Merge remote-tracking branch 'upstream/master' into Implement_convolution_#520

CHANGELOG.md

@@ -4,7 +4,16 @@ documented here.
 
 This project adheres to [Semantic Versioning](http://semver.org/).
 
-## [0.17.0] - WIP
+## [0.18.0] - WIP
+
+### Added
+  * Add `.renormalize` to `Unit<...>` and `Rotation3` to correct potential drift due to repeated operations.
+    Those drifts can cause them not to be pure rotations anymore.
+  * Add the `::from_matrix` constructor too all rotation types to extract a rotation from a raw matrix.
+  * Add the `::from_matrix_eps` constructor too all rotation types to extract a rotation from a raw matrix. This takes
+    more argument than `::from_matrix` to control the convergence of the underlying optimization algorithm.
+
+## [0.17.0]
 
 ### Added
   * Add swizzling up to dimension 3 for vectors. For example, you can do `v.zxy()` as an equivalent to `Vector3::new(v.z, v.x, v.y)`.
@@ -35,6 +44,7 @@ This project adheres to [Semantic Versioning](http://semver.org/).
   * Implement `Extend<Matrix<...>>` for matrices with dynamic storage. This will concatenate the columns of both matrices.
   * Implement `Into<Vec>` for the `MatrixVec` storage.
   * Implement `Hash` for all matrices.
+  * Add a `.len()` method to retrieve the size of a `MatrixVec`.
 
 ### Modified
   * The orthographic projection no longer require that `bottom < top`, that `left < right`, and that `znear < zfar`. The
@@ -47,6 +57,9 @@ This project adheres to [Semantic Versioning](http://semver.org/).
     This is for the case of `Unit`, `Transform`, `Orthographic3`, `Perspective3`, `Rotation`.
   * Deprecate several functions at the root of the crate (replaced by methods).
 
+### Removed
+    * Remove the `Deref` impl for `MatrixVec` as it could cause hard-to-understand compilation errors.
+
 ### nalgebra-glm
   * Add several alternative projection computations, e.g., `ortho_lh`, `ortho_lh_no`, `perspective_lh`, etc.
   * Add features matching those of nalgebra, in particular: `serde-serialize`, `abmonation-serialize`, std` (enabled by default).

Cargo.toml

@@ -1,6 +1,6 @@
 [package]
 name    = "nalgebra"
-version = "0.16.13"
+version = "0.17.2"
 authors = [ "Sébastien Crozet <developer@crozet.re>" ]
 
 description = "Linear algebra library with transformations and statically-sized or dynamically-sized matrices."
@@ -12,6 +12,8 @@ categories = [ "science" ]
 keywords = [ "linear", "algebra", "matrix", "vector", "math" ]
 license = "BSD-3-Clause"
 
+exclude = ["/ci/*", "/.travis.yml", "/Makefile"]
+
 [lib]
 name = "nalgebra"
 path = "src/lib.rs"
@@ -23,8 +25,10 @@ stdweb          = [ "rand/stdweb" ]
 arbitrary       = [ "quickcheck" ]
 serde-serialize = [ "serde", "serde_derive", "num-complex/serde" ]
 abomonation-serialize = [ "abomonation" ]
+sparse = [ ]
 debug = [ ]
 alloc = [ ]
+io = [ "pest", "pest_derive" ]
 
 [dependencies]
 typenum        = "1.10"
@@ -33,13 +37,15 @@ rand           = { version = "0.6", default-features = false }
 num-traits     = { version = "0.2", default-features = false }
 num-complex    = { version = "0.2", default-features = false }
 approx         = { version = "0.3", default-features = false }
-alga           = { version = "0.7", default-features = false }
+alga           = { version = "0.8", default-features = false }
 matrixmultiply = { version = "0.2", optional = true }
 serde          = { version = "1.0", optional = true }
 serde_derive   = { version = "1.0", optional = true }
 abomonation    = { version = "0.7", optional = true }
 mint           = { version = "0.5", optional = true }
-quickcheck     = { version = "0.7", optional = true }
+quickcheck     = { version = "0.8", optional = true }
+pest           = { version = "2.0", optional = true }
+pest_derive    = { version = "2.0", optional = true }
 
 [dev-dependencies]
 serde_json = "1.0"

ci/build.sh

@@ -11,7 +11,7 @@ if [ -z "$NO_STD" ]; then
         cargo build --verbose -p nalgebra --features "serde-serialize";
         cargo build --verbose -p nalgebra --features "abomonation-serialize";
         cargo build --verbose -p nalgebra --features "debug";
-        cargo build --verbose -p nalgebra --features "debug arbitrary mint serde-serialize abomonation-serialize";
+        cargo build --verbose -p nalgebra --all-features
     else
         cargo build -p nalgebra-lapack;
     fi

examples/matrix_construction.rs

@@ -51,8 +51,8 @@ fn main() {
             // Components listed column-by-column.
             1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0,
         ]
-            .iter()
+        .iter()
-            .cloned(),
+        .cloned(),
     );
 
     assert_eq!(dm, dm1);

nalgebra-glm/Cargo.toml

@@ -1,6 +1,6 @@
 [package]
 name = "nalgebra-glm"
-version = "0.2.1"
+version = "0.3.0"
 authors = ["sebcrozet <developer@crozet.re>"]
 
 description = "A computer-graphics oriented API for nalgebra, inspired by the C++ GLM library."
@@ -23,5 +23,5 @@ abomonation-serialize = [ "nalgebra/abomonation-serialize" ]
 [dependencies]
 num-traits = { version = "0.2", default-features = false }
 approx = { version = "0.3", default-features = false }
-alga = { version = "0.7", default-features = false }
+alga = { version = "0.8", default-features = false }
-nalgebra = { path =  "..", version = "^0.16.13", default-features = false }
+nalgebra = { path =  "..", version = "0.17", default-features = false }

nalgebra-glm/src/ext/matrix_transform.rs

@@ -9,7 +9,7 @@ where DefaultAllocator: Alloc<N, D, D> {
     TMat::<N, D, D>::identity()
 }
 
-/// Build a right hand look at view matrix
+/// Build a look at view matrix based on the right handedness.
 ///
 /// # Parameters:
 ///

nalgebra-glm/src/lib.rs

@@ -13,7 +13,7 @@
 
    ```toml
    [dependencies]
-   nalgebra-glm = "0.1"
+   nalgebra-glm = "0.3"
    ```
 
    Then, you should add an `extern crate` statement to your `lib.rs` or `main.rs` file. It is **strongly
@@ -110,6 +110,7 @@
    and keep in mind it is possible to convert, e.g., an `Isometry3` to a `Mat4` and vice-versa (see the [conversions section](#conversions)).
 */
 
+#![doc(html_favicon_url = "http://nalgebra.org/img/favicon.ico")]
 #![cfg_attr(not(feature = "std"), no_std)]
 
 extern crate num_traits as num;

nalgebra-lapack/Cargo.toml

@@ -1,6 +1,6 @@
 [package]
 name    = "nalgebra-lapack"
-version = "0.8.0"
+version = "0.9.0"
 authors = [ "Sébastien Crozet <developer@crozet.re>", "Andrew Straw <strawman@astraw.com>" ]
 
 description   = "Linear algebra library with transformations and satically-sized or dynamically-sized matrices."
@@ -22,10 +22,10 @@ accelerate = ["lapack-src/accelerate"]
 intel-mkl  = ["lapack-src/intel-mkl"]
 
 [dependencies]
-nalgebra      = { version = "0.16", path = ".." }
+nalgebra      = { version = "0.17", path = ".." }
 num-traits    = "0.2"
 num-complex   = { version = "0.2", default-features = false }
-alga          = { version = "0.7", default-features = false }
+alga          = { version = "0.8", default-features = false }
 serde         = { version = "1.0", optional = true }
 serde_derive  = { version = "1.0", optional = true }
 lapack        = { version = "0.16", default-features = false }
@@ -33,7 +33,7 @@ lapack-src    = { version = "0.2", default-features = false }
 # clippy = "*"
 
 [dev-dependencies]
-nalgebra   = { version = "0.16", path = "..", features = [ "arbitrary" ] }
+nalgebra   = { version = "0.17", path = "..", features = [ "arbitrary" ] }
-quickcheck = "0.7"
+quickcheck = "0.8"
 approx     = "0.3"
 rand       = "0.6"

nalgebra-lapack/src/cholesky.rs

@@ -62,7 +62,7 @@ where DefaultAllocator: Allocator<N, D, D>
         N::xpotrf(uplo, dim, m.as_mut_slice(), dim, &mut info);
         lapack_check!(info);
 
-        Some(Cholesky { l: m })
+        Some(Self { l: m })
     }
 
     /// Retrieves the lower-triangular factor of the cholesky decomposition.

nalgebra-lapack/src/eigen.rs

@@ -127,7 +127,7 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
                 lapack_check!(info);
 
                 if wi.iter().all(|e| e.is_zero()) {
-                    return Some(Eigen {
+                    return Some(Self {
                         eigenvalues: wr,
                         left_eigenvectors: Some(vl),
                         eigenvectors: Some(vr),
@@ -156,7 +156,7 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
                 lapack_check!(info);
 
                 if wi.iter().all(|e| e.is_zero()) {
-                    return Some(Eigen {
+                    return Some(Self {
                         eigenvalues: wr,
                         left_eigenvectors: Some(vl),
                         eigenvectors: None,
@@ -185,7 +185,7 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
                 lapack_check!(info);
 
                 if wi.iter().all(|e| e.is_zero()) {
-                    return Some(Eigen {
+                    return Some(Self {
                         eigenvalues: wr,
                         left_eigenvectors: None,
                         eigenvectors: Some(vr),
@@ -212,7 +212,7 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
                 lapack_check!(info);
 
                 if wi.iter().all(|e| e.is_zero()) {
-                    return Some(Eigen {
+                    return Some(Self {
                         eigenvalues: wr,
                         left_eigenvectors: None,
                         eigenvectors: None,

nalgebra-lapack/src/hessenberg.rs

@@ -48,7 +48,7 @@ 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> {
+    pub fn new(mut m: MatrixN<N, D>) -> Self {
         let nrows = m.data.shape().0;
         let n = nrows.value() as i32;
 
@@ -83,7 +83,7 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimDiff<D, U1>>
         );
         lapack_panic!(info);
 
-        Hessenberg { h: m, tau: tau }
+        Self { h: m, tau: tau }
     }
 
     /// Computes the hessenberg matrix of this decomposition.

nalgebra-lapack/src/lib.rs

@@ -68,8 +68,10 @@
 #![deny(unused_qualifications)]
 #![deny(unused_results)]
 #![deny(missing_docs)]
-#![doc(html_favicon_url = "http://nalgebra.org/img/favicon.ico",
+#![doc(
-       html_root_url = "http://nalgebra.org/rustdoc")]
+    html_favicon_url = "http://nalgebra.org/img/favicon.ico",
+    html_root_url = "http://nalgebra.org/rustdoc"
+)]
 
 extern crate alga;
 extern crate lapack;

nalgebra-lapack/src/lu.rs

@@ -82,7 +82,7 @@ where
         );
         lapack_panic!(info);
 
-        LU { lu: m, p: ipiv }
+        Self { lu: m, p: ipiv }
     }
 
     /// Gets the lower-triangular matrix part of the decomposition.

nalgebra-lapack/src/qr.rs

@@ -54,14 +54,14 @@ where DefaultAllocator: Allocator<N, R, 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> {
+    pub fn new(mut m: MatrixMN<N, R, C>) -> Self {
         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 };
+            return Self { qr: m, tau: tau };
         }
 
         let lwork = N::xgeqrf_work_size(
@@ -86,7 +86,7 @@ where DefaultAllocator: Allocator<N, R, C>
             &mut info,
         );
 
-        QR { qr: m, tau: tau }
+        Self { qr: m, tau: tau }
     }
 
     /// Retrieves the upper trapezoidal submatrix `R` of this decomposition.

nalgebra-lapack/src/symmetric_eigen.rs

@@ -62,7 +62,7 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
     pub fn new(m: MatrixN<N, D>) -> Self {
         let (vals, vecs) =
             Self::do_decompose(m, true).expect("SymmetricEigen: convergence failure.");
-        SymmetricEigen {
+        Self {
             eigenvalues: vals,
             eigenvectors: vecs.unwrap(),
         }

src/base/alias_slice.rs

@@ -175,24 +175,24 @@ pub type MatrixSliceXx6<'a, N, RStride = U1, CStride = Dynamic> =
     MatrixSliceMN<'a, N, Dynamic, U6, RStride, CStride>;
 
 /// A column vector slice with `D` rows.
-pub type VectorSliceN<'a, N, D, Stride = U1> =
+pub type VectorSliceN<'a, N, D, RStride = U1, CStride = D> =
-    Matrix<N, D, U1, SliceStorage<'a, N, D, U1, Stride, D>>;
+    Matrix<N, D, U1, SliceStorage<'a, N, D, U1, RStride, CStride>>;
 
 /// A column vector slice dynamic numbers of rows and columns.
-pub type DVectorSlice<'a, N, Stride = U1> = VectorSliceN<'a, N, Dynamic, Stride>;
+pub type DVectorSlice<'a, N, RStride = U1, CStride = Dynamic> = VectorSliceN<'a, N, Dynamic, RStride, CStride>;
 
 /// A 1D column vector slice.
-pub type VectorSlice1<'a, N, Stride = U1> = VectorSliceN<'a, N, U1, Stride>;
+pub type VectorSlice1<'a, N, RStride = U1, CStride = U1> = VectorSliceN<'a, N, U1, RStride, CStride>;
 /// A 2D column vector slice.
-pub type VectorSlice2<'a, N, Stride = U1> = VectorSliceN<'a, N, U2, Stride>;
+pub type VectorSlice2<'a, N, RStride = U1, CStride = U2> = VectorSliceN<'a, N, U2, RStride, CStride>;
 /// A 3D column vector slice.
-pub type VectorSlice3<'a, N, Stride = U1> = VectorSliceN<'a, N, U3, Stride>;
+pub type VectorSlice3<'a, N, RStride = U1, CStride = U3> = VectorSliceN<'a, N, U3, RStride, CStride>;
 /// A 4D column vector slice.
-pub type VectorSlice4<'a, N, Stride = U1> = VectorSliceN<'a, N, U4, Stride>;
+pub type VectorSlice4<'a, N, RStride = U1, CStride = U4> = VectorSliceN<'a, N, U4, RStride, CStride>;
 /// A 5D column vector slice.
-pub type VectorSlice5<'a, N, Stride = U1> = VectorSliceN<'a, N, U5, Stride>;
+pub type VectorSlice5<'a, N, RStride = U1, CStride = U5> = VectorSliceN<'a, N, U5, RStride, CStride>;
 /// A 6D column vector slice.
-pub type VectorSlice6<'a, N, Stride = U1> = VectorSliceN<'a, N, U6, Stride>;
+pub type VectorSlice6<'a, N, RStride = U1, CStride = U6> = VectorSliceN<'a, N, U6, RStride, CStride>;
 
 /*
  *
@@ -367,21 +367,21 @@ pub type MatrixSliceMutXx6<'a, N, RStride = U1, CStride = Dynamic> =
     MatrixSliceMutMN<'a, N, Dynamic, U6, RStride, CStride>;
 
 /// A mutable column vector slice with `D` rows.
-pub type VectorSliceMutN<'a, N, D, Stride = U1> =
+pub type VectorSliceMutN<'a, N, D, RStride = U1, CStride = D> =
-    Matrix<N, D, U1, SliceStorageMut<'a, N, D, U1, Stride, D>>;
+    Matrix<N, D, U1, SliceStorageMut<'a, N, D, U1, RStride, CStride>>;
 
 /// A mutable column vector slice dynamic numbers of rows and columns.
-pub type DVectorSliceMut<'a, N, Stride = U1> = VectorSliceMutN<'a, N, Dynamic, Stride>;
+pub type DVectorSliceMut<'a, N, RStride = U1, CStride = Dynamic> = VectorSliceMutN<'a, N, Dynamic, RStride, CStride>;
 
 /// A 1D mutable column vector slice.
-pub type VectorSliceMut1<'a, N, Stride = U1> = VectorSliceMutN<'a, N, U1, Stride>;
+pub type VectorSliceMut1<'a, N, RStride = U1, CStride = U1> = VectorSliceMutN<'a, N, U1, RStride, CStride>;
 /// A 2D mutable column vector slice.
-pub type VectorSliceMut2<'a, N, Stride = U1> = VectorSliceMutN<'a, N, U2, Stride>;
+pub type VectorSliceMut2<'a, N, RStride = U1, CStride = U2> = VectorSliceMutN<'a, N, U2, RStride, CStride>;
 /// A 3D mutable column vector slice.
-pub type VectorSliceMut3<'a, N, Stride = U1> = VectorSliceMutN<'a, N, U3, Stride>;
+pub type VectorSliceMut3<'a, N, RStride = U1, CStride = U3> = VectorSliceMutN<'a, N, U3, RStride, CStride>;
 /// A 4D mutable column vector slice.
-pub type VectorSliceMut4<'a, N, Stride = U1> = VectorSliceMutN<'a, N, U4, Stride>;
+pub type VectorSliceMut4<'a, N, RStride = U1, CStride = U4> = VectorSliceMutN<'a, N, U4, RStride, CStride>;
 /// A 5D mutable column vector slice.
-pub type VectorSliceMut5<'a, N, Stride = U1> = VectorSliceMutN<'a, N, U5, Stride>;
+pub type VectorSliceMut5<'a, N, RStride = U1, CStride = U5> = VectorSliceMutN<'a, N, U5, RStride, CStride>;
 /// A 6D mutable column vector slice.
-pub type VectorSliceMut6<'a, N, Stride = U1> = VectorSliceMutN<'a, N, U6, Stride>;
+pub type VectorSliceMut6<'a, N, RStride = U1, CStride = U6> = VectorSliceMutN<'a, N, U6, RStride, CStride>;

src/base/array_storage.rs

@@ -331,7 +331,7 @@ where
         let mut curr = 0;
 
         while let Some(value) = try!(visitor.next_element()) {
-            out[curr] = value;
+            *out.get_mut(curr).ok_or_else(|| V::Error::invalid_length(curr, &self))? = value;
             curr += 1;
         }
 

src/base/blas.rs

@@ -13,18 +13,18 @@ use base::dimension::{Dim, Dynamic, U1, U2, U3, U4};
 use base::storage::{Storage, StorageMut};
 use base::{DefaultAllocator, Matrix, Scalar, SquareMatrix, Vector};
 
-impl<N: Scalar + PartialOrd + Signed, D: Dim, S: Storage<N, D>> Vector<N, D, S> {
+impl<N: Scalar + PartialOrd, D: Dim, S: Storage<N, D>> Vector<N, D, S> {
-    /// Computes the index of the vector component with the largest value.
+    /// Computes the index and value of the vector component with the largest value.
     ///
     /// # Examples:
     ///
     /// ```
     /// # use nalgebra::Vector3;
     /// let vec = Vector3::new(11, -15, 13);
-    /// assert_eq!(vec.imax(), 2);
+    /// assert_eq!(vec.argmax(), (2, 13));
     /// ```
     #[inline]
-    pub fn imax(&self) -> usize {
+    pub fn argmax(&self) -> (usize, N) {
         assert!(!self.is_empty(), "The input vector must not be empty.");
 
         let mut the_max = unsafe { self.vget_unchecked(0) };
@@ -39,7 +39,21 @@ impl<N: Scalar + PartialOrd + Signed, D: Dim, S: Storage<N, D>> Vector<N, D, S>
             }
         }
 
-        the_i
+        (the_i, *the_max)
+    }
+
+    /// Computes the index of the vector component with the largest value.
+    ///
+    /// # Examples:
+    ///
+    /// ```
+    /// # use nalgebra::Vector3;
+    /// let vec = Vector3::new(11, -15, 13);
+    /// assert_eq!(vec.imax(), 2);
+    /// ```
+    #[inline]
+    pub fn imax(&self) -> usize {
+        self.argmax().0
     }
 
     /// Computes the index of the vector component with the largest absolute value.
@@ -52,7 +66,8 @@ impl<N: Scalar + PartialOrd + Signed, D: Dim, S: Storage<N, D>> Vector<N, D, S>
     /// assert_eq!(vec.iamax(), 1);
     /// ```
     #[inline]
-    pub fn iamax(&self) -> usize {
+    pub fn iamax(&self) -> usize
+        where N: Signed {
         assert!(!self.is_empty(), "The input vector must not be empty.");
 
         let mut the_max = unsafe { self.vget_unchecked(0).abs() };
@@ -70,6 +85,34 @@ impl<N: Scalar + PartialOrd + Signed, D: Dim, S: Storage<N, D>> Vector<N, D, S>
         the_i
     }
 
+    /// Computes the index and value of the vector component with the smallest value.
+    ///
+    /// # Examples:
+    ///
+    /// ```
+    /// # use nalgebra::Vector3;
+    /// let vec = Vector3::new(11, -15, 13);
+    /// assert_eq!(vec.argmin(), (1, -15));
+    /// ```
+    #[inline]
+    pub fn argmin(&self) -> (usize, N) {
+        assert!(!self.is_empty(), "The input vector must not be empty.");
+
+        let mut the_min = unsafe { self.vget_unchecked(0) };
+        let mut the_i = 0;
+
+        for i in 1..self.nrows() {
+            let val = unsafe { self.vget_unchecked(i) };
+
+            if val < the_min {
+                the_min = val;
+                the_i = i;
+            }
+        }
+
+        (the_i, *the_min)
+    }
+
     /// Computes the index of the vector component with the smallest value.
     ///
     /// # Examples:
@@ -81,21 +124,7 @@ impl<N: Scalar + PartialOrd + Signed, D: Dim, S: Storage<N, D>> Vector<N, D, S>
     /// ```
     #[inline]
     pub fn imin(&self) -> usize {
-        assert!(!self.is_empty(), "The input vector must not be empty.");
+        self.argmin().0
-
-        let mut the_max = unsafe { self.vget_unchecked(0) };
-        let mut the_i = 0;
-
-        for i in 1..self.nrows() {
-            let val = unsafe { self.vget_unchecked(i) };
-
-            if val < the_max {
-                the_max = val;
-                the_i = i;
-            }
-        }
-
-        the_i
     }
 
     /// Computes the index of the vector component with the smallest absolute value.
@@ -108,17 +137,18 @@ impl<N: Scalar + PartialOrd + Signed, D: Dim, S: Storage<N, D>> Vector<N, D, S>
     /// assert_eq!(vec.iamin(), 0);
     /// ```
     #[inline]
-    pub fn iamin(&self) -> usize {
+    pub fn iamin(&self) -> usize
+        where N: Signed {
         assert!(!self.is_empty(), "The input vector must not be empty.");
 
-        let mut the_max = unsafe { self.vget_unchecked(0).abs() };
+        let mut the_min = 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 {
+            if val < the_min {
-                the_max = val;
+                the_min = val;
                 the_i = i;
             }
         }
@@ -627,7 +657,6 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Matrix2x3, Matrix3x4, Matrix2x4};
     /// let mut mat1 = Matrix2x4::identity();
     /// let mat2 = Matrix2x3::new(1.0, 2.0, 3.0,
@@ -760,7 +789,6 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Matrix3x2, Matrix3x4, Matrix2x4};
     /// let mut mat1 = Matrix2x4::identity();
     /// let mat2 = Matrix3x2::new(1.0, 4.0,
@@ -879,7 +907,6 @@ where N: Scalar + Zero + One + ClosedAdd + ClosedMul
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{DMatrix, DVector};
     /// // Note that all those would also work with statically-sized matrices.
     /// // We use DMatrix/DVector since that's the only case where pre-allocating the
@@ -934,7 +961,6 @@ where N: Scalar + Zero + One + ClosedAdd + ClosedMul
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Matrix2, Matrix3, Matrix2x3, Vector2};
     /// let mut mat = Matrix2::identity();
     /// let lhs = Matrix2x3::new(1.0, 2.0, 3.0,
@@ -971,7 +997,6 @@ where N: Scalar + Zero + One + ClosedAdd + ClosedMul
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{DMatrix, DVector};
     /// // Note that all those would also work with statically-sized matrices.
     /// // We use DMatrix/DVector since that's the only case where pre-allocating the
@@ -1026,7 +1051,6 @@ where N: Scalar + Zero + One + ClosedAdd + ClosedMul
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Matrix2, Matrix3x2, Matrix3};
     /// let mut mat = Matrix2::identity();
     /// let rhs = Matrix3x2::new(1.0, 2.0,

src/base/cg.rs

@@ -130,8 +130,14 @@ impl<N: Real> Matrix4<N> {
     /// It maps the view direction `target - eye` to the positive `z` axis and the origin to the
     /// `eye`.
     #[inline]
+    pub fn face_towards(eye: &Point3<N>, target: &Point3<N>, up: &Vector3<N>) -> Self {
+        IsometryMatrix3::face_towards(eye, target, up).to_homogeneous()
+    }
+
+    /// Deprecated: Use [Matrix4::face_towards] instead.
+    #[deprecated(note="renamed to `face_towards`")]
     pub fn new_observer_frame(eye: &Point3<N>, target: &Point3<N>, up: &Vector3<N>) -> Self {
-        IsometryMatrix3::new_observer_frame(eye, target, up).to_homogeneous()
+        Matrix4::face_towards(eye, target, up)
     }
 
     /// Builds a right-handed look-at view matrix.

src/base/componentwise.rs

@@ -1,4 +1,4 @@
-// Non-conventional componentwise operators.
+// Non-conventional component-wise operators.
 
 use num::{Signed, Zero};
 use std::ops::{Add, Mul};

src/base/construction.rs

@@ -270,7 +270,7 @@ where DefaultAllocator: Allocator<N, R, C>
     /// let vec_ptr = vec.as_ptr();
     ///
     /// let matrix = Matrix::from_vec_generic(Dynamic::new(vec.len()), U1, vec);
-    /// let matrix_storage_ptr = matrix.data.as_ptr();
+    /// let matrix_storage_ptr = matrix.data.as_vec().as_ptr();
     ///
     /// // `matrix` is backed by exactly the same `Vec` as it was constructed from.
     /// assert_eq!(matrix_storage_ptr, vec_ptr);
@@ -296,7 +296,7 @@ where
     ///
     /// let m = Matrix3::from_diagonal(&Vector3::new(1.0, 2.0, 3.0));
     /// // The two additional arguments represent the matrix dimensions.
-    /// let dm = DMatrix::from_diagonal(&DVector::from_row_slice(3, &[1.0, 2.0, 3.0]));
+    /// let dm = DMatrix::from_diagonal(&DVector::from_row_slice(&[1.0, 2.0, 3.0]));
     ///
     /// assert!(m.m11 == 1.0 && m.m12 == 0.0 && m.m13 == 0.0 &&
     ///         m.m21 == 0.0 && m.m22 == 2.0 && m.m23 == 0.0 &&
@@ -444,63 +444,6 @@ macro_rules! impl_constructors(
                 Self::from_iterator_generic($($gargs, )* iter)
             }
 
-            /// Creates a matrix with its elements filled with the components provided by a slice
-            /// in row-major order.
-            ///
-            /// The order of elements in the slice must follow the usual mathematic writing, i.e.,
-            /// row-by-row.
-            ///
-            /// # Example
-            /// ```
-            /// # use nalgebra::{Matrix2x3, Vector3, DVector, DMatrix};
-            /// # use std::iter;
-            ///
-            /// let v = Vector3::from_row_slice(&[0, 1, 2]);
-            /// // The additional argument represents the vector dimension.
-            /// let dv = DVector::from_row_slice(3, &[0, 1, 2]);
-            /// let m = Matrix2x3::from_row_slice(&[0, 1, 2, 3, 4, 5]);
-            /// // The two additional arguments represent the matrix dimensions.
-            /// let dm = DMatrix::from_row_slice(2, 3, &[0, 1, 2, 3, 4, 5]);
-            ///
-            /// assert!(v.x == 0 && v.y == 1 && v.z == 2);
-            /// assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
-            /// assert!(m.m11 == 0 && m.m12 == 1 && m.m13 == 2 &&
-            ///         m.m21 == 3 && m.m22 == 4 && m.m23 == 5);
-            /// assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 1 && dm[(0, 2)] == 2 &&
-            ///         dm[(1, 0)] == 3 && dm[(1, 1)] == 4 && dm[(1, 2)] == 5);
-            /// ```
-            #[inline]
-            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.
-            ///
-            /// # Example
-            /// ```
-            /// # use nalgebra::{Matrix2x3, Vector3, DVector, DMatrix};
-            /// # use std::iter;
-            ///
-            /// let v = Vector3::from_column_slice(&[0, 1, 2]);
-            /// // The additional argument represents the vector dimension.
-            /// let dv = DVector::from_column_slice(3, &[0, 1, 2]);
-            /// let m = Matrix2x3::from_column_slice(&[0, 1, 2, 3, 4, 5]);
-            /// // The two additional arguments represent the matrix dimensions.
-            /// let dm = DMatrix::from_column_slice(2, 3, &[0, 1, 2, 3, 4, 5]);
-            ///
-            /// assert!(v.x == 0 && v.y == 1 && v.z == 2);
-            /// assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
-            /// assert!(m.m11 == 0 && m.m12 == 2 && m.m13 == 4 &&
-            ///         m.m21 == 1 && m.m22 == 3 && m.m23 == 5);
-            /// assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 2 && dm[(0, 2)] == 4 &&
-            ///         dm[(1, 0)] == 1 && dm[(1, 1)] == 3 && dm[(1, 2)] == 5);
-            /// ```
-            #[inline]
-            pub fn from_column_slice($($args: usize,)* slice: &[N]) -> Self {
-                Self::from_column_slice_generic($($gargs, )* slice)
-            }
-
             /// Creates a matrix or vector filled with the results of a function applied to each of its
             /// component coordinates.
             ///
@@ -612,32 +555,6 @@ macro_rules! impl_constructors(
             ) -> Self {
                 Self::from_distribution_generic($($gargs, )* distribution, rng)
             }
-
-            /// Creates a matrix backed by a given `Vec`.
-            ///
-            /// The output matrix is filled column-by-column.
-            ///
-            /// # Example
-            /// ```
-            /// # use nalgebra::{DMatrix, Matrix2x3};
-            ///
-            /// let m = Matrix2x3::from_vec(vec![0, 1, 2, 3, 4, 5]);
-            ///
-            /// assert!(m.m11 == 0 && m.m12 == 2 && m.m13 == 4 &&
-            ///         m.m21 == 1 && m.m22 == 3 && m.m23 == 5);
-            ///
-            ///
-            /// // The two additional arguments represent the matrix dimensions.
-            /// let dm = DMatrix::from_vec(2, 3, vec![0, 1, 2, 3, 4, 5]);
-            ///
-            /// assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 2 && dm[(0, 2)] == 4 &&
-            ///         dm[(1, 0)] == 1 && dm[(1, 1)] == 3 && dm[(1, 2)] == 5);
-            /// ```
-            #[inline]
-            #[cfg(feature = "std")]
-            pub fn from_vec($($args: usize,)* data: Vec<N>) -> Self {
-                Self::from_vec_generic($($gargs, )* data)
-            }
         }
 
         impl<N: Scalar, $($DimIdent: $DimBound, )*> MatrixMN<N $(, $Dims)*>
@@ -676,6 +593,125 @@ impl_constructors!(Dynamic, Dynamic;
                    Dynamic::new(nrows), Dynamic::new(ncols);
                    nrows, ncols);
 
