_slice: ident,
-     $generic_slice_with_steps: ident) => {
+     $generic_slice_with_steps: ident,
+     $rows_range_pair: ident,
+     $columns_range_pair: ident) => {
         /// A matrix slice.
-        pub type $MatrixSlice<'a, N, R, C, RStride, CStride, Alloc>
-        = Matrix<N, R, C, $SliceStorage<'a, N, R, C, RStride, CStride, Alloc>>;
+        pub type $MatrixSlice<'a, N, R, C, RStride, CStride>
+        = Matrix<N, R, C, $SliceStorage<'a, N, R, C, RStride, CStride>>;
 
         impl<N: Scalar, R: Dim, C: Dim, S: $Storage<N, R, C>> Matrix<N, R, C, S> {
             /*
@@ -175,73 +239,80 @@ macro_rules! matrix_slice_impl(
              * Row slicing.
              *
              */
-            /// Returns a slice containing the i-th column of this matrix.
+            /// Returns a slice containing the i-th row of this matrix.
             #[inline]
-            pub fn $row($me: $Me, i: usize) -> $MatrixSlice<N, U1, C, S::RStride, S::CStride, S::Alloc> {
+            pub fn $row($me: $Me, i: usize) -> $MatrixSlice<N, U1, C, S::RStride, S::CStride> {
                 $me.$fixed_rows::<U1>(i)
             }
 
+            /// Returns a slice containing the `n` first elements of the i-th row of this matrix.
+            #[inline]
+            pub fn $row_part($me: $Me, i: usize, n: usize) -> $MatrixSlice<N, U1, Dynamic, S::RStride, S::CStride> {
+                $me.$generic_slice((i, 0), (U1, Dynamic::new(n)))
+            }
+
             /// Extracts from this matrix a set of consecutive rows.
             #[inline]
             pub fn $rows($me: $Me, first_row: usize, nrows: usize)
-                -> $MatrixSlice<N, Dynamic, C, S::RStride, S::CStride, S::Alloc> {
+                -> $MatrixSlice<N, Dynamic, C, S::RStride, S::CStride> {
 
-                let my_shape = $me.data.shape();
-                $me.assert_slice_index((first_row, 0), (nrows, my_shape.1.value()), (1, 1));
-                let shape = (Dynamic::new(nrows), my_shape.1);
-
-                unsafe {
-                    let data = $SliceStorage::new_unchecked($data, (first_row, 0), shape);
-                    Matrix::from_data_statically_unchecked(data)
-                }
+                $me.$rows_generic(first_row, Dynamic::new(nrows))
             }
 
-            /// Extracts from this matrix a set of consecutive rows regularly spaced by `step` rows.
+            /// Extracts from this matrix a set of consecutive rows regularly skipping `step` rows.
             #[inline]
             pub fn $rows_with_step($me: $Me, first_row: usize, nrows: usize, step: usize)
-                -> $MatrixSlice<N, Dynamic, C, Dynamic, S::CStride, S::Alloc> {
+                -> $MatrixSlice<N, Dynamic, C, Dynamic, S::CStride> {
 
-                $me.$rows_generic(first_row, Dynamic::new(nrows), Dynamic::new(step))
+                $me.$rows_generic_with_step(first_row, Dynamic::new(nrows), step)
             }
 
             /// Extracts a compile-time number of consecutive rows from this matrix.
             #[inline]
-            pub fn $fixed_rows<RSlice>($me: $Me, first_row: usize)
-                -> $MatrixSlice<N, RSlice, C, S::RStride, S::CStride, S::Alloc>
-                where RSlice: DimName {
+            pub fn $fixed_rows<RSlice: DimName>($me: $Me, first_row: usize)
+                -> $MatrixSlice<N, RSlice, C, S::RStride, S::CStride> {
+
+                $me.$rows_generic(first_row, RSlice::name())
+            }
+
+            /// Extracts from this matrix a compile-time number of rows regularly skipping `step`
+            /// rows.
+            #[inline]
+            pub fn $fixed_rows_with_step<RSlice: DimName>($me: $Me, first_row: usize, step: usize)
+                -> $MatrixSlice<N, RSlice, C, Dynamic, S::CStride> {
+
+                $me.$rows_generic_with_step(first_row, RSlice::name(), step)
+            }
+
+            /// Extracts from this matrix `nrows` rows regularly skipping `step` rows. Both
+            /// argument may or may not be values known at compile-time.
+            #[inline]
+            pub fn $rows_generic<RSlice: Dim>($me: $Me, row_start: usize, nrows: RSlice)
+                -> $MatrixSlice<N, RSlice, C, S::RStride, S::CStride> {
 
                 let my_shape   = $me.data.shape();
-                $me.assert_slice_index((first_row, 0), (RSlice::dim(), my_shape.1.value()), (1, 1));
-                let shape = (RSlice::name(), my_shape.1);
+                $me.assert_slice_index((row_start, 0), (nrows.value(), my_shape.1.value()), (0, 0));
+
+                let shape = (nrows, my_shape.1);
 
                 unsafe {
-                    let data = $SliceStorage::new_unchecked($data, (first_row, 0), shape);
+                    let data = $SliceStorage::new_unchecked($data, (row_start, 0), shape);
                     Matrix::from_data_statically_unchecked(data)
                 }
             }
 
-            /// Extracts from this matrix a compile-time number of rows regularly spaced by `step` rows.
+            /// Extracts from this matrix `nrows` rows regularly skipping `step` rows. Both
+            /// argument may or may not be values known at compile-time.
             #[inline]
-            pub fn $fixed_rows_with_step<RSlice>($me: $Me, first_row: usize, step: usize)
-                -> $MatrixSlice<N, RSlice, C, Dynamic, S::CStride, S::Alloc>
-                where RSlice: DimName {
-
-                $me.$rows_generic(first_row, RSlice::name(), Dynamic::new(step))
-            }
-
-            /// Extracts from this matrix `nrows` rows regularly spaced by `step` rows. Both argument may
-            /// or may not be values known at compile-time.
-            #[inline]
-            pub fn $rows_generic<RSlice, RStep>($me: $Me, row_start: usize, nrows: RSlice, step: RStep)
-                -> $MatrixSlice<N, RSlice, C, DimProd<RStep, S::RStride>, S::CStride, S::Alloc>
-                where RSlice: Dim,
-                      RStep: DimMul<S::RStride> {
+            pub fn $rows_generic_with_step<RSlice>($me: $Me, row_start: usize, nrows: RSlice, step: usize)
+                -> $MatrixSlice<N, RSlice, C, Dynamic, S::CStride>
+                where RSlice: Dim {
 
                 let my_shape   = $me.data.shape();
                 let my_strides = $me.data.strides();
-                $me.assert_slice_index((row_start, 0), (nrows.value(), my_shape.1.value()), (step.value(), 1));
+                $me.assert_slice_index((row_start, 0), (nrows.value(), my_shape.1.value()), (step, 0));
 
-                let strides = (step.mul(my_strides.0), my_strides.1);
+                let strides = (Dynamic::new((step + 1) * my_strides.0.value()), my_strides.1);
                 let shape   = (nrows, my_shape.1);
 
                 unsafe {
@@ -257,42 +328,59 @@ macro_rules! matrix_slice_impl(
              */
             /// Returns a slice containing the i-th column of this matrix.
             #[inline]
-            pub fn $column($me: $Me, i: usize) -> $MatrixSlice<N, R, U1, S::RStride, S::CStride, S::Alloc> {
+            pub fn $column($me: $Me, i: usize) -> $MatrixSlice<N, R, U1, S::RStride, S::CStride> {
                 $me.$fixed_columns::<U1>(i)
             }
 
+            /// Returns a slice containing the `n` first elements of the i-th column of this matrix.
+            #[inline]
+            pub fn $column_part($me: $Me, i: usize, n: usize) -> $MatrixSlice<N, Dynamic, U1, S::RStride, S::CStride> {
+                $me.$generic_slice((0, i), (Dynamic::new(n), U1))
+            }
+
             /// Extracts from this matrix a set of consecutive columns.
             #[inline]
             pub fn $columns($me: $Me, first_col: usize, ncols: usize)
-                -> $MatrixSlice<N, R, Dynamic, S::RStride, S::CStride, S::Alloc> {
+                -> $MatrixSlice<N, R, Dynamic, S::RStride, S::CStride> {
 
-                let my_shape = $me.data.shape();
-                $me.assert_slice_index((0, first_col), (my_shape.0.value(), ncols), (1, 1));
-                let shape = (my_shape.0, Dynamic::new(ncols));
-
-                unsafe {
-                    let data = $SliceStorage::new_unchecked($data, (0, first_col), shape);
-                    Matrix::from_data_statically_unchecked(data)
-                }
+                $me.$columns_generic(first_col, Dynamic::new(ncols))
             }
 
-            /// Extracts from this matrix a set of consecutive columns regularly spaced by `step` columns.
+            /// Extracts from this matrix a set of consecutive columns regularly skipping `step`
+            /// columns.
             #[inline]
             pub fn $columns_with_step($me: $Me, first_col: usize, ncols: usize, step: usize)
-                -> $MatrixSlice<N, R, Dynamic, S::RStride, Dynamic, S::Alloc> {
+                -> $MatrixSlice<N, R, Dynamic, S::RStride, Dynamic> {
 
-                $me.$columns_generic(first_col, Dynamic::new(ncols), Dynamic::new(step))
+                $me.$columns_generic_with_step(first_col, Dynamic::new(ncols), step)
             }
 
             /// Extracts a compile-time number of consecutive columns from this matrix.
             #[inline]
-            pub fn $fixed_columns<CSlice>($me: $Me, first_col: usize)
-                -> $MatrixSlice<N, R, CSlice, S::RStride, S::CStride, S::Alloc>
-                where CSlice: DimName {
+            pub fn $fixed_columns<CSlice: DimName>($me: $Me, first_col: usize)
+                -> $MatrixSlice<N, R, CSlice, S::RStride, S::CStride> {
+
+                $me.$columns_generic(first_col, CSlice::name())
+            }
+
+            /// Extracts from this matrix a compile-time number of columns regularly skipping
+            /// `step` columns.
+            #[inline]
+            pub fn $fixed_columns_with_step<CSlice: DimName>($me: $Me, first_col: usize, step: usize)
+                -> $MatrixSlice<N, R, CSlice, S::RStride, Dynamic> {
+
+                $me.$columns_generic_with_step(first_col, CSlice::name(), step)
+            }
+
+            /// Extracts from this matrix `ncols` columns. The number of columns may or may not be
+            /// known at compile-time.
+            #[inline]
+            pub fn $columns_generic<CSlice: Dim>($me: $Me, first_col: usize, ncols: CSlice)
+                -> $MatrixSlice<N, R, CSlice, S::RStride, S::CStride> {
 
                 let my_shape = $me.data.shape();
-                $me.assert_slice_index((0, first_col), (my_shape.0.value(), CSlice::dim()), (1, 1));
-                let shape = (my_shape.0, CSlice::name());
+                $me.assert_slice_index((0, first_col), (my_shape.0.value(), ncols.value()), (0, 0));
+                let shape = (my_shape.0, ncols);
 
                 unsafe {
                     let data = $SliceStorage::new_unchecked($data, (0, first_col), shape);
@@ -300,30 +388,19 @@ macro_rules! matrix_slice_impl(
                 }
             }
 
-            /// Extracts from this matrix a compile-time number of columns regularly spaced by `step`
-            /// columns.
-            #[inline]
-            pub fn $fixed_columns_with_step<CSlice>($me: $Me, first_col: usize, step: usize)
-                -> $MatrixSlice<N, R, CSlice, S::RStride, Dynamic, S::Alloc>
-                where CSlice: DimName {
 
-                $me.$columns_generic(first_col, CSlice::name(), Dynamic::new(step))
-            }
-
-            /// Extracts from this matrix `ncols` columns regularly spaced by `step` columns. Both argument may
+            /// Extracts from this matrix `ncols` columns skipping `step` columns. Both argument may
             /// or may not be values known at compile-time.
             #[inline]
-            pub fn $columns_generic<CSlice, CStep>($me: $Me, first_col: usize, ncols: CSlice, step: CStep)
-                -> $MatrixSlice<N, R, CSlice, S::RStride, DimProd<CStep, S::CStride>, S::Alloc>
-                where CSlice: Dim,
-                      CStep: DimMul<S::CStride> {
+            pub fn $columns_generic_with_step<CSlice: Dim>($me: $Me, first_col: usize, ncols: CSlice, step: usize)
+                -> $MatrixSlice<N, R, CSlice, S::RStride, Dynamic> {
 
                 let my_shape   = $me.data.shape();
                 let my_strides = $me.data.strides();
 
-                $me.assert_slice_index((0, first_col), (my_shape.0.value(), ncols.value()), (1, step.value()));
+                $me.assert_slice_index((0, first_col), (my_shape.0.value(), ncols.value()), (0, step));
 
-                let strides = (my_strides.0, step.mul(my_strides.1));
+                let strides = (my_strides.0, Dynamic::new((step + 1) * my_strides.1.value()));
                 let shape   = (my_shape.0, ncols);
 
                 unsafe {
@@ -341,9 +418,9 @@ macro_rules! matrix_slice_impl(
             /// consecutive elements.
             #[inline]
             pub fn $slice($me: $Me, start: (usize, usize), shape: (usize, usize))
-                -> $MatrixSlice<N, Dynamic, Dynamic, S::RStride, S::CStride, S::Alloc> {
+                -> $MatrixSlice<N, Dynamic, Dynamic, S::RStride, S::CStride> {
 
-                $me.assert_slice_index(start, shape, (1, 1));
+                $me.assert_slice_index(start, shape, (0, 0));
                 let shape = (Dynamic::new(shape.0), Dynamic::new(shape.1));
 
                 unsafe {
@@ -359,9 +436,8 @@ macro_rules! matrix_slice_impl(
             /// original matrix.
             #[inline]
             pub fn $slice_with_steps($me: $Me, start: (usize, usize), shape: (usize, usize), steps: (usize, usize))
-                -> $MatrixSlice<N, Dynamic, Dynamic, Dynamic, Dynamic, S::Alloc> {
+                -> $MatrixSlice<N, Dynamic, Dynamic, Dynamic, Dynamic> {
                 let shape = (Dynamic::new(shape.0), Dynamic::new(shape.1));
-                let steps = (Dynamic::new(steps.0), Dynamic::new(steps.1));
 
                 $me.$generic_slice_with_steps(start, shape, steps)
             }
@@ -370,11 +446,11 @@ macro_rules! matrix_slice_impl(
             /// CSlice::dim())` consecutive components.
             #[inline]
             pub fn $fixed_slice<RSlice, CSlice>($me: $Me, irow: usize, icol: usize)
-                -> $MatrixSlice<N, RSlice, CSlice, S::RStride, S::CStride, S::Alloc>
+                -> $MatrixSlice<N, RSlice, CSlice, S::RStride, S::CStride>
                 where RSlice: DimName,
                       CSlice: DimName {
 
-                $me.assert_slice_index((irow, icol), (RSlice::dim(), CSlice::dim()), (1, 1));
+                $me.assert_slice_index((irow, icol), (RSlice::dim(), CSlice::dim()), (0, 0));
                 let shape = (RSlice::name(), CSlice::name());
 
                 unsafe {
@@ -389,22 +465,21 @@ macro_rules! matrix_slice_impl(
             /// the original matrix.
             #[inline]
             pub fn $fixed_slice_with_steps<RSlice, CSlice>($me: $Me, start: (usize, usize), steps: (usize, usize))
-                -> $MatrixSlice<N, RSlice, CSlice, Dynamic, Dynamic, S::Alloc>
+                -> $MatrixSlice<N, RSlice, CSlice, Dynamic, Dynamic>
                 where RSlice: DimName,
                       CSlice: DimName {
                 let shape = (RSlice::name(), CSlice::name());
-                let steps = (Dynamic::new(steps.0), Dynamic::new(steps.1));
                 $me.$generic_slice_with_steps(start, shape, steps)
             }
 
             /// Creates a slice that may or may not have a fixed size and stride.
             #[inline]
             pub fn $generic_slice<RSlice, CSlice>($me: $Me, start: (usize, usize), shape: (RSlice, CSlice))
-                -> $MatrixSlice<N, RSlice, CSlice, S::RStride, S::CStride, S::Alloc>
+                -> $MatrixSlice<N, RSlice, CSlice, S::RStride, S::CStride>
                 where RSlice: Dim,
                       CSlice: Dim {
 
-                $me.assert_slice_index(start, (shape.0.value(), shape.1.value()), (1, 1));
+                $me.assert_slice_index(start, (shape.0.value(), shape.1.value()), (0, 0));
 
                 unsafe {
                     let data = $SliceStorage::new_unchecked($data, start, shape);
@@ -414,69 +489,335 @@ macro_rules! matrix_slice_impl(
 
             /// Creates a slice that may or may not have a fixed size and stride.
             #[inline]
-            pub fn $generic_slice_with_steps<RSlice, CSlice, RStep, CStep>($me: $Me,
+            pub fn $generic_slice_with_steps<RSlice, CSlice>($me: $Me,
                                                              start: (usize, usize),
                                                              shape: (RSlice, CSlice),
-                                                                           steps: (RStep, CStep))
-                -> $MatrixSlice<N, RSlice, CSlice, DimProd<RStep, S::RStride>, DimProd<CStep, S::CStride>, S::Alloc>
+                                                             steps: (usize, usize))
+                -> $MatrixSlice<N, RSlice, CSlice, Dynamic, Dynamic>
                 where RSlice: Dim,
-                      CSlice: Dim,
-                      RStep: DimMul<S::RStride>,
-                      CStep: DimMul<S::CStride> {
+                      CSlice: Dim {
 
-                $me.assert_slice_index(start, (shape.0.value(), shape.1.value()), (steps.0.value(), steps.1.value()));
+                $me.assert_slice_index(start, (shape.0.value(), shape.1.value()), steps);
 
                 let my_strides = $me.data.strides();
-                let strides    = (steps.0.mul(my_strides.0), steps.1.mul(my_strides.1));
+                let strides    = (Dynamic::new((steps.0 + 1) * my_strides.0.value()),
+                                  Dynamic::new((steps.1 + 1) * my_strides.1.value()));
 
                 unsafe {
                     let data = $SliceStorage::new_with_strides_unchecked($data, start, shape, strides);
                     Matrix::from_data_statically_unchecked(data)
                 }
             }
+
+            /*
+             *
+             * Splitting.
+             *
+             */
+            /// Splits this NxM matrix into two parts delimited by two ranges.
+            ///
+            /// Panics if the ranges overlap or if the first range is empty.
+            #[inline]
+            pub fn $rows_range_pair<Range1: SliceRange<R>, Range2: SliceRange<R>>($me: $Me, r1: Range1, r2: Range2)
+                -> ($MatrixSlice<N, Range1::Size, C, S::RStride, S::CStride>,
+                    $MatrixSlice<N, Range2::Size, C, S::RStride, S::CStride>) {
+
+                let (nrows, ncols) = $me.data.shape();
+                let strides        = $me.data.strides();
+
+                let start1 = r1.begin(nrows);
+                let start2 = r2.begin(nrows);
+
+                let end1 = r1.end(nrows);
+                let end2 = r2.end(nrows);
+
+                let nrows1 = r1.size(nrows);
+                let nrows2 = r2.size(nrows);
+
+                assert!(start2 >= end1 || start1 >= end2, "Rows range pair: the slice ranges must not overlap.");
+                assert!(end2 <= nrows.value(), "Rows range pair: index out of range.");
+
+                unsafe {
+                    let ptr1 = $data.$get_addr(start1, 0);
+                    let ptr2 = $data.$get_addr(start2, 0);
+
+                    let data1  = $SliceStorage::from_raw_parts(ptr1, (nrows1, ncols), strides);
+                    let data2  = $SliceStorage::from_raw_parts(ptr2, (nrows2, ncols), strides);
+                    let slice1 = Matrix::from_data_statically_unchecked(data1);
+                    let slice2 = Matrix::from_data_statically_unchecked(data2);
+
+                    (slice1, slice2)
+                }
+            }
+
+            /// Splits this NxM matrix into two parts delimited by two ranges.
+            ///
+            /// Panics if the ranges overlap or if the first range is empty.
+            #[inline]
+            pub fn $columns_range_pair<Range1: SliceRange<C>, Range2: SliceRange<C>>($me: $Me, r1: Range1, r2: Range2)
+                -> ($MatrixSlice<N, R, Range1::Size, S::RStride, S::CStride>,
+                    $MatrixSlice<N, R, Range2::Size, S::RStride, S::CStride>) {
+
+                let (nrows, ncols) = $me.data.shape();
+                let strides        = $me.data.strides();
+
+                let start1 = r1.begin(ncols);
+                let start2 = r2.begin(ncols);
+
+                let end1 = r1.end(ncols);
+                let end2 = r2.end(ncols);
+
+                let ncols1 = r1.size(ncols);
+                let ncols2 = r2.size(ncols);
+
+                assert!(start2 >= end1 || start1 >= end2, "Columns range pair: the slice ranges must not overlap.");
+                assert!(end2 <= ncols.value(), "Columns range pair: index out of range.");
+
+                unsafe {
+                    let ptr1 = $data.$get_addr(0, start1);
+                    let ptr2 = $data.$get_addr(0, start2);
+
+                    let data1  = $SliceStorage::from_raw_parts(ptr1, (nrows, ncols1), strides);
+                    let data2  = $SliceStorage::from_raw_parts(ptr2, (nrows, ncols2), strides);
+                    let slice1 = Matrix::from_data_statically_unchecked(data1);
+                    let slice2 = Matrix::from_data_statically_unchecked(data2);
+
+                    (slice1, slice2)
+                }
+            }
         }
     }
 );
 
 matrix_slice_impl!(
-     self: &Self, MatrixSlice, SliceStorage, Storage, &self.data;
+     self: &Self, MatrixSlice, SliceStorage, Storage.get_address_unchecked(), &self.data;
      row,
+     row_part,
      rows,
      rows_with_step,
      fixed_rows,
      fixed_rows_with_step,
      rows_generic,
+     rows_generic_with_step,
      column,
+     column_part,
      columns,
      columns_with_step,
      fixed_columns,
      fixed_columns_with_step,
      columns_generic,
+     columns_generic_with_step,
      slice,
      slice_with_steps,
      fixed_slice,
      fixed_slice_with_steps,
      generic_slice,
-     generic_slice_with_steps);
+     generic_slice_with_steps,
+     rows_range_pair,
+     columns_range_pair);
 
 
 matrix_slice_impl!(
-     self: &mut Self, MatrixSliceMut, SliceStorageMut, StorageMut, &mut self.data;
+     self: &mut Self, MatrixSliceMut, SliceStorageMut, StorageMut.get_address_unchecked_mut(), &mut self.data;
      row_mut,
+     row_part_mut,
      rows_mut,
      rows_with_step_mut,
      fixed_rows_mut,
      fixed_rows_with_step_mut,
      rows_generic_mut,
+     rows_generic_with_step_mut,
      column_mut,
+     column_part_mut,
      columns_mut,
      columns_with_step_mut,
      fixed_columns_mut,
      fixed_columns_with_step_mut,
      columns_generic_mut,
+     columns_generic_with_step_mut,
      slice_mut,
      slice_with_steps_mut,
      fixed_slice_mut,
      fixed_slice_with_steps_mut,
      generic_slice_mut,
-     generic_slice_with_steps_mut);
+     generic_slice_with_steps_mut,
+     rows_range_pair_mut,
+     columns_range_pair_mut);
+
+
+/// A range with a size that may be known at compile-time.
+///
+/// This may be:
+/// * A single `usize` index, e.g., `4`
+/// * A left-open range `std::ops::RangeTo`, e.g., `.. 4`
+/// * A right-open range `std::ops::RangeFrom`, e.g., `4 ..`
+/// * A full range `std::ops::RangeFull`, e.g., `..`
+pub trait SliceRange<D: Dim> {
+    /// Type of the range size. May be a type-level integer.
+    type Size: Dim;
+
+    /// The start index of the range.
+    fn begin(&self, shape: D) -> usize;
+    // NOTE: this is the index immediatly after the last index.
+    /// The index immediatly after the last index inside of the range.
+    fn end(&self, shape: D) -> usize;
+    /// The number of elements of the range, i.e., `self.end - self.begin`.
+    fn size(&self, shape: D) -> Self::Size;
+}
+
+impl<D: Dim> SliceRange<D> for usize {
+    type Size = U1;
+
+    #[inline(always)]
+    fn begin(&self, _: D) -> usize {
+        *self
+    }
+
+    #[inline(always)]
+    fn end(&self, _: D) -> usize {
+        *self + 1
+    }
+
+    #[inline(always)]
+    fn size(&self, _: D) -> Self::Size {
+        U1
+    }
+}
+
+impl<D: Dim> SliceRange<D> for Range<usize> {
+    type Size = Dynamic;
+
+    #[inline(always)]
+    fn begin(&self, _: D) -> usize {
+        self.start
+    }
+
+    #[inline(always)]
+    fn end(&self, _: D) -> usize {
+        self.end
+    }
+
+    #[inline(always)]
+    fn size(&self, _: D) -> Self::Size {
+        Dynamic::new(self.end - self.start)
+    }
+}
+
+impl<D: Dim> SliceRange<D> for RangeFrom<usize> {
+    type Size = Dynamic;
+
+    #[inline(always)]
+    fn begin(&self, _: D) -> usize {
+        self.start
+    }
+
+    #[inline(always)]
+    fn end(&self, dim: D) -> usize {
+        dim.value()
+    }
+
+    #[inline(always)]
+    fn size(&self, dim: D) -> Self::Size {
+        Dynamic::new(dim.value() - self.start)
+    }
+}
+
+impl<D: Dim> SliceRange<D> for RangeTo<usize> {
+    type Size = Dynamic;
+
+    #[inline(always)]
+    fn begin(&self, _: D) -> usize {
+        0
+    }
+
+    #[inline(always)]
+    fn end(&self, _: D) -> usize {
+        self.end
+    }
+
+    #[inline(always)]
+    fn size(&self, _: D) -> Self::Size {
+        Dynamic::new(self.end)
+    }
+}
+
+impl<D: Dim> SliceRange<D> for RangeFull {
+    type Size = D;
+
+    #[inline(always)]
+    fn begin(&self, _: D) -> usize {
+        0
+    }
+
+    #[inline(always)]
+    fn end(&self, dim: D) -> usize {
+        dim.value()
+    }
+
+    #[inline(always)]
+    fn size(&self, dim: D) -> Self::Size {
+        dim
+    }
+}
+
+
+impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
+    /// Slices a sub-matrix containing the rows indexed by the range `rows` and the columns indexed
+    /// by the range `cols`.
+    #[inline]
+    pub fn slice_range<RowRange, ColRange>(&self, rows: RowRange, cols: ColRange)
+        -> MatrixSlice<N, RowRange::Size, ColRange::Size, S::RStride, S::CStride>
+        where RowRange: SliceRange<R>,
+              ColRange: SliceRange<C> {
+
+        let (nrows, ncols) = self.data.shape();
+        self.generic_slice((rows.begin(nrows), cols.begin(ncols)),
+                           (rows.size(nrows), cols.size(ncols)))
+    }
+
+    /// Slice containing all the rows indexed by the range `rows`.
+    #[inline]
+    pub fn rows_range<RowRange: SliceRange<R>>(&self, rows: RowRange)
+        -> MatrixSlice<N, RowRange::Size, C, S::RStride, S::CStride> {
+
+        self.slice_range(rows, ..)
+    }
+
+    /// Slice containing all the columns indexed by the range `rows`.
+    #[inline]
+    pub fn columns_range<ColRange: SliceRange<C>>(&self, cols: ColRange)
+        -> MatrixSlice<N, R, ColRange::Size, S::RStride, S::CStride> {
+
+        self.slice_range(.., cols)
+    }
+}
+
+impl<N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
+    /// Slices a mutable sub-matrix containing the rows indexed by the range `rows` and the columns
+    /// indexed by the range `cols`.
+    pub fn slice_range_mut<RowRange, ColRange>(&mut self, rows: RowRange, cols: ColRange)
+        -> MatrixSliceMut<N, RowRange::Size, ColRange::Size, S::RStride, S::CStride>
+        where RowRange: SliceRange<R>,
+              ColRange: SliceRange<C> {
+
+        let (nrows, ncols) = self.data.shape();
+        self.generic_slice_mut((rows.begin(nrows), cols.begin(ncols)),
+                               (rows.size(nrows), cols.size(ncols)))
+    }
+
+    /// Slice containing all the rows indexed by the range `rows`.
+    #[inline]
+    pub fn rows_range_mut<RowRange: SliceRange<R>>(&mut self, rows: RowRange)
+        -> MatrixSliceMut<N, RowRange::Size, C, S::RStride, S::CStride> {
+
+        self.slice_range_mut(rows, ..)
+    }
+
+    /// Slice containing all the columns indexed by the range `cols`.
+    #[inline]
+    pub fn columns_range_mut<ColRange: SliceRange<C>>(&mut self, cols: ColRange)
+        -> MatrixSliceMut<N, R, ColRange::Size, S::RStride, S::CStride> {
+
+        self.slice_range_mut(.., cols)
+    }
+}

src/core/matrix_vec.rs

@@ -2,7 +2,8 @@ use std::ops::Deref;
 
 use core::Scalar;
 use core::dimension::{Dim, DimName, Dynamic, U1};
-use core::storage::{Storage, StorageMut, Owned, OwnedStorage};
+use core::storage::{Storage, StorageMut, Owned, ContiguousStorage, ContiguousStorageMut};
+use core::allocator::Allocator;
 use core::default_allocator::DefaultAllocator;
 