+/*
+ *
+ * Constructors that don't necessarily require all dimensions
+ * to be specified whon one dimension is already known.
+ *
+ */
+macro_rules! impl_constructors_from_data(
+    ($data: ident; $($Dims: ty),*; $(=> $DimIdent: ident: $DimBound: ident),*; $($gargs: expr),*; $($args: ident),*) => {
+        impl<N: Scalar, $($DimIdent: $DimBound, )*> MatrixMN<N $(, $Dims)*>
+        where DefaultAllocator: Allocator<N $(, $Dims)*> {
+            /// Creates a matrix with its elements filled with the components provided by a slice
+            /// in row-major order.
+            ///
+            /// The order of elements in the slice must follow the usual mathematic writing, i.e.,
+            /// row-by-row.
+            ///
+            /// # Example
+            /// ```
+            /// # use nalgebra::{Matrix2x3, Vector3, DVector, DMatrix};
+            /// # use std::iter;
+            ///
+            /// let v = Vector3::from_row_slice(&[0, 1, 2]);
+            /// // The additional argument represents the vector dimension.
+            /// let dv = DVector::from_row_slice(&[0, 1, 2]);
+            /// let m = Matrix2x3::from_row_slice(&[0, 1, 2, 3, 4, 5]);
+            /// // The two additional arguments represent the matrix dimensions.
+            /// let dm = DMatrix::from_row_slice(2, 3, &[0, 1, 2, 3, 4, 5]);
+            ///
+            /// assert!(v.x == 0 && v.y == 1 && v.z == 2);
+            /// assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
+            /// assert!(m.m11 == 0 && m.m12 == 1 && m.m13 == 2 &&
+            ///         m.m21 == 3 && m.m22 == 4 && m.m23 == 5);
+            /// assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 1 && dm[(0, 2)] == 2 &&
+            ///         dm[(1, 0)] == 3 && dm[(1, 1)] == 4 && dm[(1, 2)] == 5);
+            /// ```
+            #[inline]
+            pub fn from_row_slice($($args: usize,)* $data: &[N]) -> Self {
+                Self::from_row_slice_generic($($gargs, )* $data)
+            }
+
+            /// Creates a matrix with its elements filled with the components provided by a slice
+            /// in column-major order.
+            ///
+            /// # Example
+            /// ```
+            /// # use nalgebra::{Matrix2x3, Vector3, DVector, DMatrix};
+            /// # use std::iter;
+            ///
+            /// let v = Vector3::from_column_slice(&[0, 1, 2]);
+            /// // The additional argument represents the vector dimension.
+            /// let dv = DVector::from_column_slice(&[0, 1, 2]);
+            /// let m = Matrix2x3::from_column_slice(&[0, 1, 2, 3, 4, 5]);
+            /// // The two additional arguments represent the matrix dimensions.
+            /// let dm = DMatrix::from_column_slice(2, 3, &[0, 1, 2, 3, 4, 5]);
+            ///
+            /// assert!(v.x == 0 && v.y == 1 && v.z == 2);
+            /// assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
+            /// assert!(m.m11 == 0 && m.m12 == 2 && m.m13 == 4 &&
+            ///         m.m21 == 1 && m.m22 == 3 && m.m23 == 5);
+            /// assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 2 && dm[(0, 2)] == 4 &&
+            ///         dm[(1, 0)] == 1 && dm[(1, 1)] == 3 && dm[(1, 2)] == 5);
+            /// ```
+            #[inline]
+            pub fn from_column_slice($($args: usize,)* $data: &[N]) -> Self {
+                Self::from_column_slice_generic($($gargs, )* $data)
+            }
+
+            /// Creates a matrix backed by a given `Vec`.
+            ///
+            /// The output matrix is filled column-by-column.
+            ///
+            /// # Example
+            /// ```
+            /// # use nalgebra::{DMatrix, Matrix2x3};
+            ///
+            /// let m = Matrix2x3::from_vec(vec![0, 1, 2, 3, 4, 5]);
+            ///
+            /// assert!(m.m11 == 0 && m.m12 == 2 && m.m13 == 4 &&
+            ///         m.m21 == 1 && m.m22 == 3 && m.m23 == 5);
+            ///
+            ///
+            /// // The two additional arguments represent the matrix dimensions.
+            /// let dm = DMatrix::from_vec(2, 3, vec![0, 1, 2, 3, 4, 5]);
+            ///
+            /// assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 2 && dm[(0, 2)] == 4 &&
+            ///         dm[(1, 0)] == 1 && dm[(1, 1)] == 3 && dm[(1, 2)] == 5);
+            /// ```
+            #[inline]
+            #[cfg(feature = "std")]
+            pub fn from_vec($($args: usize,)* $data: Vec<N>) -> Self {
+                Self::from_vec_generic($($gargs, )* $data)
+            }
+        }
+    }
+);
+
+// FIXME: this is not very pretty. We could find a better call syntax.
+impl_constructors_from_data!(data; R, C;                  // Arguments for Matrix<N, ..., S>
+                            => R: DimName, => C: DimName; // Type parameters for impl<N, ..., S>
+                            R::name(), C::name();         // Arguments for `_generic` constructors.
+                            ); // Arguments for non-generic constructors.
+
+impl_constructors_from_data!(data; R, Dynamic;
+                            => R: DimName;
+                            R::name(), Dynamic::new(data.len() / R::dim());
+                            );
+
+impl_constructors_from_data!(data; Dynamic, C;
+                            => C: DimName;
+                            Dynamic::new(data.len() / C::dim()), C::name();
+                            );
+
+impl_constructors_from_data!(data; Dynamic, Dynamic;
+                            ;
+                            Dynamic::new(nrows), Dynamic::new(ncols);
+                            nrows, ncols);
+
+
+
 /*
  *
  * Zero, One, Rand traits.

src/base/conversion.rs

@@ -12,8 +12,10 @@ use typenum::Prod;
 use base::allocator::{Allocator, SameShapeAllocator};
 use base::constraint::{SameNumberOfColumns, SameNumberOfRows, ShapeConstraint};
 use base::dimension::{
-    Dim, DimName, Dynamic, U1, U10, U11, U12, U13, U14, U15, U16, U2, U3, U4, U5, U6, U7, U8, U9,
+    Dim, DimName, U1, U10, U11, U12, U13, U14, U15, U16, U2, U3, U4, U5, U6, U7, U8, U9,
 };
+#[cfg(any(feature = "std", feature = "alloc"))]
+use base::dimension::Dynamic;
 use base::iter::{MatrixIter, MatrixIterMut};
 use base::storage::{ContiguousStorage, ContiguousStorageMut, Storage, StorageMut};
 #[cfg(any(feature = "std", feature = "alloc"))]

src/base/dimension.rs

@@ -22,8 +22,8 @@ pub struct Dynamic {
 impl Dynamic {
     /// A dynamic size equal to `value`.
     #[inline]
-    pub fn new(value: usize) -> Dynamic {
+    pub fn new(value: usize) -> Self {
-        Dynamic { value: value }
+        Self { value: value }
     }
 }
 
@@ -80,7 +80,7 @@ impl Dim for Dynamic {
 
     #[inline]
     fn from_usize(dim: usize) -> Self {
-        Dynamic::new(dim)
+        Self::new(dim)
     }
 
     #[inline]
@@ -93,8 +93,8 @@ impl Add<usize> for Dynamic {
     type Output = Dynamic;
 
     #[inline]
-    fn add(self, rhs: usize) -> Dynamic {
+    fn add(self, rhs: usize) -> Self {
-        Dynamic::new(self.value + rhs)
+        Self::new(self.value + rhs)
     }
 }
 
@@ -102,8 +102,8 @@ impl Sub<usize> for Dynamic {
     type Output = Dynamic;
 
     #[inline]
-    fn sub(self, rhs: usize) -> Dynamic {
+    fn sub(self, rhs: usize) -> Self {
-        Dynamic::new(self.value - rhs)
+        Self::new(self.value - rhs)
     }
 }
 
@@ -364,7 +364,8 @@ impl<
         G: Bit + Any + Debug + Copy + PartialEq + Send + Sync,
     > IsNotStaticOne
     for UInt<UInt<UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, A>, B>, C>, D>, E>, F>, G>
-{}
+{
+}
 
 impl<U: Unsigned + DimName, B: Bit + Any + Debug + Copy + PartialEq + Send + Sync> NamedDim
     for UInt<U, B>
@@ -405,4 +406,5 @@ impl<U: Unsigned + DimName, B: Bit + Any + Debug + Copy + PartialEq + Send + Syn
 
 impl<U: Unsigned + DimName, B: Bit + Any + Debug + Copy + PartialEq + Send + Sync> IsNotStaticOne
     for UInt<U, B>
-{}
+{
+}

src/base/edition.rs

@@ -1,12 +1,18 @@
 use num::{One, Zero};
 use std::cmp;
 use std::ptr;
+#[cfg(any(feature = "std", feature = "alloc"))]
+use std::iter::ExactSizeIterator;
+#[cfg(any(feature = "std", feature = "alloc"))]
+use std::mem;
 
 use base::allocator::{Allocator, Reallocator};
 use base::constraint::{DimEq, SameNumberOfColumns, SameNumberOfRows, ShapeConstraint};
 use base::dimension::{
-    Dim, DimAdd, DimDiff, DimMin, DimMinimum, DimName, DimSub, DimSum, Dynamic, U1,
+    Dim, DimAdd, DimDiff, DimMin, DimMinimum, DimName, DimSub, DimSum, U1,
 };
+#[cfg(any(feature = "std", feature = "alloc"))]
+use base::dimension::Dynamic;
 use base::storage::{Storage, StorageMut};
 #[cfg(any(feature = "std", feature = "alloc"))]
 use base::DMatrix;
@@ -23,7 +29,7 @@ impl<N: Scalar + Zero, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
         res
     }
 
-    /// Extracts the upper triangular part of this matrix (including the diagonal).
+    /// Extracts the lower triangular part of this matrix (including the diagonal).
     #[inline]
     pub fn lower_triangle(&self) -> MatrixMN<N, R, C>
     where DefaultAllocator: Allocator<N, R, C> {
@@ -32,6 +38,54 @@ impl<N: Scalar + Zero, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
 
         res
     }
+
+    /// Creates a new matrix by extracting the given set of rows from `self`.
+    #[cfg(any(feature = "std", feature = "alloc"))]
+    pub fn select_rows<'a, I>(&self, irows: I) -> MatrixMN<N, Dynamic, C>
+        where I: IntoIterator<Item = &'a usize>,
+              I::IntoIter: ExactSizeIterator + Clone,
+              DefaultAllocator: Allocator<N, Dynamic, C> {
+        let irows = irows.into_iter();
+        let ncols = self.data.shape().1;
+        let mut res = unsafe { MatrixMN::new_uninitialized_generic(Dynamic::new(irows.len()), ncols) };
+
+        // First, check that all the indices from irows are valid.
+        // This will allow us to use unchecked access in the inner loop.
+        for i in irows.clone() {
+            assert!(*i < self.nrows(), "Row index out of bounds.")
+        }
+
+        for j in 0..ncols.value() {
+            // FIXME: use unchecked column indexing
+            let mut res = res.column_mut(j);
+            let mut src = self.column(j);
+
+            for (destination, source) in irows.clone().enumerate() {
+                unsafe {
+                    *res.vget_unchecked_mut(destination) = *src.vget_unchecked(*source)
+                }
+            }
+        }
+
+        res
+    }
+
+    /// Creates a new matrix by extracting the given set of columns from `self`.
+    #[cfg(any(feature = "std", feature = "alloc"))]
+    pub fn select_columns<'a, I>(&self, icols: I) -> MatrixMN<N, R, Dynamic>
+        where I: IntoIterator<Item = &'a usize>,
+              I::IntoIter: ExactSizeIterator,
+              DefaultAllocator: Allocator<N, R, Dynamic> {
+        let icols = icols.into_iter();
+        let nrows = self.data.shape().0;
+        let mut res = unsafe { MatrixMN::new_uninitialized_generic(nrows, Dynamic::new(icols.len())) };
+
+        for (destination, source) in icols.enumerate() {
+            res.column_mut(destination).copy_from(&self.column(*source))
+        }
+
+        res
+    }
 }
 
 impl<N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
@@ -248,6 +302,7 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
 
     /// Removes `n` consecutive columns from this matrix, starting with the `i`-th (included).
     #[inline]
+    #[cfg(any(feature = "std", feature = "alloc"))]
     pub fn remove_columns(self, i: usize, n: usize) -> MatrixMN<N, R, Dynamic>
     where
         C: DimSub<Dynamic, Output = Dynamic>,
@@ -330,6 +385,7 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
 
     /// Removes `n` consecutive rows from this matrix, starting with the `i`-th (included).
     #[inline]
+    #[cfg(any(feature = "std", feature = "alloc"))]
     pub fn remove_rows(self, i: usize, n: usize) -> MatrixMN<N, Dynamic, C>
     where
         R: DimSub<Dynamic, Output = Dynamic>,
@@ -407,6 +463,7 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
 
     /// Inserts `n` columns filled with `val` starting at the `i-th` position.
     #[inline]
+    #[cfg(any(feature = "std", feature = "alloc"))]
     pub fn insert_columns(self, i: usize, n: usize, val: N) -> MatrixMN<N, R, Dynamic>
     where
         C: DimAdd<Dynamic, Output = Dynamic>,
@@ -484,6 +541,7 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
 
     /// Inserts `n` rows filled with `val` starting at the `i-th` position.
     #[inline]
+    #[cfg(any(feature = "std", feature = "alloc"))]
     pub fn insert_rows(self, i: usize, n: usize, val: N) -> MatrixMN<N, Dynamic, C>
     where
         R: DimAdd<Dynamic, Output = Dynamic>,
@@ -549,6 +607,29 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
         self.resize_generic(Dynamic::new(new_nrows), Dynamic::new(new_ncols), val)
     }
 
+    /// Resizes this matrix vertically, i.e., so that it contains `new_nrows` rows while keeping the same number of columns.
+    ///
+    /// The values are copied such that `self[(i, j)] == result[(i, j)]`. If the result has more
+    /// rows than `self`, then the extra rows are filled with `val`.
+    #[cfg(any(feature = "std", feature = "alloc"))]
+    pub fn resize_vertically(self, new_nrows: usize, val: N) -> MatrixMN<N, Dynamic, C>
+        where DefaultAllocator: Reallocator<N, R, C, Dynamic, C> {
+        let ncols = self.data.shape().1;
+        self.resize_generic(Dynamic::new(new_nrows), ncols, val)
+    }
+
+    /// Resizes this matrix horizontally, i.e., so that it contains `new_ncolumns` columns while keeping the same number of columns.
+    ///
+    /// The values are copied such that `self[(i, j)] == result[(i, j)]`. If the result has more
+    /// columns than `self`, then the extra columns are filled with `val`.
+    #[cfg(any(feature = "std", feature = "alloc"))]
+    pub fn resize_horizontally(self, new_ncols: usize, val: N) -> MatrixMN<N, R, Dynamic>
+        where DefaultAllocator: Reallocator<N, R, C, R, Dynamic> {
+        let nrows = self.data.shape().0;
+        self.resize_generic(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
@@ -626,6 +707,61 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     }
 }
 
+#[cfg(any(feature = "std", feature = "alloc"))]
+impl<N: Scalar> DMatrix<N> {
+    /// Resizes this matrix in-place.
+    ///
+    /// 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`.
+    ///
+    /// Defined only for owned fully-dynamic matrices, i.e., `DMatrix`.
+    pub fn resize_mut(&mut self, new_nrows: usize, new_ncols: usize, val: N)
+        where DefaultAllocator: Reallocator<N, Dynamic, Dynamic, Dynamic, Dynamic> {
+        let placeholder = unsafe { Self::new_uninitialized(0, 0) };
+        let old = mem::replace(self, placeholder);
+        let new = old.resize(new_nrows, new_ncols, val);
+        let _ = mem::replace(self, new);
+    }
+}
+
+#[cfg(any(feature = "std", feature = "alloc"))]
+impl<N: Scalar, C: Dim> MatrixMN<N, Dynamic, C>
+    where DefaultAllocator: Allocator<N, Dynamic, C> {
+    /// Changes the number of rows of this matrix in-place.
+    ///
+    /// The values are copied such that `self[(i, j)] == result[(i, j)]`. If the result has more
+    /// rows than `self`, then the extra rows are filled with `val`.
+    ///
+    /// Defined only for owned matrices with a dynamic number of rows (for example, `DVector`).
+    #[cfg(any(feature = "std", feature = "alloc"))]
+    pub fn resize_vertically_mut(&mut self, new_nrows: usize, val: N)
+        where DefaultAllocator: Reallocator<N, Dynamic, C, Dynamic, C> {
+        let placeholder = unsafe { Self::new_uninitialized_generic(Dynamic::new(0), self.data.shape().1) };
+        let old = mem::replace(self, placeholder);
+        let new = old.resize_vertically(new_nrows, val);
+        let _ = mem::replace(self, new);
+    }
+}
+
+#[cfg(any(feature = "std", feature = "alloc"))]
+impl<N: Scalar, R: Dim> MatrixMN<N, R, Dynamic>
+    where DefaultAllocator: Allocator<N, R, Dynamic> {
+    /// Changes the number of column of this matrix in-place.
+    ///
+    /// The values are copied such that `self[(i, j)] == result[(i, j)]`. If the result has more
+    /// columns than `self`, then the extra columns are filled with `val`.
+    ///
+    /// Defined only for owned matrices with a dynamic number of columns (for example, `DVector`).
+    #[cfg(any(feature = "std", feature = "alloc"))]
+    pub fn resize_horizontally_mut(&mut self, new_ncols: usize, val: N)
+        where DefaultAllocator: Reallocator<N, R, Dynamic, R, Dynamic> {
+        let placeholder = unsafe { Self::new_uninitialized_generic(self.data.shape().0, Dynamic::new(0)) };
+        let old = mem::replace(self, placeholder);
+        let new = old.resize_horizontally(new_ncols, val);
+        let _ = mem::replace(self, new);
+    }
+}
+
 unsafe fn compress_rows<N: Scalar>(
     data: &mut [N],
     nrows: usize,
@@ -706,6 +842,7 @@ unsafe fn extend_rows<N: Scalar>(
 
 /// Extend the number of columns of the `Matrix` with elements from
 /// a given iterator.
+#[cfg(any(feature = "std", feature = "alloc"))]
 impl<N, R, S> Extend<N> for Matrix<N, R, Dynamic, S>
 where
     N: Scalar,
@@ -753,6 +890,7 @@ where
 
 /// Extend the number of rows of the `Vector` with elements from
 /// a given iterator.
+#[cfg(any(feature = "std", feature = "alloc"))]
 impl<N, S> Extend<N> for Matrix<N, Dynamic, U1, S>
 where
     N: Scalar,
@@ -764,15 +902,16 @@ where
     /// # Example
     /// ```
     /// # use nalgebra::DVector;
-    /// let mut vector = DVector::from_vec(3, vec![0, 1, 2]);
+    /// let mut vector = DVector::from_vec(vec![0, 1, 2]);
     /// vector.extend(vec![3, 4, 5]);
-    /// assert!(vector.eq(&DVector::from_vec(6, vec![0, 1, 2, 3, 4, 5])));
+    /// assert!(vector.eq(&DVector::from_vec(vec![0, 1, 2, 3, 4, 5])));
     /// ```
     fn extend<I: IntoIterator<Item=N>>(&mut self, iter: I) {
         self.data.extend(iter);
     }
 }
 
+#[cfg(any(feature = "std", feature = "alloc"))]
 impl<N, R, S, RV, SV> Extend<Vector<N, RV, SV>> for Matrix<N, R, Dynamic, S>
 where
     N: Scalar,

src/base/iter.rs

@@ -3,9 +3,9 @@
 use std::marker::PhantomData;
 use std::mem;
 
-use base::dimension::Dim;
+use base::dimension::{Dim, U1};
 use base::storage::{Storage, StorageMut};
-use base::Scalar;
+use base::{Scalar, Matrix, MatrixSlice, MatrixSliceMut};
 
 macro_rules! iterator {
     (struct $Name:ident for $Storage:ident.$ptr: ident -> $Ptr:ty, $Ref:ty, $SRef: ty) => {
@@ -96,3 +96,226 @@ macro_rules! iterator {
 
 iterator!(struct MatrixIter for Storage.ptr -> *const N, &'a N, &'a S);
 iterator!(struct MatrixIterMut for StorageMut.ptr_mut -> *mut N, &'a mut N, &'a mut S);
+
+
+/*
+ *
+ * Row iterators.
+ *
+ */
+#[derive(Clone)]
+/// An iterator through the rows of a matrix.
+pub struct RowIter<'a, N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> {
+    mat: &'a Matrix<N, R, C, S>,
+    curr: usize
+}
+
+impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + Storage<N, R, C>> RowIter<'a, N, R, C, S> {
+    pub(crate) fn new(mat: &'a Matrix<N, R, C, S>) -> Self {
+        RowIter {
+            mat, curr: 0
+        }
+    }
+}
+
+
+impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + Storage<N, R, C>> Iterator for RowIter<'a, N, R, C, S> {
+    type Item = MatrixSlice<'a, N, U1, C, S::RStride, S::CStride>;
+
+    #[inline]
+    fn next(&mut self) -> Option<Self::Item> {
+        if self.curr < self.mat.nrows() {
+            let res = self.mat.row(self.curr);
+            self.curr += 1;
+            Some(res)
+        } else {
+            None
+        }
+    }
+
+    #[inline]
+    fn size_hint(&self) -> (usize, Option<usize>) {
+        (self.mat.nrows() - self.curr, Some(self.mat.nrows() - self.curr))
+    }
+
+    #[inline]
+    fn count(self) -> usize {
+        self.mat.nrows() - self.curr
+    }
+}
+
+impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + Storage<N, R, C>> ExactSizeIterator for RowIter<'a, N, R, C, S> {
+    #[inline]
+    fn len(&self) -> usize {
+        self.mat.nrows() - self.curr
+    }
+}
+
+
+/// An iterator through the mutable rows of a matrix.
+pub struct RowIterMut<'a, N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> {
+    mat: *mut Matrix<N, R, C, S>,
+    curr: usize,
+    phantom: PhantomData<&'a mut Matrix<N, R, C, S>>
+}
+
+impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + StorageMut<N, R, C>> RowIterMut<'a, N, R, C, S> {
+    pub(crate) fn new(mat: &'a mut Matrix<N, R, C, S>) -> Self {
+        RowIterMut {
+            mat,
+            curr: 0,
+            phantom: PhantomData
+        }
+    }
+
+    fn nrows(&self) -> usize {
+        unsafe {
+            (*self.mat).nrows()
+        }
+    }
+}
+
+
+impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + StorageMut<N, R, C>> Iterator for RowIterMut<'a, N, R, C, S> {
+    type Item = MatrixSliceMut<'a, N, U1, C, S::RStride, S::CStride>;
+
+    #[inline]
+    fn next(&mut self) -> Option<Self::Item> {
+        if self.curr < self.nrows() {
+            let res = unsafe { (*self.mat).row_mut(self.curr) };
+            self.curr += 1;
+            Some(res)
+        } else {
+            None
+        }
+    }
+
+    #[inline]
+    fn size_hint(&self) -> (usize, Option<usize>) {
+        (self.nrows() - self.curr, Some(self.nrows() - self.curr))
+    }
+
+    #[inline]
+    fn count(self) -> usize {
+        self.nrows() - self.curr
+    }
+}
+
+impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + StorageMut<N, R, C>> ExactSizeIterator for RowIterMut<'a, N, R, C, S> {
+    #[inline]
+    fn len(&self) -> usize {
+        self.nrows() - self.curr
+    }
+}
+
+
+/*
+ *
+ * Column iterators.
+ *
+ */
+#[derive(Clone)]
+/// An iterator through the columns of a matrix.
+pub struct ColumnIter<'a, N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> {
+    mat: &'a Matrix<N, R, C, S>,
+    curr: usize
+}
+
+impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + Storage<N, R, C>> ColumnIter<'a, N, R, C, S> {
+    pub(crate) fn new(mat: &'a Matrix<N, R, C, S>) -> Self {
+        ColumnIter {
+            mat, curr: 0
+        }
+    }
+}
+
+
+impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + Storage<N, R, C>> Iterator for ColumnIter<'a, N, R, C, S> {
+    type Item = MatrixSlice<'a, N, R, U1, S::RStride, S::CStride>;
+
+    #[inline]
+    fn next(&mut self) -> Option<Self::Item> {
+        if self.curr < self.mat.ncols() {
+            let res = self.mat.column(self.curr);
+            self.curr += 1;
+            Some(res)
+        } else {
+            None
+        }
+    }
+
+    #[inline]
+    fn size_hint(&self) -> (usize, Option<usize>) {
+        (self.mat.ncols() - self.curr, Some(self.mat.ncols() - self.curr))
+    }
+
+    #[inline]
+    fn count(self) -> usize {
+        self.mat.ncols() - self.curr
+    }
+}
+
+impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + Storage<N, R, C>> ExactSizeIterator for ColumnIter<'a, N, R, C, S> {
+    #[inline]
+    fn len(&self) -> usize {
+        self.mat.ncols() - self.curr
+    }
+}
+
+
+/// An iterator through the mutable columns of a matrix.
+pub struct ColumnIterMut<'a, N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> {
+    mat: *mut Matrix<N, R, C, S>,
+    curr: usize,
+    phantom: PhantomData<&'a mut Matrix<N, R, C, S>>
+}
+
+impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + StorageMut<N, R, C>> ColumnIterMut<'a, N, R, C, S> {
+    pub(crate) fn new(mat: &'a mut Matrix<N, R, C, S>) -> Self {
+        ColumnIterMut {
+            mat,
+            curr: 0,
+            phantom: PhantomData
+        }
+    }
+
+    fn ncols(&self) -> usize {
+        unsafe {
+            (*self.mat).ncols()
+        }
+    }
+}
+
+
+impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + StorageMut<N, R, C>> Iterator for ColumnIterMut<'a, N, R, C, S> {
+    type Item = MatrixSliceMut<'a, N, R, U1, S::RStride, S::CStride>;
+
+    #[inline]
+    fn next(&mut self) -> Option<Self::Item> {
+        if self.curr < self.ncols() {
+            let res = unsafe { (*self.mat).column_mut(self.curr) };
+            self.curr += 1;
+            Some(res)
+        } else {
+            None
+        }
+    }
+
+    #[inline]
+    fn size_hint(&self) -> (usize, Option<usize>) {
+        (self.ncols() - self.curr, Some(self.ncols() - self.curr))
+    }
+
+    #[inline]
+    fn count(self) -> usize {
+        self.ncols() - self.curr
+    }
+}
+
+impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + StorageMut<N, R, C>> ExactSizeIterator for ColumnIterMut<'a, N, R, C, S> {
+    #[inline]
+    fn len(&self) -> usize {
+        self.ncols() - self.curr
+    }
+}
+

src/base/matrix.rs

@@ -22,7 +22,7 @@ use alga::general::{ClosedAdd, ClosedMul, ClosedSub, Real, Ring};
 use base::allocator::{Allocator, SameShapeAllocator, SameShapeC, SameShapeR};
 use base::constraint::{DimEq, SameNumberOfColumns, SameNumberOfRows, ShapeConstraint};
 use base::dimension::{Dim, DimAdd, DimSum, IsNotStaticOne, U1, U2, U3};
-use base::iter::{MatrixIter, MatrixIterMut};
+use base::iter::{MatrixIter, MatrixIterMut, RowIter, RowIterMut, ColumnIter, ColumnIterMut};
 use base::storage::{
     ContiguousStorage, ContiguousStorageMut, Owned, SameShapeStorage, Storage, StorageMut,
 };
@@ -152,7 +152,7 @@ impl<N: Scalar, R: Dim, C: Dim, S> Matrix<N, R, C, S> {
 impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /// Creates a new matrix with the given data.
     #[inline]
-    pub fn from_data(data: S) -> Matrix<N, R, C, S> {
+    pub fn from_data(data: S) -> Self {
         unsafe { Self::from_data_statically_unchecked(data) }
     }
 
@@ -247,6 +247,37 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
         MatrixIter::new(&self.data)
     }
 
+    /// Iterate through the rows of this matrix.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::Matrix2x3;
+    /// let mut a = Matrix2x3::new(1, 2, 3,
+    ///                            4, 5, 6);
+    /// for (i, row) in a.row_iter().enumerate() {
+    ///     assert_eq!(row, a.row(i))
+    /// }
+    /// ```
+    #[inline]
+    pub fn row_iter(&self) -> RowIter<N, R, C, S> {
+        RowIter::new(self)
+    }
+
+    /// Iterate through the columns of this matrix.
+    /// # Example
+    /// ```
+    /// # use nalgebra::Matrix2x3;
+    /// let mut a = Matrix2x3::new(1, 2, 3,
+    ///                            4, 5, 6);
+    /// for (i, column) in a.column_iter().enumerate() {
+    ///     assert_eq!(column, a.column(i))
+    /// }
+    /// ```
+    #[inline]
+    pub fn column_iter(&self) -> ColumnIter<N, R, C, S> {
+        ColumnIter::new(self)
+    }
+
     /// Computes the row and column coordinates of the i-th element of this matrix seen as a
     /// vector.
     #[inline]
@@ -264,6 +295,15 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
         }
     }
 
+    /// Returns a pointer to the start of the matrix.
+    ///
+    /// If the matrix is not empty, this pointer is guaranteed to be aligned
+    /// and non-null.
+    #[inline]
+    pub fn as_ptr(&self) -> *const N {
+        self.data.ptr()
+    }
+
     /// Tests whether `self` and `rhs` are equal up to a given epsilon.
     ///
     /// See `relative_eq` from the `RelativeEq` trait for more details.
@@ -393,7 +433,7 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     }
 
     /// Returns a matrix containing the result of `f` applied to each of its entries. Unlike `map`,
-    /// `f` also gets passed the row and column index, i.e. `f(value, row, col)`.
+    /// `f` also gets passed the row and column index, i.e. `f(row, col, value)`.
     #[inline]
     pub fn map_with_location<N2: Scalar, F: FnMut(usize, usize, N) -> N2>(
         &self,
@@ -493,6 +533,57 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
         res
     }
 
+    /// Folds a function `f` on each entry of `self`.
+    #[inline]
+    pub fn fold<Acc>(&self, init: Acc, mut f: impl FnMut(Acc, N) -> Acc) -> Acc {
+        let (nrows, ncols) = self.data.shape();
+
+        let mut res = init;
+
+        for j in 0..ncols.value() {
+            for i in 0..nrows.value() {
+                unsafe {
+                    let a = *self.data.get_unchecked(i, j);
+                    res = f(res, a)
+                }
+            }
+        }
+
+        res
+    }
+
+    /// Folds a function `f` on each pairs of entries from `self` and `rhs`.
+    #[inline]
+    pub fn zip_fold<N2, R2, C2, S2, Acc>(&self, rhs: &Matrix<N2, R2, C2, S2>, init: Acc, mut f: impl FnMut(Acc, N, N2) -> Acc) -> Acc
+        where
+            N2: Scalar,
+            R2: Dim,
+            C2: Dim,
+            S2: Storage<N2, R2, C2>,
+            ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>
+    {
+        let (nrows, ncols) = self.data.shape();
+
+        let mut res = init;
+
+        assert!(
+            (nrows.value(), ncols.value()) == rhs.shape(),
+            "Matrix simultaneous traversal error: dimension mismatch."
+        );
+
+        for j in 0..ncols.value() {
+            for i in 0..nrows.value() {
+                unsafe {
+                    let a = *self.data.get_unchecked(i, j);
+                    let b = *rhs.data.get_unchecked(i, j);
+                    res = f(res, a, b)
+                }
+            }
+        }
+
+        res
+    }
+
     /// Transposes `self` and store the result into `out`.
     #[inline]
     pub fn transpose_to<R2, C2, SB>(&self, out: &mut Matrix<N, R2, C2, SB>)
@@ -540,6 +631,55 @@ impl<N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
         MatrixIterMut::new(&mut self.data)
     }
 
+    /// Returns a mutable pointer to the start of the matrix.
+    ///
+    /// If the matrix is not empty, this pointer is guaranteed to be aligned
+    /// and non-null.
+    #[inline]
+    pub fn as_mut_ptr(&mut self) -> *mut N {
+        self.data.ptr_mut()
+    }
+
+    /// Mutably iterates through this matrix rows.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::Matrix2x3;
+    /// let mut a = Matrix2x3::new(1, 2, 3,
+    ///                            4, 5, 6);
+    /// for (i, mut row) in a.row_iter_mut().enumerate() {
+    ///     row *= (i + 1) * 10;
+    /// }
+    ///
+    /// let expected = Matrix2x3::new(10, 20, 30,
+    ///                               80, 100, 120);
+    /// assert_eq!(a, expected);
+    /// ```
+    #[inline]
+    pub fn row_iter_mut(&mut self) -> RowIterMut<N, R, C, S> {
+        RowIterMut::new(self)
+    }
+
+    /// Mutably iterates through this matrix columns.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::Matrix2x3;
+    /// let mut a = Matrix2x3::new(1, 2, 3,
+    ///                            4, 5, 6);
+    /// for (i, mut col) in a.column_iter_mut().enumerate() {
+    ///     col *= (i + 1) * 10;
+    /// }
+    ///
+    /// let expected = Matrix2x3::new(10, 40, 90,
+    ///                               40, 100, 180);
+    /// assert_eq!(a, expected);
+    /// ```
+    #[inline]
+    pub fn column_iter_mut(&mut self) -> ColumnIterMut<N, R, C, S> {
+        ColumnIterMut::new(self)
+    }
+
     /// Swaps two entries without bound-checking.
     #[inline]
     pub unsafe fn swap_unchecked(&mut self, row_cols1: (usize, usize), row_cols2: (usize, usize)) {
@@ -633,8 +773,7 @@ impl<N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
 
     /// Replaces each component of `self` by the result of a closure `f` applied on it.
     #[inline]
-    pub fn apply<F: FnMut(N) -> N>(&mut self, mut f: F)
+    pub fn apply<F: FnMut(N) -> N>(&mut self, mut f: F) {
-    where DefaultAllocator: Allocator<N, R, C> {
         let (nrows, ncols) = self.shape();
 
         for j in 0..ncols {
@@ -646,6 +785,71 @@ impl<N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
             }
         }
     }
+
+    /// Replaces each component of `self` by the result of a closure `f` applied on its components
+    /// joined with the components from `rhs`.
+    #[inline]
+    pub fn zip_apply<N2, R2, C2, S2>(&mut self, rhs: &Matrix<N2, R2, C2, S2>, mut f: impl FnMut(N, N2) -> N)
+        where N2: Scalar,
+              R2: Dim,
+              C2: Dim,
+              S2: Storage<N2, R2, C2>,
+              ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2> {
+        let (nrows, ncols) = self.shape();
+
+        assert!(
+            (nrows, ncols) == rhs.shape(),
+            "Matrix simultaneous traversal error: dimension mismatch."
+        );
+
+        for j in 0..ncols {
+            for i in 0..nrows {
+                unsafe {
+                    let e = self.data.get_unchecked_mut(i, j);
+                    let rhs = rhs.get_unchecked((i, j));
+                    *e = f(*e, *rhs)
+                }
+            }
+        }
+    }
+
+
+    /// Replaces each component of `self` by the result of a closure `f` applied on its components
+    /// joined with the components from `b` and `c`.
+    #[inline]
+    pub fn zip_zip_apply<N2, R2, C2, S2, N3, R3, C3, S3>(&mut self, b: &Matrix<N2, R2, C2, S2>, c: &Matrix<N3, R3, C3, S3>, mut f: impl FnMut(N, N2, N3) -> N)
+        where N2: Scalar,
+              R2: Dim,
+              C2: Dim,
+              S2: Storage<N2, R2, C2>,
+              N3: Scalar,
+              R3: Dim,
+              C3: Dim,
+              S3: Storage<N3, R3, C3>,
+              ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
+              ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2> {
+        let (nrows, ncols) = self.shape();
+
+        assert!(
+            (nrows, ncols) == b.shape(),
+            "Matrix simultaneous traversal error: dimension mismatch."
+        );
+        assert!(
+            (nrows, ncols) == c.shape(),
+            "Matrix simultaneous traversal error: dimension mismatch."
+        );
+
+        for j in 0..ncols {
+            for i in 0..nrows {
+                unsafe {
+                    let e = self.data.get_unchecked_mut(i, j);
+                    let b = b.get_unchecked((i, j));
+                    let c = c.get_unchecked((i, j));
+                    *e = f(*e, *b, *c)
+                }
+            }
+        }
+    }
 }
 
 impl<N: Scalar, D: Dim, S: Storage<N, D>> Vector<N, D, S> {
@@ -832,14 +1036,7 @@ impl<N: Scalar + Zero, D: DimAdd<U1>, S: Storage<N, D>> Vector<N, D, S> {
     #[inline]
     pub fn to_homogeneous(&self) -> VectorN<N, DimSum<D, U1>>
     where DefaultAllocator: Allocator<N, DimSum<D, U1>> {
-        let len = self.len();
+        self.push(N::zero())
-        let hnrows = DimSum::<D, U1>::from_usize(len + 1);
-        let mut res = unsafe { VectorN::<N, _>::new_uninitialized_generic(hnrows, U1) };
-        res.generic_slice_mut((0, 0), self.data.shape())
-            .copy_from(self);
-        res[(len, 0)] = N::zero();
-
-        res
     }
 
     /// Constructs a vector from coordinates in projective space, i.e., removes a `0` at the end of
@@ -859,6 +1056,22 @@ impl<N: Scalar + Zero, D: DimAdd<U1>, S: Storage<N, D>> Vector<N, D, S> {
     }
 }
 
+impl<N: Scalar + Zero, D: DimAdd<U1>, S: Storage<N, D>> Vector<N, D, S> {
+    /// Constructs a new vector of higher dimension by appending `element` to the end of `self`.
+    #[inline]
+    pub fn push(&self, element: N) -> VectorN<N, DimSum<D, U1>>
+    where DefaultAllocator: Allocator<N, DimSum<D, U1>> {
+        let len = self.len();
+        let hnrows = DimSum::<D, U1>::from_usize(len + 1);
+        let mut res = unsafe { VectorN::<N, _>::new_uninitialized_generic(hnrows, U1) };
+        res.generic_slice_mut((0, 0), self.data.shape())
+            .copy_from(self);
+        res[(len, 0)] = element;
+
+        res
+    }
+}
+
 impl<N, R: Dim, C: Dim, S> AbsDiffEq for Matrix<N, R, C, S>
 where
     N: Scalar + AbsDiffEq,
@@ -1242,67 +1455,6 @@ impl<N: Real, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     }
 }
 
-impl<N: Real, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
-    /// The squared L2 norm of this vector.
-    #[inline]
-    pub fn norm_squared(&self) -> N {
-        let mut res = N::zero();
-
-        for i in 0..self.ncols() {
-            let col = self.column(i);
-            res += col.dot(&col)
-        }
-
-        res
-    }
-
-    /// The L2 norm of this matrix.
-    #[inline]
-    pub fn norm(&self) -> N {
-        self.norm_squared().sqrt()
-    }
-
-    /// A synonym for the norm of this matrix.
-    ///
-    /// Aka the length.
-    ///
-    /// This function is simply implemented as a call to `norm()`
-    #[inline]
-    pub fn magnitude(&self) -> N {
-        self.norm()
-    }
-
-    /// A synonym for the squared norm of this matrix.
-    ///
-    /// Aka the squared length.
-    ///
-    /// This function is simply implemented as a call to `norm_squared()`
-    #[inline]
-    pub fn magnitude_squared(&self) -> N {
-        self.norm_squared()
-    }
-
-    /// Returns a normalized version of this matrix.
-    #[inline]
-    pub fn normalize(&self) -> MatrixMN<N, R, C>
-    where DefaultAllocator: Allocator<N, R, C> {
-        self / self.norm()
-    }
-
-    /// Returns a normalized version of this matrix unless its norm as smaller or equal to `eps`.
-    #[inline]
-    pub fn try_normalize(&self, min_norm: N) -> Option<MatrixMN<N, R, C>>
-    where DefaultAllocator: Allocator<N, R, C> {
-        let n = self.norm();
-
-        if n <= min_norm {
-            None
-        } else {
-            Some(self / n)
-        }
-    }
-}
-
 impl<N: Scalar + Zero + One + ClosedAdd + ClosedSub + ClosedMul, D: Dim, S: Storage<N, D>>
     Vector<N, D, S>
 {
@@ -1377,32 +1529,6 @@ impl<N: Real, D: Dim, S: Storage<N, D>> Unit<Vector<N, D, S>> {
     }
 }
 
-impl<N: Real, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
-    /// Normalizes this matrix in-place and returns its norm.
-    #[inline]
-    pub fn normalize_mut(&mut self) -> N {
-        let n = self.norm();
-        *self /= n;
-
-        n
-    }
-
-    /// Normalizes this matrix in-place or does nothing if its norm is smaller or equal to `eps`.
-    ///
-    /// If the normalization succeeded, returns the old normal of this matrix.
-    #[inline]
-    pub fn try_normalize_mut(&mut self, min_norm: N) -> Option<N> {
-        let n = self.norm();
-
-        if n <= min_norm {
-            None
-        } else {
-            *self /= n;
-            Some(n)
-        }
-    }
-}
-
 impl<N, R: Dim, C: Dim, S> AbsDiffEq for Unit<Matrix<N, R, C, S>>
 where
     N: Scalar + AbsDiffEq,

src/base/matrix_alga.rs

@@ -6,7 +6,7 @@ use num::{One, Zero};
 use alga::general::{
     AbstractGroup, AbstractGroupAbelian, AbstractLoop, AbstractMagma, AbstractModule,
     AbstractMonoid, AbstractQuasigroup, AbstractSemigroup, Additive, ClosedAdd, ClosedMul,
-    ClosedNeg, Field, Identity, Inverse, JoinSemilattice, Lattice, MeetSemilattice, Module,
+    ClosedNeg, Field, Identity, TwoSidedInverse, JoinSemilattice, Lattice, MeetSemilattice, Module,
     Multiplicative, Real, RingCommutative,
 };
 use alga::linear::{
@@ -45,18 +45,18 @@ where
     }
 }
 
-impl<N, R: DimName, C: DimName> Inverse<Additive> for MatrixMN<N, R, C>
+impl<N, R: DimName, C: DimName> TwoSidedInverse<Additive> for MatrixMN<N, R, C>
 where
     N: Scalar + ClosedNeg,
     DefaultAllocator: Allocator<N, R, C>,
 {
     #[inline]
-    fn inverse(&self) -> MatrixMN<N, R, C> {
+    fn two_sided_inverse(&self) -> Self {
         -self
     }
 
     #[inline]
-    fn inverse_mut(&mut self) {
+    fn two_sided_inverse_mut(&mut self) {
         *self = -self.clone()
     }
 }
@@ -203,7 +203,7 @@ impl<N: Real, R: DimName, C: DimName> FiniteDimInnerSpace for MatrixMN<N, R, C>
 where DefaultAllocator: Allocator<N, R, C>
 {
     #[inline]
-    fn orthonormalize(vs: &mut [MatrixMN<N, R, C>]) -> usize {
+    fn orthonormalize(vs: &mut [Self]) -> usize {
         let mut nbasis_elements = 0;
 
         for i in 0..vs.len() {

src/base/matrix_slice.rs

@@ -4,9 +4,9 @@ use std::slice;
 
 use base::allocator::Allocator;
 use base::default_allocator::DefaultAllocator;
-use base::dimension::{Dim, DimName, Dynamic, U1};
+use base::dimension::{Dim, DimName, Dynamic, U1, IsNotStaticOne};
 use base::iter::MatrixIter;
-use base::storage::{Owned, Storage, StorageMut};
+use base::storage::{Owned, Storage, StorageMut, ContiguousStorage, ContiguousStorageMut};
 use base::{Matrix, Scalar};
 
 macro_rules! slice_storage_impl(
@@ -91,14 +91,15 @@ 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> Copy
     for SliceStorage<'a, N, R, C, RStride, CStride>
-{}
+{
+}
 
 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 {
+        Self {
             ptr: self.ptr,
             shape: self.shape,
             strides: self.strides,
@@ -146,8 +147,6 @@ macro_rules! storage_impl(
                 }
             }
 
-
-
             #[inline]
             fn into_owned(self) -> Owned<N, R, C>
                 where DefaultAllocator: Allocator<N, R, C> {
@@ -199,6 +198,14 @@ unsafe impl<'a, N: Scalar, R: Dim, C: Dim, RStride: Dim, CStride: Dim> StorageMu
     }
 }
 
+unsafe impl<'a, N: Scalar, R: Dim, CStride: Dim> ContiguousStorage<N, R, U1> for SliceStorage<'a, N, R, U1, U1, CStride> { }
+unsafe impl<'a, N: Scalar, R: Dim, CStride: Dim> ContiguousStorage<N, R, U1> for SliceStorageMut<'a, N, R, U1, U1, CStride> { }
+unsafe impl<'a, N: Scalar, R: Dim, CStride: Dim> ContiguousStorageMut<N, R, U1> for SliceStorageMut<'a, N, R, U1, U1, CStride> { }
+
+unsafe impl<'a, N: Scalar, R: DimName, C: Dim + IsNotStaticOne> ContiguousStorage<N, R, C> for SliceStorage<'a, N, R, C, U1, R> { }
+unsafe impl<'a, N: Scalar, R: DimName, C: Dim + IsNotStaticOne> ContiguousStorage<N, R, C> for SliceStorageMut<'a, N, R, C, U1, R> { }
+unsafe impl<'a, N: Scalar, R: DimName, C: Dim + IsNotStaticOne> ContiguousStorageMut<N, R, C> for SliceStorageMut<'a, N, R, C, U1, R> { }
+
 impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     #[inline]
     fn assert_slice_index(
@@ -859,3 +866,25 @@ impl<N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
         self.slice_range_mut(.., cols)
     }
 }
+
+
+impl<'a, N, R, C, RStride, CStride> From<MatrixSliceMut<'a, N, R, C, RStride, CStride>>
+for MatrixSlice<'a, N, R, C, RStride, CStride>
+    where
+        N: Scalar,
+        R: Dim,
+        C: Dim,
+        RStride: Dim,
+        CStride: Dim,
+{
+    fn from(slice_mut: MatrixSliceMut<'a, N, R, C, RStride, CStride>) -> Self {
+        let data = SliceStorage {
+            ptr:       slice_mut.data.ptr,
+            shape:     slice_mut.data.shape,
+            strides:   slice_mut.data.strides,
+            _phantoms: PhantomData,
+        };
+
+        unsafe { Matrix::from_data_statically_unchecked(data) }
+    }
+}

src/base/mod.rs

@@ -29,6 +29,8 @@ mod properties;
 mod scalar;
 mod swizzle;
 mod unit;
+mod statistics;
+mod norm;
 
 #[doc(hidden)]
 pub mod helper;
@@ -36,6 +38,7 @@ pub mod helper;
 pub use self::matrix::*;
 pub use self::scalar::*;
 pub use self::unit::*;
+pub use self::norm::*;
 
 pub use self::default_allocator::*;
 pub use self::dimension::*;

src/base/norm.rs

@@ -0,0 +1,238 @@
+use num::Signed;
+use std::cmp::PartialOrd;
+
+use allocator::Allocator;
+use ::{Real, Scalar};
+use storage::{Storage, StorageMut};
+use base::{DefaultAllocator, Matrix, Dim, MatrixMN};
+use constraint::{SameNumberOfRows, SameNumberOfColumns, ShapeConstraint};
+
+
+// FIXME: this should be be a trait on alga?
+/// A trait for abstract matrix norms.
+///
+/// This may be moved to the alga crate in the future.
+pub trait Norm<N: Scalar> {
+    /// Apply this norm to the given matrix.
+    fn norm<R, C, S>(&self, m: &Matrix<N, R, C, S>) -> N
+        where R: Dim, C: Dim, S: Storage<N, R, C>;
+    /// Use the metric induced by this norm to compute the metric distance between the two given matrices.
+    fn metric_distance<R1, C1, S1, R2, C2, S2>(&self, m1: &Matrix<N, R1, C1, S1>, m2: &Matrix<N, R2, C2, S2>) -> N
+        where R1: Dim, C1: Dim, S1: Storage<N, R1, C1>,
+              R2: Dim, C2: Dim, S2: Storage<N, R2, C2>,
+              ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>;
+}
+
+/// Euclidean norm.
+pub struct EuclideanNorm;
+/// Lp norm.
+pub struct LpNorm(pub i32);
+/// L-infinite norm aka. Chebytchev norm aka. uniform norm aka. suppremum norm.
+pub struct UniformNorm;
+
+impl<N: Real> Norm<N> for EuclideanNorm {
+    #[inline]
+    fn norm<R, C, S>(&self, m: &Matrix<N, R, C, S>) -> N
+        where R: Dim, C: Dim, S: Storage<N, R, C> {
+        m.norm_squared().sqrt()
+    }
+
+    #[inline]
+    fn metric_distance<R1, C1, S1, R2, C2, S2>(&self, m1: &Matrix<N, R1, C1, S1>, m2: &Matrix<N, R2, C2, S2>) -> N
+        where R1: Dim, C1: Dim, S1: Storage<N, R1, C1>,
+              R2: Dim, C2: Dim, S2: Storage<N, R2, C2>,
+              ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
+        m1.zip_fold(m2, N::zero(), |acc, a, b| {
+            let diff = a - b;
+            acc + diff * diff
+        }).sqrt()
+    }
+}
+
+impl<N: Real> Norm<N> for LpNorm {
+    #[inline]
+    fn norm<R, C, S>(&self, m: &Matrix<N, R, C, S>) -> N
+        where R: Dim, C: Dim, S: Storage<N, R, C> {
+        m.fold(N::zero(), |a, b| {
+            a + b.abs().powi(self.0)
+        }).powf(::convert(1.0 / (self.0 as f64)))
+    }
+
+    #[inline]
+    fn metric_distance<R1, C1, S1, R2, C2, S2>(&self, m1: &Matrix<N, R1, C1, S1>, m2: &Matrix<N, R2, C2, S2>) -> N
+        where R1: Dim, C1: Dim, S1: Storage<N, R1, C1>,
+              R2: Dim, C2: Dim, S2: Storage<N, R2, C2>,
+              ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
+        m1.zip_fold(m2, N::zero(), |acc, a, b| {
+            let diff = a - b;
+            acc + diff.abs().powi(self.0)
+        }).powf(::convert(1.0 / (self.0 as f64)))
+    }
+}
+
+impl<N: Scalar + PartialOrd + Signed> Norm<N> for UniformNorm {
+    #[inline]
+    fn norm<R, C, S>(&self, m: &Matrix<N, R, C, S>) -> N
+        where R: Dim, C: Dim, S: Storage<N, R, C> {
+        m.amax()
+    }
+
+    #[inline]
+    fn metric_distance<R1, C1, S1, R2, C2, S2>(&self, m1: &Matrix<N, R1, C1, S1>, m2: &Matrix<N, R2, C2, S2>) -> N
+        where R1: Dim, C1: Dim, S1: Storage<N, R1, C1>,
+              R2: Dim, C2: Dim, S2: Storage<N, R2, C2>,
+              ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
+        m1.zip_fold(m2, N::zero(), |acc, a, b| {
+            let val = (a - b).abs();
+            if val > acc {
+                val
+            } else {
+                acc
+            }
+        })
+    }
+}
+
+
+impl<N: Real, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
+    /// The squared L2 norm of this vector.
+    #[inline]
+    pub fn norm_squared(&self) -> N {
+        let mut res = N::zero();
+
+        for i in 0..self.ncols() {
+            let col = self.column(i);
+            res += col.dot(&col)
+        }
+
+        res
+    }
+
+    /// The L2 norm of this matrix.
+    ///
+    /// Use `.apply_norm` to apply a custom norm.
+    #[inline]
+    pub fn norm(&self) -> N {
+        self.norm_squared().sqrt()
+    }
+
+    /// Compute the distance between `self` and `rhs` using the metric induced by the euclidean norm.
+    ///
+    /// Use `.apply_metric_distance` to apply a custom norm.
+    #[inline]
+    pub fn metric_distance<R2, C2, S2>(&self, rhs: &Matrix<N, R2, C2, S2>) -> N
+        where R2: Dim, C2: Dim, S2: Storage<N, R2, C2>,
+              ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2> {
+        self.apply_metric_distance(rhs, &EuclideanNorm)
+    }
+
+    /// Uses the given `norm` to compute the norm of `self`.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// # use nalgebra::{Vector3, UniformNorm, LpNorm, EuclideanNorm};
+    ///
+    /// let v = Vector3::new(1.0, 2.0, 3.0);
+    /// assert_eq!(v.apply_norm(&UniformNorm), 3.0);
+    /// assert_eq!(v.apply_norm(&LpNorm(1)), 6.0);
+    /// assert_eq!(v.apply_norm(&EuclideanNorm), v.norm());
+    /// ```
+    #[inline]
+    pub fn apply_norm(&self, norm: &impl Norm<N>) -> N {
+        norm.norm(self)
+    }
+
+    /// Uses the metric induced by the given `norm` to compute the metric distance between `self` and `rhs`.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// # use nalgebra::{Vector3, UniformNorm, LpNorm, EuclideanNorm};
+    ///
+    /// let v1 = Vector3::new(1.0, 2.0, 3.0);
+    /// let v2 = Vector3::new(10.0, 20.0, 30.0);
+    ///
+    /// assert_eq!(v1.apply_metric_distance(&v2, &UniformNorm), 27.0);
+    /// assert_eq!(v1.apply_metric_distance(&v2, &LpNorm(1)), 27.0 + 18.0 + 9.0);
+    /// assert_eq!(v1.apply_metric_distance(&v2, &EuclideanNorm), (v1 - v2).norm());
+    /// ```
+    #[inline]
+    pub fn apply_metric_distance<R2, C2, S2>(&self, rhs: &Matrix<N, R2, C2, S2>, norm: &impl Norm<N>) -> N
+        where R2: Dim, C2: Dim, S2: Storage<N, R2, C2>,
+              ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2> {
+        norm.metric_distance(self,rhs)
+    }
+
+    /// The Lp norm of this matrix.
+    #[inline]
+    pub fn lp_norm(&self, p: i32) -> N {
+        self.apply_norm(&LpNorm(p))
+    }
+
+    /// A synonym for the norm of this matrix.
+    ///
+    /// Aka the length.
+    ///
+    /// This function is simply implemented as a call to `norm()`
+    #[inline]
+    pub fn magnitude(&self) -> N {
+        self.norm()
+    }
+
+    /// A synonym for the squared norm of this matrix.
+    ///
+    /// Aka the squared length.
+    ///
+    /// This function is simply implemented as a call to `norm_squared()`
+    #[inline]
+    pub fn magnitude_squared(&self) -> N {
+        self.norm_squared()
+    }
+
+    /// Returns a normalized version of this matrix.
+    #[inline]
+    pub fn normalize(&self) -> MatrixMN<N, R, C>
+        where DefaultAllocator: Allocator<N, R, C> {
+        self / self.norm()
+    }
+
+    /// Returns a normalized version of this matrix unless its norm as smaller or equal to `eps`.
+    #[inline]
+    pub fn try_normalize(&self, min_norm: N) -> Option<MatrixMN<N, R, C>>
+        where DefaultAllocator: Allocator<N, R, C> {
+        let n = self.norm();
+
+        if n <= min_norm {
+            None
+        } else {
+            Some(self / n)
+        }
+    }
+}
+
+impl<N: Real, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
+    /// Normalizes this matrix in-place and returns its norm.
+    #[inline]
+    pub fn normalize_mut(&mut self) -> N {
+        let n = self.norm();
+        *self /= n;
+
+        n
+    }
+
+    /// Normalizes this matrix in-place or does nothing if its norm is smaller or equal to `eps`.
+    ///
+    /// If the normalization succeeded, returns the old normal of this matrix.
+    #[inline]
+    pub fn try_normalize_mut(&mut self, min_norm: N) -> Option<N> {
+        let n = self.norm();
+
+        if n <= min_norm {
+            None
+        } else {
+            *self /= n;
+            Some(n)
+        }
+    }
+}

src/base/ops.rs

@@ -11,7 +11,7 @@ use base::allocator::{Allocator, SameShapeAllocator, SameShapeC, SameShapeR};
 use base::constraint::{
     AreMultipliable, DimEq, SameNumberOfColumns, SameNumberOfRows, ShapeConstraint,
 };
-use base::dimension::{Dim, DimMul, DimName, DimProd};
+use base::dimension::{Dim, DimMul, DimName, DimProd, Dynamic};
 use base::storage::{ContiguousStorageMut, Storage, StorageMut};
 use base::{DefaultAllocator, Matrix, MatrixMN, MatrixN, MatrixSum, Scalar};
 
@@ -24,7 +24,7 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Index<usize> for Matrix<N,
     type Output = N;
 
     #[inline]
-    fn index(&self, i: usize) -> &N {
+    fn index(&self, i: usize) -> &Self::Output {
         let ij = self.vector_to_matrix_index(i);
         &self[ij]
     }
@@ -38,7 +38,7 @@ where
     type Output = N;
 
     #[inline]
-    fn index(&self, ij: (usize, usize)) -> &N {
+    fn index(&self, ij: (usize, usize)) -> &Self::Output {
         let shape = self.shape();
         assert!(
             ij.0 < shape.0 && ij.1 < shape.1,
@@ -384,6 +384,36 @@ where
     }
 }
 
+impl<N, C: Dim> iter::Sum for MatrixMN<N, Dynamic, C>
+where
+    N: Scalar + ClosedAdd + Zero,
+    DefaultAllocator: Allocator<N, Dynamic, C>,
+{
+    /// # Example
+    /// ```
+    /// # use nalgebra::DVector;
+    /// assert_eq!(vec![DVector::repeat(3, 1.0f64),
+    ///                 DVector::repeat(3, 1.0f64),
+    ///                 DVector::repeat(3, 1.0f64)].into_iter().sum::<DVector<f64>>(),
+    ///            DVector::repeat(3, 1.0f64) + DVector::repeat(3, 1.0f64) + DVector::repeat(3, 1.0f64));
+    /// ```
+    ///
+    /// # Panics
+    /// Panics if the iterator is empty:
+    /// ```should_panic
+    /// # use std::iter;
+    /// # use nalgebra::DMatrix;
+    /// iter::empty::<DMatrix<f64>>().sum::<DMatrix<f64>>(); // panics!
+    /// ```
+    fn sum<I: Iterator<Item = MatrixMN<N, Dynamic, C>>>(mut iter: I) -> MatrixMN<N, Dynamic, C> {
+        if let Some(first) = iter.next() {
+            iter.fold(first, |acc, x| acc + x)
+        } else {
+            panic!("Cannot compute `sum` of empty iterator.")
+        }
+    }
+}
+
 impl<'a, N, R: DimName, C: DimName> iter::Sum<&'a MatrixMN<N, R, C>> for MatrixMN<N, R, C>
 where
     N: Scalar + ClosedAdd + Zero,
@@ -394,6 +424,36 @@ where
     }
 }
 
+impl<'a, N, C: Dim> iter::Sum<&'a MatrixMN<N, Dynamic, C>> for MatrixMN<N, Dynamic, C>
+where
+    N: Scalar + ClosedAdd + Zero,
+    DefaultAllocator: Allocator<N, Dynamic, C>,
+{
+    /// # Example
+    /// ```
+    /// # use nalgebra::DVector;
+    /// let v = &DVector::repeat(3, 1.0f64);
+    ///
+    /// assert_eq!(vec![v, v, v].into_iter().sum::<DVector<f64>>(),
+    ///            v + v + v);
+    /// ```
+    ///
+    /// # Panics
+    /// Panics if the iterator is empty:
+    /// ```should_panic
+    /// # use std::iter;
+    /// # use nalgebra::DMatrix;
+    /// iter::empty::<&DMatrix<f64>>().sum::<DMatrix<f64>>(); // panics!
+    /// ```
+    fn sum<I: Iterator<Item = &'a MatrixMN<N, Dynamic, C>>>(mut iter: I) -> MatrixMN<N, Dynamic, C> {
+        if let Some(first) = iter.next() {
+            iter.fold(first.clone(), |acc, x| acc + x)
+        } else {
+            panic!("Cannot compute `sum` of empty iterator.")
+        }
+    }
+}
+
 /*
  *
  * Multiplication
@@ -761,7 +821,7 @@ where
 }
 
 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.
+    /// Returns the absolute value of the component with the largest absolute value.
     #[inline]
     pub fn amax(&self) -> N {
         let mut max = N::zero();
@@ -777,7 +837,7 @@ impl<N: Scalar + PartialOrd + Signed, R: Dim, C: Dim, S: Storage<N, R, C>> Matri
         max
     }
 