 #[cfg(feature = "abomonation-serialize")]
@@ -48,6 +49,26 @@ impl<N, R: Dim, C: Dim> MatrixVec<N, R, C> {
     pub unsafe fn data_mut(&mut self) -> &mut Vec<N> {
         &mut self.data
     }
+
+    /// Resizes the undelying mutable data storage and unrwaps it.
+    ///
+    /// If `sz` is larger than the current size, additional elements are uninitialized.
+    /// If `sz` is smaller than the current size, additional elements are trucated.
+    #[inline]
+    pub unsafe fn resize(mut self, sz: usize) -> Vec<N>{
+        let len = self.len();
+
+        if sz < len {
+            self.data.set_len(sz);
+            self.data.shrink_to_fit();
+        }
+        else {
+            self.data.reserve_exact(sz - len);
+            self.data.set_len(sz);
+        }
+
+        self.data
+    }
 }
 
 impl<N, R: Dim, C: Dim> Deref for MatrixVec<N, R, C> {
@@ -65,24 +86,14 @@ impl<N, R: Dim, C: Dim> Deref for MatrixVec<N, R, C> {
  * Dynamic − Dynamic
  *
  */
-unsafe impl<N: Scalar, C: Dim> Storage<N, Dynamic, C> for MatrixVec<N, Dynamic, C> {
+unsafe impl<N: Scalar, C: Dim> Storage<N, Dynamic, C> for MatrixVec<N, Dynamic, C>
+    where DefaultAllocator: Allocator<N, Dynamic, C, Buffer = Self> {
     type RStride = U1;
     type CStride = Dynamic;
-    type Alloc   = DefaultAllocator;
-
-    #[inline]
-    fn into_owned(self) -> Owned<N, Dynamic, C, Self::Alloc> {
-        self
-    }
-
-    #[inline]
-    fn clone_owned(&self) -> Owned<N, Dynamic, C, Self::Alloc> {
-        self.clone()
-    }
 
     #[inline]
     fn ptr(&self) -> *const N {
-        self[..].as_ptr()
+        self.data.as_ptr()
     }
 
     #[inline]
@@ -94,27 +105,39 @@ unsafe impl<N: Scalar, C: Dim> Storage<N, Dynamic, C> for MatrixVec<N, Dynamic,
     fn strides(&self) -> (Self::RStride, Self::CStride) {
         (Self::RStride::name(), self.nrows)
     }
-}
-
-
-unsafe impl<N: Scalar, R: DimName> Storage<N, R, Dynamic> for MatrixVec<N, R, Dynamic> {
-    type RStride = U1;
-    type CStride = R;
-    type Alloc   = DefaultAllocator;
 
     #[inline]
-    fn into_owned(self) -> Owned<N, R, Dynamic, Self::Alloc> {
+    fn is_contiguous(&self) -> bool {
+        true
+    }
+
+    #[inline]
+    fn into_owned(self) -> Owned<N, Dynamic, C>
+        where DefaultAllocator: Allocator<N, Dynamic, C> {
         self
     }
 
     #[inline]
-    fn clone_owned(&self) -> Owned<N, R, Dynamic, Self::Alloc> {
+    fn clone_owned(&self) -> Owned<N, Dynamic, C>
+        where DefaultAllocator: Allocator<N, Dynamic, C> {
         self.clone()
     }
 
+    #[inline]
+    fn as_slice(&self) -> &[N] {
+        &self[..]
+    }
+}
+
+
+unsafe impl<N: Scalar, R: DimName> Storage<N, R, Dynamic> for MatrixVec<N, R, Dynamic>
+    where DefaultAllocator: Allocator<N, R, Dynamic, Buffer = Self> {
+    type RStride = U1;
+    type CStride = R;
+
     #[inline]
     fn ptr(&self) -> *const N {
-        self[..].as_ptr()
+        self.data.as_ptr()
     }
 
     #[inline]
@@ -126,6 +149,28 @@ unsafe impl<N: Scalar, R: DimName> Storage<N, R, Dynamic> for MatrixVec<N, R, Dy
     fn strides(&self) -> (Self::RStride, Self::CStride) {
         (Self::RStride::name(), self.nrows)
     }
+
+    #[inline]
+    fn is_contiguous(&self) -> bool {
+        true
+    }
+
+    #[inline]
+    fn into_owned(self) -> Owned<N, R, Dynamic>
+        where DefaultAllocator: Allocator<N, R, Dynamic> {
+        self
+    }
+
+    #[inline]
+    fn clone_owned(&self) -> Owned<N, R, Dynamic>
+        where DefaultAllocator: Allocator<N, R, Dynamic> {
+        self.clone()
+    }
+
+    #[inline]
+    fn as_slice(&self) -> &[N] {
+        &self[..]
+    }
 }
 
 
@@ -133,20 +178,14 @@ unsafe impl<N: Scalar, R: DimName> Storage<N, R, Dynamic> for MatrixVec<N, R, Dy
 
 /*
  *
- * StorageMut, OwnedStorage.
+ * StorageMut, ContiguousStorage.
  *
  */
-unsafe impl<N: Scalar, C: Dim> StorageMut<N, Dynamic, C> for MatrixVec<N, Dynamic, C> {
+unsafe impl<N: Scalar, C: Dim> StorageMut<N, Dynamic, C> for MatrixVec<N, Dynamic, C>
+    where DefaultAllocator: Allocator<N, Dynamic, C, Buffer = Self> {
     #[inline]
     fn ptr_mut(&mut self) -> *mut N {
-        self.as_mut_slice().as_mut_ptr()
-    }
-}
-
-unsafe impl<N: Scalar, C: Dim> OwnedStorage<N, Dynamic, C> for MatrixVec<N, Dynamic, C> {
-    #[inline]
-    fn as_slice(&self) -> &[N] {
-        &self[..]
+        self.data.as_mut_ptr()
     }
 
     #[inline]
@@ -155,18 +194,20 @@ unsafe impl<N: Scalar, C: Dim> OwnedStorage<N, Dynamic, C> for MatrixVec<N, Dyna
     }
 }
 
-
-unsafe impl<N: Scalar, R: DimName> StorageMut<N, R, Dynamic> for MatrixVec<N, R, Dynamic> {
-    #[inline]
-    fn ptr_mut(&mut self) -> *mut N {
-        self.as_mut_slice().as_mut_ptr()
-    }
+unsafe impl<N: Scalar, C: Dim> ContiguousStorage<N, Dynamic, C> for MatrixVec<N, Dynamic, C>
+    where DefaultAllocator: Allocator<N, Dynamic, C, Buffer = Self> {
 }
 
-unsafe impl<N: Scalar, R: DimName> OwnedStorage<N, R, Dynamic> for MatrixVec<N, R, Dynamic> {
+unsafe impl<N: Scalar, C: Dim> ContiguousStorageMut<N, Dynamic, C> for MatrixVec<N, Dynamic, C>
+    where DefaultAllocator: Allocator<N, Dynamic, C, Buffer = Self> {
+}
+
+
+unsafe impl<N: Scalar, R: DimName> StorageMut<N, R, Dynamic> for MatrixVec<N, R, Dynamic>
+    where DefaultAllocator: Allocator<N, R, Dynamic, Buffer = Self> {
     #[inline]
-    fn as_slice(&self) -> &[N] {
-        &self[..]
+    fn ptr_mut(&mut self) -> *mut N {
+        self.data.as_mut_ptr()
     }
 
     #[inline]
@@ -189,3 +230,11 @@ impl<N: Abomonation, R: Dim, C: Dim> Abomonation for MatrixVec<N, R, C> {
         self.data.exhume(bytes)
     }
 }
+
+unsafe impl<N: Scalar, R: DimName> ContiguousStorage<N, R, Dynamic> for MatrixVec<N, R, Dynamic>
+    where DefaultAllocator: Allocator<N, R, Dynamic, Buffer = Self> {
+}
+
+unsafe impl<N: Scalar, R: DimName> ContiguousStorageMut<N, R, Dynamic> for MatrixVec<N, R, Dynamic>
+    where DefaultAllocator: Allocator<N, R, Dynamic, Buffer = Self> {
+}

src/core/mod.rs

@@ -6,6 +6,7 @@ pub mod allocator;
 pub mod storage;
 pub mod coordinates;
 mod ops;
+mod blas;
 pub mod iter;
 pub mod default_allocator;
 
@@ -15,8 +16,6 @@ mod construction;
 mod properties;
 mod alias;
 mod matrix_alga;
-mod determinant;
-mod inverse;
 mod conversion;
 mod matrix_slice;
 mod matrix_array;
@@ -24,8 +23,7 @@ mod matrix_vec;
 mod cg;
 mod unit;
 mod componentwise;
-
-mod decompositions;
+mod edition;
 
 #[doc(hidden)]
 pub mod helper;

src/core/ops.rs

@@ -1,15 +1,16 @@
 use std::iter;
 use std::ops::{Add, AddAssign, Sub, SubAssign, Mul, MulAssign, Div, DivAssign, Neg,
                Index, IndexMut};
-use num::{Zero, One};
+use std::cmp::PartialOrd;
+use num::{Zero, One, Signed};
 
 use alga::general::{ClosedMul, ClosedDiv, ClosedAdd, ClosedSub, ClosedNeg};
 
-use core::{Scalar, Matrix, OwnedMatrix, SquareMatrix, MatrixSum, MatrixMul, MatrixTrMul};
-use core::dimension::{Dim, DimMul, DimName, DimProd};
-use core::constraint::{ShapeConstraint, SameNumberOfRows, SameNumberOfColumns, AreMultipliable};
-use core::storage::{Storage, StorageMut, OwnedStorage};
-use core::allocator::{SameShapeAllocator, Allocator, OwnedAllocator};
+use core::{DefaultAllocator, Scalar, Matrix, MatrixN, MatrixMN, MatrixSum};
+use core::dimension::{Dim, DimName, DimProd, DimMul};
+use core::constraint::{ShapeConstraint, SameNumberOfRows, SameNumberOfColumns, AreMultipliable, DimEq};
+use core::storage::{Storage, StorageMut, ContiguousStorageMut};
+use core::allocator::{SameShapeAllocator, Allocator, SameShapeR, SameShapeC};
 
 /*
  *
@@ -70,8 +71,9 @@ impl<N, R: Dim, C: Dim, S> IndexMut<(usize, usize)> for Matrix<N, R, C, S>
  */
 impl<N, R: Dim, C: Dim, S> Neg for Matrix<N, R, C, S>
     where N: Scalar + ClosedNeg,
-          S: Storage<N, R, C> {
-    type Output = OwnedMatrix<N, R, C, S::Alloc>;
+          S: Storage<N, R, C>,
+          DefaultAllocator: Allocator<N, R, C> {
+    type Output = MatrixMN<N, R, C>;
 
     #[inline]
     fn neg(self) -> Self::Output {
@@ -83,8 +85,9 @@ impl<N, R: Dim, C: Dim, S> Neg for Matrix<N, R, C, S>
 
 impl<'a, N, R: Dim, C: Dim, S> Neg for &'a Matrix<N, R, C, S>
     where N: Scalar + ClosedNeg,
-          S: Storage<N, R, C> {
-    type Output = OwnedMatrix<N, R, C, S::Alloc>;
+          S: Storage<N, R, C>,
+          DefaultAllocator: Allocator<N, R, C> {
+    type Output = MatrixMN<N, R, C>;
 
     #[inline]
     fn neg(self) -> Self::Output {
@@ -109,33 +112,156 @@ impl<N, R: Dim, C: Dim, S> Matrix<N, R, C, S>
  * Addition & Substraction
  *
  */
+
 macro_rules! componentwise_binop_impl(
     ($Trait: ident, $method: ident, $bound: ident;
-     $TraitAssign: ident, $method_assign: ident) => {
+     $TraitAssign: ident, $method_assign: ident, $method_assign_statically_unchecked: ident,
+     $method_assign_statically_unchecked_rhs: ident;
+     $method_to: ident, $method_to_statically_unchecked: ident) => {
+
+        impl<N, R1: Dim, C1: Dim, SA: Storage<N, R1, C1>> Matrix<N, R1, C1, SA>
+            where N: Scalar + $bound {
+
+            /*
+             *
+             * Methods without dimension checking at compile-time.
+             * This is useful for code reuse because the sum representative system does not plays
+             * easily with static checks.
+             *
+             */
+            #[inline]
+            fn $method_to_statically_unchecked<R2: Dim, C2: Dim, SB,
+                                               R3: Dim, C3: Dim, SC>(&self,
+                                                                     rhs: &Matrix<N, R2, C2, SB>,
+                                                                     out: &mut Matrix<N, R3, C3, SC>)
+                where SB: Storage<N, R2, C2>,
+                      SC: StorageMut<N, R3, C3> {
+                assert!(self.shape() == rhs.shape(), "Matrix addition/subtraction dimensions mismatch.");
+                assert!(self.shape() == out.shape(), "Matrix addition/subtraction output dimensions mismatch.");
+
+                // This is the most common case and should be deduced at compile-time.
+                // FIXME: use specialization instead?
+                if self.data.is_contiguous() && rhs.data.is_contiguous() && out.data.is_contiguous() {
+                    let arr1 = self.data.as_slice();
+                    let arr2 = rhs.data.as_slice();
+                    let out  = out.data.as_mut_slice();
+                    for i in 0 .. arr1.len() {
+                        unsafe {
+                            *out.get_unchecked_mut(i) = arr1.get_unchecked(i).$method(*arr2.get_unchecked(i));
+                        }
+                    }
+                }
+                else {
+                    for j in 0 .. self.ncols() {
+                        for i in 0 .. self.nrows() {
+                            unsafe {
+                                let val = self.get_unchecked(i, j).$method(*rhs.get_unchecked(i, j));
+                                *out.get_unchecked_mut(i, j) = val;
+                            }
+                        }
+                    }
+                }
+            }
+
+
+            #[inline]
+            fn $method_assign_statically_unchecked<R2, C2, SB>(&mut self, rhs: &Matrix<N, R2, C2, SB>)
+                where R2: Dim,
+                      C2: Dim,
+                      SA: StorageMut<N, R1, C1>,
+                      SB: Storage<N, R2, C2> {
+                assert!(self.shape() == rhs.shape(), "Matrix addition/subtraction dimensions mismatch.");
+
+                // This is the most common case and should be deduced at compile-time.
+                // FIXME: use specialization instead?
+                if self.data.is_contiguous() && rhs.data.is_contiguous() {
+                    let arr1 = self.data.as_mut_slice();
+                    let arr2 = rhs.data.as_slice();
+                    for i in 0 .. arr2.len() {
+                        unsafe {
+                            arr1.get_unchecked_mut(i).$method_assign(*arr2.get_unchecked(i));
+                        }
+                    }
+                }
+                else {
+                    for j in 0 .. rhs.ncols() {
+                        for i in 0 .. rhs.nrows() {
+                            unsafe {
+                                self.get_unchecked_mut(i, j).$method_assign(*rhs.get_unchecked(i, j))
+                            }
+                        }
+                    }
+                }
+            }
+
+
+            #[inline]
+            fn $method_assign_statically_unchecked_rhs<R2, C2, SB>(&self, rhs: &mut Matrix<N, R2, C2, SB>)
+                where R2: Dim,
+                      C2: Dim,
+                      SB: StorageMut<N, R2, C2> {
+                assert!(self.shape() == rhs.shape(), "Matrix addition/subtraction dimensions mismatch.");
+
+                // This is the most common case and should be deduced at compile-time.
+                // FIXME: use specialization instead?
+                if self.data.is_contiguous() && rhs.data.is_contiguous() {
+                    let arr1 = self.data.as_slice();
+                    let arr2 = rhs.data.as_mut_slice();
+                    for i in 0 .. arr1.len() {
+                        unsafe {
+                            let res = arr1.get_unchecked(i).$method(*arr2.get_unchecked(i));
+                            *arr2.get_unchecked_mut(i) = res;
+                        }
+                    }
+                }
+                else {
+                    for j in 0 .. self.ncols() {
+                        for i in 0 .. self.nrows() {
+                            unsafe {
+                                let r = rhs.get_unchecked_mut(i, j);
+                                *r = self.get_unchecked(i, j).$method(*r)
+                            }
+                        }
+                    }
+                }
+            }
+
+
+            /*
+             *
+             * Methods without dimension checking at compile-time.
+             * This is useful for code reuse because the sum representative system does not plays
+             * easily with static checks.
+             *
+             */
+            /// Equivalent to `self + rhs` but stores the result into `out` to avoid allocations.
+            #[inline]
+            pub fn $method_to<R2: Dim, C2: Dim, SB,
+                              R3: Dim, C3: Dim, SC>(&self,
+                                                    rhs: &Matrix<N, R2, C2, SB>,
+                                                    out: &mut Matrix<N, R3, C3, SC>)
+                where SB: Storage<N, R2, C2>,
+                      SC: StorageMut<N, R3, C3>,
+                      ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> +
+                                       SameNumberOfRows<R1, R3> + SameNumberOfColumns<C1, C3> {
+                self.$method_to_statically_unchecked(rhs, out)
+            }
+        }
+
         impl<'b, N, R1, C1, R2, C2, SA, SB> $Trait<&'b Matrix<N, R2, C2, SB>> for Matrix<N, R1, C1, SA>
             where R1: Dim, C1: Dim, R2: Dim, C2: Dim,
                   N: Scalar + $bound,
                   SA: Storage<N, R1, C1>,
                   SB: Storage<N, R2, C2>,
-                  SA::Alloc: SameShapeAllocator<N, R1, C1, R2, C2, SA>,
+                  DefaultAllocator: SameShapeAllocator<N, R1, C1, R2, C2>,
                   ShapeConstraint:  SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
-            type Output = MatrixSum<N, R1, C1, R2, C2, SA>;
+            type Output = MatrixSum<N, R1, C1, R2, C2>;
 
             #[inline]
-            fn $method(self, right: &'b Matrix<N, R2, C2, SB>) -> Self::Output {
-                assert!(self.shape() == right.shape(), "Matrix addition/subtraction dimensions mismatch.");
+            fn $method(self, rhs: &'b Matrix<N, R2, C2, SB>) -> Self::Output {
+                assert!(self.shape() == rhs.shape(), "Matrix addition/subtraction dimensions mismatch.");
                 let mut res = self.into_owned_sum::<R2, C2>();
-
-                // XXX: optimize our iterator!
-                //
-                // Using our own iterator prevents loop unrolling, wich breaks some optimization
-                // (like SIMD). On the other hand, using the slice iterator is 4x faster.
-
-                // for (left, right) in res.iter_mut().zip(right.iter()) {
-                for (left, right) in res.as_mut_slice().iter_mut().zip(right.iter()) {
-                    *left = left.$method(*right)
-                }
-
+                res.$method_assign_statically_unchecked(rhs);
                 res
             }
         }
@@ -145,26 +271,16 @@ macro_rules! componentwise_binop_impl(
                   N: Scalar + $bound,
                   SA: Storage<N, R1, C1>,
                   SB: Storage<N, R2, C2>,
-                  SB::Alloc: SameShapeAllocator<N, R2, C2, R1, C1, SB>,
+                  DefaultAllocator: SameShapeAllocator<N, R2, C2, R1, C1>,
                   ShapeConstraint:  SameNumberOfRows<R2, R1> + SameNumberOfColumns<C2, C1> {
-            type Output = MatrixSum<N, R2, C2, R1, C1, SB>;
+            type Output = MatrixSum<N, R2, C2, R1, C1>;
 
             #[inline]
-            fn $method(self, right: Matrix<N, R2, C2, SB>) -> Self::Output {
-                assert!(self.shape() == right.shape(), "Matrix addition/subtraction dimensions mismatch.");
-                let mut res = right.into_owned_sum::<R1, C1>();
-
-                // XXX: optimize our iterator!
-                //
-                // Using our own iterator prevents loop unrolling, wich breaks some optimization
-                // (like SIMD). On the other hand, using the slice iterator is 4x faster.
-
-                // for (left, right) in self.iter().zip(res.iter_mut()) {
-                for (left, right) in self.iter().zip(res.as_mut_slice().iter_mut()) {
-                    *right = left.$method(*right)
-                }
-
-                res
+            fn $method(self, rhs: Matrix<N, R2, C2, SB>) -> Self::Output {
+                let mut rhs = rhs.into_owned_sum::<R1, C1>();
+                assert!(self.shape() == rhs.shape(), "Matrix addition/subtraction dimensions mismatch.");
+                self.$method_assign_statically_unchecked_rhs(&mut rhs);
+                rhs
             }
         }
 
@@ -173,13 +289,13 @@ macro_rules! componentwise_binop_impl(
                   N: Scalar + $bound,
                   SA: Storage<N, R1, C1>,
                   SB: Storage<N, R2, C2>,
-                  SA::Alloc: SameShapeAllocator<N, R1, C1, R2, C2, SA>,
+                  DefaultAllocator: SameShapeAllocator<N, R1, C1, R2, C2>,
                   ShapeConstraint:  SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
-            type Output = MatrixSum<N, R1, C1, R2, C2, SA>;
+            type Output = MatrixSum<N, R1, C1, R2, C2>;
 
             #[inline]
-            fn $method(self, right: Matrix<N, R2, C2, SB>) -> Self::Output {
-                self.$method(&right)
+            fn $method(self, rhs: Matrix<N, R2, C2, SB>) -> Self::Output {
+                self.$method(&rhs)
             }
         }
 
@@ -188,13 +304,21 @@ macro_rules! componentwise_binop_impl(
                   N: Scalar + $bound,
                   SA: Storage<N, R1, C1>,
                   SB: Storage<N, R2, C2>,
-                  SA::Alloc: SameShapeAllocator<N, R1, C1, R2, C2, SA>,
+                  DefaultAllocator: SameShapeAllocator<N, R1, C1, R2, C2>,
                   ShapeConstraint:  SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
-            type Output = MatrixSum<N, R1, C1, R2, C2, SA>;
+            type Output = MatrixSum<N, R1, C1, R2, C2>;
 
             #[inline]
-            fn $method(self, right: &'b Matrix<N, R2, C2, SB>) -> Self::Output {
-                self.clone_owned().$method(right)
+            fn $method(self, rhs: &'b Matrix<N, R2, C2, SB>) -> Self::Output {
+                let mut res = unsafe {
+                    let (nrows, ncols) = self.shape();
+                    let nrows: SameShapeR<R1, R2> = Dim::from_usize(nrows);
+                    let ncols: SameShapeC<C1, C2> = Dim::from_usize(ncols);
+                    Matrix::new_uninitialized_generic(nrows, ncols)
+                };
+
+                self.$method_to_statically_unchecked(rhs, &mut res);
+                res
             }
         }
 
@@ -206,11 +330,8 @@ macro_rules! componentwise_binop_impl(
                   ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
 
             #[inline]
-            fn $method_assign(&mut self, right: &'b Matrix<N, R2, C2, SB>) {
-                assert!(self.shape() == right.shape(), "Matrix addition/subtraction dimensions mismatch.");
-                for (left, right) in self.iter_mut().zip(right.iter()) {
-                    left.$method_assign(*right)
-                }
+            fn $method_assign(&mut self, rhs: &'b Matrix<N, R2, C2, SB>) {
+                self.$method_assign_statically_unchecked(rhs)
             }
         }
 
@@ -222,32 +343,34 @@ macro_rules! componentwise_binop_impl(
                   ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
 
             #[inline]
-            fn $method_assign(&mut self, right: Matrix<N, R2, C2, SB>) {
-                self.$method_assign(&right)
+            fn $method_assign(&mut self, rhs: Matrix<N, R2, C2, SB>) {
+                self.$method_assign(&rhs)
             }
         }
     }
 );
 