-    /// Returns the absolute value of the coefficient with the smallest absolute value.
+    /// Returns the absolute value of the component with the smallest absolute value.
     #[inline]
     pub fn amin(&self) -> N {
         let mut it = self.iter();
@@ -796,4 +856,42 @@ impl<N: Scalar + PartialOrd + Signed, R: Dim, C: Dim, S: Storage<N, R, C>> Matri
 
         min
     }
+
+    /// Returns the component with the largest value.
+    #[inline]
+    pub fn max(&self) -> N {
+        let mut it = self.iter();
+        let mut max = it
+            .next()
+            .expect("max: empty matrices not supported.");
+
+        for e in it {
+            let ae = e;
+
+            if ae > max {
+                max = ae;
+            }
+        }
+
+        *max
+    }
+
+    /// Returns the component with the smallest value.
+    #[inline]
+    pub fn min(&self) -> N {
+        let mut it = self.iter();
+        let mut min = it
+            .next()
+            .expect("min: empty matrices not supported.");
+
+        for e in it {
+            let ae = e;
+
+            if ae < min {
+                min = ae;
+            }
+        }
+
+        *min
+    }
 }

src/base/statistics.rs

@@ -0,0 +1,309 @@
+use ::{Real, Dim, Matrix, VectorN, RowVectorN, DefaultAllocator, U1, VectorSliceN};
+use storage::Storage;
+use allocator::Allocator;
+
+impl<N: Real, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
+    /// Returns a row vector where each element is the result of the application of `f` on the
+    /// corresponding column of the original matrix.
+    #[inline]
+    pub fn compress_rows(&self, f: impl Fn(VectorSliceN<N, R, S::RStride, S::CStride>) -> N) -> RowVectorN<N, C>
+        where DefaultAllocator: Allocator<N, U1, C> {
+
+        let ncols = self.data.shape().1;
+        let mut res = unsafe { RowVectorN::new_uninitialized_generic(U1, ncols) };
+
+        for i in 0..ncols.value() {
+            // FIXME: avoid bound checking of column.
+            unsafe { *res.get_unchecked_mut((0, i)) = f(self.column(i)); }
+        }
+
+        res
+    }
+
+    /// Returns a column vector where each element is the result of the application of `f` on the
+    /// corresponding column of the original matrix.
+    ///
+    /// This is the same as `self.compress_rows(f).transpose()`.
+    #[inline]
+    pub fn compress_rows_tr(&self, f: impl Fn(VectorSliceN<N, R, S::RStride, S::CStride>) -> N) -> VectorN<N, C>
+        where DefaultAllocator: Allocator<N, C> {
+
+        let ncols = self.data.shape().1;
+        let mut res = unsafe { VectorN::new_uninitialized_generic(ncols, U1) };
+
+        for i in 0..ncols.value() {
+            // FIXME: avoid bound checking of column.
+            unsafe { *res.vget_unchecked_mut(i) = f(self.column(i)); }
+        }
+
+        res
+    }
+
+    /// Returns a column vector resulting from the folding of `f` on each column of this matrix.
+    #[inline]
+    pub fn compress_columns(&self, init: VectorN<N, R>, f: impl Fn(&mut VectorN<N, R>, VectorSliceN<N, R, S::RStride, S::CStride>)) -> VectorN<N, R>
+        where DefaultAllocator: Allocator<N, R> {
+        let mut res = init;
+
+        for i in 0..self.ncols() {
+            f(&mut res, self.column(i))
+        }
+
+        res
+    }
+}
+
+impl<N: Real, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
+    /*
+     *
+     * Sum computation.
+     *
+     */
+    /// The sum of all the elements of this matrix.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// # use nalgebra::Matrix2x3;
+    ///
+    /// let m = Matrix2x3::new(1.0, 2.0, 3.0,
+    ///                        4.0, 5.0, 6.0);
+    /// assert_eq!(m.sum(), 21.0);
+    /// ```
+    #[inline]
+    pub fn sum(&self) -> N {
+        self.iter().cloned().fold(N::zero(), |a, b| a + b)
+    }
+
+    /// The sum of all the rows of this matrix.
+    ///
+    /// Use `.row_variance_tr` if you need the result in a column vector instead.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// # use nalgebra::{Matrix2x3, RowVector3};
+    ///
+    /// let m = Matrix2x3::new(1.0, 2.0, 3.0,
+    ///                        4.0, 5.0, 6.0);
+    /// assert_eq!(m.row_sum(), RowVector3::new(5.0, 7.0, 9.0));
+    /// ```
+    #[inline]
+    pub fn row_sum(&self) -> RowVectorN<N, C>
+        where DefaultAllocator: Allocator<N, U1, C> {
+        self.compress_rows(|col| col.sum())
+    }
+
+    /// The sum of all the rows of this matrix. The result is transposed and returned as a column vector.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// # use nalgebra::{Matrix2x3, Vector3};
+    ///
+    /// let m = Matrix2x3::new(1.0, 2.0, 3.0,
+    ///                        4.0, 5.0, 6.0);
+    /// assert_eq!(m.row_sum_tr(), Vector3::new(5.0, 7.0, 9.0));
+    /// ```
+    #[inline]
+    pub fn row_sum_tr(&self) -> VectorN<N, C>
+        where DefaultAllocator: Allocator<N, C> {
+        self.compress_rows_tr(|col| col.sum())
+    }
+
+    /// The sum of all the columns of this matrix.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// # use nalgebra::{Matrix2x3, Vector2};
+    ///
+    /// let m = Matrix2x3::new(1.0, 2.0, 3.0,
+    ///                        4.0, 5.0, 6.0);
+    /// assert_eq!(m.column_sum(), Vector2::new(6.0, 15.0));
+    /// ```
+    #[inline]
+    pub fn column_sum(&self) -> VectorN<N, R>
+        where DefaultAllocator: Allocator<N, R> {
+        let nrows = self.data.shape().0;
+        self.compress_columns(VectorN::zeros_generic(nrows, U1), |out, col| {
+            out.axpy(N::one(), &col, N::one())
+        })
+    }
+
+    /*
+     *
+     * Variance computation.
+     *
+     */
+    /// The variance of all the elements of this matrix.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # use nalgebra::Matrix2x3;
+    ///
+    /// let m = Matrix2x3::new(1.0, 2.0, 3.0,
+    ///                        4.0, 5.0, 6.0);
+    /// assert_relative_eq!(m.variance(), 35.0 / 12.0, epsilon = 1.0e-8);
+    /// ```
+    #[inline]
+    pub fn variance(&self) -> N {
+        if self.len() == 0 {
+            N::zero()
+        } else {
+            let val = self.iter().cloned().fold((N::zero(), N::zero()), |a, b| (a.0 + b * b, a.1 + b));
+            let denom = N::one() / ::convert::<_, N>(self.len() as f64);
+            val.0 * denom - (val.1 * denom) * (val.1 * denom)
+        }
+    }
+
+    /// The variance of all the rows of this matrix.
+    ///
+    /// Use `.row_variance_tr` if you need the result in a column vector instead.
+    /// # Example
+    ///
+    /// ```
+    /// # use nalgebra::{Matrix2x3, RowVector3};
+    ///
+    /// let m = Matrix2x3::new(1.0, 2.0, 3.0,
+    ///                        4.0, 5.0, 6.0);
+    /// assert_eq!(m.row_variance(), RowVector3::new(2.25, 2.25, 2.25));
+    /// ```
+    #[inline]
+    pub fn row_variance(&self) -> RowVectorN<N, C>
+        where DefaultAllocator: Allocator<N, U1, C> {
+        self.compress_rows(|col| col.variance())
+    }
+
+    /// The variance of all the rows of this matrix. The result is transposed and returned as a column vector.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// # use nalgebra::{Matrix2x3, Vector3};
+    ///
+    /// let m = Matrix2x3::new(1.0, 2.0, 3.0,
+    ///                        4.0, 5.0, 6.0);
+    /// assert_eq!(m.row_variance_tr(), Vector3::new(2.25, 2.25, 2.25));
+    /// ```
+    #[inline]
+    pub fn row_variance_tr(&self) -> VectorN<N, C>
+        where DefaultAllocator: Allocator<N, C> {
+        self.compress_rows_tr(|col| col.variance())
+    }
+
+    /// The variance of all the columns of this matrix.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # use nalgebra::{Matrix2x3, Vector2};
+    ///
+    /// let m = Matrix2x3::new(1.0, 2.0, 3.0,
+    ///                        4.0, 5.0, 6.0);
+    /// assert_relative_eq!(m.column_variance(), Vector2::new(2.0 / 3.0, 2.0 / 3.0), epsilon = 1.0e-8);
+    /// ```
+    #[inline]
+    pub fn column_variance(&self) -> VectorN<N, R>
+        where DefaultAllocator: Allocator<N, R> {
+        let (nrows, ncols) = self.data.shape();
+
+        let mut mean = self.column_mean();
+        mean.apply(|e| -(e * e));
+
+        let denom = N::one() / ::convert::<_, N>(ncols.value() as f64);
+        self.compress_columns(mean, |out, col| {
+            for i in 0..nrows.value() {
+                unsafe {
+                    let val = col.vget_unchecked(i);
+                    *out.vget_unchecked_mut(i) += denom * *val * *val
+                }
+            }
+        })
+    }
+
+    /*
+     *
+     * Mean computation.
+     *
+     */
+    /// The mean of all the elements of this matrix.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// # use nalgebra::Matrix2x3;
+    ///
+    /// let m = Matrix2x3::new(1.0, 2.0, 3.0,
+    ///                        4.0, 5.0, 6.0);
+    /// assert_eq!(m.mean(), 3.5);
+    /// ```
+    #[inline]
+    pub fn mean(&self) -> N {
+        if self.len() == 0 {
+            N::zero()
+        } else {
+            self.sum() / ::convert(self.len() as f64)
+        }
+    }
+
+    /// The mean of all the rows of this matrix.
+    ///
+    /// Use `.row_mean_tr` if you need the result in a column vector instead.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// # use nalgebra::{Matrix2x3, RowVector3};
+    ///
+    /// let m = Matrix2x3::new(1.0, 2.0, 3.0,
+    ///                        4.0, 5.0, 6.0);
+    /// assert_eq!(m.row_mean(), RowVector3::new(2.5, 3.5, 4.5));
+    /// ```
+    #[inline]
+    pub fn row_mean(&self) -> RowVectorN<N, C>
+        where DefaultAllocator: Allocator<N, U1, C> {
+        self.compress_rows(|col| col.mean())
+    }
+
+    /// The mean of all the rows of this matrix. The result is transposed and returned as a column vector.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// # use nalgebra::{Matrix2x3, Vector3};
+    ///
+    /// let m = Matrix2x3::new(1.0, 2.0, 3.0,
+    ///                        4.0, 5.0, 6.0);
+    /// assert_eq!(m.row_mean_tr(), Vector3::new(2.5, 3.5, 4.5));
+    /// ```
+    #[inline]
+    pub fn row_mean_tr(&self) -> VectorN<N, C>
+        where DefaultAllocator: Allocator<N, C> {
+        self.compress_rows_tr(|col| col.mean())
+    }
+
+    /// The mean of all the columns of this matrix.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// # use nalgebra::{Matrix2x3, Vector2};
+    ///
+    /// let m = Matrix2x3::new(1.0, 2.0, 3.0,
+    ///                        4.0, 5.0, 6.0);
+    /// assert_eq!(m.column_mean(), Vector2::new(2.0, 5.0));
+    /// ```
+    #[inline]
+    pub fn column_mean(&self) -> VectorN<N, R>
+        where DefaultAllocator: Allocator<N, R> {
+        let (nrows, ncols) = self.data.shape();
+        let denom = N::one() / ::convert::<_, N>(ncols.value() as f64);
+        self.compress_columns(VectorN::zeros_generic(nrows, U1), |out, col| {
+            out.axpy(denom, &col, N::one())
+        })
+    }
+}

src/base/unit.rs

@@ -13,6 +13,8 @@ use abomonation::Abomonation;
 use alga::general::SubsetOf;
 use alga::linear::NormedSpace;
 
+use ::Real;
+
 /// A wrapper that ensures the underlying algebraic entity has a unit norm.
 ///
 /// Use `.as_ref()` or `.into_inner()` to obtain the underlying value by-reference or by-move.
@@ -91,11 +93,24 @@ impl<T: NormedSpace> Unit<T> {
     /// Normalizes this value again. This is useful when repeated computations
     /// might cause a drift in the norm because of float inaccuracies.
     ///
-    /// Returns the norm before re-normalization (should be close to `1.0`).
+    /// Returns the norm before re-normalization. See `.renormalize_fast` for a faster alternative
+    /// that may be slightly less accurate if `self` drifted significantly from having a unit length.
     #[inline]
     pub fn renormalize(&mut self) -> T::Field {
         self.value.normalize_mut()
     }
+
+    /// Normalizes this value again using a first-order Taylor approximation.
+    /// This is useful when repeated computations might cause a drift in the norm
+    /// because of float inaccuracies.
+    #[inline]
+    pub fn renormalize_fast(&mut self)
+        where T::Field: Real {
+        let sq_norm = self.value.norm_squared();
+        let _3: T::Field = ::convert(3.0);
+        let _0_5: T::Field = ::convert(0.5);
+        self.value *= _0_5 * (_3 - sq_norm);
+    }
 }
 
 impl<T> Unit<T> {

src/base/vec_storage.rs

@@ -1,6 +1,5 @@
 #[cfg(feature = "abomonation-serialize")]
 use std::io::{Result as IOResult, Write};
-use std::ops::Deref;
 
 #[cfg(all(feature = "alloc", not(feature = "std")))]
 use alloc::vec::Vec;
@@ -37,12 +36,12 @@ pub type MatrixVec<N, R, C> = VecStorage<N, R, C>;
 impl<N, R: Dim, C: Dim> VecStorage<N, R, C> {
     /// Creates a new dynamic matrix data storage from the given vector and shape.
     #[inline]
-    pub fn new(nrows: R, ncols: C, data: Vec<N>) -> VecStorage<N, R, C> {
+    pub fn new(nrows: R, ncols: C, data: Vec<N>) -> Self {
         assert!(
             nrows.value() * ncols.value() == data.len(),
             "Data storage buffer dimension mismatch."
         );
-        VecStorage {
+        Self {
             data: data,
             nrows: nrows,
             ncols: ncols,
@@ -51,15 +50,16 @@ impl<N, R: Dim, C: Dim> VecStorage<N, R, C> {
 
     /// The underlying data storage.
     #[inline]
-    pub fn data(&self) -> &Vec<N> {
+    pub fn as_vec(&self) -> &Vec<N> {
         &self.data
     }
 
     /// The underlying mutable data storage.
     ///
-    /// This is unsafe because this may cause UB if the vector is modified by the user.
+    /// This is unsafe because this may cause UB if the size of the vector is changed
+    /// by the user.
     #[inline]
-    pub unsafe fn data_mut(&mut self) -> &mut Vec<N> {
+    pub unsafe fn as_vec_mut(&mut self) -> &mut Vec<N> {
         &mut self.data
     }
 
@@ -81,14 +81,11 @@ impl<N, R: Dim, C: Dim> VecStorage<N, R, C> {
 
         self.data
     }
-}
-
-impl<N, R: Dim, C: Dim> Deref for VecStorage<N, R, C> {
-    type Target = Vec<N>;
 
+    /// The number of elements on the underlying vector.
     #[inline]
-    fn deref(&self) -> &Self::Target {
+    pub fn len(&self) -> usize {
-        &self.data
+        self.data.len()
     }
 }
 
@@ -145,7 +142,7 @@ where DefaultAllocator: Allocator<N, Dynamic, C, Buffer = Self>
 
     #[inline]
     fn as_slice(&self) -> &[N] {
-        &self[..]
+        &self.data
     }
 }
 
@@ -189,7 +186,7 @@ where DefaultAllocator: Allocator<N, R, Dynamic, Buffer = Self>
 
     #[inline]
     fn as_slice(&self) -> &[N] {
-        &self[..]
+        &self.data
     }
 }
 

src/geometry/isometry.rs

@@ -100,7 +100,7 @@ where DefaultAllocator: Allocator<N, D>
 {
     #[inline]
     fn clone(&self) -> Self {
-        Isometry::from_parts(self.translation.clone(), self.rotation.clone())
+        Self::from_parts(self.translation.clone(), self.rotation.clone())
     }
 }
 
@@ -113,7 +113,6 @@ where DefaultAllocator: Allocator<N, D>
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use std::f32;
     /// # use nalgebra::{Isometry3, Translation3, UnitQuaternion, Vector3, Point3};
     /// let tra = Translation3::new(0.0, 0.0, 3.0);
@@ -123,8 +122,8 @@ where DefaultAllocator: Allocator<N, D>
     /// assert_relative_eq!(iso * Point3::new(1.0, 2.0, 3.0), Point3::new(-1.0, 2.0, 0.0), epsilon = 1.0e-6);
     /// ```
     #[inline]
-    pub fn from_parts(translation: Translation<N, D>, rotation: R) -> Isometry<N, D, R> {
+    pub fn from_parts(translation: Translation<N, D>, rotation: R) -> Self {
-        Isometry {
+        Self {
             rotation: rotation,
             translation: translation,
             _noconstruct: PhantomData,
@@ -145,7 +144,7 @@ where DefaultAllocator: Allocator<N, D>
     /// assert_eq!(inv * (iso * pt), pt);
     /// ```
     #[inline]
-    pub fn inverse(&self) -> Isometry<N, D, R> {
+    pub fn inverse(&self) -> Self {
         let mut res = self.clone();
         res.inverse_mut();
         res
@@ -167,7 +166,7 @@ where DefaultAllocator: Allocator<N, D>
     /// ```
     #[inline]
     pub fn inverse_mut(&mut self) {
-        self.rotation.inverse_mut();
+        self.rotation.two_sided_inverse_mut();
         self.translation.inverse_mut();
         self.translation.vector = self.rotation.transform_vector(&self.translation.vector);
     }
@@ -197,7 +196,6 @@ where DefaultAllocator: Allocator<N, D>
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use std::f32;
     /// # use nalgebra::{Isometry2, Translation2, UnitComplex, Vector2};
     /// let mut iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::PI / 6.0);
@@ -220,7 +218,6 @@ where DefaultAllocator: Allocator<N, D>
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use std::f32;
     /// # use nalgebra::{Isometry2, Translation2, UnitComplex, Vector2, Point2};
     /// let mut iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
@@ -272,7 +269,6 @@ where DefaultAllocator: Allocator<N, D>
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use std::f32;
     /// # use nalgebra::{Isometry2, Vector2, Matrix3};
     /// let iso = Isometry2::new(Vector2::new(10.0, 20.0), f32::consts::FRAC_PI_6);
@@ -310,7 +306,7 @@ where
     DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
-    fn eq(&self, right: &Isometry<N, D, R>) -> bool {
+    fn eq(&self, right: &Self) -> bool {
         self.translation == right.translation && self.rotation == right.rotation
     }
 }

src/geometry/isometry_alga.rs

@@ -1,6 +1,6 @@
 use alga::general::{
     AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
-    AbstractSemigroup, Id, Identity, Inverse, Multiplicative, Real,
+    AbstractSemigroup, Id, Identity, TwoSidedInverse, Multiplicative, Real,
 };
 use alga::linear::Isometry as AlgaIsometry;
 use alga::linear::{
@@ -30,18 +30,18 @@ where
     }
 }
 
-impl<N: Real, D: DimName, R> Inverse<Multiplicative> for Isometry<N, D, R>
+impl<N: Real, D: DimName, R> TwoSidedInverse<Multiplicative> for Isometry<N, D, R>
 where
     R: Rotation<Point<N, D>>,
     DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
-    fn inverse(&self) -> Self {
+    fn two_sided_inverse(&self) -> Self {
         self.inverse()
     }
 
     #[inline]
-    fn inverse_mut(&mut self) {
+    fn two_sided_inverse_mut(&mut self) {
         self.inverse_mut()
     }
 }
@@ -121,7 +121,7 @@ where
     type Translation = Translation<N, D>;
 
     #[inline]
-    fn decompose(&self) -> (Translation<N, D>, R, Id, R) {
+    fn decompose(&self) -> (Self::Translation, R, Id, R) {
         (
             self.translation.clone(),
             self.rotation.clone(),

src/geometry/isometry_construction.rs

@@ -16,7 +16,7 @@ use base::{DefaultAllocator, Vector2, Vector3};
 
 use geometry::{
     Isometry, Point, Point3, Rotation, Rotation2, Rotation3, Translation, UnitComplex,
-    UnitQuaternion,
+    UnitQuaternion, Translation2, Translation3
 };
 
 impl<N: Real, D: DimName, R: AlgaRotation<Point<N, D>>> Isometry<N, D, R>
@@ -49,7 +49,6 @@ where DefaultAllocator: Allocator<N, D>
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use std::f32;
     /// # use nalgebra::{Isometry2, Point2, UnitComplex};
     /// let rot = UnitComplex::new(f32::consts::PI);
@@ -130,6 +129,18 @@ impl<N: Real> Isometry<N, U2, Rotation2<N>> {
             Rotation::<N, U2>::new(angle),
         )
     }
+
+    /// Creates a new isometry from the given translation coordinates.
+    #[inline]
+    pub fn translation(x: N, y: N) -> Self {
+        Self::new(Vector2::new(x, y), N::zero())
+    }
+
+    /// Creates a new isometry from the given rotation angle.
+    #[inline]
+    pub fn rotation(angle: N) -> Self {
+        Self::new(Vector2::zeros(), angle)
+    }
 }
 
 impl<N: Real> Isometry<N, U2, UnitComplex<N>> {
@@ -153,6 +164,18 @@ impl<N: Real> Isometry<N, U2, UnitComplex<N>> {
             UnitComplex::from_angle(angle),
         )
     }
+
+    /// Creates a new isometry from the given translation coordinates.
+    #[inline]
+    pub fn translation(x: N, y: N) -> Self {
+        Self::from_parts(Translation2::new(x, y), UnitComplex::identity())
+    }
+
+    /// Creates a new isometry from the given rotation angle.
+    #[inline]
+    pub fn rotation(angle: N) -> Self {
+        Self::new(Vector2::zeros(), angle)
+    }
 }
 
 // 3D rotation.
@@ -165,7 +188,6 @@ macro_rules! isometry_construction_impl(
             ///
             /// ```
             /// # #[macro_use] extern crate approx;
-            /// # extern crate nalgebra;
             /// # use std::f32;
             /// # use nalgebra::{Isometry3, IsometryMatrix3, Point3, Vector3};
             /// let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
@@ -191,6 +213,18 @@ macro_rules! isometry_construction_impl(
                     $RotId::<$($RotParams),*>::from_scaled_axis(axisangle))
             }
 
+            /// Creates a new isometry from the given translation coordinates.
+            #[inline]
+            pub fn translation(x: N, y: N, z: N) -> Self {
+                Self::from_parts(Translation3::new(x, y, z), $RotId::identity())
+            }
+
+            /// Creates a new isometry from the given rotation angle.
+            #[inline]
+            pub fn rotation(axisangle: Vector3<N>) -> Self {
+                Self::new(Vector3::zeros(), axisangle)
+            }
+
             /// Creates an isometry that corresponds to the local frame of an observer standing at the
             /// point `eye` and looking toward `target`.
             ///
@@ -206,7 +240,6 @@ macro_rules! isometry_construction_impl(
             ///
             /// ```
             /// # #[macro_use] extern crate approx;
-            /// # extern crate nalgebra;
             /// # use std::f32;
             /// # use nalgebra::{Isometry3, IsometryMatrix3, Point3, Vector3};
             /// let eye = Point3::new(1.0, 2.0, 3.0);
@@ -214,23 +247,32 @@ macro_rules! isometry_construction_impl(
             /// let up = Vector3::y();
             ///
             /// // Isometry with its rotation part represented as a UnitQuaternion
-            /// let iso = Isometry3::new_observer_frame(&eye, &target, &up);
+            /// let iso = Isometry3::face_towards(&eye, &target, &up);
             /// assert_eq!(iso * Point3::origin(), eye);
             /// assert_relative_eq!(iso * Vector3::z(), Vector3::x());
             ///
             /// // Isometry with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
-            /// let iso = IsometryMatrix3::new_observer_frame(&eye, &target, &up);
+            /// let iso = IsometryMatrix3::face_towards(&eye, &target, &up);
             /// assert_eq!(iso * Point3::origin(), eye);
             /// assert_relative_eq!(iso * Vector3::z(), Vector3::x());
             /// ```
             #[inline]
-            pub fn new_observer_frame(eye:    &Point3<N>,
+            pub fn face_towards(eye:    &Point3<N>,
                                       target: &Point3<N>,
                                       up:     &Vector3<N>)
                                       -> Self {
                 Self::from_parts(
                     Translation::from(eye.coords.clone()),
-                    $RotId::new_observer_frame(&(target - eye), up))
+                    $RotId::face_towards(&(target - eye), up))
+            }
+
+            /// Deprecated: Use [Isometry::face_towards] instead.
+            #[deprecated(note="renamed to `face_towards`")]
+            pub fn new_observer_frame(eye:    &Point3<N>,
+                                      target: &Point3<N>,
+                                      up:     &Vector3<N>)
+                                      -> Self {
+                Self::face_towards(eye, target, up)
             }
 
             /// Builds a right-handed look-at view matrix.
@@ -249,7 +291,6 @@ macro_rules! isometry_construction_impl(
             ///
             /// ```
             /// # #[macro_use] extern crate approx;
-            /// # extern crate nalgebra;
             /// # use std::f32;
             /// # use nalgebra::{Isometry3, IsometryMatrix3, Point3, Vector3};
             /// let eye = Point3::new(1.0, 2.0, 3.0);
@@ -293,7 +334,6 @@ macro_rules! isometry_construction_impl(
             ///
             /// ```
             /// # #[macro_use] extern crate approx;
-            /// # extern crate nalgebra;
             /// # use std::f32;
             /// # use nalgebra::{Isometry3, IsometryMatrix3, Point3, Vector3};
             /// let eye = Point3::new(1.0, 2.0, 3.0);

src/geometry/isometry_ops.rs

@@ -200,8 +200,8 @@ isometry_binop_assign_impl_all!(
     DivAssign, div_assign;
     self: Isometry<N, D, R>, rhs: R;
     // FIXME: don't invert explicitly?
-    [val] => *self *= rhs.inverse();
+    [val] => *self *= rhs.two_sided_inverse();
-    [ref] => *self *= rhs.inverse();
+    [ref] => *self *= rhs.two_sided_inverse();
 );
 
 // Isometry × R

src/geometry/mod.rs

@@ -37,6 +37,7 @@ mod translation_alga;
 mod translation_alias;
 mod translation_construction;
 mod translation_conversion;
+mod translation_coordinates;
 mod translation_ops;
 
 mod isometry;

src/geometry/orthographic.rs

@@ -26,7 +26,7 @@ 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())
+        Self::from_matrix_unchecked(self.matrix.clone())
     }
 }
 
@@ -57,7 +57,7 @@ impl<'a, N: Real + Deserialize<'a>> Deserialize<'a> for Orthographic3<N> {
     where Des: Deserializer<'a> {
         let matrix = Matrix4::<N>::deserialize(deserializer)?;
 
-        Ok(Orthographic3::from_matrix_unchecked(matrix))
+        Ok(Self::from_matrix_unchecked(matrix))
     }
 }
 
@@ -69,7 +69,6 @@ impl<N: Real> Orthographic3<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Orthographic3, Point3};
     /// let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
     /// // Check this projection actually transforms the view cuboid into the double-unit cube.
@@ -136,7 +135,7 @@ impl<N: Real> Orthographic3<N> {
     /// ```
     #[inline]
     pub fn from_matrix_unchecked(matrix: Matrix4<N>) -> Self {
-        Orthographic3 { matrix: matrix }
+        Self { matrix: matrix }
     }
 
     /// Creates a new orthographic projection matrix from an aspect ratio and the vertical field of view.
@@ -170,7 +169,6 @@ impl<N: Real> Orthographic3<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Orthographic3, Point3, Matrix4};
     /// let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
     /// let inv = proj.inverse();
@@ -271,7 +269,6 @@ impl<N: Real> Orthographic3<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Orthographic3, Point3, Matrix4};
     /// let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
     /// let expected = Matrix4::new(
@@ -299,7 +296,6 @@ impl<N: Real> Orthographic3<N> {
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Orthographic3;
     /// let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
     /// assert_relative_eq!(proj.left(), 1.0, epsilon = 1.0e-6);
@@ -316,7 +312,6 @@ impl<N: Real> Orthographic3<N> {
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Orthographic3;
     /// let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
     /// assert_relative_eq!(proj.right(), 10.0, epsilon = 1.0e-6);
@@ -333,7 +328,6 @@ impl<N: Real> Orthographic3<N> {
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Orthographic3;
     /// let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
     /// assert_relative_eq!(proj.bottom(), 2.0, epsilon = 1.0e-6);
@@ -350,7 +344,6 @@ impl<N: Real> Orthographic3<N> {
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Orthographic3;
     /// let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
     /// assert_relative_eq!(proj.top(), 20.0, epsilon = 1.0e-6);
@@ -367,7 +360,6 @@ impl<N: Real> Orthographic3<N> {
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Orthographic3;
     /// let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
     /// assert_relative_eq!(proj.znear(), 0.1, epsilon = 1.0e-6);
@@ -384,7 +376,6 @@ impl<N: Real> Orthographic3<N> {
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Orthographic3;
     /// let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
     /// assert_relative_eq!(proj.zfar(), 1000.0, epsilon = 1.0e-6);
@@ -403,7 +394,6 @@ impl<N: Real> Orthographic3<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Orthographic3, Point3};
     /// let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
     ///
@@ -439,7 +429,6 @@ impl<N: Real> Orthographic3<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Orthographic3, Point3};
     /// let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
     ///
@@ -478,7 +467,6 @@ impl<N: Real> Orthographic3<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Orthographic3, Vector3};
     /// let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
     ///
@@ -504,7 +492,6 @@ impl<N: Real> Orthographic3<N> {
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Orthographic3;
     /// let mut proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
     /// proj.set_left(2.0);
@@ -524,7 +511,6 @@ impl<N: Real> Orthographic3<N> {
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Orthographic3;
     /// let mut proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
     /// proj.set_right(15.0);
@@ -544,7 +530,6 @@ impl<N: Real> Orthographic3<N> {
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Orthographic3;
     /// let mut proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
     /// proj.set_bottom(8.0);
@@ -564,7 +549,6 @@ impl<N: Real> Orthographic3<N> {
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Orthographic3;
     /// let mut proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
     /// proj.set_top(15.0);
@@ -584,7 +568,6 @@ impl<N: Real> Orthographic3<N> {
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Orthographic3;
     /// let mut proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
     /// proj.set_znear(8.0);
@@ -604,7 +587,6 @@ impl<N: Real> Orthographic3<N> {
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Orthographic3;
     /// let mut proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
     /// proj.set_zfar(15.0);
@@ -624,7 +606,6 @@ impl<N: Real> Orthographic3<N> {
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Orthographic3;
     /// let mut proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
     /// proj.set_left_and_right(7.0, 70.0);
@@ -650,7 +631,6 @@ impl<N: Real> Orthographic3<N> {
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Orthographic3;
     /// let mut proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
     /// proj.set_bottom_and_top(7.0, 70.0);
@@ -676,7 +656,6 @@ impl<N: Real> Orthographic3<N> {
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Orthographic3;
     /// let mut proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
     /// proj.set_znear_and_zfar(50.0, 5000.0);

src/geometry/perspective.rs

@@ -27,7 +27,7 @@ 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())
+        Self::from_matrix_unchecked(self.matrix.clone())
     }
 }
 
@@ -58,7 +58,7 @@ impl<'a, N: Real + Deserialize<'a>> Deserialize<'a> for Perspective3<N> {
     where Des: Deserializer<'a> {
         let matrix = Matrix4::<N>::deserialize(deserializer)?;
 
-        Ok(Perspective3::from_matrix_unchecked(matrix))
+        Ok(Self::from_matrix_unchecked(matrix))
     }
 }
 
@@ -75,7 +75,7 @@ impl<N: Real> Perspective3<N> {
         );
 
         let matrix = Matrix4::identity();
-        let mut res = Perspective3::from_matrix_unchecked(matrix);
+        let mut res = Self::from_matrix_unchecked(matrix);
 
         res.set_fovy(fovy);
         res.set_aspect(aspect);
@@ -93,7 +93,7 @@ impl<N: Real> Perspective3<N> {
     /// projection.
     #[inline]
     pub fn from_matrix_unchecked(matrix: Matrix4<N>) -> Self {
-        Perspective3 { matrix: matrix }
+        Self { matrix: matrix }
     }
 
     /// Retrieves the inverse of the underlying homogeneous matrix.

src/geometry/point.rs

@@ -66,7 +66,7 @@ where
     where Des: Deserializer<'a> {
         let coords = VectorN::<N, D>::deserialize(deserializer)?;
 
-        Ok(Point::from(coords))
+        Ok(Self::from(coords))
     }
 }
 
@@ -126,8 +126,8 @@ where DefaultAllocator: Allocator<N, D>
     /// Creates a new point with the given coordinates.
     #[deprecated(note = "Use Point::from(vector) instead.")]
     #[inline]
-    pub fn from_coordinates(coords: VectorN<N, D>) -> Point<N, D> {
+    pub fn from_coordinates(coords: VectorN<N, D>) -> Self {
-        Point { coords: coords }
+        Self { coords: coords }
     }
 
     /// The dimension of this point.

src/geometry/point_alga.rs

@@ -54,7 +54,7 @@ where
 {
     #[inline]
     fn meet(&self, other: &Self) -> Self {
-        Point::from(self.coords.meet(&other.coords))
+        Self::from(self.coords.meet(&other.coords))
     }
 }
 
@@ -65,7 +65,7 @@ where
 {
     #[inline]
     fn join(&self, other: &Self) -> Self {
-        Point::from(self.coords.join(&other.coords))
+        Self::from(self.coords.join(&other.coords))
     }
 }
 
@@ -78,6 +78,6 @@ where
     fn meet_join(&self, other: &Self) -> (Self, Self) {
         let (meet, join) = self.coords.meet_join(&other.coords);
 
-        (Point::from(meet), Point::from(join))
+        (Self::from(meet), Self::from(join))
     }
 }

src/geometry/point_construction.rs

@@ -145,7 +145,7 @@ where
 {
     #[inline]
     fn arbitrary<G: Gen>(g: &mut G) -> Self {
-        Point::from(VectorN::arbitrary(g))
+        Self::from(VectorN::arbitrary(g))
     }
 }
 
@@ -163,7 +163,7 @@ macro_rules! componentwise_constructors_impl(
             #[doc = $doc]
             #[doc = "```"]
             #[inline]
-            pub fn new($($args: N),*) -> Point<N, $D> {
+            pub fn new($($args: N),*) -> Self {
                 unsafe {
                     let mut res = Self::new_uninitialized();
                     $( *res.get_unchecked_mut($irow) = $args; )*
@@ -194,7 +194,7 @@ macro_rules! from_array_impl(
     ($($D: ty, $len: expr);*) => {$(
       impl <N: Scalar> From<[N; $len]> for Point<N, $D> {
           fn from (coords: [N; $len]) -> Self {
-              Point {
+              Self {
                 coords: coords.into()
               }
           }

src/geometry/point_conversion.rs

@@ -45,7 +45,7 @@ where
 
     #[inline]
     unsafe fn from_superset_unchecked(m: &Point<N2, D>) -> Self {
-        Point::from(Matrix::from_superset_unchecked(&m.coords))
+        Self::from(Matrix::from_superset_unchecked(&m.coords))
     }
 }
 

src/geometry/point_ops.rs

@@ -46,11 +46,11 @@ where DefaultAllocator: Allocator<N, D>
 impl<N: Scalar + ClosedNeg, D: DimName> Neg for Point<N, D>
 where DefaultAllocator: Allocator<N, D>
 {
-    type Output = Point<N, D>;
+    type Output = Self;
 
     #[inline]
     fn neg(self) -> Self::Output {
-        Point::from(-self.coords)
+        Self::Output::from(-self.coords)
     }
 }
 