-componentwise_binop_impl!(Add, add, ClosedAdd; AddAssign, add_assign);
-componentwise_binop_impl!(Sub, sub, ClosedSub; SubAssign, sub_assign);
+componentwise_binop_impl!(Add, add, ClosedAdd;
+                          AddAssign, add_assign, add_assign_statically_unchecked, add_assign_statically_unchecked_mut;
+                          add_to, add_to_statically_unchecked);
+componentwise_binop_impl!(Sub, sub, ClosedSub;
+                          SubAssign, sub_assign, sub_assign_statically_unchecked, sub_assign_statically_unchecked_mut;
+                          sub_to, sub_to_statically_unchecked);
 
-impl<N, R: DimName, C: DimName, S> iter::Sum for Matrix<N, R, C, S>
+impl<N, R: DimName, C: DimName> iter::Sum for MatrixMN<N, R, C>
     where N: Scalar + ClosedAdd + Zero,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S>
+          DefaultAllocator: Allocator<N, R, C>
 {
-    fn sum<I: Iterator<Item = Matrix<N, R, C, S>>>(iter: I) -> Matrix<N, R, C, S> {
+    fn sum<I: Iterator<Item = MatrixMN<N, R, C>>>(iter: I) -> MatrixMN<N, R, C> {
         iter.fold(Matrix::zero(), |acc, x| acc + x)
     }
 }
 
-impl<'a, N, R: DimName, C: DimName, S> iter::Sum<&'a Matrix<N, R, C, S>> for Matrix<N, R, C, S>
+impl<'a, N, R: DimName, C: DimName> iter::Sum<&'a MatrixMN<N, R, C>> for MatrixMN<N, R, C>
     where N: Scalar + ClosedAdd + Zero,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S>
+          DefaultAllocator: Allocator<N, R, C>
 {
-    fn sum<I: Iterator<Item = &'a Matrix<N, R, C, S>>>(iter: I) -> Matrix<N, R, C, S> {
+    fn sum<I: Iterator<Item = &'a MatrixMN<N, R, C>>>(iter: I) -> MatrixMN<N, R, C> {
         iter.fold(Matrix::zero(), |acc, x| acc + x)
     }
 }
@@ -266,8 +389,9 @@ macro_rules! componentwise_scalarop_impl(
      $TraitAssign: ident, $method_assign: ident) => {
         impl<N, R: Dim, C: Dim, S> $Trait<N> for Matrix<N, R, C, S>
             where N: Scalar + $bound,
-                  S: Storage<N, R, C> {
-            type Output = OwnedMatrix<N, R, C, S::Alloc>;
+                  S: Storage<N, R, C>,
+                  DefaultAllocator: Allocator<N, R, C> {
+            type Output = MatrixMN<N, R, C>;
 
             #[inline]
             fn $method(self, rhs: N) -> Self::Output {
@@ -289,8 +413,9 @@ macro_rules! componentwise_scalarop_impl(
 
         impl<'a, N, R: Dim, C: Dim, S> $Trait<N> for &'a Matrix<N, R, C, S>
             where N: Scalar + $bound,
-                  S: Storage<N, R, C> {
-            type Output = OwnedMatrix<N, R, C, S::Alloc>;
+                  S: Storage<N, R, C>,
+                  DefaultAllocator: Allocator<N, R, C> {
+            type Output = MatrixMN<N, R, C>;
 
             #[inline]
             fn $method(self, rhs: N) -> Self::Output {
@@ -302,9 +427,11 @@ macro_rules! componentwise_scalarop_impl(
             where N: Scalar + $bound,
                   S: StorageMut<N, R, C> {
             #[inline]
-            fn $method_assign(&mut self, right: N) {
-                for left in self.iter_mut() {
-                    left.$method_assign(right)
+            fn $method_assign(&mut self, rhs: N) {
+                for j in 0 .. self.ncols() {
+                    for i in 0 .. self.nrows() {
+                        unsafe { self.get_unchecked_mut(i, j).$method_assign(rhs) };
+                    }
                 }
             }
         }
@@ -316,35 +443,35 @@ componentwise_scalarop_impl!(Div, div, ClosedDiv; DivAssign, div_assign);
 
 macro_rules! left_scalar_mul_impl(
     ($($T: ty),* $(,)*) => {$(
-        impl<R: Dim, C: Dim, S> Mul<Matrix<$T, R, C, S>> for $T
-            where S: Storage<$T, R, C> {
-            type Output = OwnedMatrix<$T, R, C, S::Alloc>;
+        impl<R: Dim, C: Dim, S: Storage<$T, R, C>> Mul<Matrix<$T, R, C, S>> for $T
+            where DefaultAllocator: Allocator<$T, R, C> {
+            type Output = MatrixMN<$T, R, C>;
 
             #[inline]
-            fn mul(self, right: Matrix<$T, R, C, S>) -> Self::Output {
-                let mut res = right.into_owned();
+            fn mul(self, rhs: Matrix<$T, R, C, S>) -> Self::Output {
+                let mut res = rhs.into_owned();
 
                 // XXX: optimize our iterator!
                 //
                 // Using our own iterator prevents loop unrolling, wich breaks some optimization
                 // (like SIMD). On the other hand, using the slice iterator is 4x faster.
 
-                // for right in res.iter_mut() {
-                for right in res.as_mut_slice().iter_mut() {
-                    *right = self * *right
+                // for rhs in res.iter_mut() {
+                for rhs in res.as_mut_slice().iter_mut() {
+                    *rhs = self * *rhs
                 }
 
                 res
             }
         }
 
-        impl<'b, R: Dim, C: Dim, S> Mul<&'b Matrix<$T, R, C, S>> for $T
-            where S: Storage<$T, R, C> {
-            type Output = OwnedMatrix<$T, R, C, S::Alloc>;
+        impl<'b, R: Dim, C: Dim, S: Storage<$T, R, C>> Mul<&'b Matrix<$T, R, C, S>> for $T
+            where DefaultAllocator: Allocator<$T, R, C> {
+            type Output = MatrixMN<$T, R, C>;
 
             #[inline]
-            fn mul(self, right: &'b Matrix<$T, R, C, S>) -> Self::Output {
-                self * right.clone_owned()
+            fn mul(self, rhs: &'b Matrix<$T, R, C, S>) -> Self::Output {
+                self * rhs.clone_owned()
             }
         }
     )*}
@@ -361,84 +488,66 @@ left_scalar_mul_impl!(
 // Matrix × Matrix
 impl<'a, 'b, N, R1: Dim, C1: Dim, R2: Dim, C2: Dim, SA, SB> Mul<&'b Matrix<N, R2, C2, SB>>
 for &'a Matrix<N, R1, C1, SA>
-    where N:  Scalar + Zero + ClosedAdd + ClosedMul,
-          SB: Storage<N, R2, C2>,
+    where N:  Scalar + Zero + One + ClosedAdd + ClosedMul,
           SA: Storage<N, R1, C1>,
-          SA::Alloc: Allocator<N, R1, C2>,
+          SB: Storage<N, R2, C2>,
+          DefaultAllocator: Allocator<N, R1, C2>,
           ShapeConstraint:  AreMultipliable<R1, C1, R2, C2> {
-    type Output = MatrixMul<N, R1, C1, C2, SA>;
+    type Output = MatrixMN<N, R1, C2>;
 
     #[inline]
-    fn mul(self, right: &'b Matrix<N, R2, C2, SB>) -> Self::Output {
-        let (nrows1, ncols1) = self.shape();
-        let (nrows2, ncols2) = right.shape();
-
-        assert!(ncols1 == nrows2, "Matrix multiplication dimensions mismatch.");
-
-        let mut res: MatrixMul<N, R1, C1, C2, SA> = unsafe {
-            Matrix::new_uninitialized_generic(self.data.shape().0, right.data.shape().1)
+    fn mul(self, rhs: &'b Matrix<N, R2, C2, SB>) -> Self::Output {
+        let mut res = unsafe {
+            Matrix::new_uninitialized_generic(self.data.shape().0, rhs.data.shape().1)
         };
 
-        for i in 0 .. nrows1 {
-            for j in 0 .. ncols2 {
-                let mut acc = N::zero();
-
-                unsafe {
-                    for k in 0 .. ncols1 {
-                        acc = acc + *self.get_unchecked(i, k) * *right.get_unchecked(k, j);
-                    }
-
-                    *res.get_unchecked_mut(i, j) = acc;
-                }
-            }
-        }
-
+        self.mul_to(rhs, &mut res);
         res
     }
 }
 
 impl<'a, N, R1: Dim, C1: Dim, R2: Dim, C2: Dim, SA, SB> Mul<Matrix<N, R2, C2, SB>>
 for &'a Matrix<N, R1, C1, SA>
-    where N:  Scalar + Zero + ClosedAdd + ClosedMul,
+    where N:  Scalar + Zero + One + ClosedAdd + ClosedMul,
           SB: Storage<N, R2, C2>,
           SA: Storage<N, R1, C1>,
-          SA::Alloc: Allocator<N, R1, C2>,
+          DefaultAllocator: Allocator<N, R1, C2>,
           ShapeConstraint:  AreMultipliable<R1, C1, R2, C2> {
-    type Output = MatrixMul<N, R1, C1, C2, SA>;
+    type Output = MatrixMN<N, R1, C2>;
 
     #[inline]
-    fn mul(self, right: Matrix<N, R2, C2, SB>) -> Self::Output {
-        self * &right
+    fn mul(self, rhs: Matrix<N, R2, C2, SB>) -> Self::Output {
+        self * &rhs
     }
 }
 
 impl<'b, N, R1: Dim, C1: Dim, R2: Dim, C2: Dim, SA, SB> Mul<&'b Matrix<N, R2, C2, SB>>
 for Matrix<N, R1, C1, SA>
-    where N:  Scalar + Zero + ClosedAdd + ClosedMul,
+    where N:  Scalar + Zero + One + ClosedAdd + ClosedMul,
           SB: Storage<N, R2, C2>,
           SA: Storage<N, R1, C1>,
-          SA::Alloc: Allocator<N, R1, C2>,
+          DefaultAllocator: Allocator<N, R1, C2>,
           ShapeConstraint:  AreMultipliable<R1, C1, R2, C2> {
-    type Output = MatrixMul<N, R1, C1, C2, SA>;
+    type Output = MatrixMN<N, R1, C2>;
 
     #[inline]
-    fn mul(self, right: &'b Matrix<N, R2, C2, SB>) -> Self::Output {
-        &self * right
+    fn mul(self, rhs: &'b Matrix<N, R2, C2, SB>) -> Self::Output {
+        &self * rhs
     }
 }
 
 impl<N, R1: Dim, C1: Dim, R2: Dim, C2: Dim, SA, SB> Mul<Matrix<N, R2, C2, SB>>
 for Matrix<N, R1, C1, SA>
-    where N:  Scalar + Zero + ClosedAdd + ClosedMul,
+    where N:  Scalar + Zero + One + ClosedAdd + ClosedMul,
           SB: Storage<N, R2, C2>,
           SA: Storage<N, R1, C1>,
-          SA::Alloc: Allocator<N, R1, C2>,
+          DefaultAllocator: Allocator<N, R1, C2>,
           ShapeConstraint:  AreMultipliable<R1, C1, R2, C2> {
-    type Output = MatrixMul<N, R1, C1, C2, SA>;
+    type Output = MatrixMN<N, R1, C2>;
 
     #[inline]
-    fn mul(self, right: Matrix<N, R2, C2, SB>) -> Self::Output {
-        &self * &right
+    fn mul(self, rhs: Matrix<N, R2, C2, SB>) -> Self::Output {
+        &self * &rhs
     }
 }
 
@@ -447,84 +556,106 @@ for Matrix<N, R1, C1, SA>
 //    − we can't use `a *= b` when C2 is not equal to C1.
 impl<N, R1, C1, R2, SA, SB> MulAssign<Matrix<N, R2, C1, SB>> for Matrix<N, R1, C1, SA>
     where R1: Dim, C1: Dim, R2: Dim,
-          N:  Scalar + Zero + ClosedAdd + ClosedMul,
+          N:  Scalar + Zero + One + ClosedAdd + ClosedMul,
           SB: Storage<N, R2, C1>,
-          SA: OwnedStorage<N, R1, C1>,
+          SA: ContiguousStorageMut<N, R1, C1> + Clone,
           ShapeConstraint:  AreMultipliable<R1, C1, R2, C1>,
-          SA::Alloc: OwnedAllocator<N, R1, C1, SA> {
+          DefaultAllocator: Allocator<N, R1, C1, Buffer = SA> {
     #[inline]
-    fn mul_assign(&mut self, right: Matrix<N, R2, C1, SB>) {
-        *self = &*self * right
+    fn mul_assign(&mut self, rhs: Matrix<N, R2, C1, SB>) {
+        *self = &*self * rhs
     }
 }
 
 impl<'b, N, R1, C1, R2, SA, SB> MulAssign<&'b Matrix<N, R2, C1, SB>> for Matrix<N, R1, C1, SA>
     where R1: Dim, C1: Dim, R2: Dim,
-          N:  Scalar + Zero + ClosedAdd + ClosedMul,
+          N:  Scalar + Zero + One + ClosedAdd + ClosedMul,
           SB: Storage<N, R2, C1>,
-          SA: OwnedStorage<N, R1, C1>,
+          SA: ContiguousStorageMut<N, R1, C1> + Clone,
           ShapeConstraint: AreMultipliable<R1, C1, R2, C1>,
           // FIXME: this is too restrictive. See comments for the non-ref version.
-          SA::Alloc: OwnedAllocator<N, R1, C1, SA> {
+          DefaultAllocator: Allocator<N, R1, C1, Buffer = SA> {
     #[inline]
-    fn mul_assign(&mut self, right: &'b Matrix<N, R2, C1, SB>) {
-        *self = &*self * right
+    fn mul_assign(&mut self, rhs: &'b Matrix<N, R2, C1, SB>) {
+        *self = &*self * rhs
     }
 }
 
 
 // Transpose-multiplication.
 impl<N, R1: Dim, C1: Dim, SA> Matrix<N, R1, C1, SA>
-    where N:  Scalar,
+    where N:  Scalar + Zero + One + ClosedAdd + ClosedMul,
           SA: Storage<N, R1, C1> {
-    /// Equivalent to `self.transpose() * right`.
+    /// Equivalent to `self.transpose() * rhs`.
     #[inline]
-    pub fn tr_mul<R2: Dim, C2: Dim, SB>(&self, right: &Matrix<N, R2, C2, SB>) -> MatrixTrMul<N, R1, C1, C2, SA>
-        where N: Zero + ClosedAdd + ClosedMul,
-              SB: Storage<N, R2, C2>,
-              SA::Alloc: Allocator<N, C1, C2>,
-              ShapeConstraint: AreMultipliable<C1, R1, R2, C2> {
+    pub fn tr_mul<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<N, R2, C2, SB>) -> MatrixMN<N, C1, C2>
+        where SB: Storage<N, R2, C2>,
+              DefaultAllocator: Allocator<N, C1, C2>,
+              ShapeConstraint: SameNumberOfRows<R1, R2> {
+
+        let mut res = unsafe {
+            Matrix::new_uninitialized_generic(self.data.shape().1, rhs.data.shape().1)
+        };
+
+        self.tr_mul_to(rhs, &mut res);
+        res
+    }
+
+    /// Equivalent to `self.transpose() * rhs` but stores the result into `out` to avoid
+    /// allocations.
+    #[inline]
+    pub fn tr_mul_to<R2: Dim, C2: Dim, SB,
+                     R3: Dim, C3: Dim, SC>(&self,
+                                           rhs: &Matrix<N, R2, C2, SB>,
+                                           out: &mut Matrix<N, R3, C3, SC>)
+        where SB: Storage<N, R2, C2>,
+              SC: StorageMut<N, R3, C3>,
+              ShapeConstraint: SameNumberOfRows<R1, R2> +
+                               DimEq<C1, R3> +
+                               DimEq<C2, C3> {
         let (nrows1, ncols1) = self.shape();
-        let (nrows2, ncols2) = right.shape();
+        let (nrows2, ncols2) = rhs.shape();
+        let (nrows3, ncols3) = out.shape();
 
         assert!(nrows1 == nrows2, "Matrix multiplication dimensions mismatch.");
-
-        let mut res: MatrixTrMul<N, R1, C1, C2, SA> = unsafe {
-            Matrix::new_uninitialized_generic(self.data.shape().1, right.data.shape().1)
-        };
+        assert!(nrows3 == ncols1 && ncols3 == ncols2, "Matrix multiplication output dimensions mismatch.");
 
         for i in 0 .. ncols1 {
             for j in 0 .. ncols2 {
-                let mut acc = N::zero();
-
-                unsafe {
-                    for k in 0 .. nrows1 {
-                        acc += *self.get_unchecked(k, i) * *right.get_unchecked(k, j);
-                    }
-
-                    *res.get_unchecked_mut(i, j) = acc;
+                let dot = self.column(i).dot(&rhs.column(j));
+                unsafe { *out.get_unchecked_mut(i, j) = dot };
             }
         }
     }
 
-        res
+    /// Equivalent to `self * rhs` but stores the result into `out` to avoid allocations.
+    #[inline]
+    pub fn mul_to<R2: Dim, C2: Dim, SB,
+                  R3: Dim, C3: Dim, SC>(&self,
+                                        rhs: &Matrix<N, R2, C2, SB>,
+                                        out: &mut Matrix<N, R3, C3, SC>)
+        where SB: Storage<N, R2, C2>,
+              SC: StorageMut<N, R3, C3>,
+              ShapeConstraint: SameNumberOfRows<R3, R1>    +
+                               SameNumberOfColumns<C3, C2> +
+                               AreMultipliable<R1, C1, R2, C2> {
+        out.gemm(N::one(), self, rhs, N::zero());
     }
 
 
     /// The kronecker product of two matrices (aka. tensor product of the corresponding linear
     /// maps).
     pub fn kronecker<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<N, R2, C2, SB>)
-                                           -> OwnedMatrix<N, DimProd<R1, R2>, DimProd<C1, C2>, SA::Alloc>
+                                           -> MatrixMN<N, DimProd<R1, R2>, DimProd<C1, C2>>
         where N:  ClosedMul,
               R1: DimMul<R2>,
               C1: DimMul<C2>,
               SB: Storage<N, R2, C2>,
-              SA::Alloc: Allocator<N, DimProd<R1, R2>, DimProd<C1, C2>> {
+              DefaultAllocator: Allocator<N, DimProd<R1, R2>, DimProd<C1, C2>> {
         let (nrows1, ncols1) = self.data.shape();
         let (nrows2, ncols2) = rhs.data.shape();
 
-        let mut res: OwnedMatrix<_, _, _, SA::Alloc> =
-            unsafe { Matrix::new_uninitialized_generic(nrows1.mul(nrows2), ncols1.mul(ncols2)) };
+        let mut res = unsafe { Matrix::new_uninitialized_generic(nrows1.mul(nrows2), ncols1.mul(ncols2)) };
 
         {
             let mut data_res = res.data.ptr_mut();
@@ -549,22 +680,76 @@ impl<N, R1: Dim, C1: Dim, SA> Matrix<N, R1, C1, SA>
     }
 }
 
-impl<N, D: DimName, S> iter::Product for SquareMatrix<N, D, S>
+impl<N: Scalar + ClosedAdd, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
+    /// Adds a scalar to `self`.
+    #[inline]
+    pub fn add_scalar(&self, rhs: N) -> MatrixMN<N, R, C>
+        where DefaultAllocator: Allocator<N, R, C> {
+        let mut res = self.clone_owned();
+        res.add_scalar_mut(rhs);
+        res
+    }
+
+    /// Adds a scalar to `self` in-place.
+    #[inline]
+    pub fn add_scalar_mut(&mut self, rhs: N)
+        where S: StorageMut<N, R, C> {
+        for e in self.iter_mut() {
+            *e += rhs
+        }
+    }
+}
+
+
+impl<N, D: DimName> iter::Product for MatrixN<N, D>
     where N: Scalar + Zero + One + ClosedMul + ClosedAdd,
-          S: OwnedStorage<N, D, D>,
-          S::Alloc: OwnedAllocator<N, D, D, S>
+          DefaultAllocator: Allocator<N, D, D>
 {
-    fn product<I: Iterator<Item = SquareMatrix<N, D, S>>>(iter: I) -> SquareMatrix<N, D, S> {
+    fn product<I: Iterator<Item = MatrixN<N, D>>>(iter: I) -> MatrixN<N, D> {
         iter.fold(Matrix::one(), |acc, x| acc * x)
     }
 }
 
-impl<'a, N, D: DimName, S> iter::Product<&'a SquareMatrix<N, D, S>> for SquareMatrix<N, D, S>
+impl<'a, N, D: DimName> iter::Product<&'a MatrixN<N, D>> for MatrixN<N, D>
     where N: Scalar + Zero + One + ClosedMul + ClosedAdd,
-          S: OwnedStorage<N, D, D>,
-          S::Alloc: OwnedAllocator<N, D, D, S>
+          DefaultAllocator: Allocator<N, D, D>
 {
-    fn product<I: Iterator<Item = &'a SquareMatrix<N, D, S>>>(iter: I) -> SquareMatrix<N, D, S> {
+    fn product<I: Iterator<Item = &'a MatrixN<N, D>>>(iter: I) -> MatrixN<N, D> {
         iter.fold(Matrix::one(), |acc, x| acc * x)
     }
 }
+
+impl<N: Scalar + PartialOrd + Signed, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
+    /// Returns the absolute value of the coefficient with the largest absolute value.
+    #[inline]
+    pub fn amax(&self) -> N {
+        let mut max = N::zero();
+
+        for e in self.iter() {
+            let ae = e.abs();
+
+            if ae > max {
+                max = ae;
+            }
+        }
+
+        max
+    }
+
+    /// Returns the absolute value of the coefficient with the smallest absolute value.
+    #[inline]
+    pub fn amin(&self) -> N {
+        let mut it = self.iter();
+        let mut min = it.next().expect("amin: empty matrices not supported.").abs();
+
+        for e in it {
+            let ae = e.abs();
+
+            if ae < min {
+                min = ae;
+            }
+        }
+
+        min
+    }
+}

src/core/properties.rs

@@ -2,33 +2,38 @@
 use num::{Zero, One};
 use approx::ApproxEq;
 
-use alga::general::{ClosedAdd, ClosedMul, ClosedSub, Field};
+use alga::general::{ClosedAdd, ClosedMul, Real};
 
-use core::{Scalar, Matrix, SquareMatrix};
-use core::dimension::Dim;
+use core::{DefaultAllocator, Scalar, Matrix, SquareMatrix};
+use core::dimension::{Dim, DimMin};
 use core::storage::Storage;
+use core::allocator::Allocator;
 
 
 impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /// Indicates if this is a square matrix.
     #[inline]
-    pub fn is_square(&self) -> bool {
-        let shape = self.shape();
-        shape.0 == shape.1
+    pub fn is_empty(&self) -> bool {
+        let (nrows, ncols) = self.shape();
+        nrows == 0 || ncols == 0
+    }
+
+    /// Indicates if this is a square matrix.
+    #[inline]
+    pub fn is_square(&self) -> bool {
+        let (nrows, ncols) = self.shape();
+        nrows == ncols
     }
-}
 
-impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S>
     // FIXME: ApproxEq prevents us from using those methods on integer matrices…
-    where N: ApproxEq,
-          N::Epsilon: Copy {
     /// Indicated if this is the identity matrix within a relative error of `eps`.
     ///
     /// If the matrix is diagonal, this checks that diagonal elements (i.e. at coordinates `(i, i)`
     /// for i from `0` to `min(R, C)`) are equal one; and that all other elements are zero.
     #[inline]
     pub fn is_identity(&self, eps: N::Epsilon) -> bool
-        where N: Zero + One {
+    where N: Zero + One + ApproxEq,
+          N::Epsilon: Copy {
         let (nrows, ncols) = self.shape();
         let d;
 
@@ -75,32 +80,35 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S>
 
         true
     }
-}
 
-
-impl<N: Scalar + ApproxEq, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S>
-    where N: Zero + One + ClosedAdd + ClosedMul,
-          N::Epsilon: Copy {
-    /// Checks that this matrix is orthogonal, i.e., that it is square and `M × Mᵀ = Id`.
+    /// Checks that `Mᵀ × M = Id`.
     ///
     /// In this definition `Id` is approximately equal to the identity matrix with a relative error
     /// equal to `eps`.
     #[inline]
-    pub fn is_orthogonal(&self, eps: N::Epsilon) -> bool {
-        self.is_square() && (self.tr_mul(self)).is_identity(eps)
+    pub fn is_orthogonal(&self, eps: N::Epsilon) -> bool
+        where N: Zero + One + ClosedAdd + ClosedMul + ApproxEq,
+              S: Storage<N, R, C>,
+              N::Epsilon: Copy,
+              DefaultAllocator: Allocator<N, C, C> {
+        (self.tr_mul(self)).is_identity(eps)
     }
+}
 
+
+impl<N: Real, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S>
+    where DefaultAllocator: Allocator<N, D, D> {
     /// Checks that this matrix is orthogonal and has a determinant equal to 1.
     #[inline]
-    pub fn is_special_orthogonal(&self, eps: N::Epsilon) -> bool
-        where N: ClosedSub + PartialOrd {
-            self.is_orthogonal(eps) && self.determinant() > N::zero()
+    pub fn is_special_orthogonal(&self, eps: N) -> bool
+        where D: DimMin<D, Output = D>,
+              DefaultAllocator: Allocator<(usize, usize), D> {
+            self.is_square() && self.is_orthogonal(eps) && self.determinant() > N::zero()
     }
 
     /// Returns `true` if this matrix is invertible.
     #[inline]
-    pub fn is_invertible(&self) -> bool
-        where N: Field {
+    pub fn is_invertible(&self) -> bool {
         // FIXME: improve this?
         self.clone_owned().try_inverse().is_some()
     }

src/core/scalar.rs

@@ -1,3 +1,4 @@
+use std::any::TypeId;
 use std::fmt::Debug;
 use std::any::Any;
 
@@ -5,5 +6,12 @@ use std::any::Any;
 ///
 /// This does not make any assumption on the algebraic properties of `Self`.
 pub trait Scalar: Copy + PartialEq + Debug + Any {
+    #[inline]
+    /// Tests if `Self` the the same as the type `T`
+    ///
+    /// Typically used to test of `Self` is a f32 or a f64 with `N::is::<f32>()`.
+    fn is<T: Scalar>() -> bool {
+        TypeId::of::<Self>() == TypeId::of::<T>()
+    }
 }
 impl<T: Copy + PartialEq + Debug + Any> Scalar for T { }

src/core/storage.rs

@@ -1,39 +1,28 @@
 //! Abstract definition of a matrix data storage.
 