@@ -61,7 +61,7 @@ where DefaultAllocator: Allocator<N, D>
 
     #[inline]
     fn neg(self) -> Self::Output {
-        Point::from(-&self.coords)
+        Self::Output::from(-&self.coords)
     }
 }
 

src/geometry/quaternion.rs

@@ -68,7 +68,7 @@ impl<N: Real> Copy for Quaternion<N> {}
 impl<N: Real> Clone for Quaternion<N> {
     #[inline]
     fn clone(&self) -> Self {
-        Quaternion::from(self.coords.clone())
+        Self::from(self.coords.clone())
     }
 }
 
@@ -90,7 +90,7 @@ where Owned<N, U4>: Deserialize<'a>
     where Des: Deserializer<'a> {
         let coords = Vector4::<N>::deserialize(deserializer)?;
 
-        Ok(Quaternion::from(coords))
+        Ok(Self::from(coords))
     }
 }
 
@@ -98,15 +98,15 @@ impl<N: Real> Quaternion<N> {
     /// Moves this unit quaternion into one that owns its data.
     #[inline]
     #[deprecated(note = "This method is a no-op and will be removed in a future release.")]
-    pub fn into_owned(self) -> Quaternion<N> {
+    pub fn into_owned(self) -> Self {
         self
     }
 
     /// Clones this unit quaternion into one that owns its data.
     #[inline]
     #[deprecated(note = "This method is a no-op and will be removed in a future release.")]
-    pub fn clone_owned(&self) -> Quaternion<N> {
+    pub fn clone_owned(&self) -> Self {
-        Quaternion::from(self.coords.clone_owned())
+        Self::from(self.coords.clone_owned())
     }
 
     /// Normalizes this quaternion.
@@ -114,15 +114,14 @@ impl<N: Real> Quaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Quaternion;
     /// let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
     /// let q_normalized = q.normalize();
     /// relative_eq!(q_normalized.norm(), 1.0);
     /// ```
     #[inline]
-    pub fn normalize(&self) -> Quaternion<N> {
+    pub fn normalize(&self) -> Self {
-        Quaternion::from(self.coords.normalize())
+        Self::from(self.coords.normalize())
     }
 
     /// The conjugate of this quaternion.
@@ -135,14 +134,14 @@ impl<N: Real> Quaternion<N> {
     /// assert!(conj.i == -2.0 && conj.j == -3.0 && conj.k == -4.0 && conj.w == 1.0);
     /// ```
     #[inline]
-    pub fn conjugate(&self) -> Quaternion<N> {
+    pub fn conjugate(&self) -> Self {
         let v = Vector4::new(
             -self.coords[0],
             -self.coords[1],
             -self.coords[2],
             self.coords[3],
         );
-        Quaternion::from(v)
+        Self::from(v)
     }
 
     /// Inverts this quaternion if it is not zero.
@@ -150,7 +149,6 @@ impl<N: Real> Quaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Quaternion;
     /// let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
     /// let inv_q = q.try_inverse();
@@ -165,8 +163,8 @@ impl<N: Real> Quaternion<N> {
     /// assert!(inv_q.is_none());
     /// ```
     #[inline]
-    pub fn try_inverse(&self) -> Option<Quaternion<N>> {
+    pub fn try_inverse(&self) -> Option<Self> {
-        let mut res = Quaternion::from(self.coords.clone_owned());
+        let mut res = Self::from(self.coords.clone_owned());
 
         if res.try_inverse_mut() {
             Some(res)
@@ -188,7 +186,7 @@ impl<N: Real> Quaternion<N> {
     /// assert_eq!(q1.lerp(&q2, 0.1), Quaternion::new(1.9, 3.8, 5.7, 7.6));
     /// ```
     #[inline]
-    pub fn lerp(&self, other: &Quaternion<N>, t: N) -> Quaternion<N> {
+    pub fn lerp(&self, other: &Self, t: N) -> Self {
         self * (N::one() - t) + other * t
     }
 
@@ -240,7 +238,6 @@ impl<N: Real> Quaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Quaternion;
     /// let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
     /// assert_relative_eq!(q.norm(), 5.47722557, epsilon = 1.0e-6);
@@ -258,7 +255,6 @@ impl<N: Real> Quaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Quaternion;
     /// let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
     /// assert_relative_eq!(q.magnitude(), 5.47722557, epsilon = 1.0e-6);
@@ -345,18 +341,17 @@ impl<N: Real> Quaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Quaternion;
     /// let q = Quaternion::new(2.0, 5.0, 0.0, 0.0);
     /// assert_relative_eq!(q.ln(), Quaternion::new(1.683647, 1.190289, 0.0, 0.0), epsilon = 1.0e-6)
     /// ```
     #[inline]
-    pub fn ln(&self) -> Quaternion<N> {
+    pub fn ln(&self) -> Self {
         let n = self.norm();
         let v = self.vector();
         let s = self.scalar();
 
-        Quaternion::from_parts(n.ln(), v.normalize() * (s / n).acos())
+        Self::from_parts(n.ln(), v.normalize() * (s / n).acos())
     }
 
     /// Compute the exponential of a quaternion.
@@ -364,13 +359,12 @@ impl<N: Real> Quaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Quaternion;
     /// let q = Quaternion::new(1.683647, 1.190289, 0.0, 0.0);
     /// assert_relative_eq!(q.exp(), Quaternion::new(2.0, 5.0, 0.0, 0.0), epsilon = 1.0e-5)
     /// ```
     #[inline]
-    pub fn exp(&self) -> Quaternion<N> {
+    pub fn exp(&self) -> Self {
         self.exp_eps(N::default_epsilon())
     }
 
@@ -380,7 +374,6 @@ impl<N: Real> Quaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Quaternion;
     /// let q = Quaternion::new(1.683647, 1.190289, 0.0, 0.0);
     /// assert_relative_eq!(q.exp_eps(1.0e-6), Quaternion::new(2.0, 5.0, 0.0, 0.0), epsilon = 1.0e-5);
@@ -390,18 +383,18 @@ impl<N: Real> Quaternion<N> {
     /// assert_eq!(q.exp_eps(1.0e-6), Quaternion::identity());
     /// ```
     #[inline]
-    pub fn exp_eps(&self, eps: N) -> Quaternion<N> {
+    pub fn exp_eps(&self, eps: N) -> Self {
         let v = self.vector();
         let nn = v.norm_squared();
 
         if nn <= eps * eps {
-            Quaternion::identity()
+            Self::identity()
         } else {
             let w_exp = self.scalar().exp();
             let n = nn.sqrt();
             let nv = v * (w_exp * n.sin() / n);
 
-            Quaternion::from_parts(w_exp * n.cos(), nv)
+            Self::from_parts(w_exp * n.cos(), nv)
         }
     }
 
@@ -410,13 +403,12 @@ impl<N: Real> Quaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Quaternion;
     /// let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
     /// assert_relative_eq!(q.powf(1.5), Quaternion::new( -6.2576659, 4.1549037, 6.2323556, 8.3098075), epsilon = 1.0e-6);
     /// ```
     #[inline]
-    pub fn powf(&self, n: N) -> Quaternion<N> {
+    pub fn powf(&self, n: N) -> Self {
         (self.ln() * n).exp()
     }
 
@@ -476,7 +468,6 @@ impl<N: Real> Quaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Quaternion;
     /// let mut q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
     ///
@@ -506,7 +497,6 @@ impl<N: Real> Quaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Quaternion;
     /// let mut q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
     /// q.normalize_mut();
@@ -530,7 +520,7 @@ impl<N: Real + AbsDiffEq<Epsilon = N>> AbsDiffEq for Quaternion<N> {
     fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool {
         self.as_vector().abs_diff_eq(other.as_vector(), epsilon) ||
         // Account for the double-covering of S², i.e. q = -q
-       self.as_vector().iter().zip(other.as_vector().iter()).all(|(a, b)| a.abs_diff_eq(&-*b, epsilon))
+        self.as_vector().iter().zip(other.as_vector().iter()).all(|(a, b)| a.abs_diff_eq(&-*b, epsilon))
     }
 }
 
@@ -550,7 +540,7 @@ impl<N: Real + RelativeEq<Epsilon = N>> RelativeEq for Quaternion<N> {
     {
         self.as_vector().relative_eq(other.as_vector(), epsilon, max_relative) ||
         // Account for the double-covering of S², i.e. q = -q
-       self.as_vector().iter().zip(other.as_vector().iter()).all(|(a, b)| a.relative_eq(&-*b, epsilon, max_relative))
+        self.as_vector().iter().zip(other.as_vector().iter()).all(|(a, b)| a.relative_eq(&-*b, epsilon, max_relative))
     }
 }
 
@@ -564,7 +554,7 @@ impl<N: Real + UlpsEq<Epsilon = N>> UlpsEq for Quaternion<N> {
     fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool {
         self.as_vector().ulps_eq(other.as_vector(), epsilon, max_ulps) ||
         // Account for the double-covering of S², i.e. q = -q.
-       self.as_vector().iter().zip(other.as_vector().iter()).all(|(a, b)| a.ulps_eq(&-*b, epsilon, max_ulps))
+        self.as_vector().iter().zip(other.as_vector().iter()).all(|(a, b)| a.ulps_eq(&-*b, epsilon, max_ulps))
     }
 }
 
@@ -587,7 +577,7 @@ impl<N: Real> UnitQuaternion<N> {
     #[deprecated(
         note = "This method is unnecessary and will be removed in a future release. Use `.clone()` instead."
     )]
-    pub fn into_owned(self) -> UnitQuaternion<N> {
+    pub fn into_owned(self) -> Self {
         self
     }
 
@@ -596,7 +586,7 @@ impl<N: Real> UnitQuaternion<N> {
     #[deprecated(
         note = "This method is unnecessary and will be removed in a future release. Use `.clone()` instead."
     )]
-    pub fn clone_owned(&self) -> UnitQuaternion<N> {
+    pub fn clone_owned(&self) -> Self {
         *self
     }
 
@@ -647,8 +637,8 @@ impl<N: Real> UnitQuaternion<N> {
     /// assert_eq!(conj, UnitQuaternion::from_axis_angle(&-axis, 1.78));
     /// ```
     #[inline]
-    pub fn conjugate(&self) -> UnitQuaternion<N> {
+    pub fn conjugate(&self) -> Self {
-        UnitQuaternion::new_unchecked(self.as_ref().conjugate())
+        Self::new_unchecked(self.as_ref().conjugate())
     }
 
     /// Inverts this quaternion if it is not zero.
@@ -663,7 +653,7 @@ impl<N: Real> UnitQuaternion<N> {
     /// assert_eq!(inv * rot, UnitQuaternion::identity());
     /// ```
     #[inline]
-    pub fn inverse(&self) -> UnitQuaternion<N> {
+    pub fn inverse(&self) -> Self {
         self.conjugate()
     }
 
@@ -672,14 +662,13 @@ impl<N: Real> UnitQuaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{UnitQuaternion, Vector3};
     /// let rot1 = UnitQuaternion::from_axis_angle(&Vector3::y_axis(), 1.0);
     /// let rot2 = UnitQuaternion::from_axis_angle(&Vector3::x_axis(), 0.1);
     /// assert_relative_eq!(rot1.angle_to(&rot2), 1.0045657, epsilon = 1.0e-6);
     /// ```
     #[inline]
-    pub fn angle_to(&self, other: &UnitQuaternion<N>) -> N {
+    pub fn angle_to(&self, other: &Self) -> N {
         let delta = self.rotation_to(other);
         delta.angle()
     }
@@ -691,7 +680,6 @@ impl<N: Real> UnitQuaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{UnitQuaternion, Vector3};
     /// let rot1 = UnitQuaternion::from_axis_angle(&Vector3::y_axis(), 1.0);
     /// let rot2 = UnitQuaternion::from_axis_angle(&Vector3::x_axis(), 0.1);
@@ -699,7 +687,7 @@ impl<N: Real> UnitQuaternion<N> {
     /// assert_relative_eq!(rot_to * rot1, rot2, epsilon = 1.0e-6);
     /// ```
     #[inline]
-    pub fn rotation_to(&self, other: &UnitQuaternion<N>) -> UnitQuaternion<N> {
+    pub fn rotation_to(&self, other: &Self) -> Self{
         other / self
     }
 
@@ -715,7 +703,7 @@ impl<N: Real> UnitQuaternion<N> {
     /// assert_eq!(q1.lerp(&q2, 0.1), Quaternion::new(0.9, 0.1, 0.0, 0.0));
     /// ```
     #[inline]
-    pub fn lerp(&self, other: &UnitQuaternion<N>, t: N) -> Quaternion<N> {
+    pub fn lerp(&self, other: &Self, t: N) -> Quaternion<N> {
         self.as_ref().lerp(other.as_ref(), t)
     }
 
@@ -731,11 +719,11 @@ impl<N: Real> UnitQuaternion<N> {
     /// assert_eq!(q1.nlerp(&q2, 0.1), UnitQuaternion::new_normalize(Quaternion::new(0.9, 0.1, 0.0, 0.0)));
     /// ```
     #[inline]
-    pub fn nlerp(&self, other: &UnitQuaternion<N>, t: N) -> UnitQuaternion<N> {
+    pub fn nlerp(&self, other: &Self, t: N) -> Self {
         let mut res = self.lerp(other, t);
         let _ = res.normalize_mut();
 
-        UnitQuaternion::new_unchecked(res)
+        Self::new_unchecked(res)
     }
 
     /// Spherical linear interpolation between two unit quaternions.
@@ -743,7 +731,7 @@ impl<N: Real> UnitQuaternion<N> {
     /// Panics if the angle between both quaternion is 180 degrees (in which case the interpolation
     /// is not well-defined). Use `.try_slerp` instead to avoid the panic.
     #[inline]
-    pub fn slerp(&self, other: &UnitQuaternion<N>, t: N) -> UnitQuaternion<N> {
+    pub fn slerp(&self, other: &Self, t: N) -> Self {
         Unit::new_unchecked(Quaternion::from(
             Unit::new_unchecked(self.coords)
                 .slerp(&Unit::new_unchecked(other.coords), t)
@@ -764,10 +752,10 @@ impl<N: Real> UnitQuaternion<N> {
     #[inline]
     pub fn try_slerp(
         &self,
-        other: &UnitQuaternion<N>,
+        other: &Self,
         t: N,
         epsilon: N,
-    ) -> Option<UnitQuaternion<N>>
+    ) -> Option<Self>
     {
         Unit::new_unchecked(self.coords)
             .try_slerp(&Unit::new_unchecked(other.coords), t, epsilon)
@@ -785,7 +773,6 @@ impl<N: Real> UnitQuaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{UnitQuaternion, Vector3, Unit};
     /// let axisangle = Vector3::new(0.1, 0.2, 0.3);
     /// let mut rot = UnitQuaternion::new(axisangle);
@@ -828,7 +815,6 @@ impl<N: Real> UnitQuaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{UnitQuaternion, Vector3, Unit};
     /// let axisangle = Vector3::new(0.1, 0.2, 0.3);
     /// let rot = UnitQuaternion::new(axisangle);
@@ -885,7 +871,6 @@ impl<N: Real> UnitQuaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Vector3, UnitQuaternion};
     /// let axisangle = Vector3::new(0.1, 0.2, 0.3);
     /// let q = UnitQuaternion::new(axisangle);
@@ -908,7 +893,6 @@ impl<N: Real> UnitQuaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{UnitQuaternion, Vector3, Unit};
     /// let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
     /// let angle = 1.2;
@@ -918,11 +902,11 @@ impl<N: Real> UnitQuaternion<N> {
     /// assert_eq!(pow.angle(), 2.4);
     /// ```
     #[inline]
-    pub fn powf(&self, n: N) -> UnitQuaternion<N> {
+    pub fn powf(&self, n: N) -> Self {
         if let Some(v) = self.axis() {
-            UnitQuaternion::from_axis_angle(&v, self.angle() * n)
+            Self::from_axis_angle(&v, self.angle() * n)
         } else {
-            UnitQuaternion::identity()
+            Self::identity()
         }
     }
 
@@ -932,7 +916,6 @@ impl<N: Real> UnitQuaternion<N> {
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use std::f32;
     /// # use nalgebra::{UnitQuaternion, Vector3, Matrix3};
     /// let q = UnitQuaternion::from_axis_angle(&Vector3::z_axis(), f32::consts::FRAC_PI_6);
@@ -990,7 +973,6 @@ impl<N: Real> UnitQuaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::UnitQuaternion;
     /// let rot = UnitQuaternion::from_euler_angles(0.1, 0.2, 0.3);
     /// let euler = rot.euler_angles();
@@ -1009,7 +991,6 @@ impl<N: Real> UnitQuaternion<N> {
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use std::f32;
     /// # use nalgebra::{UnitQuaternion, Vector3, Matrix4};
     /// let rot = UnitQuaternion::from_axis_angle(&Vector3::z_axis(), f32::consts::FRAC_PI_6);

src/geometry/quaternion_alga.rs

@@ -2,7 +2,7 @@ use num::Zero;
 
 use alga::general::{
     AbstractGroup, AbstractGroupAbelian, AbstractLoop, AbstractMagma, AbstractModule,
-    AbstractMonoid, AbstractQuasigroup, AbstractSemigroup, Additive, Id, Identity, Inverse, Module,
+    AbstractMonoid, AbstractQuasigroup, AbstractSemigroup, Additive, Id, Identity, TwoSidedInverse, Module,
     Multiplicative, Real,
 };
 use alga::linear::{
@@ -42,9 +42,9 @@ impl<N: Real> AbstractMagma<Additive> for Quaternion<N> {
     }
 }
 
-impl<N: Real> Inverse<Additive> for Quaternion<N> {
+impl<N: Real> TwoSidedInverse<Additive> for Quaternion<N> {
     #[inline]
-    fn inverse(&self) -> Self {
+    fn two_sided_inverse(&self) -> Self {
         -self
     }
 }
@@ -173,14 +173,14 @@ impl<N: Real> AbstractMagma<Multiplicative> for UnitQuaternion<N> {
     }
 }
 
-impl<N: Real> Inverse<Multiplicative> for UnitQuaternion<N> {
+impl<N: Real> TwoSidedInverse<Multiplicative> for UnitQuaternion<N> {
     #[inline]
-    fn inverse(&self) -> Self {
+    fn two_sided_inverse(&self) -> Self {
         self.inverse()
     }
 
     #[inline]
-    fn inverse_mut(&mut self) {
+    fn two_sided_inverse_mut(&mut self) {
         self.inverse_mut()
     }
 }

src/geometry/quaternion_construction.rs

@@ -15,9 +15,9 @@ use base::dimension::U3;
 use base::storage::Storage;
 #[cfg(feature = "arbitrary")]
 use base::Vector3;
-use base::{Unit, Vector, Vector4};
+use base::{Unit, Vector, Vector4, Matrix3};
 
-use geometry::{Quaternion, Rotation, UnitQuaternion};
+use geometry::{Quaternion, Rotation3, UnitQuaternion};
 
 impl<N: Real> Quaternion<N> {
     /// Creates a quaternion from a 4D vector. The quaternion scalar part corresponds to the `w`
@@ -25,7 +25,7 @@ impl<N: Real> Quaternion<N> {
     #[inline]
     #[deprecated(note = "Use `::from` instead.")]
     pub fn from_vector(vector: Vector4<N>) -> Self {
-        Quaternion { coords: vector }
+        Self { coords: vector }
     }
 
     /// Creates a new quaternion from its individual components. Note that the arguments order does
@@ -130,7 +130,7 @@ where Owned<N, U4>: Send
 {
     #[inline]
     fn arbitrary<G: Gen>(g: &mut G) -> Self {
-        Quaternion::new(
+        Self::new(
             N::arbitrary(g),
             N::arbitrary(g),
             N::arbitrary(g),
@@ -166,7 +166,6 @@ impl<N: Real> UnitQuaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use std::f32;
     /// # use nalgebra::{UnitQuaternion, Point3, Vector3};
     /// let axis = Vector3::y_axis();
@@ -208,7 +207,6 @@ impl<N: Real> UnitQuaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::UnitQuaternion;
     /// let rot = UnitQuaternion::from_euler_angles(0.1, 0.2, 0.3);
     /// let euler = rot.euler_angles();
@@ -237,7 +235,6 @@ impl<N: Real> UnitQuaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Rotation3, UnitQuaternion, Vector3};
     /// let axis = Vector3::y_axis();
     /// let angle = 0.1;
@@ -248,7 +245,7 @@ impl<N: Real> UnitQuaternion<N> {
     /// assert_relative_eq!(q.angle(), rot.angle(), epsilon = 1.0e-6);
     /// ```
     #[inline]
-    pub fn from_rotation_matrix(rotmat: &Rotation<N, U3>) -> Self {
+    pub fn from_rotation_matrix(rotmat: &Rotation3<N>) -> Self {
         // Robust matrix to quaternion transformation.
         // See http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion
         let tr = rotmat[(0, 0)] + rotmat[(1, 1)] + rotmat[(2, 2)];
@@ -296,13 +293,38 @@ impl<N: Real> UnitQuaternion<N> {
         Self::new_unchecked(res)
     }
 
+    /// Builds an unit quaternion by extracting the rotation part of the given transformation `m`.
+    ///
+    /// This is an iterative method. See `.from_matrix_eps` to provide mover
+    /// convergence parameters and starting solution.
+    /// This implements "A Robust Method to Extract the Rotational Part of Deformations" by Müller et al.
+    pub fn from_matrix(m: &Matrix3<N>) -> Self {
+        Rotation3::from_matrix(m).into()
+    }
+
+    /// Builds an unit quaternion by extracting the rotation part of the given transformation `m`.
+    ///
+    /// This implements "A Robust Method to Extract the Rotational Part of Deformations" by Müller et al.
+    ///
+    /// # Parameters
+    ///
+    /// * `m`: the matrix from which the rotational part is to be extracted.
+    /// * `eps`: the angular errors tolerated between the current rotation and the optimal one.
+    /// * `max_iter`: the maximum number of iterations. Loops indefinitely until convergence if set to `0`.
+    /// * `guess`: an estimate of the solution. Convergence will be significantly faster if an initial solution close
+    ///           to the actual solution is provided. Can be set to `UnitQuaternion::identity()` if no other
+    ///           guesses come to mind.
+    pub fn from_matrix_eps(m: &Matrix3<N>, eps: N, max_iter: usize, guess: Self) -> Self {
+        let guess = Rotation3::from(guess);
+        Rotation3::from_matrix_eps(m, eps, max_iter, guess).into()
+    }
+
     /// The unit quaternion needed to make `a` and `b` be collinear and point toward the same
     /// direction.
     ///
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Vector3, UnitQuaternion};
     /// let a = Vector3::new(1.0, 2.0, 3.0);
     /// let b = Vector3::new(3.0, 1.0, 2.0);
@@ -325,7 +347,6 @@ impl<N: Real> UnitQuaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Vector3, UnitQuaternion};
     /// let a = Vector3::new(1.0, 2.0, 3.0);
     /// let b = Vector3::new(3.0, 1.0, 2.0);
@@ -361,7 +382,6 @@ impl<N: Real> UnitQuaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Unit, Vector3, UnitQuaternion};
     /// let a = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
     /// let b = Unit::new_normalize(Vector3::new(3.0, 1.0, 2.0));
@@ -387,7 +407,6 @@ impl<N: Real> UnitQuaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Unit, Vector3, UnitQuaternion};
     /// let a = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
     /// let b = Unit::new_normalize(Vector3::new(3.0, 1.0, 2.0));
@@ -446,22 +465,31 @@ impl<N: Real> UnitQuaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use std::f32;
     /// # use nalgebra::{UnitQuaternion, Vector3};
     /// let dir = Vector3::new(1.0, 2.0, 3.0);
     /// let up = Vector3::y();
     ///
-    /// let q = UnitQuaternion::new_observer_frame(&dir, &up);
+    /// let q = UnitQuaternion::face_towards(&dir, &up);
     /// assert_relative_eq!(q * Vector3::z(), dir.normalize());
     /// ```
     #[inline]
-    pub fn new_observer_frame<SB, SC>(dir: &Vector<N, U3, SB>, up: &Vector<N, U3, SC>) -> Self
+    pub fn face_towards<SB, SC>(dir: &Vector<N, U3, SB>, up: &Vector<N, U3, SC>) -> Self
     where
         SB: Storage<N, U3>,
         SC: Storage<N, U3>,
     {
-        Self::from_rotation_matrix(&Rotation::<N, U3>::new_observer_frame(dir, up))
+        Self::from_rotation_matrix(&Rotation3::face_towards(dir, up))
+    }
+
+    /// Deprecated: Use [UnitQuaternion::face_towards] instead.
+    #[deprecated(note="renamed to `face_towards`")]
+    pub fn new_observer_frames<SB, SC>(dir: &Vector<N, U3, SB>, up: &Vector<N, U3, SC>) -> Self
+    where
+        SB: Storage<N, U3>,
+        SC: Storage<N, U3>,
+    {
+        Self::face_towards(dir, up)
     }
 
     /// Builds a right-handed look-at view matrix without translation.
@@ -478,7 +506,6 @@ impl<N: Real> UnitQuaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use std::f32;
     /// # use nalgebra::{UnitQuaternion, Vector3};
     /// let dir = Vector3::new(1.0, 2.0, 3.0);
@@ -493,7 +520,7 @@ impl<N: Real> UnitQuaternion<N> {
         SB: Storage<N, U3>,
         SC: Storage<N, U3>,
     {
-        Self::new_observer_frame(&-dir, up).inverse()
+        Self::face_towards(&-dir, up).inverse()
     }
 
     /// Builds a left-handed look-at view matrix without translation.
@@ -510,7 +537,6 @@ impl<N: Real> UnitQuaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use std::f32;
     /// # use nalgebra::{UnitQuaternion, Vector3};
     /// let dir = Vector3::new(1.0, 2.0, 3.0);
@@ -525,7 +551,7 @@ impl<N: Real> UnitQuaternion<N> {
         SB: Storage<N, U3>,
         SC: Storage<N, U3>,
     {
-        Self::new_observer_frame(dir, up).inverse()
+        Self::face_towards(dir, up).inverse()
     }
 
     /// Creates a new unit quaternion rotation from a rotation axis scaled by the rotation angle.
@@ -535,7 +561,6 @@ impl<N: Real> UnitQuaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use std::f32;
     /// # use nalgebra::{UnitQuaternion, Point3, Vector3};
     /// let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
@@ -565,7 +590,6 @@ impl<N: Real> UnitQuaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use std::f32;
     /// # use nalgebra::{UnitQuaternion, Point3, Vector3};
     /// let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
@@ -596,7 +620,6 @@ impl<N: Real> UnitQuaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use std::f32;
     /// # use nalgebra::{UnitQuaternion, Point3, Vector3};
     /// let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
@@ -625,7 +648,6 @@ impl<N: Real> UnitQuaternion<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use std::f32;
     /// # use nalgebra::{UnitQuaternion, Point3, Vector3};
     /// let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
@@ -687,7 +709,7 @@ where
     #[inline]
     fn arbitrary<G: Gen>(g: &mut G) -> Self {
         let axisangle = Vector3::arbitrary(g);
-        UnitQuaternion::from_scaled_axis(axisangle)
+        Self::from_scaled_axis(axisangle)
     }
 }
 

src/geometry/quaternion_conversion.rs

@@ -103,7 +103,7 @@ impl<N1, N2, R> SubsetOf<Isometry<N2, U3, R>> for UnitQuaternion<N1>
 where
     N1: Real,
     N2: Real + SupersetOf<N1>,
-    R: AlgaRotation<Point3<N2>> + SupersetOf<UnitQuaternion<N1>>,
+    R: AlgaRotation<Point3<N2>> + SupersetOf<Self>,
 {
     #[inline]
     fn to_superset(&self) -> Isometry<N2, U3, R> {
@@ -125,7 +125,7 @@ impl<N1, N2, R> SubsetOf<Similarity<N2, U3, R>> for UnitQuaternion<N1>
 where
     N1: Real,
     N2: Real + SupersetOf<N1>,
-    R: AlgaRotation<Point3<N2>> + SupersetOf<UnitQuaternion<N1>>,
+    R: AlgaRotation<Point3<N2>> + SupersetOf<Self>,
 {
     #[inline]
     fn to_superset(&self) -> Similarity<N2, U3, R> {
@@ -186,7 +186,7 @@ impl<N1: Real, N2: Real + SupersetOf<N1>> SubsetOf<Matrix4<N2>> for UnitQuaterni
 #[cfg(feature = "mint")]
 impl<N: Real> From<mint::Quaternion<N>> for Quaternion<N> {
     fn from(q: mint::Quaternion<N>) -> Self {
-        Quaternion::new(q.s, q.v.x, q.v.y, q.v.z)
+        Self::new(q.s, q.v.x, q.v.y, q.v.z)
     }
 }
 
@@ -220,14 +220,28 @@ impl<N: Real> Into<mint::Quaternion<N>> for UnitQuaternion<N> {
 
 impl<N: Real> From<UnitQuaternion<N>> for Matrix4<N> {
     #[inline]
-    fn from(q: UnitQuaternion<N>) -> Matrix4<N> {
+    fn from(q: UnitQuaternion<N>) -> Self {
         q.to_homogeneous()
     }
 }
 
+impl<N: Real> From<UnitQuaternion<N>> for Rotation3<N> {
+    #[inline]
+    fn from(q: UnitQuaternion<N>) -> Self {
+        q.to_rotation_matrix()
+    }
+}
+
+impl<N: Real> From<Rotation3<N>> for UnitQuaternion<N> {
+    #[inline]
+    fn from(q: Rotation3<N>) -> Self {
+        Self::from_rotation_matrix(&q)
+    }
+}
+
 impl<N: Real> From<UnitQuaternion<N>> for Matrix3<N> {
     #[inline]
-    fn from(q: UnitQuaternion<N>) -> Matrix3<N> {
+    fn from(q: UnitQuaternion<N>) -> Self {
         q.to_rotation_matrix().into_inner()
     }
 }
@@ -235,6 +249,6 @@ impl<N: Real> From<UnitQuaternion<N>> for Matrix3<N> {
 impl<N: Real> From<Vector4<N>> for Quaternion<N> {
     #[inline]
     fn from(coords: Vector4<N>) -> Self {
-        Quaternion { coords }
+        Self { coords }
     }
 }

src/geometry/quaternion_ops.rs

@@ -67,7 +67,7 @@ impl<N: Real> Index<usize> for Quaternion<N> {
     type Output = N;
 
     #[inline]
-    fn index(&self, i: usize) -> &N {
+    fn index(&self, i: usize) -> &Self::Output {
         &self.coords[i]
     }
 }

src/geometry/reflection.rs

@@ -18,8 +18,8 @@ impl<N: Real, D: Dim, S: Storage<N, D>> Reflection<N, D, S> {
     ///
     /// The bias is the position of the plane on the axis. In particular, a bias equal to zero
     /// represents a plane that passes through the origin.
-    pub fn new(axis: Unit<Vector<N, D, S>>, bias: N) -> Reflection<N, D, S> {
+    pub fn new(axis: Unit<Vector<N, D, S>>, bias: N) -> Self {
-        Reflection {
+        Self {
             axis: axis.into_inner(),
             bias: bias,
         }
@@ -30,7 +30,7 @@ impl<N: Real, D: Dim, S: Storage<N, D>> Reflection<N, D, S> {
     pub fn new_containing_point(
         axis: Unit<Vector<N, D, S>>,
         pt: &Point<N, D>,
-    ) -> Reflection<N, D, S>
+    ) -> Self
     where
         D: DimName,
         DefaultAllocator: Allocator<N, D>,

src/geometry/rotation.rs

@@ -53,7 +53,7 @@ where
 {
     #[inline]
     fn clone(&self) -> Self {
-        Rotation::from_matrix_unchecked(self.matrix.clone())
+        Self::from_matrix_unchecked(self.matrix.clone())
     }
 }
 
@@ -100,7 +100,7 @@ where
     where Des: Deserializer<'a> {
         let matrix = MatrixN::<N, D>::deserialize(deserializer)?;
 
-        Ok(Rotation::from_matrix_unchecked(matrix))
+        Ok(Self::from_matrix_unchecked(matrix))
     }
 }
 
@@ -241,13 +241,13 @@ where DefaultAllocator: Allocator<N, D, D>
     /// assert_eq!(*rot.matrix(), mat);
     /// ```
     #[inline]
-    pub fn from_matrix_unchecked(matrix: MatrixN<N, D>) -> Rotation<N, D> {
+    pub fn from_matrix_unchecked(matrix: MatrixN<N, D>) -> Self {
         assert!(
             matrix.is_square(),
             "Unable to create a rotation from a non-square matrix."
         );
 