+use std::fmt::Debug;
 use std::mem;
-use std::any::Any;
 
 use core::Scalar;
-use dimension::Dim;
-use allocator::{Allocator, SameShapeR, SameShapeC};
+use core::default_allocator::DefaultAllocator;
+use core::dimension::{Dim, U1};
+use core::allocator::{Allocator, SameShapeR, SameShapeC};
 
 /*
- * Aliases for sum storage.
+ * Aliases for allocation results.
  */
 /// The data storage for the sum of two matrices with dimensions `(R1, C1)` and `(R2, C2)`.
-pub type SumStorage<N, R1, C1, R2, C2, SA> =
-    <<SA as Storage<N, R1, C1>>::Alloc as Allocator<N, SameShapeR<R1, R2>, SameShapeC<C1, C2>>>::Buffer;
+pub type SameShapeStorage<N, R1, C1, R2, C2> = <DefaultAllocator as Allocator<N, SameShapeR<R1, R2>, SameShapeC<C1, C2>>>::Buffer;
 
-/*
- * Aliases for multiplication storage.
- */
-/// The data storage for the multiplication of two matrices with dimensions `(R1, C1)` on the left
-/// hand side, and with `C2` columns on the right hand side.
-pub type MulStorage<N, R1, C1, C2, SA> =
-    <<SA as Storage<N, R1, C1>>::Alloc as Allocator<N, R1, C2>>::Buffer;
-
-/// The data storage for the multiplication of two matrices with dimensions `(R1, C1)` on the left
-/// hand side, and with `C2` columns on the right hand side. The first matrix is implicitly
-/// transposed.
-pub type TrMulStorage<N, R1, C1, C2, SA> =
-    <<SA as Storage<N, R1, C1>>::Alloc as Allocator<N, C1, C2>>::Buffer;
-
-/*
- * Alias for allocation result.
- */
+// FIXME: better name than Owned ?
 /// The owned data storage that can be allocated from `S`.
-pub type Owned<N, R, C, A> =
-    <A as Allocator<N, R, C>>::Buffer;
+pub type Owned<N, R, C = U1> = <DefaultAllocator as Allocator<N, R, C>>::Buffer;
+
+/// The row-stride of the owned data storage for a buffer of dimension `(R, C)`.
+pub type RStride<N, R, C = U1> = <<DefaultAllocator as Allocator<N, R, C>>::Buffer as Storage<N, R, C>>::RStride;
+
+/// The column-stride of the owned data storage for a buffer of dimension `(R, C)`.
+pub type CStride<N, R, C = U1> = <<DefaultAllocator as Allocator<N, R, C>>::Buffer as Storage<N, R, C>>::CStride;
 
 
 /// The trait shared by all matrix data storage.
@@ -45,22 +34,13 @@ pub type Owned<N, R, C, A> =
 /// should **not** allow the user to modify the size of the underlying buffer with safe methods
 /// (for example the `MatrixVec::data_mut` method is unsafe because the user could change the
 /// vector's size so that it no longer contains enough elements: this will lead to UB.
-pub unsafe trait Storage<N: Scalar, R: Dim, C: Dim>: Sized {
+pub unsafe trait Storage<N: Scalar, R: Dim, C: Dim = U1>: Debug + Sized {
     /// The static stride of this storage's rows.
     type RStride: Dim;
 
     /// The static stride of this storage's columns.
     type CStride: Dim;
 
-    /// The allocator for this family of storage.
-    type Alloc: Allocator<N, R, C>;
-
-    /// Builds a matrix data storage that does not contain any reference.
-    fn into_owned(self) -> Owned<N, R, C, Self::Alloc>;
-
-    /// Clones this data storage into one that does not contain any reference.
-    fn clone_owned(&self) -> Owned<N, R, C, Self::Alloc>;
-
     /// The matrix data pointer.
     fn ptr(&self) -> *const N;
 
@@ -110,6 +90,24 @@ pub unsafe trait Storage<N: Scalar, R: Dim, C: Dim>: Sized {
     unsafe fn get_unchecked(&self, irow: usize, icol: usize) -> &N {
         self.get_unchecked_linear(self.linear_index(irow, icol))
     }
+
+    /// Indicates whether this data buffer stores its elements contiguously.
+    #[inline]
+    fn is_contiguous(&self) -> bool;
+
+    /// Retrieves the data buffer as a contiguous slice.
+    ///
+    /// The matrix components may not be stored in a contiguous way, depending on the strides.
+    #[inline]
+    fn as_slice(&self) -> &[N];
+
+    /// Builds a matrix data storage that does not contain any reference.
+    fn into_owned(self) -> Owned<N, R, C>
+        where DefaultAllocator: Allocator<N, R, C>;
+
+    /// Clones this data storage to one that does not contain any reference.
+    fn clone_owned(&self) -> Owned<N, R, C>
+        where DefaultAllocator: Allocator<N, R, C>;
 }
 
 
@@ -118,7 +116,7 @@ pub unsafe trait Storage<N: Scalar, R: Dim, C: Dim>: Sized {
 /// Note that a mutable access does not mean that the matrix owns its data. For example, a mutable
 /// matrix slice can provide mutable access to its elements even if it does not own its data (it
 /// contains only an internal reference to them).
-pub unsafe trait StorageMut<N: Scalar, R: Dim, C: Dim>: Storage<N, R, C> {
+pub unsafe trait StorageMut<N: Scalar, R: Dim, C: Dim = U1>: Storage<N, R, C> {
     /// The matrix mutable data pointer.
     fn ptr_mut(&mut self) -> *mut N;
 
@@ -163,22 +161,24 @@ pub unsafe trait StorageMut<N: Scalar, R: Dim, C: Dim>: Storage<N, R, C> {
 
         self.swap_unchecked_linear(lid1, lid2)
     }
-}
 
-/// A matrix storage that does not contain any reference and that is stored contiguously in memory.
-///
-/// The storage requirement means that for any value of `i` in `[0, nrows * ncols[`, the value
-/// `.get_unchecked_linear` succeeds. This trait is unsafe because failing to comply to this may
-/// cause Undefined Behaviors.
-pub unsafe trait OwnedStorage<N: Scalar, R: Dim, C: Dim>: StorageMut<N, R, C> + Clone + Any
-    where Self::Alloc: Allocator<N, R, C, Buffer = Self> {
-    // NOTE: We could auto-impl those two methods but we don't to make sure the user is aware that
-    // data must be contiguous.
-    /// Converts this data storage to a slice.
-    #[inline]
-    fn as_slice(&self) -> &[N];
-
-    /// Converts this data storage to a mutable slice.
+    /// Retrieves the mutable data buffer as a contiguous slice.
+    ///
+    /// Matrix components may not be contiguous, depending on its strides.
     #[inline]
     fn as_mut_slice(&mut self) -> &mut [N];
 }
+
+/// A matrix storage that is stored contiguously in memory.
+///
+/// The storage requirement means that for any value of `i` in `[0, nrows * ncols[`, the value
+/// `.get_unchecked_linear` returns one of the matrix component. This trait is unsafe because
+/// failing to comply to this may cause Undefined Behaviors.
+pub unsafe trait ContiguousStorage<N: Scalar, R: Dim, C: Dim = U1>: Storage<N, R, C> { }
+
+/// A mutable matrix storage that is stored contiguously in memory.
+///
+/// The storage requirement means that for any value of `i` in `[0, nrows * ncols[`, the value
+/// `.get_unchecked_linear` returns one of the matrix component. This trait is unsafe because
+/// failing to comply to this may cause Undefined Behaviors.
+pub unsafe trait ContiguousStorageMut<N: Scalar, R: Dim, C: Dim = U1>: ContiguousStorage<N, R, C> + StorageMut<N, R, C> { }

src/debug/mod.rs

@@ -0,0 +1,8 @@
+//! Various tools useful for testing/debugging/benchmarking.
+
+
+mod random_orthogonal;
+mod random_sdp;
+
+pub use self::random_orthogonal::*;
+pub use self::random_sdp::*;

src/debug/random_orthogonal.rs

@@ -0,0 +1,51 @@
+#[cfg(feature = "arbitrary")]
+use quickcheck::{Arbitrary, Gen};
+#[cfg(feature = "arbitrary")]
+use core::storage::Owned;
+
+use num_complex::Complex;
+use alga::general::Real;
+use core::{DefaultAllocator, MatrixN};
+use core::dimension::{Dim, Dynamic, U2};
+use core::allocator::Allocator;
+use geometry::UnitComplex;
+
+/// A random orthogonal matrix.
+#[derive(Clone, Debug)]
+pub struct RandomOrthogonal<N: Real, D: Dim = Dynamic>
+    where DefaultAllocator: Allocator<N, D, D> {
+    m: MatrixN<N, D>
+}
+
+
+impl<N: Real, D: Dim> RandomOrthogonal<N, D>
+    where DefaultAllocator: Allocator<N, D, D> {
+    /// Retrieve the generated matrix.
+    pub fn unwrap(self) -> MatrixN<N, D> {
+        self.m
+    }
+
+    /// Creates a new random orthogonal matrix from its dimension and a random reals generators.
+    pub fn new<Rand: FnMut() -> N>(dim: D, mut rand: Rand) -> Self {
+        let mut res = MatrixN::identity_generic(dim, dim);
+
+        // Create an orthogonal matrix by compositing planar 2D rotations.
+        for i in 0 .. dim.value() - 1 {
+            let c = Complex::new(rand(), rand());
+            let rot: UnitComplex<N> = UnitComplex::from_complex(c);
+            rot.rotate(&mut res.fixed_rows_mut::<U2>(i));
+        }
+
+        RandomOrthogonal { m: res }
+    }
+}
+
+#[cfg(feature = "arbitrary")]
+impl<N: Real + Arbitrary + Send, D: Dim> Arbitrary for RandomOrthogonal<N, D>
+    where DefaultAllocator: Allocator<N, D, D>,
+          Owned<N, D, D>: Clone + Send {
+    fn arbitrary<G: Gen>(g: &mut G) -> Self {
+        let dim = D::try_to_usize().unwrap_or(g.gen_range(1, 50));
+        Self::new(D::from_usize(dim), || N::arbitrary(g))
+    }
+}

src/debug/random_sdp.rs

@@ -0,0 +1,54 @@
+#[cfg(feature = "arbitrary")]
+use quickcheck::{Arbitrary, Gen};
+#[cfg(feature = "arbitrary")]
+use core::storage::Owned;
+
+use alga::general::Real;
+use core::{DefaultAllocator, MatrixN};
+use core::dimension::{Dim, Dynamic};
+use core::allocator::Allocator;
+
+use debug::RandomOrthogonal;
+
+
+/// A random, well-conditioned, symmetric definite-positive matrix.
+#[derive(Clone, Debug)]
+pub struct RandomSDP<N: Real, D: Dim = Dynamic>
+    where DefaultAllocator: Allocator<N, D, D> {
+    m: MatrixN<N, D>
+}
+
+
+impl<N: Real, D: Dim> RandomSDP<N, D>
+    where DefaultAllocator: Allocator<N, D, D> {
+
+    /// Retrieve the generated matrix.
+    pub fn unwrap(self) -> MatrixN<N, D> {
+        self.m
+    }
+
+    /// Creates a new well conditioned symmetric definite-positive matrix from its dimension and a
+    /// random reals generators.
+    pub fn new<Rand: FnMut() -> N>(dim: D, mut rand: Rand) -> Self {
+        let mut m = RandomOrthogonal::new(dim, || rand()).unwrap();
+        let mt = m.transpose();
+
+        for i in 0 .. dim.value() {
+            let mut col = m.column_mut(i);
+            let eigenval = N::one() + rand().abs();
+            col *= eigenval;
+        }
+
+        RandomSDP { m: m * mt }
+    }
+}
+
+#[cfg(feature = "arbitrary")]
+impl<N: Real + Arbitrary + Send, D: Dim> Arbitrary for RandomSDP<N, D>
+    where DefaultAllocator: Allocator<N, D, D>,
+          Owned<N, D, D>: Clone + Send {
+    fn arbitrary<G: Gen>(g: &mut G) -> Self {
+        let dim = D::try_to_usize().unwrap_or(g.gen_range(1, 50));
+        Self::new(D::from_usize(dim), || N::arbitrary(g))
+    }
+}

src/geometry/isometry.rs

@@ -1,33 +1,43 @@
 use std::fmt;
+use std::hash;
 use std::marker::PhantomData;
 use approx::ApproxEq;
 
-use alga::general::{Real, SubsetOf};
-use alga::linear::Rotation;
-
-use core::{Scalar, OwnedSquareMatrix};
-use core::dimension::{DimName, DimNameSum, DimNameAdd, U1};
-use core::storage::{Storage, OwnedStorage};
-use core::allocator::{Allocator, OwnedAllocator};
-use geometry::{TranslationBase, PointBase};
+#[cfg(feature = "serde-serialize")]
+use serde;
 
 #[cfg(feature = "abomonation-serialize")]
 use abomonation::Abomonation;
 
+use alga::general::{Real, SubsetOf};
+use alga::linear::Rotation;
 
-/// An isometry that uses a data storage deduced from the allocator `A`.
-pub type OwnedIsometryBase<N, D, A, R> =
-    IsometryBase<N, D, <A as Allocator<N, D, U1>>::Buffer, R>;
+use core::{DefaultAllocator, MatrixN};
+use core::dimension::{DimName, DimNameSum, DimNameAdd, U1};
+use core::storage::Owned;
+use core::allocator::Allocator;
+use geometry::{Translation, Point};
 
 /// A direct isometry, i.e., a rotation followed by a translation.
 #[repr(C)]
-#[derive(Hash, Debug, Clone, Copy)]
+#[derive(Debug)]
 #[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
-pub struct IsometryBase<N: Scalar, D: DimName, S, R> {
+#[cfg_attr(feature = "serde-serialize",
+    serde(bound(
+        serialize = "R: serde::Serialize,
+                     DefaultAllocator: Allocator<N, D>,
+                     Owned<N, D>: serde::Serialize")))]
+#[cfg_attr(feature = "serde-serialize",
+    serde(bound(
+        deserialize = "R: serde::Deserialize<'de>,
+                       DefaultAllocator: Allocator<N, D>,
+                       Owned<N, D>: serde::Deserialize<'de>")))]
+pub struct Isometry<N: Real, D: DimName, R>
+    where DefaultAllocator: Allocator<N, D> {
     /// The pure rotational part of this isometry.
     pub rotation:    R,
     /// The pure translational part of this isometry.
-    pub translation: TranslationBase<N, D, S>,
+    pub translation: Translation<N, D>,
 
 
     // One dummy private field just to prevent explicit construction.
@@ -36,11 +46,12 @@ pub struct IsometryBase<N: Scalar, D: DimName, S, R> {
 }
 
 #[cfg(feature = "abomonation-serialize")]
-impl<N, D, S, R> Abomonation for IsometryBase<N, D, S, R>
+impl<N, D, R> Abomonation for IsometryBase<N, D, R>
     where N: Scalar,
           D: DimName,
           R: Abomonation,
-          TranslationBase<N, D, S>: Abomonation
+          TranslationBase<N, D>: Abomonation,
+          DefaultAllocator: Allocator<N, D>
 {
     unsafe fn entomb(&self, writer: &mut Vec<u8>) {
         self.rotation.entomb(writer);
@@ -58,15 +69,35 @@ impl<N, D, S, R> Abomonation for IsometryBase<N, D, S, R>
     }
 }
 
-impl<N, D: DimName, S, R> IsometryBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real + hash::Hash, D: DimName + hash::Hash, R: hash::Hash> hash::Hash for Isometry<N, D, R>
+    where DefaultAllocator: Allocator<N, D>,
+          Owned<N, D>: hash::Hash {
+    fn hash<H: hash::Hasher>(&self, state: &mut H) {
+        self.translation.hash(state);
+        self.rotation.hash(state);
+    }
+}
+
+impl<N: Real, D: DimName + Copy, R: Rotation<Point<N, D>> + Copy> Copy for Isometry<N, D, R>
+    where DefaultAllocator: Allocator<N, D>,
+          Owned<N, D>: Copy {
+}
+
+impl<N: Real, D: DimName, R: Rotation<Point<N, D>> + Clone> Clone for Isometry<N, D, R>
+    where DefaultAllocator: Allocator<N, D> {
+    #[inline]
+    fn clone(&self) -> Self {
+        Isometry::from_parts(self.translation.clone(), self.rotation.clone())
+    }
+}
+
+impl<N: Real, D: DimName, R: Rotation<Point<N, D>>> Isometry<N, D, R>
+    where DefaultAllocator: Allocator<N, D> {
+
     /// Creates a new isometry from its rotational and translational parts.
     #[inline]
-    pub fn from_parts(translation: TranslationBase<N, D, S>, rotation: R) -> IsometryBase<N, D, S, R> {
-        IsometryBase {
+    pub fn from_parts(translation: Translation<N, D>, rotation: R) -> Isometry<N, D, R> {
+        Isometry {
             rotation:     rotation,
             translation:  translation,
             _noconstruct: PhantomData
@@ -75,7 +106,7 @@ impl<N, D: DimName, S, R> IsometryBase<N, D, S, R>
 
     /// Inverts `self`.
     #[inline]
-    pub fn inverse(&self) -> IsometryBase<N, D, S, R> {
+    pub fn inverse(&self) -> Isometry<N, D, R> {
         let mut res = self.clone();
         res.inverse_mut();
         res
@@ -91,7 +122,7 @@ impl<N, D: DimName, S, R> IsometryBase<N, D, S, R>
 
     /// Appends to `self` the given translation in-place.
     #[inline]
-    pub fn append_translation_mut(&mut self, t: &TranslationBase<N, D, S>) {
+    pub fn append_translation_mut(&mut self, t: &Translation<N, D>) {
         self.translation.vector += &t.vector
     }
 
@@ -105,7 +136,7 @@ impl<N, D: DimName, S, R> IsometryBase<N, D, S, R>
     /// Appends in-place to `self` a rotation centered at the point `p`, i.e., the rotation that
     /// lets `p` invariant.
     #[inline]
-    pub fn append_rotation_wrt_point_mut(&mut self, r: &R, p: &PointBase<N, D, S>) {
+    pub fn append_rotation_wrt_point_mut(&mut self, r: &R, p: &Point<N, D>) {
         self.translation.vector -= &p.coords;
         self.append_rotation_mut(r);
         self.translation.vector += &p.coords;
@@ -115,7 +146,7 @@ impl<N, D: DimName, S, R> IsometryBase<N, D, S, R>
     /// `self.translation`.
     #[inline]
     pub fn append_rotation_wrt_center_mut(&mut self, r: &R) {
-        let center = PointBase::from_coordinates(self.translation.vector.clone());
+        let center = Point::from_coordinates(self.translation.vector.clone());
         self.append_rotation_wrt_point_mut(r, &center)
     }
 }
@@ -124,16 +155,15 @@ impl<N, D: DimName, S, R> IsometryBase<N, D, S, R>
 // and makes it hard to use it, e.g., for Transform × Isometry implementation.
 // This is OK since all constructors of the isometry enforce the Rotation bound already (and
 // explicit struct construction is prevented by the dummy ZST field).
-impl<N, D: DimName, S, R> IsometryBase<N, D, S, R>
-    where N: Scalar,
-          S: Storage<N, D, U1> {
+impl<N: Real, D: DimName, R> Isometry<N, D, R>
+    where DefaultAllocator: Allocator<N, D> {
     /// Converts this isometry into its equivalent homogeneous transformation matrix.
     #[inline]
-    pub fn to_homogeneous(&self) -> OwnedSquareMatrix<N, DimNameSum<D, U1>, S::Alloc>
+    pub fn to_homogeneous(&self) -> MatrixN<N, DimNameSum<D, U1>>
         where D: DimNameAdd<U1>,
-              R: SubsetOf<OwnedSquareMatrix<N, DimNameSum<D, U1>, S::Alloc>>,
-              S::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
-        let mut res: OwnedSquareMatrix<N, _, S::Alloc> = ::convert_ref(&self.rotation);
+              R: SubsetOf<MatrixN<N, DimNameSum<D, U1>>>,
+              DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
+        let mut res: MatrixN<N, _> = ::convert_ref(&self.rotation);
         res.fixed_slice_mut::<D, U1>(0, D::dim()).copy_from(&self.translation.vector);
 
         res
@@ -141,30 +171,24 @@ impl<N, D: DimName, S, R> IsometryBase<N, D, S, R>
 }
 
 
-impl<N, D: DimName, S, R> Eq for IsometryBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>> + Eq,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R> Eq for Isometry<N, D, R>
+    where R: Rotation<Point<N, D>> + Eq,
+          DefaultAllocator: Allocator<N, D> {
 }
 
-impl<N, D: DimName, S, R> PartialEq for IsometryBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>> + PartialEq,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R> PartialEq for Isometry<N, D, R>
+    where R: Rotation<Point<N, D>> + PartialEq,
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
-    fn eq(&self, right: &IsometryBase<N, D, S, R>) -> bool {
+    fn eq(&self, right: &Isometry<N, D, R>) -> bool {
         self.translation == right.translation &&
         self.rotation    == right.rotation
     }
 }
 
-impl<N, D: DimName, S, R> ApproxEq for IsometryBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>> + ApproxEq<Epsilon = N::Epsilon>,
-          S::Alloc: OwnedAllocator<N, D, U1, S>,
+impl<N: Real, D: DimName, R> ApproxEq for Isometry<N, D, R>
+    where R: Rotation<Point<N, D>> + ApproxEq<Epsilon = N::Epsilon>,
+          DefaultAllocator: Allocator<N, D>,
           N::Epsilon: Copy {
     type Epsilon = N::Epsilon;
 
@@ -201,32 +225,16 @@ impl<N, D: DimName, S, R> ApproxEq for IsometryBase<N, D, S, R>
  * Display
  *
  */
-impl<N, D: DimName, S, R> fmt::Display for IsometryBase<N, D, S, R>
-    where N: Real + fmt::Display,
-          S: OwnedStorage<N, D, U1>,
-          R: fmt::Display,
-          S::Alloc: OwnedAllocator<N, D, U1, S> + Allocator<usize, D, U1> {
+impl<N: Real + fmt::Display, D: DimName, R> fmt::Display for Isometry<N, D, R>
+    where R: fmt::Display,
+          DefaultAllocator: Allocator<N, D> +
+                            Allocator<usize, D> {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         let precision = f.precision().unwrap_or(3);
 
-        try!(writeln!(f, "IsometryBase {{"));
+        try!(writeln!(f, "Isometry {{"));
         try!(write!(f, "{:.*}", precision, self.translation));
         try!(write!(f, "{:.*}", precision, self.rotation));
         writeln!(f, "}}")
     }
 }
-
-
-//         /*
-//          *
-//          * Absolute
-//          *
-//          */
-//         impl<N: Absolute> Absolute for $t<N> {
-//             type AbsoluteValue = $submatrix<N::AbsoluteValue>;
-//
-//             #[inline]
-//             fn abs(m: &$t<N>) -> $submatrix<N::AbsoluteValue> {
-//                 Absolute::abs(&m.submatrix)
-//             }
-//         }

src/geometry/isometry_alga.rs

@@ -1,14 +1,14 @@
 use alga::general::{AbstractMagma, AbstractGroup, AbstractLoop, AbstractMonoid, AbstractQuasigroup,
                     AbstractSemigroup, Real, Inverse, Multiplicative, Identity, Id};
-use alga::linear::{Transformation, Similarity, AffineTransformation, DirectIsometry, Isometry,
+use alga::linear::{Transformation, Similarity, AffineTransformation, DirectIsometry,
                    Rotation, ProjectiveTransformation};
+use alga::linear::Isometry as AlgaIsometry;
 
-use core::ColumnVector;
-use core::dimension::{DimName, U1};
-use core::storage::OwnedStorage;
-use core::allocator::OwnedAllocator;
+use core::{DefaultAllocator, VectorN};
+use core::dimension::DimName;
+use core::allocator::Allocator;
 
-use geometry::{IsometryBase, TranslationBase, PointBase};
+use geometry::{Isometry, Translation, Point};
 
 
 /*
@@ -16,22 +16,18 @@ use geometry::{IsometryBase, TranslationBase, PointBase};
  * Algebraic structures.
  *
  */
-impl<N, D: DimName, S, R> Identity<Multiplicative> for IsometryBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R> Identity<Multiplicative> for Isometry<N, D, R>
+    where R: Rotation<Point<N, D>>,
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn identity() -> Self {
         Self::identity()
     }
 }
 
-impl<N, D: DimName, S, R> Inverse<Multiplicative> for IsometryBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R> Inverse<Multiplicative> for Isometry<N, D, R>
+    where R: Rotation<Point<N, D>>,
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn inverse(&self) -> Self {
         self.inverse()
@@ -43,11 +39,9 @@ impl<N, D: DimName, S, R> Inverse<Multiplicative> for IsometryBase<N, D, S, R>
     }
 }
 
-impl<N, D: DimName, S, R> AbstractMagma<Multiplicative> for IsometryBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R> AbstractMagma<Multiplicative> for Isometry<N, D, R>
+    where R: Rotation<Point<N, D>>,
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn operate(&self, rhs: &Self) -> Self {
         self * rhs
@@ -56,11 +50,9 @@ impl<N, D: DimName, S, R> AbstractMagma<Multiplicative> for IsometryBase<N, D, S
 
 macro_rules! impl_multiplicative_structures(
     ($($marker: ident<$operator: ident>),* $(,)*) => {$(
-        impl<N, D: DimName, S, R> $marker<$operator> for IsometryBase<N, D, S, R>
-            where N: Real,
-                  S: OwnedStorage<N, D, U1>,
-                  R: Rotation<PointBase<N, D, S>>,
-                  S::Alloc: OwnedAllocator<N, D, U1, S> { }
+        impl<N: Real, D: DimName, R> $marker<$operator> for Isometry<N, D, R>
+            where R: Rotation<Point<N, D>>,
+                  DefaultAllocator: Allocator<N, D> { }
     )*}
 );
 
@@ -77,49 +69,43 @@ impl_multiplicative_structures!(
  * Transformation groups.
  *
  */
-impl<N, D: DimName, S, R> Transformation<PointBase<N, D, S>> for IsometryBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R> Transformation<Point<N, D>> for Isometry<N, D, R>
+    where R: Rotation<Point<N, D>>,
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
-    fn transform_point(&self, pt: &PointBase<N, D, S>) -> PointBase<N, D, S> {
+    fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
         self * pt
     }
 
     #[inline]
-    fn transform_vector(&self, v: &ColumnVector<N, D, S>) -> ColumnVector<N, D, S> {
+    fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
         self * v
     }
 }
 
-impl<N, D: DimName, S, R> ProjectiveTransformation<PointBase<N, D, S>> for IsometryBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R> ProjectiveTransformation<Point<N, D>> for Isometry<N, D, R>
+    where R: Rotation<Point<N, D>>,
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
-    fn inverse_transform_point(&self, pt: &PointBase<N, D, S>) -> PointBase<N, D, S> {
+    fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
         self.rotation.inverse_transform_point(&(pt - &self.translation.vector))
     }
 
     #[inline]
-    fn inverse_transform_vector(&self, v: &ColumnVector<N, D, S>) -> ColumnVector<N, D, S> {
+    fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
         self.rotation.inverse_transform_vector(v)
     }
 }
 
-impl<N, D: DimName, S, R> AffineTransformation<PointBase<N, D, S>> for IsometryBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R> AffineTransformation<Point<N, D>> for Isometry<N, D, R>
+    where R: Rotation<Point<N, D>>,
+          DefaultAllocator: Allocator<N, D> {
     type Rotation          = R;
     type NonUniformScaling = Id;
-    type Translation       = TranslationBase<N, D, S>;
+    type Translation       = Translation<N, D>;
 
     #[inline]
-    fn decompose(&self) -> (TranslationBase<N, D, S>, R, Id, R) {
+    fn decompose(&self) -> (Translation<N, D>, R, Id, R) {
         (self.translation.clone(), self.rotation.clone(), Id::new(), R::identity())
     }
 
@@ -136,7 +122,7 @@ impl<N, D: DimName, S, R> AffineTransformation<PointBase<N, D, S>> for IsometryB
     #[inline]
     fn append_rotation(&self, r: &Self::Rotation) -> Self {
         let shift = r.transform_vector(&self.translation.vector);
-        IsometryBase::from_parts(TranslationBase::from_vector(shift), r.clone() * self.rotation.clone())
+        Isometry::from_parts(Translation::from_vector(shift), r.clone() * self.rotation.clone())
     }
 
     #[inline]
@@ -155,22 +141,20 @@ impl<N, D: DimName, S, R> AffineTransformation<PointBase<N, D, S>> for IsometryB
     }
 
     #[inline]
-    fn append_rotation_wrt_point(&self, r: &Self::Rotation, p: &PointBase<N, D, S>) -> Option<Self> {
+    fn append_rotation_wrt_point(&self, r: &Self::Rotation, p: &Point<N, D>) -> Option<Self> {
         let mut res = self.clone();
         res.append_rotation_wrt_point_mut(r, p);
         Some(res)
     }
 }
 
-impl<N, D: DimName, S, R> Similarity<PointBase<N, D, S>> for IsometryBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R> Similarity<Point<N, D>> for Isometry<N, D, R>
+    where R: Rotation<Point<N, D>>,
+          DefaultAllocator: Allocator<N, D> {
     type Scaling = Id;
 
     #[inline]
-    fn translation(&self) -> TranslationBase<N, D, S> {
+    fn translation(&self) -> Translation<N, D> {
         self.translation.clone()
     }
 
@@ -187,12 +171,10 @@ impl<N, D: DimName, S, R> Similarity<PointBase<N, D, S>> for IsometryBase<N, D,
 
 macro_rules! marker_impl(
     ($($Trait: ident),*) => {$(
-        impl<N, D: DimName, S, R> $Trait<PointBase<N, D, S>> for IsometryBase<N, D, S, R>
-        where N: Real,
-              S: OwnedStorage<N, D, U1>,
-              R: Rotation<PointBase<N, D, S>>,
-              S::Alloc: OwnedAllocator<N, D, U1, S> { }
+        impl<N: Real, D: DimName, R> $Trait<Point<N, D>> for Isometry<N, D, R>
+        where R: Rotation<Point<N, D>>,
+              DefaultAllocator: Allocator<N, D> { }
     )*}
 );
 
-marker_impl!(Isometry, DirectIsometry);
+marker_impl!(AlgaIsometry, DirectIsometry);

src/geometry/isometry_alias.rs

@@ -1,19 +1,16 @@
-use core::MatrixArray;
-use core::dimension::{U1, U2, U3};
+use core::dimension::{U2, U3};
 
-use geometry::{Rotation, IsometryBase, UnitQuaternion, UnitComplex};
+use geometry::{Isometry, Rotation2, Rotation3, UnitQuaternion, UnitComplex};
 
-/// A D-dimensional isometry.
-pub type Isometry<N, D> = IsometryBase<N, D, MatrixArray<N, D, U1>, Rotation<N, D>>;
 
 /// A 2-dimensional isometry using a unit complex number for its rotational part.
-pub type Isometry2<N> = IsometryBase<N, U2, MatrixArray<N, U2, U1>, UnitComplex<N>>;
+pub type Isometry2<N> = Isometry<N, U2, UnitComplex<N>>;
 
 /// A 3-dimensional isometry using a unit quaternion for its rotational part.
-pub type Isometry3<N> = IsometryBase<N, U3, MatrixArray<N, U3, U1>, UnitQuaternion<N>>;
+pub type Isometry3<N> = Isometry<N, U3, UnitQuaternion<N>>;
 
-/// A 2-dimensional isometry using a rotation matrix for its rotation part.
-pub type IsometryMatrix2<N> = Isometry<N, U2>;
+/// A 2-dimensional isometry using a rotation matrix for its rotational part.
+pub type IsometryMatrix2<N> = Isometry<N, U2, Rotation2<N>>;
 
-/// A 3-dimensional isometry using a rotation matrix for its rotation part.
-pub type IsometryMatrix3<N> = Isometry<N, U3>;
+/// A 3-dimensional isometry using a rotation matrix for its rotational part.
+pub type IsometryMatrix3<N> = Isometry<N, U3, Rotation3<N>>;

src/geometry/isometry_construction.rs

@@ -1,5 +1,7 @@
 #[cfg(feature = "arbitrary")]
 use quickcheck::{Arbitrary, Gen};
+#[cfg(feature = "arbitrary")]
+use core::storage::Owned;
 
 use num::One;
 use rand::{Rng, Rand};
@@ -7,31 +9,33 @@ use rand::{Rng, Rand};
 use alga::general::Real;
 use alga::linear::Rotation as AlgaRotation;
 
-use core::ColumnVector;
-use core::dimension::{DimName, U1, U2, U3, U4};
-use core::allocator::{OwnedAllocator, Allocator};
-use core::storage::OwnedStorage;
+use core::{DefaultAllocator, Vector2, Vector3};
+use core::dimension::{DimName, U2, U3};
+use core::allocator::Allocator;
 
-use geometry::{PointBase, TranslationBase, RotationBase, IsometryBase, UnitQuaternionBase, UnitComplex};
+use geometry::{Point, Translation, Rotation, Isometry, UnitQuaternion, UnitComplex,
+               Point3, Rotation2, Rotation3};
 
 
-impl<N, D: DimName, S, R> IsometryBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: AlgaRotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R: AlgaRotation<Point<N, D>>> Isometry<N, D, R>
+    where DefaultAllocator: Allocator<N, D> {
     /// Creates a new identity isometry.
     #[inline]
     pub fn identity() -> Self {
-        Self::from_parts(TranslationBase::identity(), R::identity())
+        Self::from_parts(Translation::identity(), R::identity())
+    }
+
+    /// The isometry that applies the rotation `r` with its axis passing through the point `p`.
+    /// This effectively lets `p` invariant.
+    #[inline]
+    pub fn rotation_wrt_point(r: R, p: Point<N, D>) -> Self {
+        let shift = r.transform_vector(&-&p.coords);
+        Self::from_parts(Translation::from_vector(shift + p.coords), r)
     }
 }
 
-impl<N, D: DimName, S, R> One for IsometryBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: AlgaRotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R: AlgaRotation<Point<N, D>>> One for Isometry<N, D, R>
+    where DefaultAllocator: Allocator<N, D> {
     /// Creates a new identity isometry.
     #[inline]
     fn one() -> Self {
@@ -39,37 +43,21 @@ impl<N, D: DimName, S, R> One for IsometryBase<N, D, S, R>
     }
 }
 
-impl<N, D: DimName, S, R> Rand for IsometryBase<N, D, S, R>
-    where N: Real + Rand,
-          S: OwnedStorage<N, D, U1>,
-          R: AlgaRotation<PointBase<N, D, S>> + Rand,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real + Rand, D: DimName, R> Rand for Isometry<N, D, R>
+    where R: AlgaRotation<Point<N, D>> + Rand,
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn rand<G: Rng>(rng: &mut G) -> Self {
         Self::from_parts(rng.gen(), rng.gen())
     }
 }
 
-impl<N, D: DimName, S, R> IsometryBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: AlgaRotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
-    /// The isometry that applies the rotation `r` with its axis passing through the point `p`.
-    /// This effectively lets `p` invariant.
-    #[inline]
-    pub fn rotation_wrt_point(r: R, p: PointBase<N, D, S>) -> Self {
-        let shift = r.transform_vector(&-&p.coords);
-        Self::from_parts(TranslationBase::from_vector(shift + p.coords), r)
-    }
-}
-
 #[cfg(feature = "arbitrary")]
-impl<N, D: DimName, S, R> Arbitrary for IsometryBase<N, D, S, R>
+impl<N, D: DimName, R> Arbitrary for Isometry<N, D, R>
     where N: Real + Arbitrary + Send,
-          S: OwnedStorage<N, D, U1> + Send,
-          R: AlgaRotation<PointBase<N, D, S>> + Arbitrary + Send,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+          R: AlgaRotation<Point<N, D>> + Arbitrary + Send,
+          Owned<N, D>: Send,
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn arbitrary<G: Gen>(rng: &mut G) -> Self {
         Self::from_parts(Arbitrary::arbitrary(rng), Arbitrary::arbitrary(rng))
@@ -83,45 +71,31 @@ impl<N, D: DimName, S, R> Arbitrary for IsometryBase<N, D, S, R>
  */
 
 // 2D rotation.
-impl<N, S, SR> IsometryBase<N, U2, S, RotationBase<N, U2, SR>>
-    where N: Real,
-          S:  OwnedStorage<N, U2, U1, Alloc = SR::Alloc>,
-          SR: OwnedStorage<N, U2, U2>,
-          S::Alloc:  OwnedAllocator<N, U2, U1, S>,
-          SR::Alloc: OwnedAllocator<N, U2, U2, SR> {
+impl<N: Real> Isometry<N, U2, Rotation2<N>> {
     /// Creates a new isometry from a translation and a rotation angle.
     #[inline]
-    pub fn new(translation: ColumnVector<N, U2, S>, angle: N) -> Self {
-        Self::from_parts(TranslationBase::from_vector(translation), RotationBase::<N, U2, SR>::new(angle))
+    pub fn new(translation: Vector2<N>, angle: N) -> Self {
+        Self::from_parts(Translation::from_vector(translation), Rotation::<N, U2>::new(angle))
     }
 }
 
-impl<N, S> IsometryBase<N, U2, S, UnitComplex<N>>
-    where N: Real,
-          S: OwnedStorage<N, U2, U1>,
-          S::Alloc:  OwnedAllocator<N, U2, U1, S> {
+impl<N: Real> Isometry<N, U2, UnitComplex<N>> {
     /// Creates a new isometry from a translation and a rotation angle.
     #[inline]
-    pub fn new(translation: ColumnVector<N, U2, S>, angle: N) -> Self {
-        Self::from_parts(TranslationBase::from_vector(translation), UnitComplex::from_angle(angle))
+    pub fn new(translation: Vector2<N>, angle: N) -> Self {
+        Self::from_parts(Translation::from_vector(translation), UnitComplex::from_angle(angle))
     }
 }
 
 // 3D rotation.
 macro_rules! isometry_construction_impl(
     ($RotId: ident < $($RotParams: ident),*>, $RRDim: ty, $RCDim: ty) => {
-        impl<N, S, SR> IsometryBase<N, U3, S, $RotId<$($RotParams),*>>
-            where N: Real,
-                  S:  OwnedStorage<N, U3, U1, Alloc = SR::Alloc>,
-                  SR: OwnedStorage<N, $RRDim, $RCDim>,
-                  S::Alloc:  OwnedAllocator<N, U3, U1, S>,
-                  SR::Alloc: OwnedAllocator<N, $RRDim, $RCDim, SR> +
-                             Allocator<N, U3, U3> {
+        impl<N: Real> Isometry<N, U3, $RotId<$($RotParams),*>> {
             /// Creates a new isometry from a translation and a rotation axis-angle.
             #[inline]
-            pub fn new(translation: ColumnVector<N, U3, S>, axisangle: ColumnVector<N, U3, S>) -> Self {
+            pub fn new(translation: Vector3<N>, axisangle: Vector3<N>) -> Self {
                 Self::from_parts(
-                    TranslationBase::from_vector(translation),
+                    Translation::from_vector(translation),
                     $RotId::<$($RotParams),*>::from_scaled_axis(axisangle))
             }
 
@@ -137,12 +111,12 @@ macro_rules! isometry_construction_impl(
             ///   * up - Vertical direction. The only requirement of this parameter is to not be collinear
             ///   to `eye - at`. Non-collinearity is not checked.
             #[inline]
-            pub fn new_observer_frame(eye:    &PointBase<N, U3, S>,
-                                      target: &PointBase<N, U3, S>,
-                                      up:     &ColumnVector<N, U3, S>)
+            pub fn new_observer_frame(eye:    &Point3<N>,
+                                      target: &Point3<N>,
+                                      up:     &Vector3<N>)
                                       -> Self {
                 Self::from_parts(
-                    TranslationBase::from_vector(eye.coords.clone()),
+                    Translation::from_vector(eye.coords.clone()),
                     $RotId::new_observer_frame(&(target - eye), up))
             }
 
@@ -157,14 +131,14 @@ macro_rules! isometry_construction_impl(
             ///   * up - A vector approximately aligned with required the vertical axis. The only
             ///   requirement of this parameter is to not be collinear to `target - eye`.
             #[inline]
-            pub fn look_at_rh(eye:    &PointBase<N, U3, S>,
-                              target: &PointBase<N, U3, S>,
-                              up:     &ColumnVector<N, U3, S>)
+            pub fn look_at_rh(eye:    &Point3<N>,
+                              target: &Point3<N>,
+                              up:     &Vector3<N>)
                               -> Self {
                 let rotation = $RotId::look_at_rh(&(target - eye), up);
                 let trans    = &rotation * (-eye);
 
-                Self::from_parts(TranslationBase::from_vector(trans.coords), rotation)
+                Self::from_parts(Translation::from_vector(trans.coords), rotation)
             }
 
             /// Builds a left-handed look-at view matrix.
@@ -178,18 +152,18 @@ macro_rules! isometry_construction_impl(
             ///   * up - A vector approximately aligned with required the vertical axis. The only
             ///   requirement of this parameter is to not be collinear to `target - eye`.
             #[inline]
-            pub fn look_at_lh(eye:    &PointBase<N, U3, S>,
-                              target: &PointBase<N, U3, S>,
-                              up:     &ColumnVector<N, U3, S>)
+            pub fn look_at_lh(eye:    &Point3<N>,
+                              target: &Point3<N>,
+                              up:     &Vector3<N>)
                               -> Self {
                 let rotation = $RotId::look_at_lh(&(target - eye), up);
                 let trans    = &rotation * (-eye);
 
-                Self::from_parts(TranslationBase::from_vector(trans.coords), rotation)
+                Self::from_parts(Translation::from_vector(trans.coords), rotation)
             }
         }
     }
 );
 
-isometry_construction_impl!(RotationBase<N, U3, SR>, U3, U3);
-isometry_construction_impl!(UnitQuaternionBase<N, SR>, U4, U1);
+isometry_construction_impl!(Rotation3<N>, U3, U3);
+isometry_construction_impl!(UnitQuaternion<N>, U4, U1);

src/geometry/isometry_conversion.rs

@@ -1,50 +1,47 @@
 use alga::general::{Real, SubsetOf, SupersetOf};
 use alga::linear::Rotation;
 
-use core::{SquareMatrix, OwnedSquareMatrix};
-use core::dimension::{DimName, DimNameAdd, DimNameSum, U1};
-use core::storage::OwnedStorage;
-use core::allocator::{Allocator, OwnedAllocator};
+use core::{DefaultAllocator, MatrixN};
+use core::dimension::{DimName, DimNameAdd, DimNameSum, DimMin, U1};
+use core::allocator::Allocator;
 
-use geometry::{PointBase, TranslationBase, IsometryBase, SimilarityBase, TransformBase, SuperTCategoryOf, TAffine};
+use geometry::{Point, Translation, Isometry, Similarity, Transform, SuperTCategoryOf, TAffine};
 
 /*
  * This file provides the following conversions:
  * =============================================
  *
- * IsometryBase -> IsometryBase
- * IsometryBase -> SimilarityBase
- * IsometryBase -> TransformBase
- * IsometryBase -> Matrix (homogeneous)
+ * Isometry -> Isometry
+ * Isometry -> Similarity
+ * Isometry -> Transform
+ * Isometry -> Matrix (homogeneous)
  */
 
 
-impl<N1, N2, D: DimName, SA, SB, R1, R2> SubsetOf<IsometryBase<N2, D, SB, R2>> for IsometryBase<N1, D, SA, R1>
+impl<N1, N2, D: DimName, R1, R2> SubsetOf<Isometry<N2, D, R2>> for Isometry<N1, D, R1>
     where N1: Real,
           N2: Real + SupersetOf<N1>,
-          R1: Rotation<PointBase<N1, D, SA>> + SubsetOf<R2>,
-          R2: Rotation<PointBase<N2, D, SB>>,
-          SA: OwnedStorage<N1, D, U1>,
-          SB: OwnedStorage<N2, D, U1>,
-          SA::Alloc: OwnedAllocator<N1, D, U1, SA>,
-          SB::Alloc: OwnedAllocator<N2, D, U1, SB> {
+          R1: Rotation<Point<N1, D>> + SubsetOf<R2>,
+          R2: Rotation<Point<N2, D>>,
+          DefaultAllocator: Allocator<N1, D> +
+                            Allocator<N2, D> {
     #[inline]
-    fn to_superset(&self) -> IsometryBase<N2, D, SB, R2> {
-        IsometryBase::from_parts(
+    fn to_superset(&self) -> Isometry<N2, D, R2> {
+        Isometry::from_parts(
             self.translation.to_superset(),
             self.rotation.to_superset()
         )
     }
 
     #[inline]
-    fn is_in_subset(iso: &IsometryBase<N2, D, SB, R2>) -> bool {
-        ::is_convertible::<_, TranslationBase<N1, D, SA>>(&iso.translation) &&
+    fn is_in_subset(iso: &Isometry<N2, D, R2>) -> bool {
+        ::is_convertible::<_, Translation<N1, D>>(&iso.translation) &&
         ::is_convertible::<_, R1>(&iso.rotation)
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(iso: &IsometryBase<N2, D, SB, R2>) -> Self {
-        IsometryBase::from_parts(
+    unsafe fn from_superset_unchecked(iso: &Isometry<N2, D, R2>) -> Self {
+        Isometry::from_parts(
             iso.translation.to_subset_unchecked(),
             iso.rotation.to_subset_unchecked()
         )
@@ -52,95 +49,91 @@ impl<N1, N2, D: DimName, SA, SB, R1, R2> SubsetOf<IsometryBase<N2, D, SB, R2>> f
 }
 
 
-impl<N1, N2, D: DimName, SA, SB, R1, R2> SubsetOf<SimilarityBase<N2, D, SB, R2>> for IsometryBase<N1, D, SA, R1>
+impl<N1, N2, D: DimName, R1, R2> SubsetOf<Similarity<N2, D, R2>> for Isometry<N1, D, R1>
     where N1: Real,
           N2: Real + SupersetOf<N1>,
-          R1: Rotation<PointBase<N1, D, SA>> + SubsetOf<R2>,
-          R2: Rotation<PointBase<N2, D, SB>>,
-          SA: OwnedStorage<N1, D, U1>,
-          SB: OwnedStorage<N2, D, U1>,
-          SA::Alloc: OwnedAllocator<N1, D, U1, SA>,
-          SB::Alloc: OwnedAllocator<N2, D, U1, SB> {
+          R1: Rotation<Point<N1, D>> + SubsetOf<R2>,
+          R2: Rotation<Point<N2, D>>,
+          DefaultAllocator: Allocator<N1, D> +
+                            Allocator<N2, D> {
     #[inline]
-    fn to_superset(&self) -> SimilarityBase<N2, D, SB, R2> {
-        SimilarityBase::from_isometry(
+    fn to_superset(&self) -> Similarity<N2, D, R2> {
+        Similarity::from_isometry(
             self.to_superset(),
             N2::one()
         )
     }
 
     #[inline]
-    fn is_in_subset(sim: &SimilarityBase<N2, D, SB, R2>) -> bool {
-        ::is_convertible::<_, IsometryBase<N1, D, SA, R1>>(&sim.isometry) &&
+    fn is_in_subset(sim: &Similarity<N2, D, R2>) -> bool {
+        ::is_convertible::<_, Isometry<N1, D, R1>>(&sim.isometry) &&
         sim.scaling() == N2::one()
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(sim: &SimilarityBase<N2, D, SB, R2>) -> Self {
+    unsafe fn from_superset_unchecked(sim: &Similarity<N2, D, R2>) -> Self {
         ::convert_ref_unchecked(&sim.isometry)
     }
 }
 
 
-impl<N1, N2, D, SA, SB, R, C> SubsetOf<TransformBase<N2, D, SB, C>> for IsometryBase<N1, D, SA, R>
+impl<N1, N2, D, R, C> SubsetOf<Transform<N2, D, C>> for Isometry<N1, D, R>
     where N1: Real,
           N2: Real + SupersetOf<N1>,
-          SA: OwnedStorage<N1, D, U1>,
-          SB: OwnedStorage<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>,
           C:  SuperTCategoryOf<TAffine>,
-          R: Rotation<PointBase<N1, D, SA>> +
-             SubsetOf<OwnedSquareMatrix<N1, DimNameSum<D, U1>, SA::Alloc>> + // needed by: .to_homogeneous()
-             SubsetOf<SquareMatrix<N2, DimNameSum<D, U1>, SB>>,              // needed by: ::convert_unchecked(mm)
-          D:  DimNameAdd<U1>,
-          SA::Alloc: OwnedAllocator<N1, D, U1, SA> +
+          R: Rotation<Point<N1, D>> +
+             SubsetOf<MatrixN<N1, DimNameSum<D, U1>>> +
+             SubsetOf<MatrixN<N2, DimNameSum<D, U1>>>,
+          D: DimNameAdd<U1> +
+             DimMin<D, Output = D>, // needed by .is_special_orthogonal()
+          DefaultAllocator: Allocator<N1, D>     +
                             Allocator<N1, D, D>  +                                // needed by R
                             Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>> + // needed by: .to_homogeneous()
-                     Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>,  // needed by R
-          SB::Alloc: OwnedAllocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>, SB> +
-                     Allocator<N2, D, D> +  // needed by: mm.fixed_slice_mut
-                     Allocator<N2, D, U1> + // needed by: m.fixed_slice
-                     Allocator<N2, U1, D> { // needed by: m.fixed_slice
+                            Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>> + // needed by R
+                            Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>> +
+                            Allocator<(usize, usize), D> + // needed by .is_special_orthogonal()
+                            Allocator<N2, D, D> +
+                            Allocator<N2, D>    {
     #[inline]
-    fn to_superset(&self) -> TransformBase<N2, D, SB, C> {
-        TransformBase::from_matrix_unchecked(self.to_homogeneous().to_superset())
+    fn to_superset(&self) -> Transform<N2, D, C> {
+        Transform::from_matrix_unchecked(self.to_homogeneous().to_superset())
     }
 
     #[inline]
-    fn is_in_subset(t: &TransformBase<N2, D, SB, C>) -> bool {
+    fn is_in_subset(t: &Transform<N2, D, C>) -> bool {
         <Self as SubsetOf<_>>::is_in_subset(t.matrix())
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(t: &TransformBase<N2, D, SB, C>) -> Self {
+    unsafe fn from_superset_unchecked(t: &Transform<N2, D, C>) -> Self {
         Self::from_superset_unchecked(t.matrix())
     }
 }
 
 
-impl<N1, N2, D, SA, SB, R> SubsetOf<SquareMatrix<N2, DimNameSum<D, U1>, SB>> for IsometryBase<N1, D, SA, R>
+impl<N1, N2, D, R> SubsetOf<MatrixN<N2, DimNameSum<D, U1>>> for Isometry<N1, D, R>
     where N1: Real,
           N2: Real + SupersetOf<N1>,
-          SA: OwnedStorage<N1, D, U1>,
-          SB: OwnedStorage<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>,
-          R: Rotation<PointBase<N1, D, SA>> +
-             SubsetOf<OwnedSquareMatrix<N1, DimNameSum<D, U1>, SA::Alloc>> + // needed by: .to_homogeneous()
-             SubsetOf<SquareMatrix<N2, DimNameSum<D, U1>, SB>>,              // needed by: ::convert_unchecked(mm)
-          D:  DimNameAdd<U1>,
-          SA::Alloc: OwnedAllocator<N1, D, U1, SA> +
+          R: Rotation<Point<N1, D>> +
+             SubsetOf<MatrixN<N1, DimNameSum<D, U1>>> +
+             SubsetOf<MatrixN<N2, DimNameSum<D, U1>>>,
+          D: DimNameAdd<U1> +
+             DimMin<D, Output = D>, // needed by .is_special_orthogonal()
+          DefaultAllocator: Allocator<N1, D>     +
                             Allocator<N1, D, D>  +                                // needed by R
                             Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>> + // needed by: .to_homogeneous()
-                     Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>,  // needed by R
-          SB::Alloc: OwnedAllocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>, SB> +
-                     Allocator<N2, D, D> +  // needed by: mm.fixed_slice_mut
-                     Allocator<N2, D, U1> + // needed by: m.fixed_slice
-                     Allocator<N2, U1, D> { // needed by: m.fixed_slice
+                            Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>> + // needed by R
+                            Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>> +
+                            Allocator<(usize, usize), D> + // needed by .is_special_orthogonal()
+                            Allocator<N2, D, D> +
+                            Allocator<N2, D>    {
     #[inline]
-    fn to_superset(&self) -> SquareMatrix<N2, DimNameSum<D, U1>, SB> {
+    fn to_superset(&self) -> MatrixN<N2, DimNameSum<D, U1>> {
         self.to_homogeneous().to_superset()
     }
 