-        Rotation { matrix: matrix }
+        Self { matrix: matrix }
     }
 
     /// Transposes `self`.
@@ -257,7 +257,6 @@ where DefaultAllocator: Allocator<N, D, D>
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Rotation2, Rotation3, Vector3};
     /// let rot = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
     /// let tr_rot = rot.transpose();
@@ -270,8 +269,8 @@ where DefaultAllocator: Allocator<N, D, D>
     /// assert_relative_eq!(tr_rot * rot, Rotation2::identity(), epsilon = 1.0e-6);
     /// ```
     #[inline]
-    pub fn transpose(&self) -> Rotation<N, D> {
+    pub fn transpose(&self) -> Self {
-        Rotation::from_matrix_unchecked(self.matrix.transpose())
+        Self::from_matrix_unchecked(self.matrix.transpose())
     }
 
     /// Inverts `self`.
@@ -281,7 +280,6 @@ where DefaultAllocator: Allocator<N, D, D>
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Rotation2, Rotation3, Vector3};
     /// let rot = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
     /// let inv = rot.inverse();
@@ -294,7 +292,7 @@ where DefaultAllocator: Allocator<N, D, D>
     /// assert_relative_eq!(inv * rot, Rotation2::identity(), epsilon = 1.0e-6);
     /// ```
     #[inline]
-    pub fn inverse(&self) -> Rotation<N, D> {
+    pub fn inverse(&self) -> Self {
         self.transpose()
     }
 
@@ -305,7 +303,6 @@ where DefaultAllocator: Allocator<N, D, D>
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Rotation2, Rotation3, Vector3};
     /// let rot = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
     /// let mut tr_rot = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
@@ -333,7 +330,6 @@ where DefaultAllocator: Allocator<N, D, D>
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Rotation2, Rotation3, Vector3};
     /// let rot = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
     /// let mut inv = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
@@ -361,7 +357,7 @@ impl<N: Scalar + PartialEq, D: DimName> PartialEq for Rotation<N, D>
 where DefaultAllocator: Allocator<N, D, D>
 {
     #[inline]
-    fn eq(&self, right: &Rotation<N, D>) -> bool {
+    fn eq(&self, right: &Self) -> bool {
         self.matrix == right.matrix
     }
 }

src/geometry/rotation_alga.rs

@@ -1,6 +1,6 @@
 use alga::general::{
     AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
-    AbstractSemigroup, Id, Identity, Inverse, Multiplicative, Real,
+    AbstractSemigroup, Id, Identity, TwoSidedInverse, Multiplicative, Real,
 };
 use alga::linear::{
     self, AffineTransformation, DirectIsometry, Isometry, OrthogonalTransformation,
@@ -27,16 +27,16 @@ where DefaultAllocator: Allocator<N, D, D>
     }
 }
 
-impl<N: Real, D: DimName> Inverse<Multiplicative> for Rotation<N, D>
+impl<N: Real, D: DimName> TwoSidedInverse<Multiplicative> for Rotation<N, D>
 where DefaultAllocator: Allocator<N, D, D>
 {
     #[inline]
-    fn inverse(&self) -> Self {
+    fn two_sided_inverse(&self) -> Self {
         self.transpose()
     }
 
     #[inline]
-    fn inverse_mut(&mut self) {
+    fn two_sided_inverse_mut(&mut self) {
         self.transpose_mut()
     }
 }

src/geometry/rotation_conversion.rs

@@ -102,7 +102,7 @@ impl<N1, N2, D: DimName, R> SubsetOf<Isometry<N2, D, R>> for Rotation<N1, D>
 where
     N1: Real,
     N2: Real + SupersetOf<N1>,
-    R: AlgaRotation<Point<N2, D>> + SupersetOf<Rotation<N1, D>>,
+    R: AlgaRotation<Point<N2, D>> + SupersetOf<Self>,
     DefaultAllocator: Allocator<N1, D, D> + Allocator<N2, D>,
 {
     #[inline]
@@ -125,7 +125,7 @@ impl<N1, N2, D: DimName, R> SubsetOf<Similarity<N2, D, R>> for Rotation<N1, D>
 where
     N1: Real,
     N2: Real + SupersetOf<N1>,
-    R: AlgaRotation<Point<N2, D>> + SupersetOf<Rotation<N1, D>>,
+    R: AlgaRotation<Point<N2, D>> + SupersetOf<Self>,
     DefaultAllocator: Allocator<N1, D, D> + Allocator<N2, D>,
 {
     #[inline]
@@ -219,28 +219,28 @@ impl<N: Real> From<mint::EulerAngles<N, mint::IntraXYZ>> for Rotation3<N> {
 
 impl<N: Real> From<Rotation2<N>> for Matrix3<N> {
     #[inline]
-    fn from(q: Rotation2<N>) -> Matrix3<N> {
+    fn from(q: Rotation2<N>) ->Self {
         q.to_homogeneous()
     }
 }
 
 impl<N: Real> From<Rotation2<N>> for Matrix2<N> {
     #[inline]
-    fn from(q: Rotation2<N>) -> Matrix2<N> {
+    fn from(q: Rotation2<N>) -> Self {
         q.into_inner()
     }
 }
 
 impl<N: Real> From<Rotation3<N>> for Matrix4<N> {
     #[inline]
-    fn from(q: Rotation3<N>) -> Matrix4<N> {
+    fn from(q: Rotation3<N>) -> Self {
         q.to_homogeneous()
     }
 }
 
 impl<N: Real> From<Rotation3<N>> for Matrix3<N> {
     #[inline]
-    fn from(q: Rotation3<N>) -> Matrix3<N> {
+    fn from(q: Rotation3<N>) -> Self {
         q.into_inner()
     }
 }

src/geometry/rotation_specialization.rs

@@ -11,9 +11,9 @@ use std::ops::Neg;
 
 use base::dimension::{U1, U2, U3};
 use base::storage::Storage;
-use base::{MatrixN, Unit, Vector, Vector1, Vector3, VectorN};
+use base::{Matrix2, Matrix3, MatrixN, Unit, Vector, Vector1, Vector3, VectorN};
 
-use geometry::{Rotation2, Rotation3, UnitComplex};
+use geometry::{Rotation2, Rotation3, UnitComplex, UnitQuaternion};
 
 /*
  *
@@ -27,7 +27,6 @@ impl<N: Real> Rotation2<N> {
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use std::f32;
     /// # use nalgebra::{Rotation2, Point2};
     /// let rot = Rotation2::new(f32::consts::FRAC_PI_2);
@@ -36,7 +35,7 @@ impl<N: Real> Rotation2<N> {
     /// ```
     pub fn new(angle: N) -> Self {
         let (sia, coa) = angle.sin_cos();
-        Self::from_matrix_unchecked(MatrixN::<N, U2>::new(coa, -sia, sia, coa))
+        Self::from_matrix_unchecked(Matrix2::new(coa, -sia, sia, coa))
     }
 
     /// Builds a 2 dimensional rotation matrix from an angle in radian wrapped in a 1-dimensional vector.
@@ -49,6 +48,51 @@ impl<N: Real> Rotation2<N> {
         Self::new(axisangle[0])
     }
 
+    /// Builds a rotation matrix by extracting the rotation part of the given transformation `m`.
+    ///
+    /// This is an iterative method. See `.from_matrix_eps` to provide mover
+    /// convergence parameters and starting solution.
+    /// This implements "A Robust Method to Extract the Rotational Part of Deformations" by Müller et al.
+    pub fn from_matrix(m: &Matrix2<N>) -> Self {
+        Self::from_matrix_eps(m, N::default_epsilon(), 0, Self::identity())
+    }
+
+    /// Builds a rotation matrix by extracting the rotation part of the given transformation `m`.
+    ///
+    /// This implements "A Robust Method to Extract the Rotational Part of Deformations" by Müller et al.
+    ///
+    /// # Parameters
+    ///
+    /// * `m`: the matrix from which the rotational part is to be extracted.
+    /// * `eps`: the angular errors tolerated between the current rotation and the optimal one.
+    /// * `max_iter`: the maximum number of iterations. Loops indefinitely until convergence if set to `0`.
+    /// * `guess`: an estimate of the solution. Convergence will be significantly faster if an initial solution close
+    ///           to the actual solution is provided. Can be set to `Rotation2::identity()` if no other
+    ///           guesses come to mind.
+    pub fn from_matrix_eps(m: &Matrix2<N>, eps: N, mut max_iter: usize, guess: Self) -> Self {
+        if max_iter == 0 {
+            max_iter = usize::max_value();
+        }
+
+        let mut rot = guess.into_inner();
+
+        for _ in 0..max_iter {
+            let axis = rot.column(0).perp(&m.column(0)) +
+                rot.column(1).perp(&m.column(1));
+            let denom = rot.column(0).dot(&m.column(0)) +
+                rot.column(1).dot(&m.column(1));
+
+            let angle = axis / (denom.abs() + N::default_epsilon());
+            if angle.abs() > eps {
+                rot = Self::new(angle) * rot;
+            } else {
+                break;
+            }
+        }
+
+        Self::from_matrix_unchecked(rot)
+    }
+
     /// The rotation matrix required to align `a` and `b` but with its angle.
     ///
     /// This is the rotation `R` such that `(R * a).angle(b) == 0 && (R * a).dot(b).is_positive()`.
@@ -56,7 +100,6 @@ impl<N: Real> Rotation2<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Vector2, Rotation2};
     /// let a = Vector2::new(1.0, 2.0);
     /// let b = Vector2::new(2.0, 1.0);
@@ -79,7 +122,6 @@ impl<N: Real> Rotation2<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Vector2, Rotation2};
     /// let a = Vector2::new(1.0, 2.0);
     /// let b = Vector2::new(2.0, 1.0);
@@ -100,15 +142,12 @@ impl<N: Real> Rotation2<N> {
     {
         ::convert(UnitComplex::scaled_rotation_between(a, b, s).to_rotation_matrix())
     }
-}
 
-impl<N: Real> Rotation2<N> {
     /// The rotation angle.
     ///
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Rotation2;
     /// let rot = Rotation2::new(1.78);
     /// assert_relative_eq!(rot.angle(), 1.78);
@@ -123,14 +162,13 @@ impl<N: Real> Rotation2<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Rotation2;
     /// let rot1 = Rotation2::new(0.1);
     /// let rot2 = Rotation2::new(1.7);
     /// assert_relative_eq!(rot1.angle_to(&rot2), 1.6);
     /// ```
     #[inline]
-    pub fn angle_to(&self, other: &Rotation2<N>) -> N {
+    pub fn angle_to(&self, other: &Self) -> N {
         self.rotation_to(other).angle()
     }
 
@@ -141,7 +179,6 @@ impl<N: Real> Rotation2<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Rotation2;
     /// let rot1 = Rotation2::new(0.1);
     /// let rot2 = Rotation2::new(1.7);
@@ -151,24 +188,37 @@ impl<N: Real> Rotation2<N> {
     /// assert_relative_eq!(rot_to.inverse() * rot2, rot1);
     /// ```
     #[inline]
-    pub fn rotation_to(&self, other: &Rotation2<N>) -> Rotation2<N> {
+    pub fn rotation_to(&self, other: &Self) -> Self {
         other * self.inverse()
     }
 
+
+    /* FIXME: requires alga v0.9 to be released so that Complex implements VectorSpace.
+    /// Ensure this rotation is an orthonormal rotation matrix. This is useful when repeated
+    /// computations might cause the matrix from progressively not being orthonormal anymore.
+    #[inline]
+    pub fn renormalize(&mut self) {
+        let mut c = UnitComplex::from(*self);
+        let _ = c.renormalize();
+
+        *self = Self::from_matrix_eps(self.matrix(), N::default_epsilon(), 0, c.into())
+    }
+    */
+
+
     /// Raise the quaternion to a given floating power, i.e., returns the rotation with the angle
     /// of `self` multiplied by `n`.
     ///
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Rotation2;
     /// let rot = Rotation2::new(0.78);
     /// let pow = rot.powf(2.0);
     /// assert_relative_eq!(pow.angle(), 2.0 * 0.78);
     /// ```
     #[inline]
-    pub fn powf(&self, n: N) -> Rotation2<N> {
+    pub fn powf(&self, n: N) -> Self {
         Self::new(self.angle() * n)
     }
 
@@ -217,7 +267,6 @@ impl<N: Real> Rotation3<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use std::f32;
     /// # use nalgebra::{Rotation3, Point3, Vector3};
     /// let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
@@ -238,6 +287,54 @@ impl<N: Real> Rotation3<N> {
         Self::from_axis_angle(&axis, angle)
     }
 
+    /// Builds a rotation matrix by extracting the rotation part of the given transformation `m`.
+    ///
+    /// This is an iterative method. See `.from_matrix_eps` to provide mover
+    /// convergence parameters and starting solution.
+    /// This implements "A Robust Method to Extract the Rotational Part of Deformations" by Müller et al.
+    pub fn from_matrix(m: &Matrix3<N>) -> Self {
+        Self::from_matrix_eps(m, N::default_epsilon(), 0, Self::identity())
+    }
+
+    /// Builds a rotation matrix by extracting the rotation part of the given transformation `m`.
+    ///
+    /// This implements "A Robust Method to Extract the Rotational Part of Deformations" by Müller et al.
+    ///
+    /// # Parameters
+    ///
+    /// * `m`: the matrix from which the rotational part is to be extracted.
+    /// * `eps`: the angular errors tolerated between the current rotation and the optimal one.
+    /// * `max_iter`: the maximum number of iterations. Loops indefinitely until convergence if set to `0`.
+    /// * `guess`: a guess of the solution. Convergence will be significantly faster if an initial solution close
+    ///           to the actual solution is provided. Can be set to `Rotation3::identity()` if no other
+    ///           guesses come to mind.
+    pub fn from_matrix_eps(m: &Matrix3<N>, eps: N, mut max_iter: usize, guess: Self) -> Self {
+        if max_iter == 0 {
+            max_iter = usize::max_value();
+        }
+
+        let mut rot = guess.into_inner();
+
+        for _ in 0..max_iter {
+            let axis = rot.column(0).cross(&m.column(0)) +
+                rot.column(1).cross(&m.column(1)) +
+                rot.column(2).cross(&m.column(2));
+            let denom = rot.column(0).dot(&m.column(0)) +
+                rot.column(1).dot(&m.column(1)) +
+                rot.column(2).dot(&m.column(2));
+
+            let axisangle = axis / (denom.abs() + N::default_epsilon());
+
+            if let Some((axis, angle)) = Unit::try_new_and_get(axisangle, eps) {
+                rot = Rotation3::from_axis_angle(&axis, angle) * rot;
+            } else {
+                break;
+            }
+        }
+
+        Self::from_matrix_unchecked(rot)
+    }
+
     /// Builds a 3D rotation matrix from an axis scaled by the rotation angle.
     ///
     /// This is the same as `Self::new(axisangle)`.
@@ -245,7 +342,6 @@ impl<N: Real> Rotation3<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use std::f32;
     /// # use nalgebra::{Rotation3, Point3, Vector3};
     /// let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
@@ -269,7 +365,6 @@ impl<N: Real> Rotation3<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use std::f32;
     /// # use nalgebra::{Rotation3, Point3, Vector3};
     /// let axis = Vector3::y_axis();
@@ -322,7 +417,6 @@ impl<N: Real> Rotation3<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Rotation3;
     /// let rot = Rotation3::from_euler_angles(0.1, 0.2, 0.3);
     /// let euler = rot.euler_angles();
@@ -363,7 +457,6 @@ impl<N: Real> Rotation3<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::Rotation3;
     /// let rot = Rotation3::from_euler_angles(0.1, 0.2, 0.3);
     /// let euler = rot.euler_angles();
@@ -390,6 +483,16 @@ impl<N: Real> Rotation3<N> {
         }
     }
 
+    /// Ensure this rotation is an orthonormal rotation matrix. This is useful when repeated
+    /// computations might cause the matrix from progressively not being orthonormal anymore.
+    #[inline]
+    pub fn renormalize(&mut self) {
+        let mut c = UnitQuaternion::from(*self);
+        let _ = c.renormalize();
+
+        *self = Self::from_matrix_eps(self.matrix(), N::default_epsilon(), 0, c.into())
+    }
+
     /// Creates a rotation that corresponds to the local frame of an observer standing at the
     /// origin and looking toward `dir`.
     ///
@@ -403,17 +506,16 @@ impl<N: Real> Rotation3<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use std::f32;
     /// # use nalgebra::{Rotation3, Vector3};
     /// let dir = Vector3::new(1.0, 2.0, 3.0);
     /// let up = Vector3::y();
     ///
-    /// let rot = Rotation3::new_observer_frame(&dir, &up);
+    /// let rot = Rotation3::face_towards(&dir, &up);
     /// assert_relative_eq!(rot * Vector3::z(), dir.normalize());
     /// ```
     #[inline]
-    pub fn new_observer_frame<SB, SC>(dir: &Vector<N, U3, SB>, up: &Vector<N, U3, SC>) -> Self
+    pub fn face_towards<SB, SC>(dir: &Vector<N, U3, SB>, up: &Vector<N, U3, SC>) -> Self
     where
         SB: Storage<N, U3>,
         SC: Storage<N, U3>,
@@ -427,6 +529,16 @@ impl<N: Real> Rotation3<N> {
         ))
     }
 
+    /// Deprecated: Use [Rotation3::face_towards] instead.
+    #[deprecated(note="renamed to `face_towards`")]
+    pub fn new_observer_frames<SB, SC>(dir: &Vector<N, U3, SB>, up: &Vector<N, U3, SC>) -> Self
+    where
+        SB: Storage<N, U3>,
+        SC: Storage<N, U3>,
+    {
+        Self::face_towards(dir, up)
+    }
+
     /// Builds a right-handed look-at view matrix without translation.
     ///
     /// It maps the view direction `dir` to the **negative** `z` axis.
@@ -441,7 +553,6 @@ impl<N: Real> Rotation3<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use std::f32;
     /// # use nalgebra::{Rotation3, Vector3};
     /// let dir = Vector3::new(1.0, 2.0, 3.0);
@@ -456,7 +567,7 @@ impl<N: Real> Rotation3<N> {
         SB: Storage<N, U3>,
         SC: Storage<N, U3>,
     {
-        Self::new_observer_frame(&dir.neg(), up).inverse()
+        Self::face_towards(&dir.neg(), up).inverse()
     }
 
     /// Builds a left-handed look-at view matrix without translation.
@@ -473,7 +584,6 @@ impl<N: Real> Rotation3<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use std::f32;
     /// # use nalgebra::{Rotation3, Vector3};
     /// let dir = Vector3::new(1.0, 2.0, 3.0);
@@ -488,7 +598,7 @@ impl<N: Real> Rotation3<N> {
         SB: Storage<N, U3>,
         SC: Storage<N, U3>,
     {
-        Self::new_observer_frame(dir, up).inverse()
+        Self::face_towards(dir, up).inverse()
     }
 
     /// The rotation matrix required to align `a` and `b` but with its angle.
@@ -498,7 +608,6 @@ impl<N: Real> Rotation3<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Vector3, Rotation3};
     /// let a = Vector3::new(1.0, 2.0, 3.0);
     /// let b = Vector3::new(3.0, 1.0, 2.0);
@@ -521,7 +630,6 @@ impl<N: Real> Rotation3<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Vector3, Rotation3};
     /// let a = Vector3::new(1.0, 2.0, 3.0);
     /// let b = Vector3::new(3.0, 1.0, 2.0);
@@ -566,7 +674,6 @@ impl<N: Real> Rotation3<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Unit, Rotation3, Vector3};
     /// let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
     /// let rot = Rotation3::from_axis_angle(&axis, 1.78);
@@ -584,7 +691,6 @@ impl<N: Real> Rotation3<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Rotation3, Vector3, Unit};
     /// let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
     /// let angle = 1.2;
@@ -611,7 +717,6 @@ impl<N: Real> Rotation3<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Rotation3, Vector3, Unit};
     /// let axisangle = Vector3::new(0.1, 0.2, 0.3);
     /// let rot = Rotation3::new(axisangle);
@@ -633,7 +738,6 @@ impl<N: Real> Rotation3<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Rotation3, Vector3, Unit};
     /// let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
     /// let angle = 1.2;
@@ -660,14 +764,13 @@ impl<N: Real> Rotation3<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Rotation3, Vector3};
     /// let rot1 = Rotation3::from_axis_angle(&Vector3::y_axis(), 1.0);
     /// let rot2 = Rotation3::from_axis_angle(&Vector3::x_axis(), 0.1);
     /// assert_relative_eq!(rot1.angle_to(&rot2), 1.0045657, epsilon = 1.0e-6);
     /// ```
     #[inline]
-    pub fn angle_to(&self, other: &Rotation3<N>) -> N {
+    pub fn angle_to(&self, other: &Self) -> N {
         self.rotation_to(other).angle()
     }
 
@@ -678,7 +781,6 @@ impl<N: Real> Rotation3<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Rotation3, Vector3};
     /// let rot1 = Rotation3::from_axis_angle(&Vector3::y_axis(), 1.0);
     /// let rot2 = Rotation3::from_axis_angle(&Vector3::x_axis(), 0.1);
@@ -686,7 +788,7 @@ impl<N: Real> Rotation3<N> {
     /// assert_relative_eq!(rot_to * rot1, rot2, epsilon = 1.0e-6);
     /// ```
     #[inline]
-    pub fn rotation_to(&self, other: &Rotation3<N>) -> Rotation3<N> {
+    pub fn rotation_to(&self, other: &Self) -> Self {
         other * self.inverse()
     }
 
@@ -696,7 +798,6 @@ impl<N: Real> Rotation3<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Rotation3, Vector3, Unit};
     /// let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
     /// let angle = 1.2;
@@ -706,7 +807,7 @@ impl<N: Real> Rotation3<N> {
     /// assert_eq!(pow.angle(), 2.4);
     /// ```
     #[inline]
-    pub fn powf(&self, n: N) -> Rotation3<N> {
+    pub fn powf(&self, n: N) -> Self {
         if let Some(axis) = self.axis() {
             Self::from_axis_angle(&axis, self.angle() * n)
         } else if self.matrix()[(0, 0)] < N::zero() {

src/geometry/similarity.rs

@@ -106,20 +106,20 @@ where
         translation: Translation<N, D>,
         rotation: R,
         scaling: N,
-    ) -> Similarity<N, D, R>
+    ) -> Self
     {
-        Similarity::from_isometry(Isometry::from_parts(translation, rotation), scaling)
+        Self::from_isometry(Isometry::from_parts(translation, rotation), scaling)
     }
 
     /// Creates a new similarity from its rotational and translational parts.
     #[inline]
-    pub fn from_isometry(isometry: Isometry<N, D, R>, scaling: N) -> Similarity<N, D, R> {
+    pub fn from_isometry(isometry: Isometry<N, D, R>, scaling: N) -> Self {
         assert!(
             !relative_eq!(scaling, N::zero()),
             "The scaling factor must not be zero."
         );
 
-        Similarity {
+        Self {
             isometry: isometry,
             scaling: scaling,
         }
@@ -127,13 +127,13 @@ where
 
     /// Creates a new similarity that applies only a scaling factor.
     #[inline]
-    pub fn from_scaling(scaling: N) -> Similarity<N, D, R> {
+    pub fn from_scaling(scaling: N) -> Self {
         Self::from_isometry(Isometry::identity(), scaling)
     }
 
     /// Inverts `self`.
     #[inline]
-    pub fn inverse(&self) -> Similarity<N, D, R> {
+    pub fn inverse(&self) -> Self {
         let mut res = self.clone();
         res.inverse_mut();
         res
@@ -277,7 +277,7 @@ where
     DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
-    fn eq(&self, right: &Similarity<N, D, R>) -> bool {
+    fn eq(&self, right: &Self) -> bool {
         self.isometry == right.isometry && self.scaling == right.scaling
     }
 }

src/geometry/similarity_alga.rs

@@ -1,6 +1,6 @@
 use alga::general::{
     AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
-    AbstractSemigroup, Identity, Inverse, Multiplicative, Real,
+    AbstractSemigroup, Identity, TwoSidedInverse, Multiplicative, Real,
 };
 use alga::linear::Similarity as AlgaSimilarity;
 use alga::linear::{AffineTransformation, ProjectiveTransformation, Rotation, Transformation};
@@ -27,18 +27,18 @@ where
     }
 }
 
-impl<N: Real, D: DimName, R> Inverse<Multiplicative> for Similarity<N, D, R>
+impl<N: Real, D: DimName, R> TwoSidedInverse<Multiplicative> for Similarity<N, D, R>
 where
     R: Rotation<Point<N, D>>,
     DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
-    fn inverse(&self) -> Self {
+    fn two_sided_inverse(&self) -> Self {
         self.inverse()
     }
 
     #[inline]
-    fn inverse_mut(&mut self) {
+    fn two_sided_inverse_mut(&mut self) {
         self.inverse_mut()
     }
 }

src/geometry/similarity_construction.rs

@@ -86,7 +86,6 @@ where
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use std::f32;
     /// # use nalgebra::{Similarity2, Point2, UnitComplex};
     /// let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
@@ -135,7 +134,6 @@ impl<N: Real> Similarity<N, U2, Rotation2<N>> {
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use std::f32;
     /// # use nalgebra::{SimilarityMatrix2, Vector2, Point2};
     /// let sim = SimilarityMatrix2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2, 3.0);
@@ -159,7 +157,6 @@ impl<N: Real> Similarity<N, U2, UnitComplex<N>> {
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use std::f32;
     /// # use nalgebra::{Similarity2, Vector2, Point2};
     /// let sim = Similarity2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2, 3.0);
@@ -187,7 +184,6 @@ macro_rules! similarity_construction_impl(
             ///
             /// ```
             /// # #[macro_use] extern crate approx;
-            /// # extern crate nalgebra;
             /// # use std::f32;
             /// # use nalgebra::{Similarity3, SimilarityMatrix3, Point3, Vector3};
             /// let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
@@ -227,7 +223,6 @@ macro_rules! similarity_construction_impl(
             ///
             /// ```
             /// # #[macro_use] extern crate approx;
-            /// # extern crate nalgebra;
             /// # use std::f32;
             /// # use nalgebra::{Similarity3, SimilarityMatrix3, Point3, Vector3};
             /// let eye = Point3::new(1.0, 2.0, 3.0);
@@ -235,22 +230,32 @@ macro_rules! similarity_construction_impl(
             /// let up = Vector3::y();
             ///
             /// // Similarity with its rotation part represented as a UnitQuaternion
-            /// let sim = Similarity3::new_observer_frame(&eye, &target, &up, 3.0);
+            /// let sim = Similarity3::face_towards(&eye, &target, &up, 3.0);
             /// assert_eq!(sim * Point3::origin(), eye);
             /// assert_relative_eq!(sim * Vector3::z(), Vector3::x() * 3.0, epsilon = 1.0e-6);
             ///
             /// // Similarity with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
-            /// let sim = SimilarityMatrix3::new_observer_frame(&eye, &target, &up, 3.0);
+            /// let sim = SimilarityMatrix3::face_towards(&eye, &target, &up, 3.0);
             /// assert_eq!(sim * Point3::origin(), eye);
             /// assert_relative_eq!(sim * Vector3::z(), Vector3::x() * 3.0, epsilon = 1.0e-6);
             /// ```
             #[inline]
-            pub fn new_observer_frame(eye:    &Point3<N>,
+            pub fn face_towards(eye:    &Point3<N>,
                                       target: &Point3<N>,
                                       up:     &Vector3<N>,
                                       scaling: N)
                                       -> Self {
-                Self::from_isometry(Isometry::<_, U3, $Rot>::new_observer_frame(eye, target, up), scaling)
+                Self::from_isometry(Isometry::<_, U3, $Rot>::face_towards(eye, target, up), scaling)
+            }
+
+            /// Deprecated: Use [SimilarityMatrix3::face_towards] instead.
+            #[deprecated(note="renamed to `face_towards`")]
+            pub fn new_observer_frames(eye:    &Point3<N>,
+                                      target: &Point3<N>,
+                                      up:     &Vector3<N>,
+                                      scaling: N)
+                                      -> Self {
+                Self::face_towards(eye, target, up, scaling)
             }
 
             /// Builds a right-handed look-at view matrix including scaling factor.
@@ -268,7 +273,6 @@ macro_rules! similarity_construction_impl(
             ///
             /// ```
             /// # #[macro_use] extern crate approx;
-            /// # extern crate nalgebra;
             /// # use std::f32;
             /// # use nalgebra::{Similarity3, SimilarityMatrix3, Point3, Vector3};
             /// let eye = Point3::new(1.0, 2.0, 3.0);
@@ -307,7 +311,6 @@ macro_rules! similarity_construction_impl(
             ///
             /// ```
             /// # #[macro_use] extern crate approx;
-            /// # extern crate nalgebra;
             /// # use std::f32;
             /// # use nalgebra::{Similarity3, SimilarityMatrix3, Point3, Vector3};
             /// let eye = Point3::new(1.0, 2.0, 3.0);

src/geometry/similarity_ops.rs

@@ -222,8 +222,8 @@ similarity_binop_assign_impl_all!(
     DivAssign, div_assign;
     self: Similarity<N, D, R>, rhs: R;
     // FIXME: don't invert explicitly?
-    [val] => *self *= rhs.inverse();
+    [val] => *self *= rhs.two_sided_inverse();
-    [ref] => *self *= rhs.inverse();
+    [ref] => *self *= rhs.two_sided_inverse();
 );
 
 // Similarity × R

src/geometry/transform.rs

@@ -350,7 +350,6 @@ where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
     /// # Examples
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Matrix3, Transform2};
     ///
     /// let m = Matrix3::new(2.0, 2.0, -0.3,
@@ -383,7 +382,6 @@ where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
     /// # Examples
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Matrix3, Projective2};
     ///
     /// let m = Matrix3::new(2.0, 2.0, -0.3,
@@ -407,7 +405,6 @@ where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
     /// # Examples
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Matrix3, Transform2};
     ///
     /// let m = Matrix3::new(2.0, 2.0, -0.3,
@@ -437,7 +434,6 @@ where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
     /// # Examples
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Matrix3, Projective2};
     ///
     /// let m = Matrix3::new(2.0, 2.0, -0.3,

src/geometry/transform_alga.rs

@@ -1,6 +1,6 @@
 use alga::general::{
     AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
-    AbstractSemigroup, Identity, Inverse, Multiplicative, Real,
+    AbstractSemigroup, Identity, TwoSidedInverse, Multiplicative, Real,
 };
 use alga::linear::{ProjectiveTransformation, Transformation};
 
@@ -26,18 +26,18 @@ where
     }
 }
 
-impl<N: Real, D: DimNameAdd<U1>, C> Inverse<Multiplicative> for Transform<N, D, C>
+impl<N: Real, D: DimNameAdd<U1>, C> TwoSidedInverse<Multiplicative> for Transform<N, D, C>
 where
     C: SubTCategoryOf<TProjective>,
     DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
 {
     #[inline]
-    fn inverse(&self) -> Self {
+    fn two_sided_inverse(&self) -> Self {
         self.clone().inverse()
     }
 
     #[inline]
-    fn inverse_mut(&mut self) {
+    fn two_sided_inverse_mut(&mut self) {
         self.inverse_mut()
     }
 }
@@ -116,12 +116,12 @@ where
 {
     #[inline]
     fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
-        self.inverse() * pt
+        self.two_sided_inverse() * pt
     }
 
     #[inline]
     fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
-        self.inverse() * v
+        self.two_sided_inverse() * v
     }
 }
 

src/geometry/transform_conversion.rs

@@ -57,7 +57,7 @@ where
 
     #[inline]
     unsafe fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self {
-        Transform::from_matrix_unchecked(::convert_ref_unchecked(m))
+        Self::from_matrix_unchecked(::convert_ref_unchecked(m))
     }
 }
 

src/geometry/translation_alga.rs

@@ -1,6 +1,6 @@
 use alga::general::{
     AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
-    AbstractSemigroup, Id, Identity, Inverse, Multiplicative, Real,
+    AbstractSemigroup, Id, Identity, TwoSidedInverse, Multiplicative, Real,
 };
 use alga::linear::Translation as AlgaTranslation;
 use alga::linear::{
@@ -28,16 +28,16 @@ where DefaultAllocator: Allocator<N, D>
     }
 }
 