     #[inline]
-    fn is_in_subset(m: &SquareMatrix<N2, DimNameSum<D, U1>, SB>) -> bool {
+    fn is_in_subset(m: &MatrixN<N2, DimNameSum<D, U1>>) -> bool {
         let rot    = m.fixed_slice::<D, D>(0, 0);
         let bottom = m.fixed_slice::<U1, D>(D::dim(), 0);
 
@@ -154,9 +147,9 @@ impl<N1, N2, D, SA, SB, R> SubsetOf<SquareMatrix<N2, DimNameSum<D, U1>, SB>> for
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(m: &SquareMatrix<N2, DimNameSum<D, U1>, SB>) -> Self {
+    unsafe fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self {
         let t = m.fixed_slice::<D, U1>(0, D::dim()).into_owned();
-        let t = TranslationBase::from_vector(::convert_unchecked(t));
+        let t = Translation::from_vector(::convert_unchecked(t));
 
         Self::from_parts(t, ::convert_unchecked(m.clone_owned()))
     }

src/geometry/isometry_ops.rs

@@ -1,14 +1,13 @@
 use std::ops::{Mul, MulAssign, Div, DivAssign};
 
 use alga::general::Real;
-use alga::linear::Rotation;
+use alga::linear::Rotation as AlgaRotation;
 
-use core::ColumnVector;
+use core::{DefaultAllocator, VectorN};
 use core::dimension::{DimName, U1, U3, U4};
-use core::storage::OwnedStorage;
-use core::allocator::OwnedAllocator;
+use core::allocator::Allocator;
 
-use geometry::{PointBase, RotationBase, IsometryBase, TranslationBase, UnitQuaternionBase};
+use geometry::{Point, Rotation, Isometry, Translation, UnitQuaternion};
 
 // FIXME: there are several cloning of rotations that we could probably get rid of (but we didn't
 // yet because that would require to add a bound like `where for<'a, 'b> &'a R: Mul<&'b R, Output = R>`
@@ -22,41 +21,41 @@ use geometry::{PointBase, RotationBase, IsometryBase, TranslationBase, UnitQuate
  *
  * (Operators)
  *
- * IsometryBase × IsometryBase
- * IsometryBase × R
+ * Isometry × Isometry
+ * Isometry × R
  *
  *
- * IsometryBase ÷ IsometryBase
- * IsometryBase ÷ R
+ * Isometry ÷ Isometry
+ * Isometry ÷ R
  *
- * IsometryBase × PointBase
- * IsometryBase × ColumnVector
+ * Isometry × Point
+ * Isometry × Vector
  *
  *
- * IsometryBase    × TranslationBase
- * TranslationBase × IsometryBase
- * TranslationBase × R           -> IsometryBase<R>
+ * Isometry    × Translation
+ * Translation × Isometry
+ * Translation × R           -> Isometry<R>
  *
- * NOTE: The following are provided explicitly because we can't have R × IsometryBase.
- * RotationBase   × IsometryBase<RotationBase>
- * UnitQuaternion × IsometryBase<UnitQuaternion>
+ * NOTE: The following are provided explicitly because we can't have R × Isometry.
+ * Rotation       × Isometry<Rotation>
+ * UnitQuaternion × Isometry<UnitQuaternion>
  *
- * RotationBase   ÷ IsometryBase<RotationBase>
- * UnitQuaternion ÷ IsometryBase<UnitQuaternion>
+ * Rotation       ÷ Isometry<Rotation>
+ * UnitQuaternion ÷ Isometry<UnitQuaternion>
  *
- * RotationBase   × TranslationBase -> IsometryBase<RotationBase>
- * UnitQuaternion × TranslationBase -> IsometryBase<UnitQuaternion>
+ * Rotation       × Translation -> Isometry<Rotation>
+ * UnitQuaternion × Translation -> Isometry<UnitQuaternion>
  *
  *
  * (Assignment Operators)
  *
- * IsometryBase ×= TranslationBase
+ * Isometry ×= Translation
  *
- * IsometryBase ×= IsometryBase
- * IsometryBase ×= R
+ * Isometry ×= Isometry
+ * Isometry ×= R
  *
- * IsometryBase ÷= IsometryBase
- * IsometryBase ÷= R
+ * Isometry ÷= Isometry
+ * Isometry ÷= R
  *
  */
 
@@ -65,11 +64,9 @@ macro_rules! isometry_binop_impl(
     ($Op: ident, $op: ident;
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Output: ty;
      $action: expr; $($lives: tt),*) => {
-        impl<$($lives ,)* N, D: DimName, S, R> $Op<$Rhs> for $Lhs
-            where N: Real,
-                  S: OwnedStorage<N, D, U1>,
-                  R: Rotation<PointBase<N, D, S>>,
-                  S::Alloc: OwnedAllocator<N, D, U1, S> {
+        impl<$($lives ,)* N: Real, D: DimName, R> $Op<$Rhs> for $Lhs
+            where R: AlgaRotation<Point<N, D>>,
+                  DefaultAllocator: Allocator<N, D> {
             type Output = $Output;
 
             #[inline]
@@ -114,22 +111,18 @@ macro_rules! isometry_binop_assign_impl_all(
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty;
      [val] => $action_val: expr;
      [ref] => $action_ref: expr;) => {
-        impl<N, D: DimName, S, R> $OpAssign<$Rhs> for $Lhs
-            where N: Real,
-                  S: OwnedStorage<N, D, U1>,
-                  R: Rotation<PointBase<N, D, S>>,
-                  S::Alloc: OwnedAllocator<N, D, U1, S> {
+        impl<N: Real, D: DimName, R> $OpAssign<$Rhs> for $Lhs
+            where R: AlgaRotation<Point<N, D>>,
+                  DefaultAllocator: Allocator<N, D> {
             #[inline]
             fn $op_assign(&mut $lhs, $rhs: $Rhs) {
                 $action_val
             }
         }
 
-        impl<'b, N, D: DimName, S, R> $OpAssign<&'b $Rhs> for $Lhs
-            where N: Real,
-                  S: OwnedStorage<N, D, U1>,
-                  R: Rotation<PointBase<N, D, S>>,
-                  S::Alloc: OwnedAllocator<N, D, U1, S> {
+        impl<'b, N: Real, D: DimName, R> $OpAssign<&'b $Rhs> for $Lhs
+            where R: AlgaRotation<Point<N, D>>,
+                  DefaultAllocator: Allocator<N, D> {
             #[inline]
             fn $op_assign(&mut $lhs, $rhs: &'b $Rhs) {
                 $action_ref
@@ -138,18 +131,18 @@ macro_rules! isometry_binop_assign_impl_all(
     }
 );
 
-// IsometryBase × IsometryBase
-// IsometryBase ÷ IsometryBase
+// Isometry × Isometry
+// Isometry ÷ Isometry
 isometry_binop_impl_all!(
     Mul, mul;
-    self: IsometryBase<N, D, S, R>, rhs: IsometryBase<N, D, S, R>, Output = IsometryBase<N, D, S, R>;
+    self: Isometry<N, D, R>, rhs: Isometry<N, D, R>, Output = Isometry<N, D, R>;
     [val val] => &self * &rhs;
     [ref val] => self * &rhs;
     [val ref] => &self * rhs;
     [ref ref] => {
         let shift = self.rotation.transform_vector(&rhs.translation.vector);
 
-        IsometryBase::from_parts(TranslationBase::from_vector(&self.translation.vector + shift),
+        Isometry::from_parts(Translation::from_vector(&self.translation.vector + shift),
                              self.rotation.clone() * rhs.rotation.clone()) // FIXME: too bad we have to clone.
     };
 );
@@ -157,7 +150,7 @@ isometry_binop_impl_all!(
 
 isometry_binop_impl_all!(
     Div, div;
-    self: IsometryBase<N, D, S, R>, rhs: IsometryBase<N, D, S, R>, Output = IsometryBase<N, D, S, R>;
+    self: Isometry<N, D, R>, rhs: Isometry<N, D, R>, Output = Isometry<N, D, R>;
     [val val] => self * rhs.inverse();
     [ref val] => self * rhs.inverse();
     [val ref] => self * rhs.inverse();
@@ -165,10 +158,10 @@ isometry_binop_impl_all!(
 );
 
 
-// IsometryBase ×= TranslationBase
+// Isometry ×= Translation
 isometry_binop_assign_impl_all!(
     MulAssign, mul_assign;
-    self: IsometryBase<N, D, S, R>, rhs: TranslationBase<N, D, S>;
+    self: Isometry<N, D, R>, rhs: Translation<N, D>;
     [val] => *self *= &rhs;
     [ref] => {
         let shift = self.rotation.transform_vector(&rhs.vector);
@@ -176,11 +169,11 @@ isometry_binop_assign_impl_all!(
     };
 );
 
-// IsometryBase ×= IsometryBase
-// IsometryBase ÷= IsometryBase
+// Isometry ×= Isometry
+// Isometry ÷= Isometry
 isometry_binop_assign_impl_all!(
     MulAssign, mul_assign;
-    self: IsometryBase<N, D, S, R>, rhs: IsometryBase<N, D, S, R>;
+    self: Isometry<N, D, R>, rhs: Isometry<N, D, R>;
     [val] => *self *= &rhs;
     [ref] => {
         let shift = self.rotation.transform_vector(&rhs.translation.vector);
@@ -191,55 +184,55 @@ isometry_binop_assign_impl_all!(
 
 isometry_binop_assign_impl_all!(
     DivAssign, div_assign;
-    self: IsometryBase<N, D, S, R>, rhs: IsometryBase<N, D, S, R>;
+    self: Isometry<N, D, R>, rhs: Isometry<N, D, R>;
     [val] => *self /= &rhs;
     [ref] => *self *= rhs.inverse();
 );
 
-// IsometryBase ×= R
-// IsometryBase ÷= R
+// Isometry ×= R
+// Isometry ÷= R
 isometry_binop_assign_impl_all!(
     MulAssign, mul_assign;
-    self: IsometryBase<N, D, S, R>, rhs: R;
+    self: Isometry<N, D, R>, rhs: R;
     [val] => self.rotation *= rhs;
     [ref] => self.rotation *= rhs.clone();
 );
 
 isometry_binop_assign_impl_all!(
     DivAssign, div_assign;
-    self: IsometryBase<N, D, S, R>, rhs: R;
+    self: Isometry<N, D, R>, rhs: R;
     // FIXME: don't invert explicitly?
     [val] => *self *= rhs.inverse();
     [ref] => *self *= rhs.inverse();
 );
 
 
-// IsometryBase × R
-// IsometryBase ÷ R
+// Isometry × R
+// Isometry ÷ R
 isometry_binop_impl_all!(
     Mul, mul;
-    self: IsometryBase<N, D, S, R>, rhs: R, Output = IsometryBase<N, D, S, R>;
-    [val val] => IsometryBase::from_parts(self.translation, self.rotation * rhs);
-    [ref val] => IsometryBase::from_parts(self.translation.clone(), self.rotation.clone() * rhs); // FIXME: do not clone.
-    [val ref] => IsometryBase::from_parts(self.translation, self.rotation * rhs.clone());
-    [ref ref] => IsometryBase::from_parts(self.translation.clone(), self.rotation.clone() * rhs.clone());
+    self: Isometry<N, D, R>, rhs: R, Output = Isometry<N, D, R>;
+    [val val] => Isometry::from_parts(self.translation, self.rotation * rhs);
+    [ref val] => Isometry::from_parts(self.translation.clone(), self.rotation.clone() * rhs); // FIXME: do not clone.
+    [val ref] => Isometry::from_parts(self.translation, self.rotation * rhs.clone());
+    [ref ref] => Isometry::from_parts(self.translation.clone(), self.rotation.clone() * rhs.clone());
 );
 
 
 isometry_binop_impl_all!(
     Div, div;
-    self: IsometryBase<N, D, S, R>, rhs: R, Output = IsometryBase<N, D, S, R>;
-    [val val] => IsometryBase::from_parts(self.translation, self.rotation / rhs);
-    [ref val] => IsometryBase::from_parts(self.translation.clone(), self.rotation.clone() / rhs);
-    [val ref] => IsometryBase::from_parts(self.translation, self.rotation / rhs.clone());
-    [ref ref] => IsometryBase::from_parts(self.translation.clone(), self.rotation.clone() / rhs.clone());
+    self: Isometry<N, D, R>, rhs: R, Output = Isometry<N, D, R>;
+    [val val] => Isometry::from_parts(self.translation, self.rotation / rhs);
+    [ref val] => Isometry::from_parts(self.translation.clone(), self.rotation.clone() / rhs);
+    [val ref] => Isometry::from_parts(self.translation, self.rotation / rhs.clone());
+    [ref ref] => Isometry::from_parts(self.translation.clone(), self.rotation.clone() / rhs.clone());
 );
 
 
-// IsometryBase × PointBase
+// Isometry × Point
 isometry_binop_impl_all!(
     Mul, mul;
-    self: IsometryBase<N, D, S, R>, right: PointBase<N, D, S>, Output = PointBase<N, D, S>;
+    self: Isometry<N, D, R>, right: Point<N, D>, Output = Point<N, D>;
     [val val] => self.translation  * self.rotation.transform_point(&right);
     [ref val] => &self.translation * self.rotation.transform_point(&right);
     [val ref] => self.translation  * self.rotation.transform_point(right);
@@ -247,10 +240,12 @@ isometry_binop_impl_all!(
 );
 
 
-// IsometryBase × Vector
+// Isometry × Vector
 isometry_binop_impl_all!(
     Mul, mul;
-    self: IsometryBase<N, D, S, R>, right: ColumnVector<N, D, S>, Output = ColumnVector<N, D, S>;
+    // FIXME: because of `transform_vector`, we cant use a generic storage type for the rhs vector,
+    // i.e., right: Vector<N, D, S> where S: Storage<N, D>.
+    self: Isometry<N, D, R>, right: VectorN<N, D>, Output = VectorN<N, D>;
     [val val] => self.rotation.transform_vector(&right);
     [ref val] => self.rotation.transform_vector(&right);
     [val ref] => self.rotation.transform_vector(right);
@@ -258,38 +253,38 @@ isometry_binop_impl_all!(
 );
 
 
-// IsometryBase × TranslationBase
+// Isometry × Translation
 isometry_binop_impl_all!(
     Mul, mul;
-    self: IsometryBase<N, D, S, R>, right: TranslationBase<N, D, S>, Output = IsometryBase<N, D, S, R>;
+    self: Isometry<N, D, R>, right: Translation<N, D>, Output = Isometry<N, D, R>;
     [val val] => &self * &right;
     [ref val] => self * &right;
     [val ref] => &self * right;
     [ref ref] => {
         let new_tr = &self.translation.vector + self.rotation.transform_vector(&right.vector);
-        IsometryBase::from_parts(TranslationBase::from_vector(new_tr), self.rotation.clone())
+        Isometry::from_parts(Translation::from_vector(new_tr), self.rotation.clone())
     };
 );
 
-// TranslationBase × IsometryBase
+// Translation × Isometry
 isometry_binop_impl_all!(
     Mul, mul;
-    self: TranslationBase<N, D, S>, right: IsometryBase<N, D, S, R>, Output = IsometryBase<N, D, S, R>;
-    [val val] => IsometryBase::from_parts(self * right.translation, right.rotation);
-    [ref val] => IsometryBase::from_parts(self * &right.translation, right.rotation);
-    [val ref] => IsometryBase::from_parts(self * &right.translation, right.rotation.clone());
-    [ref ref] => IsometryBase::from_parts(self * &right.translation, right.rotation.clone());
+    self: Translation<N, D>, right: Isometry<N, D, R>, Output = Isometry<N, D, R>;
+    [val val] => Isometry::from_parts(self * right.translation, right.rotation);
+    [ref val] => Isometry::from_parts(self * &right.translation, right.rotation);
+    [val ref] => Isometry::from_parts(self * &right.translation, right.rotation.clone());
+    [ref ref] => Isometry::from_parts(self * &right.translation, right.rotation.clone());
 );
 
 
-// TranslationBase × R
+// Translation × R
 isometry_binop_impl_all!(
     Mul, mul;
-    self: TranslationBase<N, D, S>, right: R, Output = IsometryBase<N, D, S, R>;
-    [val val] => IsometryBase::from_parts(self, right);
-    [ref val] => IsometryBase::from_parts(self.clone(), right);
-    [val ref] => IsometryBase::from_parts(self, right.clone());
-    [ref ref] => IsometryBase::from_parts(self.clone(), right.clone());
+    self: Translation<N, D>, right: R, Output = Isometry<N, D, R>;
+    [val val] => Isometry::from_parts(self, right);
+    [ref val] => Isometry::from_parts(self.clone(), right);
+    [val ref] => Isometry::from_parts(self, right.clone());
+    [ref ref] => Isometry::from_parts(self.clone(), right.clone());
 );
 
 
@@ -300,12 +295,9 @@ macro_rules! isometry_from_composition_impl(
      ($R1: ty, $C1: ty),($R2: ty, $C2: ty) $(for $Dims: ident: $DimsBound: ident),*;
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Output: ty;
      $action: expr; $($lives: tt),*) => {
-        impl<$($lives ,)* N $(, $Dims: $DimsBound)*, SA, SB> $Op<$Rhs> for $Lhs
-            where N: Real,
-                  SA: OwnedStorage<N, $R1, $C1>,
-                  SB: OwnedStorage<N, $R2, $C2, Alloc = SA::Alloc>,
-                  SA::Alloc: OwnedAllocator<N, $R1, $C1, SA>,
-                  SB::Alloc: OwnedAllocator<N, $R2, $C2, SB> {
+        impl<$($lives ,)* N: Real $(, $Dims: $DimsBound)*> $Op<$Rhs> for $Lhs
+            where DefaultAllocator: Allocator<N, $R1, $C1> +
+                                    Allocator<N, $R2, $C2> {
             type Output = $Output;
 
             #[inline]
@@ -352,51 +344,51 @@ macro_rules! isometry_from_composition_impl_all(
 );
 
 
-// RotationBase × TranslationBase
+// Rotation × Translation
 isometry_from_composition_impl_all!(
     Mul, mul;
     (D, D), (D, U1) for D: DimName;
-    self: RotationBase<N, D, SA>, right: TranslationBase<N, D, SB>, Output = IsometryBase<N, D, SB, RotationBase<N, D, SA>>;
-    [val val] => IsometryBase::from_parts(TranslationBase::from_vector(&self * right.vector),  self);
-    [ref val] => IsometryBase::from_parts(TranslationBase::from_vector(self * right.vector),   self.clone());
-    [val ref] => IsometryBase::from_parts(TranslationBase::from_vector(&self * &right.vector), self);
-    [ref ref] => IsometryBase::from_parts(TranslationBase::from_vector(self * &right.vector),  self.clone());
+    self: Rotation<N, D>, right: Translation<N, D>, Output = Isometry<N, D, Rotation<N, D>>;
+    [val val] => Isometry::from_parts(Translation::from_vector(&self * right.vector),  self);
+    [ref val] => Isometry::from_parts(Translation::from_vector(self * right.vector),   self.clone());
+    [val ref] => Isometry::from_parts(Translation::from_vector(&self * &right.vector), self);
+    [ref ref] => Isometry::from_parts(Translation::from_vector(self * &right.vector),  self.clone());
 );
 
 
-// UnitQuaternionBase × TranslationBase
+// UnitQuaternion × Translation
 isometry_from_composition_impl_all!(
     Mul, mul;
     (U4, U1), (U3, U1);
-    self: UnitQuaternionBase<N, SA>, right: TranslationBase<N, U3, SB>,
-    Output = IsometryBase<N, U3, SB, UnitQuaternionBase<N, SA>>;
-    [val val] => IsometryBase::from_parts(TranslationBase::from_vector(&self *  right.vector), self);
-    [ref val] => IsometryBase::from_parts(TranslationBase::from_vector( self *  right.vector), self.clone());
-    [val ref] => IsometryBase::from_parts(TranslationBase::from_vector(&self * &right.vector), self);
-    [ref ref] => IsometryBase::from_parts(TranslationBase::from_vector( self * &right.vector), self.clone());
+    self: UnitQuaternion<N>, right: Translation<N, U3>,
+    Output = Isometry<N, U3, UnitQuaternion<N>>;
+    [val val] => Isometry::from_parts(Translation::from_vector(&self *  right.vector), self);
+    [ref val] => Isometry::from_parts(Translation::from_vector( self *  right.vector), self.clone());
+    [val ref] => Isometry::from_parts(Translation::from_vector(&self * &right.vector), self);
+    [ref ref] => Isometry::from_parts(Translation::from_vector( self * &right.vector), self.clone());
 );
 
-// RotationBase × IsometryBase
+// Rotation × Isometry
 isometry_from_composition_impl_all!(
     Mul, mul;
     (D, D), (D, U1) for D: DimName;
-    self: RotationBase<N, D, SA>, right: IsometryBase<N, D, SB, RotationBase<N, D, SA>>,
-    Output = IsometryBase<N, D, SB, RotationBase<N, D, SA>>;
+    self: Rotation<N, D>, right: Isometry<N, D, Rotation<N, D>>,
+    Output = Isometry<N, D, Rotation<N, D>>;
     [val val] => &self * &right;
     [ref val] =>  self * &right;
     [val ref] => &self * right;
     [ref ref] => {
         let shift = self * &right.translation.vector;
-        IsometryBase::from_parts(TranslationBase::from_vector(shift), self * &right.rotation)
+        Isometry::from_parts(Translation::from_vector(shift), self * &right.rotation)
     };
 );
 
-// RotationBase ÷ IsometryBase
+// Rotation ÷ Isometry
 isometry_from_composition_impl_all!(
     Div, div;
     (D, D), (D, U1) for D: DimName;
-    self: RotationBase<N, D, SA>, right: IsometryBase<N, D, SB, RotationBase<N, D, SA>>,
-    Output = IsometryBase<N, D, SB, RotationBase<N, D, SA>>;
+    self: Rotation<N, D>, right: Isometry<N, D, Rotation<N, D>>,
+    Output = Isometry<N, D, Rotation<N, D>>;
     // FIXME: don't call iverse explicitly?
     [val val] => self * right.inverse();
     [ref val] => self * right.inverse();
@@ -405,28 +397,28 @@ isometry_from_composition_impl_all!(
 );
 
 
-// UnitQuaternion × IsometryBase
+// UnitQuaternion × Isometry
 isometry_from_composition_impl_all!(
     Mul, mul;
     (U4, U1), (U3, U1);
-    self: UnitQuaternionBase<N, SA>, right: IsometryBase<N, U3, SB, UnitQuaternionBase<N, SA>>,
-    Output = IsometryBase<N, U3, SB, UnitQuaternionBase<N, SA>>;
+    self: UnitQuaternion<N>, right: Isometry<N, U3, UnitQuaternion<N>>,
+    Output = Isometry<N, U3, UnitQuaternion<N>>;
     [val val] => &self * &right;
     [ref val] =>  self * &right;
     [val ref] => &self * right;
     [ref ref] => {
         let shift = self * &right.translation.vector;
-        IsometryBase::from_parts(TranslationBase::from_vector(shift), self * &right.rotation)
+        Isometry::from_parts(Translation::from_vector(shift), self * &right.rotation)
     };
 );
 
 
-// UnitQuaternion ÷ IsometryBase
+// UnitQuaternion ÷ Isometry
 isometry_from_composition_impl_all!(
     Div, div;
     (U4, U1), (U3, U1);
-    self: UnitQuaternionBase<N, SA>, right: IsometryBase<N, U3, SB, UnitQuaternionBase<N, SA>>,
-    Output = IsometryBase<N, U3, SB, UnitQuaternionBase<N, SA>>;
+    self: UnitQuaternion<N>, right: Isometry<N, U3, UnitQuaternion<N>>,
+    Output = Isometry<N, U3, UnitQuaternion<N>>;
     // FIXME: don't call inverse explicitly?
     [val val] => self * right.inverse();
     [ref val] => self * right.inverse();

src/geometry/mod.rs

@@ -14,7 +14,7 @@ mod point_coordinates;
 mod rotation;
 mod rotation_construction;
 mod rotation_ops;
-mod rotation_alga; // FIXME: implement RotationBase methods.
+mod rotation_alga; // FIXME: implement Rotation methods.
 mod rotation_conversion;
 mod rotation_alias;
 mod rotation_specialization;
@@ -23,9 +23,8 @@ mod quaternion;
 mod quaternion_construction;
 mod quaternion_ops;
 mod quaternion_alga;
-mod quaternion_alias;
-mod quaternion_coordinates;
 mod quaternion_conversion;
+mod quaternion_coordinates;
 
 mod unit_complex;
 mod unit_complex_construction;
@@ -61,6 +60,8 @@ mod transform_alga;
 mod transform_conversion;
 mod transform_alias;
 
+mod reflection;
+
 mod orthographic;
 mod perspective;
 
@@ -71,7 +72,6 @@ pub use self::rotation::*;
 pub use self::rotation_alias::*;
 
 pub use self::quaternion::*;
-pub use self::quaternion_alias::*;
 
 pub use self::unit_complex::*;
 
@@ -87,5 +87,7 @@ pub use self::similarity_alias::*;
 pub use self::transform::*;
 pub use self::transform_alias::*;
 
-pub use self::orthographic::{OrthographicBase, Orthographic3};
-pub use self::perspective::{PerspectiveBase, Perspective3};
+pub use self::reflection::*;
+
+pub use self::orthographic::Orthographic3;
+pub use self::perspective::Perspective3;

src/geometry/op_macros.rs

@@ -8,7 +8,7 @@ macro_rules! md_impl(
     // Operator, operator method, and calar bounds.
      $Op: ident, $op: ident $(where N: $($ScalarBounds: ident),*)*;
      // Storage dimensions, and dimension bounds.
-     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) for $($Dims: ident: $DimsBound: ident $(<$BoundParam: ty>)*),+
+     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) for $($Dims: ident: $DimsBound: ident $(<$($BoundParam: ty),*>)*),+
      // [Optional] Extra allocator bounds.
      $(where $ConstraintType: ty: $ConstraintBound: ident<$($ConstraintBoundParams: ty $( = $EqBound: ty )*),*> )*;
      // Argument identifiers and types + output.
@@ -17,10 +17,11 @@ macro_rules! md_impl(
      $action: expr;
      // Lifetime.
      $($lives: tt),*) => {
-        impl<$($lives ,)* N $(, $Dims: $DimsBound $(<$BoundParam>)*)*, SA, SB> $Op<$Rhs> for $Lhs
-            where N:  Scalar + Zero + ClosedAdd + ClosedMul $($(+ $ScalarBounds)*)*,
-                  SA: Storage<N, $R1, $C1>,
-                  SB: Storage<N, $R2, $C2>,
+        impl<$($lives ,)* N $(, $Dims: $DimsBound $(<$($BoundParam),*>)*)*> $Op<$Rhs> for $Lhs
+            where N: Scalar + Zero + One + ClosedAdd + ClosedMul $($(+ $ScalarBounds)*)*,
+                  DefaultAllocator: Allocator<N, $R1, $C1> +
+                                    Allocator<N, $R2, $C2> +
+                                    Allocator<N, $R1, $C2>,
                   $( $ConstraintType: $ConstraintBound<$( $ConstraintBoundParams $( = $EqBound )*),*> ),*
                    {
             type Output = $Result;
@@ -41,7 +42,7 @@ macro_rules! md_impl_all(
      // Operator, operator method, and calar bounds.
      $Op: ident, $op: ident $(where N: $($ScalarBounds: ident),*)*;
      // Storage dimensions, and dimension bounds.
-     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) for $($Dims: ident: $DimsBound: ident $(<$BoundParam: ty>)*),+
+     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) for $($Dims: ident: $DimsBound: ident $(<$($BoundParam: ty),*>)*),+
      // [Optional] Extra allocator bounds.
      $(where $ConstraintType: ty: $ConstraintBound: ident<$($ConstraintBoundParams: ty $( = $EqBound: ty )*),*> )*;
      // Argument identifiers and types + output.
@@ -54,28 +55,28 @@ macro_rules! md_impl_all(
 
         md_impl!(
             $Op, $op $(where N: $($ScalarBounds),*)*;
-            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$BoundParam>)*),+
+            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$($BoundParam),*>)*),+
             $(where $ConstraintType: $ConstraintBound<$($ConstraintBoundParams $( = $EqBound )*),*>)*;
             $lhs: $Lhs, $rhs: $Rhs, Output = $Result;
             $action_val_val; );
 
         md_impl!(
             $Op, $op $(where N: $($ScalarBounds),*)*;
-            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$BoundParam>)*),+
+            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$($BoundParam),*>)*),+
             $(where $ConstraintType: $ConstraintBound<$($ConstraintBoundParams $( = $EqBound )*),*>)*;
             $lhs: &'a $Lhs, $rhs: $Rhs, Output = $Result;
             $action_ref_val; 'a);
 
         md_impl!(
             $Op, $op $(where N: $($ScalarBounds),*)*;
-            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$BoundParam>)*),+
+            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$($BoundParam),*>)*),+
             $(where $ConstraintType: $ConstraintBound<$($ConstraintBoundParams $( = $EqBound )*),*>)*;
             $lhs: $Lhs, $rhs: &'b $Rhs, Output = $Result;
             $action_val_ref; 'b);
 
         md_impl!(
             $Op, $op $(where N: $($ScalarBounds),*)*;
-            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$BoundParam>)*),+
+            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$($BoundParam),*>)*),+
             $(where $ConstraintType: $ConstraintBound<$($ConstraintBoundParams $( = $EqBound )*),*>)*;
             $lhs: &'a $Lhs, $rhs: &'b $Rhs, Output = $Result;
             $action_ref_ref; 'a, 'b);
@@ -89,19 +90,18 @@ macro_rules! md_assign_impl(
      // Operator, operator method, and scalar bounds.
      $Op: ident, $op: ident $(where N: $($ScalarBounds: ident),*)*;
      // Storage dimensions, and dimension bounds.
-     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) for $($Dims: ident: $DimsBound: ident $(<$BoundParam: ty>)*),+
+     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) for $($Dims: ident: $DimsBound: ident $(<$($BoundParam: ty),*>)*),+
      // [Optional] Extra allocator bounds.
-     $(where $ConstraintType: ty: $ConstraintBound: ident<$($ConstraintBoundParams: ty $( = $EqBound: ty )*),*> )*;
+     $(where $ConstraintType: ty: $ConstraintBound: ident $(<$($ConstraintBoundParams: ty $( = $EqBound: ty )*),*>)* )*;
      // Argument identifiers and types.
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty;
      // Actual implementation and lifetimes.
      $action: expr; $($lives: tt),*) => {
-        impl<$($lives ,)* N $(, $Dims: $DimsBound $(<$BoundParam>)*)*, SA, SB> $Op<$Rhs> for $Lhs
-            where N:  Scalar + Zero + ClosedAdd + ClosedMul $($(+ $ScalarBounds)*)*,
-                  SA: OwnedStorage<N, $R1, $C1>, // FIXME: this is too restrictive.
-                  SB: Storage<N, $R2, $C2>,
-                  SA::Alloc: OwnedAllocator<N, $R1, $C1, SA>,
-                  $( $ConstraintType: $ConstraintBound<$( $ConstraintBoundParams $( = $EqBound )*),*> ),*
+        impl<$($lives ,)* N $(, $Dims: $DimsBound $(<$($BoundParam),*>)*)*> $Op<$Rhs> for $Lhs
+            where N:  Scalar + Zero + One + ClosedAdd + ClosedMul $($(+ $ScalarBounds)*)*,
+                  DefaultAllocator: Allocator<N, $R1, $C1> +
+                                    Allocator<N, $R2, $C2>,
+                  $( $ConstraintType: $ConstraintBound $(<$( $ConstraintBoundParams $( = $EqBound )*),*>)* ),*
         {
             #[inline]
             fn $op(&mut $lhs, $rhs: $Rhs) {
@@ -118,9 +118,9 @@ macro_rules! md_assign_impl_all(
      // Operator, operator method, and scalar bounds.
      $Op: ident, $op: ident $(where N: $($ScalarBounds: ident),*)*;
      // Storage dimensions, and dimension bounds.
-     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) for $($Dims: ident: $DimsBound: ident $(<$BoundParam: ty>)*),+
+     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) for $($Dims: ident: $DimsBound: ident $(<$($BoundParam: ty),*>)*),+
      // [Optional] Extra allocator bounds.
-     $(where $ConstraintType: ty: $ConstraintBound: ident<$($ConstraintBoundParams: ty $( = $EqBound: ty )*),*> )*;
+     $(where $ConstraintType: ty: $ConstraintBound: ident$(<$($ConstraintBoundParams: ty $( = $EqBound: ty )*),*>)* )*;
      // Argument identifiers and types.
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty;
      // Actual implementation and lifetimes.
@@ -128,15 +128,15 @@ macro_rules! md_assign_impl_all(
      [ref] => $action_ref: expr;) => {
         md_assign_impl!(
             $Op, $op $(where N: $($ScalarBounds),*)*;
-            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$BoundParam>)*),+
-            $(where $ConstraintType: $ConstraintBound<$($ConstraintBoundParams $( = $EqBound )*),*>)*;
+            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$($BoundParam),*>)*),+
+            $(where $ConstraintType: $ConstraintBound $(<$($ConstraintBoundParams $( = $EqBound )*),*>)*)*;
             $lhs: $Lhs, $rhs: $Rhs;
             $action_val; );
 
         md_assign_impl!(
             $Op, $op $(where N: $($ScalarBounds),*)*;
-            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$BoundParam>)*),+
-            $(where $ConstraintType: $ConstraintBound<$($ConstraintBoundParams $( = $EqBound )*),*>)*;
+            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$($BoundParam),*>)*),+
+            $(where $ConstraintType: $ConstraintBound $(<$($ConstraintBoundParams $( = $EqBound )*),*>)*)*;
             $lhs: $Lhs, $rhs: &'b $Rhs;
             $action_ref; 'b);
     }
@@ -146,14 +146,14 @@ macro_rules! md_assign_impl_all(
 /// Macro for the implementation of addition and subtraction.
 macro_rules! add_sub_impl(
     ($Op: ident, $op: ident, $bound: ident;
-     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) $(-> ($RRes: ty))* for $($Dims: ident: $DimsBound: ident),+;
+     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) $(-> ($RRes: ty))* for $($Dims: ident: $DimsBound: ident $(<$($BoundParam: ty),*>)*),+;
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Result: ty;
      $action: expr; $($lives: tt),*) => {
-        impl<$($lives ,)* N $(, $Dims: $DimsBound)*, SA, SB> $Op<$Rhs> for $Lhs
+        impl<$($lives ,)* N $(, $Dims: $DimsBound $(<$($BoundParam),*>)*)*> $Op<$Rhs> for $Lhs
             where N: Scalar + $bound,
-                  SA: Storage<N, $R1, $C1>,
-                  SB: Storage<N, $R2, $C2>,
-                  SA::Alloc: SameShapeAllocator<N, $R1, $C1, $R2, $C2, SA>,
+                  DefaultAllocator: Allocator<N, $R1, $C1> +
+                                    Allocator<N, $R2, $C2> +
+                                    SameShapeAllocator<N, $R1, $C1, $R2, $C2>,
                   ShapeConstraint: SameNumberOfRows<$R1, $R2 $(, Representative = $RRes)*> +
                                    SameNumberOfColumns<$C1, $C2> {
             type Output = $Result;
@@ -173,11 +173,10 @@ macro_rules! add_sub_assign_impl(
      ($R1: ty, $C1: ty),($R2: ty, $C2: ty) for $($Dims: ident: $DimsBound: ident),+;
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty;
      $action: expr; $($lives: tt),*) => {
-        impl<$($lives ,)* N $(, $Dims: $DimsBound)*, SA, SB> $Op<$Rhs> for $Lhs
+        impl<$($lives ,)* N $(, $Dims: $DimsBound)*> $Op<$Rhs> for $Lhs
             where N: Scalar + $bound,
-                  SA: OwnedStorage<N, $R1, $C1>, // FIXME: this is too restrictive.
-                  SB: Storage<N, $R2, $C2>,
-                  SA::Alloc: OwnedAllocator<N, $R1, $C1, SA>,
+                  DefaultAllocator: Allocator<N, $R1, $C1> +
+                                    Allocator<N, $R2, $C2>,
                   ShapeConstraint: SameNumberOfRows<$R1, $R2> + SameNumberOfColumns<$C1, $C2> {
             #[inline]
             fn $op(&mut $lhs, $rhs: $Rhs) {

src/geometry/orthographic.rs

@@ -1,70 +1,65 @@
 #[cfg(feature="arbitrary")]
 use quickcheck::{Arbitrary, Gen};
 use rand::{Rand, Rng};
-
 #[cfg(feature = "serde-serialize")]
-use serde::{Serialize, Serializer, Deserialize, Deserializer};
+use serde;
+use std::fmt;
 
 use alga::general::Real;
 
-use core::{Scalar, SquareMatrix, OwnedSquareMatrix, ColumnVector, OwnedColumnVector, MatrixArray};
-use core::dimension::{U1, U3, U4};
-use core::storage::{OwnedStorage, Storage, StorageMut};
-use core::allocator::OwnedAllocator;
+use core::{Matrix4, Vector, Vector3};
+use core::dimension::U3;
+use core::storage::Storage;
 use core::helper;
 
-use geometry::{PointBase, OwnedPoint};
+use geometry::Point3;
 
 /// A 3D orthographic projection stored as an homogeneous 4x4 matrix.
-#[derive(Debug, Clone, Copy)] // FIXME: Hash
-pub struct OrthographicBase<N: Scalar, S: Storage<N, U4, U4>> {
-    matrix: SquareMatrix<N, U4, S>
+pub struct Orthographic3<N: Real> {
+    matrix: Matrix4<N>
 }
 
-#[cfg(feature = "serde-serialize")]
-impl<N, S> Serialize for OrthographicBase<N, S>
-    where N: Scalar,
-          S: Storage<N, U4, U4>,
-          SquareMatrix<N, U4, S>: Serialize,
-{
-    fn serialize<T>(&self, serializer: T) -> Result<T::Ok, T::Error>
-        where T: Serializer
-    {
-        self.matrix.serialize(serializer)
+impl<N: Real> Copy for Orthographic3<N> { }
+
+impl<N: Real> Clone for Orthographic3<N> {
+    #[inline]
+    fn clone(&self) -> Self {
+        Orthographic3::from_matrix_unchecked(self.matrix.clone())
     }
 }
 
-#[cfg(feature = "serde-serialize")]
-impl<'de, N, S> Deserialize<'de> for OrthographicBase<N, S>
-    where N: Scalar,
-          S: Storage<N, U4, U4>,
-          SquareMatrix<N, U4, S>: Deserialize<'de>,
-{
-    fn deserialize<T>(deserializer: T) -> Result<Self, T::Error>
-        where T: Deserializer<'de>
-    {
-        SquareMatrix::deserialize(deserializer).map(|x| OrthographicBase { matrix: x })
+impl<N: Real> fmt::Debug for Orthographic3<N> {
+    fn fmt(&self, f: &mut fmt::Formatter) -> Result<(), fmt::Error> {
+        self.matrix.fmt(f)
     }
 }
 
-/// A 3D orthographic projection stored as a static homogeneous 4x4 matrix.
-pub type Orthographic3<N> = OrthographicBase<N, MatrixArray<N, U4, U4>>;
-
-impl<N, S> Eq for OrthographicBase<N, S>
-    where N: Scalar + Eq,
-          S: Storage<N, U4, U4> { }
-
-impl<N: Scalar, S: Storage<N, U4, U4>> PartialEq for OrthographicBase<N, S> {
+impl<N: Real> PartialEq for Orthographic3<N> {
     #[inline]
     fn eq(&self, right: &Self) -> bool {
         self.matrix == right.matrix
     }
 }
 
-impl<N, S> OrthographicBase<N, S>
-    where N: Real,
-          S: OwnedStorage<N, U4, U4>,
-          S::Alloc: OwnedAllocator<N, U4, U4, S> {
+#[cfg(feature = "serde-serialize")]
+impl<N: Real + serde::Serialize> serde::Serialize for Orthographic3<N> {
+    fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
+        where S: serde::Serializer {
+            self.matrix.serialize(serializer)
+        }
+}
+
+#[cfg(feature = "serde-serialize")]
+impl<'a, N: Real + serde::Deserialize<'a>> serde::Deserialize<'a> for Orthographic3<N> {
+    fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
+        where Des: serde::Deserializer<'a> {
+            let matrix = Matrix4::<N>::deserialize(deserializer)?;
+
+            Ok(Orthographic3::from_matrix_unchecked(matrix))
+        }
+}
+
+impl<N: Real> Orthographic3<N> {
     /// Creates a new orthographic projection matrix.
     #[inline]
     pub fn new(left: N, right: N, bottom: N, top: N, znear: N, zfar: N) -> Self {
@@ -72,7 +67,7 @@ impl<N, S> OrthographicBase<N, S>
         assert!(bottom < top, "The top corner must be higher than the bottom corner.");
         assert!(znear < zfar, "The far plane must be farther than the near plane.");
 
-        let matrix = SquareMatrix::<N, U4, S>::identity();
+        let matrix = Matrix4::<N>::identity();
         let mut res = Self::from_matrix_unchecked(matrix);
 
         res.set_left_and_right(left, right);
@@ -87,8 +82,8 @@ impl<N, S> OrthographicBase<N, S>
     /// It is not checked whether or not the given matrix actually represents an orthographic
     /// projection.
     #[inline]
-    pub fn from_matrix_unchecked(matrix: SquareMatrix<N, U4, S>) -> Self {
-        OrthographicBase {
+    pub fn from_matrix_unchecked(matrix: Matrix4<N>) -> Self {
+        Orthographic3 {
             matrix: matrix
         }
     }
@@ -105,24 +100,10 @@ impl<N, S> OrthographicBase<N, S>
 
         Self::new(-width * half, width * half, -height * half, height * half, znear, zfar)
     }
-}
-
-impl<N: Real, S: Storage<N, U4, U4>> OrthographicBase<N, S> {
-    /// A reference to the underlying homogeneous transformation matrix.
-    #[inline]
-    pub fn as_matrix(&self) -> &SquareMatrix<N, U4, S> {
-        &self.matrix
-    }
-
-    /// Retrieves the underlying homogeneous matrix.
-    #[inline]
-    pub fn unwrap(self) -> SquareMatrix<N, U4, S> {
-        self.matrix
-    }
 
     /// Retrieves the inverse of the underlying homogeneous matrix.
     #[inline]
-    pub fn inverse(&self) -> OwnedSquareMatrix<N, U4, S::Alloc> {
+    pub fn inverse(&self) -> Matrix4<N> {
         let mut res = self.to_homogeneous();
 
         let inv_m11 = N::one() / self.matrix[(0, 0)];
@@ -142,10 +123,22 @@ impl<N: Real, S: Storage<N, U4, U4>> OrthographicBase<N, S> {
 
     /// Computes the corresponding homogeneous matrix.
     #[inline]
-    pub fn to_homogeneous(&self) -> OwnedSquareMatrix<N, U4, S::Alloc> {
+    pub fn to_homogeneous(&self) -> Matrix4<N> {
         self.matrix.clone_owned()
     }
 
+    /// A reference to the underlying homogeneous transformation matrix.
+    #[inline]
+    pub fn as_matrix(&self) -> &Matrix4<N> {
+        &self.matrix
+    }
+
+    /// Retrieves the underlying homogeneous matrix.
+    #[inline]
+    pub fn unwrap(self) -> Matrix4<N> {
+        self.matrix
+    }
+
     /// The smallest x-coordinate of the view cuboid.
     #[inline]
     pub fn left(&self) -> N {
@@ -185,10 +178,8 @@ impl<N: Real, S: Storage<N, U4, U4>> OrthographicBase<N, S> {
     // FIXME: when we get specialization, specialize the Mul impl instead.
     /// Projects a point. Faster than matrix multiplication.
     #[inline]
-    pub fn project_point<SB>(&self, p: &PointBase<N, U3, SB>) -> OwnedPoint<N, U3, SB::Alloc>
-        where SB: Storage<N, U3, U1> {
-
-        OwnedPoint::<N, U3, SB::Alloc>::new(
+    pub fn project_point(&self, p: &Point3<N>) -> Point3<N> {
+        Point3::new(
             self.matrix[(0, 0)] * p[0] + self.matrix[(0, 3)],
             self.matrix[(1, 1)] * p[1] + self.matrix[(1, 3)],
             self.matrix[(2, 2)] * p[2] + self.matrix[(2, 3)]
@@ -197,10 +188,9 @@ impl<N: Real, S: Storage<N, U4, U4>> OrthographicBase<N, S> {
 
     /// Un-projects a point. Faster than multiplication by the underlying matrix inverse.
     #[inline]
-    pub fn unproject_point<SB>(&self, p: &PointBase<N, U3, SB>) -> OwnedPoint<N, U3, SB::Alloc>
-        where SB: Storage<N, U3, U1> {
+    pub fn unproject_point(&self, p: &Point3<N>) -> Point3<N> {
 
-        OwnedPoint::<N, U3, SB::Alloc>::new(
+        Point3::new(
             (p[0] - self.matrix[(0, 3)]) / self.matrix[(0, 0)],
             (p[1] - self.matrix[(1, 3)]) / self.matrix[(1, 1)],
             (p[2] - self.matrix[(2, 3)]) / self.matrix[(2, 2)]
@@ -210,18 +200,16 @@ impl<N: Real, S: Storage<N, U4, U4>> OrthographicBase<N, S> {
     // FIXME: when we get specialization, specialize the Mul impl instead.
     /// Projects a vector. Faster than matrix multiplication.
     #[inline]
-    pub fn project_vector<SB>(&self, p: &ColumnVector<N, U3, SB>) -> OwnedColumnVector<N, U3, SB::Alloc>
-        where SB: Storage<N, U3, U1> {
+    pub fn project_vector<SB>(&self, p: &Vector<N, U3, SB>) -> Vector3<N>
+        where SB: Storage<N, U3> {
 
-        OwnedColumnVector::<N, U3, SB::Alloc>::new(
+        Vector3::new(
             self.matrix[(0, 0)] * p[0],
             self.matrix[(1, 1)] * p[1],
             self.matrix[(2, 2)] * p[2]
         )
     }
-}
 
-impl<N: Real, S: StorageMut<N, U4, U4>> OrthographicBase<N, S> {
     /// Sets the smallest x-coordinate of the view cuboid.
     #[inline]
     pub fn set_left(&mut self, left: N) {
@@ -289,10 +277,7 @@ impl<N: Real, S: StorageMut<N, U4, U4>> OrthographicBase<N, S> {
     }
 }
 
-impl<N, S> Rand for OrthographicBase<N, S>
-    where N: Real + Rand,
-          S: OwnedStorage<N, U4, U4>,
-          S::Alloc: OwnedAllocator<N, U4, U4, S> {
+impl<N: Real + Rand> Rand for Orthographic3<N> {
     fn rand<R: Rng>(r: &mut R) -> Self {
         let left   = Rand::rand(r);
         let right  = helper::reject_rand(r, |x: &N| *x > left);
@@ -306,10 +291,8 @@ impl<N, S> Rand for OrthographicBase<N, S>
 }
 
 #[cfg(feature="arbitrary")]
-impl<N, S> Arbitrary for OrthographicBase<N, S>
-    where N: Real + Arbitrary,
-          S: OwnedStorage<N, U4, U4> + Send,
-          S::Alloc: OwnedAllocator<N, U4, U4, S> {
+impl<N: Real + Arbitrary> Arbitrary for Orthographic3<N>
+    where Matrix4<N>: Send {
     fn arbitrary<G: Gen>(g: &mut G) -> Self {
         let left   = Arbitrary::arbitrary(g);
         let right  = helper::reject(g, |x: &N| *x > left);

src/geometry/perspective.rs

@@ -3,77 +3,71 @@ use quickcheck::{Arbitrary, Gen};
 use rand::{Rand, Rng};
 
 #[cfg(feature = "serde-serialize")]
-use serde::{Serialize, Serializer, Deserialize, Deserializer};
+use serde;
+use std::fmt;
 
 use alga::general::Real;
 
-use core::{Scalar, SquareMatrix, OwnedSquareMatrix, ColumnVector, OwnedColumnVector, MatrixArray};
-use core::dimension::{U1, U3, U4};
-use core::storage::{OwnedStorage, Storage, StorageMut};
-use core::allocator::OwnedAllocator;
+use core::{Scalar, Matrix4, Vector, Vector3};
+use core::dimension::U3;
+use core::storage::Storage;
 use core::helper;
 
-use geometry::{PointBase, OwnedPoint};
+use geometry::Point3;
 
 /// A 3D perspective projection stored as an homogeneous 4x4 matrix.
-#[derive(Debug, Clone, Copy)] // FIXME: Hash
-pub struct PerspectiveBase<N: Scalar, S: Storage<N, U4, U4>> {
-    matrix: SquareMatrix<N, U4, S>
+pub struct Perspective3<N: Scalar> {
+    matrix: Matrix4<N>
 }
 
-#[cfg(feature = "serde-serialize")]
-impl<N, S> Serialize for PerspectiveBase<N, S>
-    where N: Scalar,
-          S: Storage<N, U4, U4>,
-          SquareMatrix<N, U4, S>: Serialize,
-{
-    fn serialize<T>(&self, serializer: T) -> Result<T::Ok, T::Error>
-        where T: Serializer
-    {
-        self.matrix.serialize(serializer)
+impl<N: Real> Copy for Perspective3<N> { }
+
+impl<N: Real> Clone for Perspective3<N> {
+    #[inline]
+    fn clone(&self) -> Self {
+        Perspective3::from_matrix_unchecked(self.matrix.clone())
     }
 }
 
-#[cfg(feature = "serde-serialize")]
-impl<'de, N, S> Deserialize<'de> for PerspectiveBase<N, S>
-    where N: Scalar,
-          S: Storage<N, U4, U4>,
-          SquareMatrix<N, U4, S>: Deserialize<'de>,
-{
-    fn deserialize<T>(deserializer: T) -> Result<Self, T::Error>
-        where T: Deserializer<'de>
-    {
-        SquareMatrix::deserialize(deserializer).map(|x| PerspectiveBase { matrix: x })
+impl<N: Real> fmt::Debug for Perspective3<N> {
+    fn fmt(&self, f: &mut fmt::Formatter) -> Result<(), fmt::Error> {
+        self.matrix.fmt(f)
     }
 }
 
-/// A 3D perspective projection stored as a static homogeneous 4x4 matrix.
-pub type Perspective3<N> = PerspectiveBase<N, MatrixArray<N, U4, U4>>;
-
-impl<N, S> Eq for PerspectiveBase<N, S>
-    where N: Scalar + Eq,
-          S: Storage<N, U4, U4> { }
-
-impl<N, S> PartialEq for PerspectiveBase<N, S>
-    where N: Scalar,
-          S: Storage<N, U4, U4> {
+impl<N: Real> PartialEq for Perspective3<N> {
     #[inline]
     fn eq(&self, right: &Self) -> bool {
         self.matrix == right.matrix
     }
 }
 
-impl<N, S> PerspectiveBase<N, S>
-    where N: Real,
-          S: OwnedStorage<N, U4, U4>,
-          S::Alloc: OwnedAllocator<N, U4, U4, S> {
+#[cfg(feature = "serde-serialize")]
+impl<N: Real + serde::Serialize> serde::Serialize for Perspective3<N> {
+    fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
+        where S: serde::Serializer {
+            self.matrix.serialize(serializer)
+        }
+}
+
+#[cfg(feature = "serde-serialize")]
+impl<'a, N: Real + serde::Deserialize<'a>> serde::Deserialize<'a> for Perspective3<N> {
+    fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
+        where Des: serde::Deserializer<'a> {
+            let matrix = Matrix4::<N>::deserialize(deserializer)?;
+
+            Ok(Perspective3::from_matrix_unchecked(matrix))
+        }
+}
+
+impl<N: Real> Perspective3<N> {
     /// Creates a new perspective matrix from the aspect ratio, y field of view, and near/far planes.
     pub fn new(aspect: N, fovy: N, znear: N, zfar: N) -> Self {
         assert!(!relative_eq!(zfar - znear, N::zero()), "The near-plane and far-plane must not be superimposed.");
         assert!(!relative_eq!(aspect, N::zero()), "The apsect ratio must not be zero.");
 
-        let matrix = SquareMatrix::<N, U4, S>::identity();
-        let mut res = PerspectiveBase::from_matrix_unchecked(matrix);
+        let matrix = Matrix4::identity();
+        let mut res = Perspective3::from_matrix_unchecked(matrix);
 
         res.set_fovy(fovy);
         res.set_aspect(aspect);
@@ -91,32 +85,15 @@ impl<N, S> PerspectiveBase<N, S>
     /// It is not checked whether or not the given matrix actually represents an orthographic
     /// projection.
     #[inline]
-    pub fn from_matrix_unchecked(matrix: SquareMatrix<N, U4, S>) -> Self {
-        PerspectiveBase {
+    pub fn from_matrix_unchecked(matrix: Matrix4<N>) -> Self {
+        Perspective3 {
             matrix: matrix
         }
     }
-}
-
-impl<N, S> PerspectiveBase<N, S>
-    where N: Real,
-          S: Storage<N, U4, U4> {
-
-    /// A reference to the underlying homogeneous transformation matrix.
-    #[inline]
-    pub fn as_matrix(&self) -> &SquareMatrix<N, U4, S> {
-        &self.matrix
-    }
-
-    /// Retrieves the underlying homogeneous matrix.
-    #[inline]
-    pub fn unwrap(self) -> SquareMatrix<N, U4, S> {
-        self.matrix
-    }
 