-impl<N: Real, D: DimName> Inverse<Multiplicative> for Translation<N, D>
+impl<N: Real, D: DimName> TwoSidedInverse<Multiplicative> for Translation<N, D>
 where DefaultAllocator: Allocator<N, D>
 {
     #[inline]
-    fn inverse(&self) -> Self {
+    fn two_sided_inverse(&self) -> Self {
         self.inverse()
     }
 
     #[inline]
-    fn inverse_mut(&mut self) {
+    fn two_sided_inverse_mut(&mut self) {
         self.inverse_mut()
     }
 }

src/geometry/translation_coordinates.rs

@@ -0,0 +1,44 @@
+use std::mem;
+use std::ops::{Deref, DerefMut};
+
+use base::allocator::Allocator;
+use base::coordinates::{X, XY, XYZ, XYZW, XYZWA, XYZWAB};
+use base::dimension::{U1, U2, U3, U4, U5, U6};
+use base::{DefaultAllocator, Scalar};
+
+use geometry::Translation;
+
+/*
+ *
+ * Give coordinates to Translation{1 .. 6}
+ *
+ */
+
+macro_rules! deref_impl(
+    ($D: ty, $Target: ident $(, $comps: ident)*) => {
+        impl<N: Scalar> Deref for Translation<N, $D>
+            where DefaultAllocator: Allocator<N, $D> {
+            type Target = $Target<N>;
+
+            #[inline]
+            fn deref(&self) -> &Self::Target {
+                unsafe { mem::transmute(self) }
+            }
+        }
+
+        impl<N: Scalar> DerefMut for Translation<N, $D>
+            where DefaultAllocator: Allocator<N, $D> {
+            #[inline]
+            fn deref_mut(&mut self) -> &mut Self::Target {
+                unsafe { mem::transmute(self) }
+            }
+        }
+    }
+);
+
+deref_impl!(U1, X, x);
+deref_impl!(U2, XY, x, y);
+deref_impl!(U3, XYZ, x, y, z);
+deref_impl!(U4, XYZW, x, y, z, w);
+deref_impl!(U5, XYZWA, x, y, z, w, a);
+deref_impl!(U6, XYZWAB, x, y, z, w, a, b);

src/geometry/unit_complex.rs

@@ -85,7 +85,6 @@ impl<N: Real> UnitComplex<N> {
     /// # Example
     /// ```
     /// # extern crate num_complex;
-    /// # extern crate nalgebra;
     /// # use num_complex::Complex;
     /// # use nalgebra::UnitComplex;
     /// let angle = 1.78f32;
@@ -109,7 +108,7 @@ impl<N: Real> UnitComplex<N> {
     /// ```
     #[inline]
     pub fn conjugate(&self) -> Self {
-        UnitComplex::new_unchecked(self.conj())
+        Self::new_unchecked(self.conj())
     }
 
     /// Inverts this complex number if it is not zero.
@@ -117,7 +116,6 @@ impl<N: Real> UnitComplex<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::UnitComplex;
     /// let rot = UnitComplex::new(1.2);
     /// let inv = rot.inverse();
@@ -134,7 +132,6 @@ impl<N: Real> UnitComplex<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::UnitComplex;
     /// let rot1 = UnitComplex::new(0.1);
     /// let rot2 = UnitComplex::new(1.7);
@@ -153,7 +150,6 @@ impl<N: Real> UnitComplex<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::UnitComplex;
     /// let rot1 = UnitComplex::new(0.1);
     /// let rot2 = UnitComplex::new(1.7);
@@ -172,7 +168,6 @@ impl<N: Real> UnitComplex<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::UnitComplex;
     /// let angle = 1.7;
     /// let rot = UnitComplex::new(angle);
@@ -192,7 +187,6 @@ impl<N: Real> UnitComplex<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::UnitComplex;
     /// let angle = 1.7;
     /// let mut rot = UnitComplex::new(angle);
@@ -213,7 +207,6 @@ impl<N: Real> UnitComplex<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::UnitComplex;
     /// let rot = UnitComplex::new(0.78);
     /// let pow = rot.powf(2.0);
@@ -311,17 +304,3 @@ impl<N: Real> UlpsEq for UnitComplex<N> {
             && self.im.ulps_eq(&other.im, epsilon, max_ulps)
     }
 }
-
-impl<N: Real> From<UnitComplex<N>> for Matrix3<N> {
-    #[inline]
-    fn from(q: UnitComplex<N>) -> Matrix3<N> {
-        q.to_homogeneous()
-    }
-}
-
-impl<N: Real> From<UnitComplex<N>> for Matrix2<N> {
-    #[inline]
-    fn from(q: UnitComplex<N>) -> Matrix2<N> {
-        q.to_rotation_matrix().into_inner()
-    }
-}

src/geometry/unit_complex_alga.rs

@@ -1,6 +1,6 @@
 use alga::general::{
     AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
-    AbstractSemigroup, Id, Identity, Inverse, Multiplicative, Real,
+    AbstractSemigroup, Id, Identity, TwoSidedInverse, Multiplicative, Real,
 };
 use alga::linear::{
     AffineTransformation, DirectIsometry, Isometry, OrthogonalTransformation,
@@ -31,14 +31,14 @@ impl<N: Real> AbstractMagma<Multiplicative> for UnitComplex<N> {
     }
 }
 
-impl<N: Real> Inverse<Multiplicative> for UnitComplex<N> {
+impl<N: Real> TwoSidedInverse<Multiplicative> for UnitComplex<N> {
     #[inline]
-    fn inverse(&self) -> Self {
+    fn two_sided_inverse(&self) -> Self {
         self.inverse()
     }
 
     #[inline]
-    fn inverse_mut(&mut self) {
+    fn two_sided_inverse_mut(&mut self) {
         self.inverse_mut()
     }
 }

src/geometry/unit_complex_construction.rs

@@ -9,7 +9,7 @@ use rand::Rng;
 use alga::general::Real;
 use base::dimension::{U1, U2};
 use base::storage::Storage;
-use base::{Unit, Vector};
+use base::{Unit, Vector, Matrix2};
 use geometry::{Rotation2, UnitComplex};
 
 impl<N: Real> UnitComplex<N> {
@@ -35,7 +35,6 @@ impl<N: Real> UnitComplex<N> {
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use std::f32;
     /// # use nalgebra::{UnitComplex, Point2};
     /// let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
@@ -56,7 +55,6 @@ impl<N: Real> UnitComplex<N> {
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use std::f32;
     /// # use nalgebra::{UnitComplex, Point2};
     /// let rot = UnitComplex::from_angle(f32::consts::FRAC_PI_2);
@@ -78,7 +76,6 @@ impl<N: Real> UnitComplex<N> {
     ///
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use std::f32;
     /// # use nalgebra::{UnitComplex, Vector2, Point2};
     /// let angle = f32::consts::FRAC_PI_2;
@@ -88,7 +85,7 @@ impl<N: Real> UnitComplex<N> {
     /// ```
     #[inline]
     pub fn from_cos_sin_unchecked(cos: N, sin: N) -> Self {
-        UnitComplex::new_unchecked(Complex::new(cos, sin))
+        Self::new_unchecked(Complex::new(cos, sin))
     }
 
     /// Builds a unit complex rotation from an angle in radian wrapped in a 1-dimensional vector.
@@ -132,13 +129,38 @@ impl<N: Real> UnitComplex<N> {
         Self::new_unchecked(Complex::new(rotmat[(0, 0)], rotmat[(1, 0)]))
     }
 
+    /// Builds an unit complex by extracting the rotation part of the given transformation `m`.
+    ///
+    /// This is an iterative method. See `.from_matrix_eps` to provide mover
+    /// convergence parameters and starting solution.
+    /// This implements "A Robust Method to Extract the Rotational Part of Deformations" by Müller et al.
+    pub fn from_matrix(m: &Matrix2<N>) -> Self {
+        Rotation2::from_matrix(m).into()
+    }
+
+    /// Builds an unit complex by extracting the rotation part of the given transformation `m`.
+    ///
+    /// This implements "A Robust Method to Extract the Rotational Part of Deformations" by Müller et al.
+    ///
+    /// # Parameters
+    ///
+    /// * `m`: the matrix from which the rotational part is to be extracted.
+    /// * `eps`: the angular errors tolerated between the current rotation and the optimal one.
+    /// * `max_iter`: the maximum number of iterations. Loops indefinitely until convergence if set to `0`.
+    /// * `guess`: an estimate of the solution. Convergence will be significantly faster if an initial solution close
+    ///           to the actual solution is provided. Can be set to `UnitQuaternion::identity()` if no other
+    ///           guesses come to mind.
+    pub fn from_matrix_eps(m: &Matrix2<N>, eps: N, max_iter: usize, guess: Self) -> Self {
+        let guess = Rotation2::from(guess);
+        Rotation2::from_matrix_eps(m, eps, max_iter, guess).into()
+    }
+
     /// The unit complex needed to make `a` and `b` be collinear and point toward the same
     /// direction.
     ///
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Vector2, UnitComplex};
     /// let a = Vector2::new(1.0, 2.0);
     /// let b = Vector2::new(2.0, 1.0);
@@ -161,7 +183,6 @@ impl<N: Real> UnitComplex<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Vector2, UnitComplex};
     /// let a = Vector2::new(1.0, 2.0);
     /// let b = Vector2::new(2.0, 1.0);
@@ -197,7 +218,6 @@ impl<N: Real> UnitComplex<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Unit, Vector2, UnitComplex};
     /// let a = Unit::new_normalize(Vector2::new(1.0, 2.0));
     /// let b = Unit::new_normalize(Vector2::new(2.0, 1.0));
@@ -223,7 +243,6 @@ impl<N: Real> UnitComplex<N> {
     /// # Example
     /// ```
     /// # #[macro_use] extern crate approx;
-    /// # extern crate nalgebra;
     /// # use nalgebra::{Unit, Vector2, UnitComplex};
     /// let a = Unit::new_normalize(Vector2::new(1.0, 2.0));
     /// let b = Unit::new_normalize(Vector2::new(2.0, 1.0));

src/geometry/unit_complex_conversion.rs

@@ -5,10 +5,10 @@ use alga::general::{Real, SubsetOf, SupersetOf};
 use alga::linear::Rotation as AlgaRotation;
 
 use base::dimension::U2;
-use base::Matrix3;
+use base::{Matrix2, Matrix3};
 use geometry::{
     Isometry, Point2, Rotation2, Similarity, SuperTCategoryOf, TAffine, Transform, Translation,
-    UnitComplex,
+    UnitComplex
 };
 
 /*
@@ -74,7 +74,7 @@ impl<N1, N2, R> SubsetOf<Isometry<N2, U2, R>> for UnitComplex<N1>
 where
     N1: Real,
     N2: Real + SupersetOf<N1>,
-    R: AlgaRotation<Point2<N2>> + SupersetOf<UnitComplex<N1>>,
+    R: AlgaRotation<Point2<N2>> + SupersetOf<Self>,
 {
     #[inline]
     fn to_superset(&self) -> Isometry<N2, U2, R> {
@@ -96,7 +96,7 @@ impl<N1, N2, R> SubsetOf<Similarity<N2, U2, R>> for UnitComplex<N1>
 where
     N1: Real,
     N2: Real + SupersetOf<N1>,
-    R: AlgaRotation<Point2<N2>> + SupersetOf<UnitComplex<N1>>,
+    R: AlgaRotation<Point2<N2>> + SupersetOf<Self>,
 {
     #[inline]
     fn to_superset(&self) -> Similarity<N2, U2, R> {
@@ -153,3 +153,32 @@ impl<N1: Real, N2: Real + SupersetOf<N1>> SubsetOf<Matrix3<N2>> for UnitComplex<
         Self::from_rotation_matrix(&rot)
     }
 }
+
+
+impl<N: Real> From<UnitComplex<N>> for Rotation2<N> {
+    #[inline]
+    fn from(q: UnitComplex<N>) -> Self {
+        q.to_rotation_matrix()
+    }
+}
+
+impl<N: Real> From<Rotation2<N>> for UnitComplex<N> {
+    #[inline]
+    fn from(q: Rotation2<N>) -> Self {
+        Self::from_rotation_matrix(&q)
+    }
+}
+
+impl<N: Real> From<UnitComplex<N>> for Matrix3<N> {
+    #[inline]
+    fn from(q: UnitComplex<N>) -> Matrix3<N> {
+        q.to_homogeneous()
+    }
+}
+
+impl<N: Real> From<UnitComplex<N>> for Matrix2<N> {
+    #[inline]
+    fn from(q: UnitComplex<N>) -> Self {
+        q.to_rotation_matrix().into_inner()
+    }
+}

src/geometry/unit_complex_ops.rs

@@ -45,11 +45,11 @@ use geometry::{Isometry, Point2, Rotation, Similarity, Translation, UnitComplex}
  */
 
 // UnitComplex × UnitComplex
-impl<N: Real> Mul<UnitComplex<N>> for UnitComplex<N> {
+impl<N: Real> Mul<Self> for UnitComplex<N> {
-    type Output = UnitComplex<N>;
+    type Output = Self;
 
     #[inline]
-    fn mul(self, rhs: UnitComplex<N>) -> UnitComplex<N> {
+    fn mul(self, rhs: Self) -> Self {
         Unit::new_unchecked(self.into_inner() * rhs.into_inner())
     }
 }
@@ -58,16 +58,16 @@ impl<'a, N: Real> Mul<UnitComplex<N>> for &'a UnitComplex<N> {
     type Output = UnitComplex<N>;
 
     #[inline]
-    fn mul(self, rhs: UnitComplex<N>) -> UnitComplex<N> {
+    fn mul(self, rhs: UnitComplex<N>) -> Self::Output {
         Unit::new_unchecked(self.complex() * rhs.into_inner())
     }
 }
 
 impl<'b, N: Real> Mul<&'b UnitComplex<N>> for UnitComplex<N> {
-    type Output = UnitComplex<N>;
+    type Output = Self;
 
     #[inline]
-    fn mul(self, rhs: &'b UnitComplex<N>) -> UnitComplex<N> {
+    fn mul(self, rhs: &'b UnitComplex<N>) -> Self::Output {
         Unit::new_unchecked(self.into_inner() * rhs.complex())
     }
 }
@@ -76,17 +76,17 @@ impl<'a, 'b, N: Real> Mul<&'b UnitComplex<N>> for &'a UnitComplex<N> {
     type Output = UnitComplex<N>;
 
     #[inline]
-    fn mul(self, rhs: &'b UnitComplex<N>) -> UnitComplex<N> {
+    fn mul(self, rhs: &'b UnitComplex<N>) -> Self::Output {
         Unit::new_unchecked(self.complex() * rhs.complex())
     }
 }
 
 // UnitComplex ÷ UnitComplex
-impl<N: Real> Div<UnitComplex<N>> for UnitComplex<N> {
+impl<N: Real> Div<Self> for UnitComplex<N> {
-    type Output = UnitComplex<N>;
+    type Output = Self;
 
     #[inline]
-    fn div(self, rhs: UnitComplex<N>) -> UnitComplex<N> {
+    fn div(self, rhs: Self) -> Self::Output {
         Unit::new_unchecked(self.into_inner() * rhs.conjugate().into_inner())
     }
 }
@@ -95,16 +95,16 @@ impl<'a, N: Real> Div<UnitComplex<N>> for &'a UnitComplex<N> {
     type Output = UnitComplex<N>;
 
     #[inline]
-    fn div(self, rhs: UnitComplex<N>) -> UnitComplex<N> {
+    fn div(self, rhs: UnitComplex<N>) -> Self::Output {
         Unit::new_unchecked(self.complex() * rhs.conjugate().into_inner())
     }
 }
 
 impl<'b, N: Real> Div<&'b UnitComplex<N>> for UnitComplex<N> {
-    type Output = UnitComplex<N>;
+    type Output = Self;
 
     #[inline]
-    fn div(self, rhs: &'b UnitComplex<N>) -> UnitComplex<N> {
+    fn div(self, rhs: &'b UnitComplex<N>) -> Self::Output {
         Unit::new_unchecked(self.into_inner() * rhs.conjugate().into_inner())
     }
 }
@@ -113,7 +113,7 @@ impl<'a, 'b, N: Real> Div<&'b UnitComplex<N>> for &'a UnitComplex<N> {
     type Output = UnitComplex<N>;
 
     #[inline]
-    fn div(self, rhs: &'b UnitComplex<N>) -> UnitComplex<N> {
+    fn div(self, rhs: &'b UnitComplex<N>) -> Self::Output {
         Unit::new_unchecked(self.complex() * rhs.conjugate().into_inner())
     }
 }

src/io/matrix_market.pest

@@ -0,0 +1,16 @@
+WHITESPACE = _{ " " }
+
+Comments = _{ "%" ~ (!NEWLINE ~ ANY)* }
+Header = { "%%" ~ (!NEWLINE ~ ANY)* }
+Shape = { Dimension ~ Dimension ~ Dimension }
+Document = {
+    SOI ~
+    NEWLINE* ~
+    Header ~
+    (NEWLINE ~ Comments)* ~
+    (NEWLINE ~ Shape) ~
+    (NEWLINE ~ Entry?)*
+}
+Dimension = @{ ASCII_DIGIT+ }
+Value = @{ ("+" | "-")? ~ NUMBER+ ~ ("." ~ NUMBER+)? ~ ("e" ~ ("+" | "-")? ~ NUMBER+)? }
+Entry = { Dimension ~ Dimension ~ Value }

src/io/matrix_market.rs

@@ -0,0 +1,53 @@
+use std::fs;
+use std::path::Path;
+
+use pest::Parser;
+use sparse::CsMatrix;
+use Real;
+
+#[derive(Parser)]
+#[grammar = "io/matrix_market.pest"]
+struct MatrixMarketParser;
+
+// FIXME: return an Error instead of an Option.
+/// Parses a Matrix Market file at the given path, and returns the corresponding sparse matrix.
+pub fn cs_matrix_from_matrix_market<N: Real, P: AsRef<Path>>(path: P) -> Option<CsMatrix<N>> {
+    let file = fs::read_to_string(path).ok()?;
+    cs_matrix_from_matrix_market_str(&file)
+}
+
+// FIXME: return an Error instead of an Option.
+/// Parses a Matrix Market file described by the given string, and returns the corresponding sparse matrix.
+pub fn cs_matrix_from_matrix_market_str<N: Real>(data: &str) -> Option<CsMatrix<N>> {
+    let file = MatrixMarketParser::parse(Rule::Document, data)
+        .unwrap()
+        .next()?;
+    let mut shape = (0, 0, 0);
+    let mut rows: Vec<usize> = Vec::new();
+    let mut cols: Vec<usize> = Vec::new();
+    let mut data: Vec<N> = Vec::new();
+
+    for line in file.into_inner() {
+        match line.as_rule() {
+            Rule::Header => {}
+            Rule::Shape => {
+                let mut inner = line.into_inner();
+                shape.0 = inner.next()?.as_str().parse::<usize>().ok()?;
+                shape.1 = inner.next()?.as_str().parse::<usize>().ok()?;
+                shape.2 = inner.next()?.as_str().parse::<usize>().ok()?;
+            }
+            Rule::Entry => {
+                let mut inner = line.into_inner();
+                // NOTE: indices are 1-based.
+                rows.push(inner.next()?.as_str().parse::<usize>().ok()? - 1);
+                cols.push(inner.next()?.as_str().parse::<usize>().ok()? - 1);
+                data.push(::convert(inner.next()?.as_str().parse::<f64>().ok()?));
+            }
+            _ => return None, // FIXME: return an Err instead.
+        }
+    }
+
+    Some(CsMatrix::from_triplet(
+        shape.0, shape.1, &rows, &cols, &data,
+    ))
+}

src/io/mod.rs

@@ -0,0 +1,5 @@
+//! Parsers for various matrix formats.
+
+pub use self::matrix_market::{cs_matrix_from_matrix_market, cs_matrix_from_matrix_market_str};
+
+mod matrix_market;

src/lib.rs

@@ -15,7 +15,7 @@ Simply add the following to your `Cargo.toml` file:
 
 ```.ignore
 [dependencies]
-nalgebra = "0.16"
+nalgebra = "0.17"
 ```
 
 
@@ -83,8 +83,10 @@ an optimized set of tools for computer graphics and physics. Those features incl
 #![deny(unused_results)]
 #![deny(missing_docs)]
 #![warn(incoherent_fundamental_impls)]
-#![doc(html_favicon_url = "http://nalgebra.org/img/favicon.ico",
+#![doc(
-       html_root_url = "http://nalgebra.org/rustdoc")]
+    html_favicon_url = "http://nalgebra.org/img/favicon.ico",
+    html_root_url = "http://nalgebra.org/rustdoc"
+)]
 #![cfg_attr(not(feature = "std"), no_std)]
 #![cfg_attr(all(feature = "alloc", not(feature = "std")), feature(alloc))]
 
@@ -121,11 +123,21 @@ extern crate alloc;
 #[cfg(not(feature = "std"))]
 extern crate core as std;
 
+#[cfg(feature = "io")]
+extern crate pest;
+#[macro_use]
+#[cfg(feature = "io")]
+extern crate pest_derive;
+
 pub mod base;
 #[cfg(feature = "debug")]
 pub mod debug;
 pub mod geometry;
+#[cfg(feature = "io")]
+pub mod io;
 pub mod linalg;
+#[cfg(feature = "sparse")]
+pub mod sparse;
 
 #[cfg(feature = "std")]
 #[deprecated(
@@ -135,11 +147,13 @@ pub use base as core;
 pub use base::*;
 pub use geometry::*;
 pub use linalg::*;
+#[cfg(feature = "sparse")]
+pub use sparse::*;
 
 use std::cmp::{self, Ordering, PartialOrd};
 
 use alga::general::{
-    Additive, AdditiveGroup, Identity, Inverse, JoinSemilattice, Lattice, MeetSemilattice,
+    Additive, AdditiveGroup, Identity, TwoSidedInverse, JoinSemilattice, Lattice, MeetSemilattice,
     Multiplicative, SupersetOf,
 };
 use alga::linear::SquareMatrix as AlgaSquareMatrix;
@@ -413,8 +427,8 @@ pub fn try_inverse<M: AlgaSquareMatrix>(m: &M) -> Option<M> {
 ///
 /// * [`try_inverse`](fn.try_inverse.html)
 #[inline]
-pub fn inverse<M: Inverse<Multiplicative>>(m: &M) -> M {
+pub fn inverse<M: TwoSidedInverse<Multiplicative>>(m: &M) -> M {
-    m.inverse()
+    m.two_sided_inverse()
 }
 
 /*

src/linalg/full_piv_lu.rs

@@ -61,7 +61,7 @@ where DefaultAllocator: Allocator<N, R, C> + Allocator<(usize, usize), DimMinimu
         let mut q = PermutationSequence::identity_generic(min_nrows_ncols);
 
         if min_nrows_ncols.value() == 0 {
-            return FullPivLU {
+            return Self {
                 lu: matrix,
                 p: p,
                 q: q,
@@ -91,7 +91,7 @@ where DefaultAllocator: Allocator<N, R, C> + Allocator<(usize, usize), DimMinimu
             }
         }
 
-        FullPivLU {
+        Self {
             lu: matrix,
             p: p,
             q: q,

src/linalg/permutation_sequence.rs

@@ -69,7 +69,7 @@ where DefaultAllocator: Allocator<(usize, usize), D>
     #[inline]
     pub fn identity_generic(dim: D) -> Self {
         unsafe {
-            PermutationSequence {
+            Self {
                 len: 0,
                 ipiv: VectorN::new_uninitialized_generic(dim, U1),
             }

src/linalg/schur.rs

@@ -55,7 +55,7 @@ where
         + Allocator<N, D>,
 {
     /// Computes the Schur decomposition of a square matrix.
-    pub fn new(m: MatrixN<N, D>) -> RealSchur<N, D> {
+    pub fn new(m: MatrixN<N, D>) -> Self {
         Self::try_new(m, N::default_epsilon(), 0).unwrap()
     }
 
@@ -70,7 +70,7 @@ where
     /// * `max_niter` − maximum total number of iterations performed by the algorithm. If this
     /// number of iteration is exceeded, `None` is returned. If `niter == 0`, then the algorithm
     /// continues indefinitely until convergence.
-    pub fn try_new(m: MatrixN<N, D>, eps: N, max_niter: usize) -> Option<RealSchur<N, D>> {
+    pub fn try_new(m: MatrixN<N, D>, eps: N, max_niter: usize) -> Option<Self> {
         let mut work = unsafe { VectorN::new_uninitialized_generic(m.data.shape().0, U1) };
 
         Self::do_decompose(m, &mut work, eps, max_niter, true).map(|(q, t)| RealSchur {

src/linalg/svd.rs

@@ -271,7 +271,7 @@ where
             }
         }
 
-        Some(SVD {
+        Some(Self {
             u: u,
             v_t: v_t,
             singular_values: b.diagonal,

src/linalg/symmetric_tridiagonal.rs

@@ -83,7 +83,7 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimDiff<D, U1>>
             }
         }
 
-        SymmetricTridiagonal {
+        Self {
             tri: m,
             off_diagonal: off_diagonal,
         }