     /// Retrieves the inverse of the underlying homogeneous matrix.
     #[inline]
-    pub fn inverse(&self) -> OwnedSquareMatrix<N, U4, S::Alloc> {
+    pub fn inverse(&self) -> Matrix4<N> {
         let mut res = self.to_homogeneous();
 
         res[(0, 0)] = N::one() / self.matrix[(0, 0)];
@@ -135,10 +112,22 @@ impl<N, S> PerspectiveBase<N, S>
 
     /// Computes the corresponding homogeneous matrix.
     #[inline]
-    pub fn to_homogeneous(&self) -> OwnedSquareMatrix<N, U4, S::Alloc> {
+    pub fn to_homogeneous(&self) -> Matrix4<N> {
         self.matrix.clone_owned()
     }
 
+    /// A reference to the underlying homogeneous transformation matrix.
+    #[inline]
+    pub fn as_matrix(&self) -> &Matrix4<N> {
+        &self.matrix
+    }
+
+    /// Retrieves the underlying homogeneous matrix.
+    #[inline]
+    pub fn unwrap(self) -> Matrix4<N> {
+        self.matrix
+    }
+
     /// Gets the `width / height` aspect ratio of the view frustrum.
     #[inline]
     pub fn aspect(&self) -> N {
@@ -174,11 +163,9 @@ impl<N, S> PerspectiveBase<N, S>
     // FIXME: when we get specialization, specialize the Mul impl instead.
     /// Projects a point. Faster than matrix multiplication.
     #[inline]
-    pub fn project_point<SB>(&self, p: &PointBase<N, U3, SB>) -> OwnedPoint<N, U3, SB::Alloc>
-        where SB: Storage<N, U3, U1> {
-
+    pub fn project_point(&self, p: &Point3<N>) -> Point3<N> {
         let inverse_denom = -N::one() / p[2];
-        OwnedPoint::<N, U3, SB::Alloc>::new(
+        Point3::new(
              self.matrix[(0, 0)] * p[0] * inverse_denom,
              self.matrix[(1, 1)] * p[1] * inverse_denom,
             (self.matrix[(2, 2)] * p[2] + self.matrix[(2, 3)]) * inverse_denom
@@ -187,12 +174,10 @@ impl<N, S> PerspectiveBase<N, S>
 
     /// Un-projects a point. Faster than multiplication by the matrix inverse.
     #[inline]
-    pub fn unproject_point<SB>(&self, p: &PointBase<N, U3, SB>) -> OwnedPoint<N, U3, SB::Alloc>
-        where SB: Storage<N, U3, U1> {
-
+    pub fn unproject_point(&self, p: &Point3<N>) -> Point3<N> {
         let inverse_denom = self.matrix[(2, 3)] / (p[2] + self.matrix[(2, 2)]);
 
-        OwnedPoint::<N, U3, SB::Alloc>::new(
+        Point3::new(
             p[0] * inverse_denom / self.matrix[(0, 0)],
             p[1] * inverse_denom / self.matrix[(1, 1)],
             -inverse_denom
@@ -202,22 +187,17 @@ impl<N, S> PerspectiveBase<N, S>
     // FIXME: when we get specialization, specialize the Mul impl instead.
     /// Projects a vector. Faster than matrix multiplication.
     #[inline]
-    pub fn project_vector<SB>(&self, p: &ColumnVector<N, U3, SB>) -> OwnedColumnVector<N, U3, SB::Alloc>
-        where SB: Storage<N, U3, U1> {
+    pub fn project_vector<SB>(&self, p: &Vector<N, U3, SB>) -> Vector3<N>
+        where SB: Storage<N, U3> {
 
         let inverse_denom = -N::one() / p[2];
-        OwnedColumnVector::<N, U3, SB::Alloc>::new(
+        Vector3::new(
             self.matrix[(0, 0)] * p[0] * inverse_denom,
             self.matrix[(1, 1)] * p[1] * inverse_denom,
             self.matrix[(2, 2)]
         )
     }
-}
 
-
-impl<N, S> PerspectiveBase<N, S>
-    where N: Real,
-          S: StorageMut<N, U4, U4> {
     /// Updates this perspective matrix with a new `width / height` aspect ratio of the view
     /// frustrum.
     #[inline]
@@ -256,10 +236,7 @@ impl<N, S> PerspectiveBase<N, S>
     }
 }
 
-impl<N, S> Rand for PerspectiveBase<N, S>
-    where N: Real + Rand,
-          S: OwnedStorage<N, U4, U4>,
-          S::Alloc: OwnedAllocator<N, U4, U4, S> {
+impl<N: Real + Rand> Rand for Perspective3<N> {
     fn rand<R: Rng>(r: &mut R) -> Self {
         let znear  = Rand::rand(r);
         let zfar   = helper::reject_rand(r, |&x: &N| !(x - znear).is_zero());
@@ -270,10 +247,7 @@ impl<N, S> Rand for PerspectiveBase<N, S>
 }
 
 #[cfg(feature="arbitrary")]
-impl<N, S> Arbitrary for PerspectiveBase<N, S>
-    where N: Real + Arbitrary,
-          S: OwnedStorage<N, U4, U4> + Send,
-          S::Alloc: OwnedAllocator<N, U4, U4, S> {
+impl<N: Real + Arbitrary> Arbitrary for Perspective3<N> {
     fn arbitrary<G: Gen>(g: &mut G) -> Self {
         let znear  = Arbitrary::arbitrary(g);
         let zfar   = helper::reject(g, |&x: &N| !(x - znear).is_zero());

src/geometry/point.rs

@@ -1,89 +1,81 @@
 use num::One;
+use std::hash;
 use std::fmt;
 use std::cmp::Ordering;
 use approx::ApproxEq;
 
 #[cfg(feature = "serde-serialize")]
-use serde::{Serialize, Serializer, Deserialize, Deserializer};
+use serde;
 
 #[cfg(feature = "abomonation-serialize")]
 use abomonation::Abomonation;
 
-use core::{Scalar, ColumnVector, OwnedColumnVector};
+use core::{DefaultAllocator, Scalar, VectorN};
 use core::iter::{MatrixIter, MatrixIterMut};
 use core::dimension::{DimName, DimNameSum, DimNameAdd, U1};
-use core::storage::{Storage, StorageMut, MulStorage};
-use core::allocator::{Allocator, SameShapeR};
-
-// XXX Bad name: we can't even add points…
-/// The type of the result of the sum of a point with a vector.
-pub type PointSum<N, D1, D2, SA> =
-    PointBase<N, SameShapeR<D1, D2>,
-    <<SA as Storage<N, D1, U1>>::Alloc as Allocator<N, SameShapeR<D1, D2>, U1>>::Buffer>;
-
-/// The type of the result of the multiplication of a point by a matrix.
-pub type PointMul<N, R1, C1, SA> = PointBase<N, R1, MulStorage<N, R1, C1, U1, SA>>;
-
-/// A point with an owned storage.
-pub type OwnedPoint<N, D, A> = PointBase<N, D, <A as Allocator<N, D, U1>>::Buffer>;
+use core::allocator::Allocator;
 
 /// A point in a n-dimensional euclidean space.
 #[repr(C)]
-#[derive(Hash, Debug)]
-pub struct PointBase<N: Scalar, D: DimName, S: Storage<N, D, U1>> {
+#[derive(Debug)]
+pub struct Point<N: Scalar, D: DimName>
+    where DefaultAllocator: Allocator<N, D> {
     /// The coordinates of this point, i.e., the shift from the origin.
-    pub coords: ColumnVector<N, D, S>
+    pub coords: VectorN<N, D>
 }
 
-impl<N, D, S> Copy for PointBase<N, D, S>
-    where N: Scalar,
-          D: DimName,
-          S: Storage<N, D, U1> + Copy { }
+impl<N: Scalar + hash::Hash, D: DimName + hash::Hash> hash::Hash for Point<N, D>
+    where DefaultAllocator: Allocator<N, D>,
+          <DefaultAllocator as Allocator<N, D>>::Buffer: hash::Hash {
+    fn hash<H: hash::Hasher>(&self, state: &mut H) {
+        self.coords.hash(state)
+    }
+}
 
-impl<N, D, S> Clone for PointBase<N, D, S>
-    where N: Scalar,
-          D: DimName,
-          S: Storage<N, D, U1> + Clone {
+impl<N: Scalar, D: DimName> Copy for Point<N, D>
+    where DefaultAllocator: Allocator<N, D>,
+          <DefaultAllocator as Allocator<N, D>>::Buffer: Copy { }
+
+impl<N: Scalar, D: DimName> Clone for Point<N, D>
+    where DefaultAllocator: Allocator<N, D>,
+          <DefaultAllocator as Allocator<N, D>>::Buffer: Clone {
     #[inline]
     fn clone(&self) -> Self {
-        PointBase::from_coordinates(self.coords.clone())
+        Point::from_coordinates(self.coords.clone())
     }
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<N, D, S> Serialize for PointBase<N, D, S>
-    where N: Scalar,
-          D: DimName,
-          S: Storage<N, D, U1>,
-          ColumnVector<N, D, S>: Serialize,
-{
-    fn serialize<T>(&self, serializer: T) -> Result<T::Ok, T::Error>
-        where T: Serializer
-    {
+impl<N: Scalar, D: DimName> serde::Serialize for Point<N, D>
+where DefaultAllocator: Allocator<N, D>,
+      <DefaultAllocator as Allocator<N, D>>::Buffer: serde::Serialize {
+
+    fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
+        where S: serde::Serializer {
             self.coords.serialize(serializer)
         }
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<'de, N, D, S> Deserialize<'de> for PointBase<N, D, S>
-    where N: Scalar,
-          D: DimName,
-          S: Storage<N, D, U1>,
-          ColumnVector<N, D, S>: Deserialize<'de>,
-{
-    fn deserialize<T>(deserializer: T) -> Result<Self, T::Error>
-        where T: Deserializer<'de>
-    {
-        ColumnVector::deserialize(deserializer).map(|x| PointBase { coords: x })
+impl<'a, N: Scalar, D: DimName> serde::Deserialize<'a> for Point<N, D>
+where DefaultAllocator: Allocator<N, D>,
+      <DefaultAllocator as Allocator<N, D>>::Buffer: serde::Deserialize<'a> {
+
+    fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
+        where Des: serde::Deserializer<'a> {
+            let coords = VectorN::<N, D>::deserialize(deserializer)?;
+
+            Ok(Point::from_coordinates(coords))
         }
 }
 
+
 #[cfg(feature = "abomonation-serialize")]
-impl<N, D, S> Abomonation for PointBase<N, D, S>
+impl<N, D> Abomonation for PointBase<N, D>
     where N: Scalar,
           D: DimName,
-          S: Storage<N, D, U1>,
-          ColumnVector<N, D, S>: Abomonation
+          ColumnVector<N, D>: Abomonation,
+          DefaultAllocator: Allocator<N, D>
 {
     unsafe fn entomb(&self, writer: &mut Vec<u8>) {
         self.coords.entomb(writer)
@@ -98,27 +90,38 @@ impl<N, D, S> Abomonation for PointBase<N, D, S>
     }
 }
 
-impl<N: Scalar, D: DimName, S: Storage<N, D, U1>> PointBase<N, D, S> {
-    /// Creates a new point with the given coordinates.
-    #[inline]
-    pub fn from_coordinates(coords: ColumnVector<N, D, S>) -> PointBase<N, D, S> {
-        PointBase {
-            coords: coords
-        }
-    }
-}
-
-impl<N: Scalar, D: DimName, S: Storage<N, D, U1>> PointBase<N, D, S> {
-    /// Moves this point into one that owns its data.
-    #[inline]
-    pub fn into_owned(self) -> OwnedPoint<N, D, S::Alloc> {
-        PointBase::from_coordinates(self.coords.into_owned())
-    }
+impl<N: Scalar, D: DimName> Point<N, D>
+    where DefaultAllocator: Allocator<N, D> {
 
     /// Clones this point into one that owns its data.
     #[inline]
-    pub fn clone_owned(&self) -> OwnedPoint<N, D, S::Alloc> {
-        PointBase::from_coordinates(self.coords.clone_owned())
+    pub fn clone(&self) -> Point<N, D> {
+        Point::from_coordinates(self.coords.clone_owned())
+    }
+
+    /// Converts this point into a vector in homogeneous coordinates, i.e., appends a `1` at the
+    /// end of it.
+    #[inline]
+    pub fn to_homogeneous(&self) -> VectorN<N, DimNameSum<D, U1>>
+        where N: One,
+              D: DimNameAdd<U1>,
+              DefaultAllocator: Allocator<N, DimNameSum<D, U1>> {
+
+        let mut res = unsafe {
+            VectorN::<_, DimNameSum<D, U1>>::new_uninitialized()
+        };
+        res.fixed_slice_mut::<D, U1>(0, 0).copy_from(&self.coords);
+        res[(D::dim(), 0)] = N::one();
+
+        res
+    }
+
+    /// Creates a new point with the given coordinates.
+    #[inline]
+    pub fn from_coordinates(coords: VectorN<N, D>) -> Point<N, D> {
+        Point {
+            coords: coords
+        }
     }
 
     /// The dimension of this point.
@@ -136,44 +139,26 @@ impl<N: Scalar, D: DimName, S: Storage<N, D, U1>> PointBase<N, D, S> {
 
     /// Iterates through this point coordinates.
     #[inline]
-    pub fn iter(&self) -> MatrixIter<N, D, U1, S> {
+    pub fn iter(&self) -> MatrixIter<N, D, U1, <DefaultAllocator as Allocator<N, D>>::Buffer> {
         self.coords.iter()
     }
 
     /// Gets a reference to i-th element of this point without bound-checking.
     #[inline]
     pub unsafe fn get_unchecked(&self, i: usize) -> &N {
-        self.coords.get_unchecked(i, 0)
+        self.coords.vget_unchecked(i)
     }
 
-
-    /// Converts this point into a vector in homogeneous coordinates, i.e., appends a `1` at the
-    /// end of it.
-    #[inline]
-    pub fn to_homogeneous(&self) -> OwnedColumnVector<N, DimNameSum<D, U1>, S::Alloc>
-        where N: One,
-              D: DimNameAdd<U1>,
-              S::Alloc: Allocator<N, DimNameSum<D, U1>, U1> {
-
-        let mut res = unsafe { OwnedColumnVector::<N, _, S::Alloc>::new_uninitialized() };
-        res.fixed_slice_mut::<D, U1>(0, 0).copy_from(&self.coords);
-        res[(D::dim(), 0)] = N::one();
-
-        res
-    }
-}
-
-impl<N: Scalar, D: DimName, S: StorageMut<N, D, U1>> PointBase<N, D, S> {
     /// Mutably iterates through this point coordinates.
     #[inline]
-    pub fn iter_mut(&mut self) -> MatrixIterMut<N, D, U1, S> {
+    pub fn iter_mut(&mut self) -> MatrixIterMut<N, D, U1, <DefaultAllocator as Allocator<N, D>>::Buffer> {
         self.coords.iter_mut()
     }
 
     /// Gets a mutable reference to i-th element of this point without bound-checking.
     #[inline]
     pub unsafe fn get_unchecked_mut(&mut self, i: usize) -> &mut N {
-        self.coords.get_unchecked_mut(i, 0)
+        self.coords.vget_unchecked_mut(i)
     }
 
     /// Swaps two entries without bound-checking.
@@ -183,9 +168,8 @@ impl<N: Scalar, D: DimName, S: StorageMut<N, D, U1>> PointBase<N, D, S> {
     }
 }
 
-impl<N, D: DimName, S> ApproxEq for PointBase<N, D, S>
-    where N: Scalar + ApproxEq,
-          S: Storage<N, D, U1>,
+impl<N: Scalar + ApproxEq, D: DimName> ApproxEq for Point<N, D>
+    where DefaultAllocator: Allocator<N, D>,
           N::Epsilon: Copy {
     type Epsilon = N::Epsilon;
 
@@ -215,22 +199,19 @@ impl<N, D: DimName, S> ApproxEq for PointBase<N, D, S>
     }
 }
 
-impl<N, D: DimName, S> Eq for PointBase<N, D, S>
-    where N: Scalar + Eq,
-          S: Storage<N, D, U1> { }
+impl<N: Scalar + Eq, D: DimName> Eq for Point<N, D>
+    where DefaultAllocator: Allocator<N, D> { }
 
-impl<N, D: DimName, S> PartialEq for PointBase<N, D, S>
-    where N: Scalar,
-          S: Storage<N, D, U1> {
+impl<N: Scalar, D: DimName> PartialEq for Point<N, D>
+    where DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn eq(&self, right: &Self) -> bool {
         self.coords == right.coords
     }
 }
 
-impl<N, D: DimName, S> PartialOrd for PointBase<N, D, S>
-    where N: Scalar + PartialOrd,
-          S: Storage<N, D, U1> {
+impl<N: Scalar + PartialOrd, D: DimName> PartialOrd for Point<N, D>
+    where DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
         self.coords.partial_cmp(&other.coords)
@@ -262,9 +243,8 @@ impl<N, D: DimName, S> PartialOrd for PointBase<N, D, S>
  * Display
  *
  */
-impl<N, D: DimName, S> fmt::Display for PointBase<N, D, S>
-    where N: Scalar + fmt::Display,
-          S: Storage<N, D, U1> {
+impl<N: Scalar + fmt::Display, D: DimName> fmt::Display for Point<N, D>
+    where DefaultAllocator: Allocator<N, D> {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         try!(write!(f, "{{"));
 

src/geometry/point_alga.rs

@@ -1,26 +1,22 @@
 use alga::general::{Field, Real, MeetSemilattice, JoinSemilattice, Lattice};
 use alga::linear::{AffineSpace, EuclideanSpace};
 
-use core::{ColumnVector, Scalar};
-use core::dimension::{DimName, U1};
-use core::storage::OwnedStorage;
-use core::allocator::OwnedAllocator;
+use core::{DefaultAllocator, Scalar, VectorN};
+use core::dimension::DimName;
+use core::allocator::Allocator;
 
-use geometry::PointBase;
+use geometry::Point;
 
 
-impl<N, D: DimName, S> AffineSpace for PointBase<N, D, S>
+impl<N: Scalar + Field, D: DimName> AffineSpace for Point<N, D>
     where N: Scalar + Field,
-          S: OwnedStorage<N, D, U1>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
-    type Translation = ColumnVector<N, D, S>;
+          DefaultAllocator: Allocator<N, D> {
+    type Translation = VectorN<N, D>;
 }
 
-impl<N, D: DimName, S> EuclideanSpace for PointBase<N, D, S>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
-    type Coordinates = ColumnVector<N, D, S>;
+impl<N: Real, D: DimName> EuclideanSpace for Point<N, D>
+    where DefaultAllocator: Allocator<N, D> {
+    type Coordinates = VectorN<N, D>;
     type Real        = N;
 
     #[inline]
@@ -49,35 +45,32 @@ impl<N, D: DimName, S> EuclideanSpace for PointBase<N, D, S>
  * Ordering
  *
  */
-impl<N, D: DimName, S> MeetSemilattice for PointBase<N, D, S>
+impl<N, D: DimName> MeetSemilattice for Point<N, D>
     where N: Scalar + MeetSemilattice,
-          S: OwnedStorage<N, D, U1>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn meet(&self, other: &Self) -> Self {
-        PointBase::from_coordinates(self.coords.meet(&other.coords))
+        Point::from_coordinates(self.coords.meet(&other.coords))
     }
 }
 
-impl<N, D: DimName, S> JoinSemilattice for PointBase<N, D, S>
+impl<N, D: DimName> JoinSemilattice for Point<N, D>
     where N: Scalar + JoinSemilattice,
-          S: OwnedStorage<N, D, U1>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn join(&self, other: &Self) -> Self {
-        PointBase::from_coordinates(self.coords.join(&other.coords))
+        Point::from_coordinates(self.coords.join(&other.coords))
     }
 }
 
 
-impl<N, D: DimName, S> Lattice for PointBase<N, D, S>
+impl<N, D: DimName> Lattice for Point<N, D>
     where N: Scalar + Lattice,
-          S: OwnedStorage<N, D, U1>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn meet_join(&self, other: &Self) -> (Self, Self) {
         let (meet, join) = self.coords.meet_join(&other.coords);
 
-        (PointBase::from_coordinates(meet), PointBase::from_coordinates(join))
+        (Point::from_coordinates(meet), Point::from_coordinates(join))
     }
 }

src/geometry/point_alias.rs

@@ -1,10 +1,6 @@
-use core::MatrixArray;
 use core::dimension::{U1, U2, U3, U4, U5, U6};
 
-use geometry::PointBase;
-
-/// A statically sized D-dimensional column point.
-pub type Point<N, D> = PointBase<N, D, MatrixArray<N, D, U1>>;
+use geometry::Point;
 
 /// A statically sized 1-dimensional column point.
 pub type Point1<N> = Point<N, U1>;

src/geometry/point_construction.rs

@@ -5,28 +5,25 @@ use rand::{Rand, Rng};
 use num::{Zero, One, Bounded};
 
 use alga::general::ClosedDiv;
-use core::{Scalar, ColumnVector};
-use core::storage::{Storage, OwnedStorage};
-use core::allocator::{Allocator, OwnedAllocator};
+use core::{DefaultAllocator, Scalar, VectorN};
+use core::allocator::Allocator;
 use core::dimension::{DimName, DimNameAdd, DimNameSum, U1, U2, U3, U4, U5, U6};
 
-use geometry::PointBase;
+use geometry::Point;
 
-impl<N, D: DimName, S> PointBase<N, D, S>
-    where N: Scalar,
-          S: OwnedStorage<N, D, U1>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Scalar, D: DimName> Point<N, D>
+    where DefaultAllocator: Allocator<N, D> {
     /// Creates a new point with uninitialized coordinates.
     #[inline]
     pub unsafe fn new_uninitialized() -> Self {
-        Self::from_coordinates(ColumnVector::<_, D, _>::new_uninitialized())
+        Self::from_coordinates(VectorN::new_uninitialized())
     }
 
     /// Creates a new point with all coordinates equal to zero.
     #[inline]
     pub fn origin() -> Self
         where N: Zero {
-        Self::from_coordinates(ColumnVector::<_, D, _>::from_element(N::zero()))
+        Self::from_coordinates(VectorN::from_element(N::zero()))
     }
 
     /// Creates a new point from its homogeneous vector representation.
@@ -34,11 +31,10 @@ impl<N, D: DimName, S> PointBase<N, D, S>
     /// In practice, this builds a D-dimensional points with the same first D component as `v`
     /// divided by the last component of `v`. Returns `None` if this divisor is zero.
     #[inline]
-    pub fn from_homogeneous<SB>(v: ColumnVector<N, DimNameSum<D, U1>, SB>) -> Option<Self>
+    pub fn from_homogeneous(v: VectorN<N, DimNameSum<D, U1>>) -> Option<Self>
         where N: Scalar + Zero + One + ClosedDiv,
               D: DimNameAdd<U1>,
-              SB: Storage<N, DimNameSum<D, U1>, U1, Alloc = S::Alloc>,
-              S::Alloc: Allocator<N, DimNameSum<D, U1>, U1> {
+              DefaultAllocator: Allocator<N, DimNameSum<D, U1>> {
 
         if !v[D::dim()].is_zero() {
             let coords =  v.fixed_slice::<D, U1>(0, 0) / v[D::dim()];
@@ -56,39 +52,34 @@ impl<N, D: DimName, S> PointBase<N, D, S>
  * Traits that buid points.
  *
  */
-impl<N, D: DimName, S> Bounded for PointBase<N, D, S>
-    where N: Scalar + Bounded,
-          S: OwnedStorage<N, D, U1>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Scalar + Bounded, D: DimName> Bounded for Point<N, D>
+    where DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn max_value() -> Self {
-        Self::from_coordinates(ColumnVector::max_value())
+        Self::from_coordinates(VectorN::max_value())
     }
 
     #[inline]
     fn min_value() -> Self {
-        Self::from_coordinates(ColumnVector::min_value())
+        Self::from_coordinates(VectorN::min_value())
     }
 }
 
-impl<N, D: DimName, S> Rand for PointBase<N, D, S>
-    where N: Scalar + Rand,
-          S: OwnedStorage<N, D, U1>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Scalar + Rand, D: DimName> Rand for Point<N, D>
+    where DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn rand<G: Rng>(rng: &mut G) -> Self {
-        PointBase::from_coordinates(rng.gen())
+        Point::from_coordinates(rng.gen())
     }
 }
 
 #[cfg(feature="arbitrary")]
-impl<N, D: DimName, S> Arbitrary for PointBase<N, D, S>
-    where N: Scalar + Arbitrary + Send,
-          S: OwnedStorage<N, D, U1> + Send,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Scalar + Arbitrary + Send, D: DimName> Arbitrary for Point<N, D>
+    where DefaultAllocator: Allocator<N, D>,
+          <DefaultAllocator as Allocator<N, D>>::Buffer: Send {
     #[inline]
     fn arbitrary<G: Gen>(g: &mut G) -> Self {
-        PointBase::from_coordinates(ColumnVector::arbitrary(g))
+        Point::from_coordinates(VectorN::arbitrary(g))
     }
 }
 
@@ -99,13 +90,11 @@ impl<N, D: DimName, S> Arbitrary for PointBase<N, D, S>
  */
 macro_rules! componentwise_constructors_impl(
     ($($D: ty, $($args: ident:$irow: expr),*);* $(;)*) => {$(
-        impl<N, S> PointBase<N, $D, S>
-            where N: Scalar,
-                  S: OwnedStorage<N, $D, U1>,
-                  S::Alloc: OwnedAllocator<N, $D, U1, S> {
+        impl<N: Scalar> Point<N, $D>
+            where DefaultAllocator: Allocator<N, $D> {
             /// Initializes this matrix from its components.
             #[inline]
-            pub fn new($($args: N),*) -> PointBase<N, $D, S> {
+            pub fn new($($args: N),*) -> Point<N, $D> {
                 unsafe {
                     let mut res = Self::new_uninitialized();
                     $( *res.get_unchecked_mut($irow) = $args; )*