src/sparse/cs_matrix.rs

@@ -0,0 +1,517 @@
+use alga::general::ClosedAdd;
+use num::Zero;
+use std::iter;
+use std::marker::PhantomData;
+use std::ops::Range;
+use std::slice;
+
+use allocator::Allocator;
+use sparse::cs_utils;
+use {
+    DefaultAllocator, Dim, Dynamic, Scalar, Vector, VectorN, U1
+};
+
+pub struct ColumnEntries<'a, N> {
+    curr: usize,
+    i: &'a [usize],
+    v: &'a [N],
+}
+
+impl<'a, N> ColumnEntries<'a, N> {
+    #[inline]
+    pub fn new(i: &'a [usize], v: &'a [N]) -> Self {
+        assert_eq!(i.len(), v.len());
+        Self { curr: 0, i, v }
+    }
+}
+
+impl<'a, N: Copy> Iterator for ColumnEntries<'a, N> {
+    type Item = (usize, N);
+
+    #[inline]
+    fn next(&mut self) -> Option<Self::Item> {
+        if self.curr >= self.i.len() {
+            None
+        } else {
+            let res = Some((unsafe { *self.i.get_unchecked(self.curr) }, unsafe {
+                *self.v.get_unchecked(self.curr)
+            }));
+            self.curr += 1;
+            res
+        }
+    }
+}
+
+// FIXME: this structure exists for now only because impl trait
+// cannot be used for trait method return types.
+/// Trait for iterable compressed-column matrix storage.
+pub trait CsStorageIter<'a, N, R, C = U1> {
+    /// Iterator through all the rows of a specific columns.
+    ///
+    /// The elements are given as a tuple (row_index, value).
+    type ColumnEntries: Iterator<Item = (usize, N)>;
+    /// Iterator through the row indices of a specific column.
+    type ColumnRowIndices: Iterator<Item = usize>;
+
+    /// Iterates through all the row indices of the j-th column.
+    fn column_row_indices(&'a self, j: usize) -> Self::ColumnRowIndices;
+    #[inline(always)]
+    /// Iterates through all the entries of the j-th column.
+    fn column_entries(&'a self, j: usize) -> Self::ColumnEntries;
+}
+
+/// Trait for mutably iterable compressed-column sparse matrix storage.
+pub trait CsStorageIterMut<'a, N: 'a, R, C = U1> {
+    /// Mutable iterator through all the values of the sparse matrix.
+    type ValuesMut: Iterator<Item = &'a mut N>;
+    /// Mutable iterator through all the rows of a specific columns.
+    ///
+    /// The elements are given as a tuple (row_index, value).
+    type ColumnEntriesMut: Iterator<Item = (usize, &'a mut N)>;
+
+    /// A mutable iterator through the values buffer of the sparse matrix.
+    fn values_mut(&'a mut self) -> Self::ValuesMut;
+    /// Iterates mutably through all the entries of the j-th column.
+    fn column_entries_mut(&'a mut self, j: usize) -> Self::ColumnEntriesMut;
+}
+
+/// Trait for compressed column sparse matrix storage.
+pub trait CsStorage<N, R, C = U1>: for<'a> CsStorageIter<'a, N, R, C> {
+    /// The shape of the stored matrix.
+    fn shape(&self) -> (R, C);
+    /// Retrieve the i-th row index of the underlying row index buffer.
+    ///
+    /// No bound-checking is performed.
+    unsafe fn row_index_unchecked(&self, i: usize) -> usize;
+    /// The i-th value on the contiguous value buffer of this storage.
+    ///
+    /// No bound-checking is performed.
+    unsafe fn get_value_unchecked(&self, i: usize) -> &N;
+    /// The i-th value on the contiguous value buffer of this storage.
+    fn get_value(&self, i: usize) -> &N;
+    /// Retrieve the i-th row index of the underlying row index buffer.
+    fn row_index(&self, i: usize) -> usize;
+    /// The value indices for the `i`-th column.
+    fn column_range(&self, i: usize) -> Range<usize>;
+    /// The size of the value buffer (i.e. the entries known as possibly being non-zero).
+    fn len(&self) -> usize;
+}
+
+/// Trait for compressed column sparse matrix mutable storage.
+pub trait CsStorageMut<N, R, C = U1>:
+    CsStorage<N, R, C> + for<'a> CsStorageIterMut<'a, N, R, C>
+{
+}
+
+/// A storage of column-compressed sparse matrix based on a Vec.
+#[derive(Clone, Debug, PartialEq)]
+pub struct CsVecStorage<N: Scalar, R: Dim, C: Dim>
+where DefaultAllocator: Allocator<usize, C>
+{
+    pub(crate) shape: (R, C),
+    pub(crate) p: VectorN<usize, C>,
+    pub(crate) i: Vec<usize>,
+    pub(crate) vals: Vec<N>,
+}
+
+impl<N: Scalar, R: Dim, C: Dim> CsVecStorage<N, R, C>
+where DefaultAllocator: Allocator<usize, C>
+{
+    /// The value buffer of this storage.
+    pub fn values(&self) -> &[N] {
+        &self.vals
+    }
+
+    /// The column shifts buffer.
+    pub fn p(&self) -> &[usize] {
+        self.p.as_slice()
+    }
+
+    /// The row index buffers.
+    pub fn i(&self) -> &[usize] {
+        &self.i
+    }
+}
+
+impl<N: Scalar, R: Dim, C: Dim> CsVecStorage<N, R, C> where DefaultAllocator: Allocator<usize, C> {}
+
+impl<'a, N: Scalar, R: Dim, C: Dim> CsStorageIter<'a, N, R, C> for CsVecStorage<N, R, C>
+where DefaultAllocator: Allocator<usize, C>
+{
+    type ColumnEntries = ColumnEntries<'a, N>;
+    type ColumnRowIndices = iter::Cloned<slice::Iter<'a, usize>>;
+
+    #[inline]
+    fn column_entries(&'a self, j: usize) -> Self::ColumnEntries {
+        let rng = self.column_range(j);
+        ColumnEntries::new(&self.i[rng.clone()], &self.vals[rng])
+    }
+
+    #[inline]
+    fn column_row_indices(&'a self, j: usize) -> Self::ColumnRowIndices {
+        let rng = self.column_range(j);
+        self.i[rng.clone()].iter().cloned()
+    }
+}
+
+impl<N: Scalar, R: Dim, C: Dim> CsStorage<N, R, C> for CsVecStorage<N, R, C>
+where DefaultAllocator: Allocator<usize, C>
+{
+    #[inline]
+    fn shape(&self) -> (R, C) {
+        self.shape
+    }
+
+    #[inline]
+    fn len(&self) -> usize {
+        self.vals.len()
+    }
+
+    #[inline]
+    fn row_index(&self, i: usize) -> usize {
+        self.i[i]
+    }
+
+    #[inline]
+    unsafe fn row_index_unchecked(&self, i: usize) -> usize {
+        *self.i.get_unchecked(i)
+    }
+
+    #[inline]
+    unsafe fn get_value_unchecked(&self, i: usize) -> &N {
+        self.vals.get_unchecked(i)
+    }
+
+    #[inline]
+    fn get_value(&self, i: usize) -> &N {
+        &self.vals[i]
+    }
+
+    #[inline]
+    fn column_range(&self, j: usize) -> Range<usize> {
+        let end = if j + 1 == self.p.len() {
+            self.len()
+        } else {
+            self.p[j + 1]
+        };
+
+        self.p[j]..end
+    }
+}
+
+impl<'a, N: Scalar, R: Dim, C: Dim> CsStorageIterMut<'a, N, R, C> for CsVecStorage<N, R, C>
+where DefaultAllocator: Allocator<usize, C>
+{
+    type ValuesMut = slice::IterMut<'a, N>;
+    type ColumnEntriesMut = iter::Zip<iter::Cloned<slice::Iter<'a, usize>>, slice::IterMut<'a, N>>;
+
+    #[inline]
+    fn values_mut(&'a mut self) -> Self::ValuesMut {
+        self.vals.iter_mut()
+    }
+
+    #[inline]
+    fn column_entries_mut(&'a mut self, j: usize) -> Self::ColumnEntriesMut {
+        let rng = self.column_range(j);
+        self.i[rng.clone()]
+            .iter()
+            .cloned()
+            .zip(self.vals[rng].iter_mut())
+    }
+}
+
+impl<N: Scalar, R: Dim, C: Dim> CsStorageMut<N, R, C> for CsVecStorage<N, R, C> where DefaultAllocator: Allocator<usize, C>
+{}
+
+/*
+pub struct CsSliceStorage<'a, N: Scalar, R: Dim, C: DimAdd<U1>> {
+    shape: (R, C),
+    p: VectorSlice<usize, DimSum<C, U1>>,
+    i: VectorSlice<usize, Dynamic>,
+    vals: VectorSlice<N, Dynamic>,
+}*/
+
+/// A compressed sparse column matrix.
+#[derive(Clone, Debug, PartialEq)]
+pub struct CsMatrix<
+    N: Scalar,
+    R: Dim = Dynamic,
+    C: Dim = Dynamic,
+    S: CsStorage<N, R, C> = CsVecStorage<N, R, C>,
+> {
+    pub(crate) data: S,
+    _phantoms: PhantomData<(N, R, C)>,
+}
+
+/// A column compressed sparse vector.
+pub type CsVector<N, R = Dynamic, S = CsVecStorage<N, R, U1>> = CsMatrix<N, R, U1, S>;
+
+impl<N: Scalar, R: Dim, C: Dim> CsMatrix<N, R, C>
+where DefaultAllocator: Allocator<usize, C>
+{
+    /// Creates a new compressed sparse column matrix with the specified dimension and
+    /// `nvals` possible non-zero values.
+    pub fn new_uninitialized_generic(nrows: R, ncols: C, nvals: usize) -> Self {
+        let mut i = Vec::with_capacity(nvals);
+        unsafe {
+            i.set_len(nvals);
+        }
+        i.shrink_to_fit();
+
+        let mut vals = Vec::with_capacity(nvals);
+        unsafe {
+            vals.set_len(nvals);
+        }
+        vals.shrink_to_fit();
+
+        CsMatrix {
+            data: CsVecStorage {
+                shape: (nrows, ncols),
+                p: VectorN::zeros_generic(ncols, U1),
+                i,
+                vals,
+            },
+            _phantoms: PhantomData,
+        }
+    }
+
+    /*
+    pub(crate) fn from_parts_generic(
+        nrows: R,
+        ncols: C,
+        p: VectorN<usize, C>,
+        i: Vec<usize>,
+        vals: Vec<N>,
+    ) -> Self
+    where
+        N: Zero + ClosedAdd,
+        DefaultAllocator: Allocator<N, R>,
+    {
+        assert_eq!(ncols.value(), p.len(), "Invalid inptr size.");
+        assert_eq!(i.len(), vals.len(), "Invalid value size.");
+
+        // Check p.
+        for ptr in &p {
+            assert!(*ptr < i.len(), "Invalid inptr value.");
+        }
+
+        for ptr in p.as_slice().windows(2) {
+            assert!(ptr[0] <= ptr[1], "Invalid inptr ordering.");
+        }
+
+        // Check i.
+        for i in &i {
+            assert!(*i < nrows.value(), "Invalid row ptr value.")
+        }
+
+        let mut res = CsMatrix {
+            data: CsVecStorage {
+                shape: (nrows, ncols),
+                p,
+                i,
+                vals,
+            },
+            _phantoms: PhantomData,
+        };
+
+        // Sort and remove duplicates.
+        res.sort();
+        res.dedup();
+
+        res
+    }*/
+}
+
+/*
+impl<N: Scalar + Zero + ClosedAdd> CsMatrix<N> {
+    pub(crate) fn from_parts(
+        nrows: usize,
+        ncols: usize,
+        p: Vec<usize>,
+        i: Vec<usize>,
+        vals: Vec<N>,
+    ) -> Self
+    {
+        let nrows = Dynamic::new(nrows);
+        let ncols = Dynamic::new(ncols);
+        let p = DVector::from_data(VecStorage::new(ncols, U1, p));
+        Self::from_parts_generic(nrows, ncols, p, i, vals)
+    }
+}
+*/
+
+impl<N: Scalar, R: Dim, C: Dim, S: CsStorage<N, R, C>> CsMatrix<N, R, C, S> {
+    pub(crate) fn from_data(data: S) -> Self {
+        CsMatrix {
+            data,
+            _phantoms: PhantomData,
+        }
+    }
+
+    /// The size of the data buffer.
+    pub fn len(&self) -> usize {
+        self.data.len()
+    }
+
+    /// The number of rows of this matrix.
+    pub fn nrows(&self) -> usize {
+        self.data.shape().0.value()
+    }
+
+    /// The number of rows of this matrix.
+    pub fn ncols(&self) -> usize {
+        self.data.shape().1.value()
+    }
+
+    /// The shape of this matrix.
+    pub fn shape(&self) -> (usize, usize) {
+        let (nrows, ncols) = self.data.shape();
+        (nrows.value(), ncols.value())
+    }
+
+    /// Whether this matrix is square or not.
+    pub fn is_square(&self) -> bool {
+        let (nrows, ncols) = self.data.shape();
+        nrows.value() == ncols.value()
+    }
+
+    /// Should always return `true`.
+    ///
+    /// This method is generally used for debugging and should typically not be called in user code.
+    /// This checks that the row inner indices of this matrix are sorted. It takes `O(n)` time,
+    /// where n` is `self.len()`.
+    /// All operations of CSC matrices on nalgebra assume, and will return, sorted indices.
+    /// If at any time this `is_sorted` method returns `false`, then, something went wrong
+    /// and an issue should be open on the nalgebra repository with details on how to reproduce
+    /// this.
+    pub fn is_sorted(&self) -> bool {
+        for j in 0..self.ncols() {
+            let mut curr = None;
+            for idx in self.data.column_row_indices(j) {
+                if let Some(curr) = curr {
+                    if idx <= curr {
+                        return false;
+                    }
+                }
+
+                curr = Some(idx);
+            }
+        }
+
+        true
+    }
+
+    /// Computes the transpose of this sparse matrix.
+    pub fn transpose(&self) -> CsMatrix<N, C, R>
+    where DefaultAllocator: Allocator<usize, R> {
+        let (nrows, ncols) = self.data.shape();
+
+        let nvals = self.len();
+        let mut res = CsMatrix::new_uninitialized_generic(ncols, nrows, nvals);
+        let mut workspace = Vector::zeros_generic(nrows, U1);
+
+        // Compute p.
+        for i in 0..nvals {
+            let row_id = self.data.row_index(i);
+            workspace[row_id] += 1;
+        }
+
+        let _ = cs_utils::cumsum(&mut workspace, &mut res.data.p);
+
+        // Fill the result.
+        for j in 0..ncols.value() {
+            for (row_id, value) in self.data.column_entries(j) {
+                let shift = workspace[row_id];
+
+                res.data.vals[shift] = value;
+                res.data.i[shift] = j;
+                workspace[row_id] += 1;
+            }
+        }
+
+        res
+    }
+}
+
+impl<N: Scalar, R: Dim, C: Dim, S: CsStorageMut<N, R, C>> CsMatrix<N, R, C, S> {
+    /// Iterator through all the mutable values of this sparse matrix.
+    #[inline]
+    pub fn values_mut(&mut self) -> impl Iterator<Item = &mut N> {
+        self.data.values_mut()
+    }
+}
+
+impl<N: Scalar, R: Dim, C: Dim> CsMatrix<N, R, C>
+where DefaultAllocator: Allocator<usize, C>
+{
+    pub(crate) fn sort(&mut self)
+    where DefaultAllocator: Allocator<N, R> {
+        // Size = R
+        let nrows = self.data.shape().0;
+        let mut workspace = unsafe { VectorN::new_uninitialized_generic(nrows, U1) };
+        self.sort_with_workspace(workspace.as_mut_slice());
+    }
+
+    pub(crate) fn sort_with_workspace(&mut self, workspace: &mut [N]) {
+        assert!(
+            workspace.len() >= self.nrows(),
+            "Workspace must be able to hold at least self.nrows() elements."
+        );
+
+        for j in 0..self.ncols() {
+            // Scatter the row in the workspace.
+            for (irow, val) in self.data.column_entries(j) {
+                workspace[irow] = val;
+            }
+
+            // Sort the index vector.
+            let range = self.data.column_range(j);
+            self.data.i[range.clone()].sort();
+
+            // Permute the values too.
+            for (i, irow) in range.clone().zip(self.data.i[range].iter().cloned()) {
+                self.data.vals[i] = workspace[irow];
+            }
+        }
+    }
+
+    // Remove dupliate entries on a sorted CsMatrix.
+    pub(crate) fn dedup(&mut self)
+    where N: Zero + ClosedAdd {
+        let mut curr_i = 0;
+
+        for j in 0..self.ncols() {
+            let range = self.data.column_range(j);
+            self.data.p[j] = curr_i;
+
+            if range.start != range.end {
+                let mut value = N::zero();
+                let mut irow = self.data.i[range.start];
+
+                for idx in range {
+                    let curr_irow = self.data.i[idx];
+
+                    if curr_irow == irow {
+                        value += self.data.vals[idx];
+                    } else {
+                        self.data.i[curr_i] = irow;
+                        self.data.vals[curr_i] = value;
+                        value = self.data.vals[idx];
+                        irow = curr_irow;
+                        curr_i += 1;
+                    }
+                }
+
+                // Handle the last entry.
+                self.data.i[curr_i] = irow;
+                self.data.vals[curr_i] = value;
+                curr_i += 1;
+            }
+        }
+
+        self.data.i.truncate(curr_i);
+        self.data.i.shrink_to_fit();
+        self.data.vals.truncate(curr_i);
+        self.data.vals.shrink_to_fit();
+    }
+}

src/sparse/cs_matrix_cholesky.rs

@@ -0,0 +1,408 @@
+use std::iter;
+use std::mem;
+
+use allocator::Allocator;
+use sparse::{CsMatrix, CsStorage, CsStorageIter, CsStorageIterMut, CsVecStorage};
+use {DefaultAllocator, Dim, Real, VectorN, U1};
+
+/// The cholesky decomposition of a column compressed sparse matrix.
+pub struct CsCholesky<N: Real, D: Dim>
+where DefaultAllocator: Allocator<usize, D> + Allocator<N, D>
+{
+    // Non-zero pattern of the original matrix upper-triangular part.
+    // Unlike the original matrix, the `original_p` array does contain the last sentinel value
+    // equal to `original_i.len()` at the end.
+    original_p: Vec<usize>,
+    original_i: Vec<usize>,
+    // Decomposition result.
+    l: CsMatrix<N, D, D>,
+    // Used only for the pattern.
+    // FIXME: store only the nonzero pattern instead.
+    u: CsMatrix<N, D, D>,
+    ok: bool,
+    // Workspaces.
+    work_x: VectorN<N, D>,
+    work_c: VectorN<usize, D>,
+}
+
+impl<N: Real, D: Dim> CsCholesky<N, D>
+where DefaultAllocator: Allocator<usize, D> + Allocator<N, D>
+{
+    /// Computes the cholesky decomposition of the sparse matrix `m`.
+    pub fn new(m: &CsMatrix<N, D, D>) -> Self {
+        let mut me = Self::new_symbolic(m);
+        let _ = me.decompose_left_looking(&m.data.vals);
+        me
+    }
+    /// Perform symbolic analysis for the given matrix.
+    ///
+    /// This does not access the numerical values of `m`.
+    pub fn new_symbolic(m: &CsMatrix<N, D, D>) -> Self {
+        assert!(
+            m.is_square(),
+            "The matrix `m` must be square to compute its elimination tree."
+        );
+
+        let (l, u) = Self::nonzero_pattern(m);
+
+        // Workspaces.
+        let work_x = unsafe { VectorN::new_uninitialized_generic(m.data.shape().0, U1) };
+        let work_c = unsafe { VectorN::new_uninitialized_generic(m.data.shape().1, U1) };
+        let mut original_p = m.data.p.as_slice().to_vec();
+        original_p.push(m.data.i.len());
+
+        CsCholesky {
+            original_p,
+            original_i: m.data.i.clone(),
+            l,
+            u,
+            ok: false,
+            work_x,
+            work_c,
+        }
+    }
+
+    /// The lower-triangular matrix of the cholesky decomposition.
+    pub fn l(&self) -> Option<&CsMatrix<N, D, D>> {
+        if self.ok {
+            Some(&self.l)
+        } else {
+            None
+        }
+    }
+
+    /// Extracts the lower-triangular matrix of the cholesky decomposition.
+    pub fn unwrap_l(self) -> Option<CsMatrix<N, D, D>> {
+        if self.ok {
+            Some(self.l)
+        } else {
+            None
+        }
+    }
+
+    /// Perform a numerical left-looking cholesky decomposition of a matrix with the same structure as the
+    /// one used to initialize `self`, but with different non-zero values provided by `values`.
+    pub fn decompose_left_looking(&mut self, values: &[N]) -> bool {
+        assert!(
+            values.len() >= self.original_i.len(),
+            "The set of values is too small."
+        );
+
+        let n = self.l.nrows();
+
+        // Reset `work_c` to the column pointers of `l`.
+        self.work_c.copy_from(&self.l.data.p);
+
+        unsafe {
+            for k in 0..n {
+                // Scatter the k-th column of the original matrix with the values provided.
+                let range_k =
+                    *self.original_p.get_unchecked(k)..*self.original_p.get_unchecked(k + 1);
+
+                *self.work_x.vget_unchecked_mut(k) = N::zero();
+                for p in range_k.clone() {
+                    let irow = *self.original_i.get_unchecked(p);
+
+                    if irow >= k {
+                        *self.work_x.vget_unchecked_mut(irow) = *values.get_unchecked(p);
+                    }
+                }
+
+                for j in self.u.data.column_row_indices(k) {
+                    let factor = -*self
+                        .l
+                        .data
+                        .vals
+                        .get_unchecked(*self.work_c.vget_unchecked(j));
+                    *self.work_c.vget_unchecked_mut(j) += 1;
+
+                    if j < k {
+                        for (z, val) in self.l.data.column_entries(j) {
+                            if z >= k {
+                                *self.work_x.vget_unchecked_mut(z) += val * factor;
+                            }
+                        }
+                    }
+                }
+
+                let diag = *self.work_x.vget_unchecked(k);
+
+                if diag > N::zero() {
+                    let denom = diag.sqrt();
+                    *self
+                        .l
+                        .data
+                        .vals
+                        .get_unchecked_mut(*self.l.data.p.vget_unchecked(k)) = denom;
+
+                    for (p, val) in self.l.data.column_entries_mut(k) {
+                        *val = *self.work_x.vget_unchecked(p) / denom;
+                        *self.work_x.vget_unchecked_mut(p) = N::zero();
+                    }
+                } else {
+                    self.ok = false;
+                    return false;
+                }
+            }
+        }
+
+        self.ok = true;
+        true
+    }
+
+    /// Perform a numerical up-looking cholesky decomposition of a matrix with the same structure as the
+    /// one used to initialize `self`, but with different non-zero values provided by `values`.
+    pub fn decompose_up_looking(&mut self, values: &[N]) -> bool {
+        assert!(
+            values.len() >= self.original_i.len(),
+            "The set of values is too small."
+        );
+
+        // Reset `work_c` to the column pointers of `l`.
+        self.work_c.copy_from(&self.l.data.p);
+
+        // Perform the decomposition.
+        for k in 0..self.l.nrows() {
+            unsafe {
+                // Scatter the k-th column of the original matrix with the values provided.
+                let column_range =
+                    *self.original_p.get_unchecked(k)..*self.original_p.get_unchecked(k + 1);
+
+                *self.work_x.vget_unchecked_mut(k) = N::zero();
+                for p in column_range.clone() {
+                    let irow = *self.original_i.get_unchecked(p);
+
+                    if irow <= k {
+                        *self.work_x.vget_unchecked_mut(irow) = *values.get_unchecked(p);
+                    }
+                }
+
+                let mut diag = *self.work_x.vget_unchecked(k);
+                *self.work_x.vget_unchecked_mut(k) = N::zero();
+
+                // Triangular solve.
+                for irow in self.u.data.column_row_indices(k) {
+                    if irow >= k {
+                        continue;
+                    }
+
+                    let lki = *self.work_x.vget_unchecked(irow)
+                        / *self
+                            .l
+                            .data
+                            .vals
+                            .get_unchecked(*self.l.data.p.vget_unchecked(irow));
+                    *self.work_x.vget_unchecked_mut(irow) = N::zero();
+
+                    for p in
+                        *self.l.data.p.vget_unchecked(irow) + 1..*self.work_c.vget_unchecked(irow)
+                    {
+                        *self
+                            .work_x
+                            .vget_unchecked_mut(*self.l.data.i.get_unchecked(p)) -=
+                            *self.l.data.vals.get_unchecked(p) * lki;
+                    }
+
+                    diag -= lki * lki;
+                    let p = *self.work_c.vget_unchecked(irow);
+                    *self.work_c.vget_unchecked_mut(irow) += 1;
+                    *self.l.data.i.get_unchecked_mut(p) = k;
+                    *self.l.data.vals.get_unchecked_mut(p) = lki;
+                }
+
+                if diag <= N::zero() {
+                    self.ok = false;
+                    return false;
+                }
+
+                // Deal with the diagonal element.
+                let p = *self.work_c.vget_unchecked(k);
+                *self.work_c.vget_unchecked_mut(k) += 1;
+                *self.l.data.i.get_unchecked_mut(p) = k;
+                *self.l.data.vals.get_unchecked_mut(p) = diag.sqrt();
+            }
+        }
+
+        self.ok = true;
+        true
+    }
+
+    fn elimination_tree<S: CsStorage<N, D, D>>(m: &CsMatrix<N, D, D, S>) -> Vec<usize> {
+        let nrows = m.nrows();
+        let mut forest: Vec<_> = iter::repeat(usize::max_value()).take(nrows).collect();
+        let mut ancestor: Vec<_> = iter::repeat(usize::max_value()).take(nrows).collect();
+
+        for k in 0..nrows {
+            for irow in m.data.column_row_indices(k) {
+                let mut i = irow;
+
+                while i < k {
+                    let i_ancestor = ancestor[i];
+                    ancestor[i] = k;
+
+                    if i_ancestor == usize::max_value() {
+                        forest[i] = k;
+                        break;
+                    }
+
+                    i = i_ancestor;
+                }
+            }
+        }
+
+        forest
+    }
+
+    fn reach<S: CsStorage<N, D, D>>(
+        m: &CsMatrix<N, D, D, S>,
+        j: usize,
+        max_j: usize,
+        tree: &[usize],
+        marks: &mut Vec<bool>,
+        out: &mut Vec<usize>,
+    )
+    {
+        marks.clear();
+        marks.resize(tree.len(), false);
+
+        // FIXME: avoid all those allocations.
+        let mut tmp = Vec::new();
+        let mut res = Vec::new();
+
+        for irow in m.data.column_row_indices(j) {
+            let mut curr = irow;
+            while curr != usize::max_value() && curr <= max_j && !marks[curr] {
+                marks[curr] = true;
+                tmp.push(curr);
+                curr = tree[curr];
+            }
+
+            tmp.append(&mut res);
+            mem::swap(&mut tmp, &mut res);
+        }
+
+        out.append(&mut res);
+    }
+
+    fn nonzero_pattern<S: CsStorage<N, D, D>>(
+        m: &CsMatrix<N, D, D, S>,
+    ) -> (CsMatrix<N, D, D>, CsMatrix<N, D, D>) {
+        let etree = Self::elimination_tree(m);
+        let (nrows, ncols) = m.data.shape();
+        let mut rows = Vec::with_capacity(m.len());
+        let mut cols = unsafe { VectorN::new_uninitialized_generic(m.data.shape().0, U1) };
+        let mut marks = Vec::new();
+
+        // NOTE: the following will actually compute the non-zero pattern of
+        // the transpose of l.
+        for i in 0..nrows.value() {
+            cols[i] = rows.len();
+            Self::reach(m, i, i, &etree, &mut marks, &mut rows);
+        }
+
+        let mut vals = Vec::with_capacity(rows.len());
+        unsafe {
+            vals.set_len(rows.len());
+        }
+        vals.shrink_to_fit();
+
+        let data = CsVecStorage {
+            shape: (nrows, ncols),
+            p: cols,
+            i: rows,
+            vals,
+        };
+
+        let u = CsMatrix::from_data(data);
+        // XXX: avoid this transpose.
+        let l = u.transpose();
+
+        (l, u)
+    }
+
+    /*
+     *
+     * NOTE: All the following methods are untested and currently unused.
+     *
+     *
+    fn column_counts<S: CsStorage<N, D, D>>(
+        m: &CsMatrix<N, D, D, S>,
+        tree: &[usize],
+    ) -> Vec<usize> {
+        let len = m.data.shape().0.value();
+        let mut counts: Vec<_> = iter::repeat(0).take(len).collect();
+        let mut reach = Vec::new();
+        let mut marks = Vec::new();
+    
+        for i in 0..len {
+            Self::reach(m, i, i, tree, &mut marks, &mut reach);
+    
+            for j in reach.drain(..) {
+                counts[j] += 1;
+            }
+        }
+    
+        counts
+    }
+    
+    fn tree_postorder(tree: &[usize]) -> Vec<usize> {
+        // FIXME: avoid all those allocations?
+        let mut first_child: Vec<_> = iter::repeat(usize::max_value()).take(tree.len()).collect();
+        let mut other_children: Vec<_> =
+            iter::repeat(usize::max_value()).take(tree.len()).collect();
+    
+        // Build the children list from the parent list.
+        // The set of children of the node `i` is given by the linked list
+        // starting at `first_child[i]`. The nodes of this list are then:
+        // { first_child[i], other_children[first_child[i]], other_children[other_children[first_child[i]], ... }
+        for (i, parent) in tree.iter().enumerate() {
+            if *parent != usize::max_value() {
+                let brother = first_child[*parent];
+                first_child[*parent] = i;
+                other_children[i] = brother;
+            }
+        }
+    
+        let mut stack = Vec::with_capacity(tree.len());
+        let mut postorder = Vec::with_capacity(tree.len());
+    
+        for (i, node) in tree.iter().enumerate() {
+            if *node == usize::max_value() {
+                Self::dfs(
+                    i,
+                    &mut first_child,
+                    &other_children,
+                    &mut stack,
+                    &mut postorder,
+                )
+            }
+        }
+    
+        postorder
+    }
+    
+    fn dfs(
+        i: usize,
+        first_child: &mut [usize],
+        other_children: &[usize],
+        stack: &mut Vec<usize>,
+        result: &mut Vec<usize>,
+    ) {
+        stack.clear();
+        stack.push(i);
+    
+        while let Some(n) = stack.pop() {
+            let child = first_child[n];
+    
+            if child == usize::max_value() {
+                // No children left.
+                result.push(n);
+            } else {
+                stack.push(n);
+                stack.push(child);
+                first_child[n] = other_children[child];
+            }
+        }
+    }
+    */
+}

src/sparse/cs_matrix_conversion.rs

@@ -0,0 +1,114 @@
+use alga::general::ClosedAdd;
+use num::Zero;
+
+use allocator::Allocator;
+use sparse::cs_utils;
+use sparse::{CsMatrix, CsStorage};
+use storage::Storage;
+use {DefaultAllocator, Dim, Dynamic, Matrix, MatrixMN, Scalar};
+
+impl<'a, N: Scalar + Zero + ClosedAdd> CsMatrix<N> {
+    /// Creates a column-compressed sparse matrix from a sparse matrix in triplet form.
+    pub fn from_triplet(
+        nrows: usize,
+        ncols: usize,
+        irows: &[usize],
+        icols: &[usize],
+        vals: &[N],
+    ) -> Self
+    {
+        Self::from_triplet_generic(Dynamic::new(nrows), Dynamic::new(ncols), irows, icols, vals)
+    }
+}
+
+impl<'a, N: Scalar + Zero + ClosedAdd, R: Dim, C: Dim> CsMatrix<N, R, C>
+where DefaultAllocator: Allocator<usize, C> + Allocator<N, R>
+{
+    /// Creates a column-compressed sparse matrix from a sparse matrix in triplet form.
+    pub fn from_triplet_generic(
+        nrows: R,
+        ncols: C,
+        irows: &[usize],
+        icols: &[usize],
+        vals: &[N],
+    ) -> Self
+    {
+        assert!(vals.len() == irows.len());
+        assert!(vals.len() == icols.len());
+
+        let mut res = CsMatrix::new_uninitialized_generic(nrows, ncols, vals.len());
+        let mut workspace = res.data.p.clone();
+
+        // Column count.
+        for j in icols.iter().cloned() {
+            workspace[j] += 1;
+        }
+
+        let _ = cs_utils::cumsum(&mut workspace, &mut res.data.p);
+
+        // Fill i and vals.
+        for ((i, j), val) in irows
+            .iter()
+            .cloned()
+            .zip(icols.iter().cloned())
+            .zip(vals.iter().cloned())
+        {
+            let offset = workspace[j];
+            res.data.i[offset] = i;
+            res.data.vals[offset] = val;
+            workspace[j] = offset + 1;
+        }
+
+        // Sort the result.
+        res.sort();
+        res.dedup();
+        res
+    }
+}
+
+impl<'a, N: Scalar + Zero, R: Dim, C: Dim, S> From<CsMatrix<N, R, C, S>> for MatrixMN<N, R, C>
+where
+    S: CsStorage<N, R, C>,
+    DefaultAllocator: Allocator<N, R, C>,
+{
+    fn from(m: CsMatrix<N, R, C, S>) -> Self {
+        let (nrows, ncols) = m.data.shape();
+        let mut res = MatrixMN::zeros_generic(nrows, ncols);
+
+        for j in 0..ncols.value() {
+            for (i, val) in m.data.column_entries(j) {
+                res[(i, j)] = val;
+            }
+        }
+
+        res
+    }
+}
+
+impl<'a, N: Scalar + Zero, R: Dim, C: Dim, S> From<Matrix<N, R, C, S>> for CsMatrix<N, R, C>
+where
+    S: Storage<N, R, C>,
+    DefaultAllocator: Allocator<N, R, C> + Allocator<usize, C>,
+{
+    fn from(m: Matrix<N, R, C, S>) -> Self {
+        let (nrows, ncols) = m.data.shape();
+        let len = m.iter().filter(|e| !e.is_zero()).count();
+        let mut res = CsMatrix::new_uninitialized_generic(nrows, ncols, len);
+        let mut nz = 0;
+
+        for j in 0..ncols.value() {
+            let column = m.column(j);
+            res.data.p[j] = nz;
+
+            for i in 0..nrows.value() {
+                if !column[i].is_zero() {
+                    res.data.i[nz] = i;
+                    res.data.vals[nz] = column[i];
+                    nz += 1;
+                }
+            }
+        }
+
+        res
+    }
+}

src/sparse/cs_matrix_ops.rs

@@ -0,0 +1,304 @@
+use alga::general::{ClosedAdd, ClosedMul};
+use num::{One, Zero};
+use std::ops::{Add, Mul};
+
+use allocator::Allocator;
+use constraint::{AreMultipliable, DimEq, ShapeConstraint};
+use sparse::{CsMatrix, CsStorage, CsStorageMut, CsVector};
+use storage::StorageMut;
+use {DefaultAllocator, Dim, Scalar, Vector, VectorN, U1};
+
+impl<N: Scalar, R: Dim, C: Dim, S: CsStorage<N, R, C>> CsMatrix<N, R, C, S> {
+    fn scatter<R2: Dim, C2: Dim>(
+        &self,
+        j: usize,
+        beta: N,
+        timestamps: &mut [usize],
+        timestamp: usize,
+        workspace: &mut [N],
+        mut nz: usize,
+        res: &mut CsMatrix<N, R2, C2>,
+    ) -> usize
+    where
+        N: ClosedAdd + ClosedMul,
+        DefaultAllocator: Allocator<usize, C2>,
+    {
+        for (i, val) in self.data.column_entries(j) {
+            if timestamps[i] < timestamp {
+                timestamps[i] = timestamp;
+                res.data.i[nz] = i;
+                nz += 1;
+                workspace[i] = val * beta;
+            } else {
+                workspace[i] += val * beta;
+            }
+        }
+
+        nz
+    }
+}
+
+/*
+impl<N: Scalar, R, S> CsVector<N, R, S> {
+    pub fn axpy(&mut self, alpha: N, x: CsVector<N, R, S>, beta: N) {
+        // First, compute the number of non-zero entries.
+        let mut nnzero = 0;
+
+        // Allocate a size large enough.
+        self.data.set_column_len(0, nnzero);
+
+        // Fill with the axpy.
+        let mut i = self.len();
+        let mut j = x.len();
+        let mut k = nnzero - 1;
+        let mut rid1 = self.data.row_index(0, i - 1);
+        let mut rid2 = x.data.row_index(0, j - 1);
+
+        while k > 0 {
+            if rid1 == rid2 {
+                self.data.set_row_index(0, k, rid1);
+                self[k] = alpha * x[j] + beta * self[k];
+                i -= 1;
+                j -= 1;
+            } else if rid1 < rid2 {
+                self.data.set_row_index(0, k, rid1);
+                self[k] = beta * self[i];
+                i -= 1;
+            } else {
+                self.data.set_row_index(0, k, rid2);
+                self[k] = alpha * x[j];
+                j -= 1;
+            }
+
+            k -= 1;
+        }
+    }
+}
+*/
+
+impl<N: Scalar + Zero + ClosedAdd + ClosedMul, D: Dim, S: StorageMut<N, D>> Vector<N, D, S> {
+    /// Perform a sparse axpy operation: `self = alpha * x + beta * self` operation.
+    pub fn axpy_cs<D2: Dim, S2>(&mut self, alpha: N, x: &CsVector<N, D2, S2>, beta: N)
+    where
+        S2: CsStorage<N, D2>,
+        ShapeConstraint: DimEq<D, D2>,
+    {
+        if beta.is_zero() {
+            for i in 0..x.len() {
+                unsafe {
+                    let k = x.data.row_index_unchecked(i);
+                    let y = self.vget_unchecked_mut(k);
+                    *y = alpha * *x.data.get_value_unchecked(i);
+                }
+            }
+        } else {
+            // Needed to be sure even components not present on `x` are multiplied.
+            *self *= beta;
+
+            for i in 0..x.len() {
+                unsafe {
+                    let k = x.data.row_index_unchecked(i);
+                    let y = self.vget_unchecked_mut(k);
+                    *y += alpha * *x.data.get_value_unchecked(i);
+                }
+            }
+        }
+    }
+
+    /*
+    pub fn gemv_sparse<R2: Dim, C2: Dim, S2>(&mut self, alpha: N, a: &CsMatrix<N, R2, C2, S2>, x: &DVector<N>, beta: N)
+        where
+            S2: CsStorage<N, R2, C2> {
+        let col2 = a.column(0);
+        let val = unsafe { *x.vget_unchecked(0) };
+        self.axpy_sparse(alpha * val, &col2, beta);
+    
+        for j in 1..ncols2 {
+            let col2 = a.column(j);
+            let val = unsafe { *x.vget_unchecked(j) };
+    
+            self.axpy_sparse(alpha * val, &col2, N::one());
+        }
+    }
+    */
+}
+
+impl<'a, 'b, N, R1, R2, C1, C2, S1, S2> Mul<&'b CsMatrix<N, R2, C2, S2>>
+    for &'a CsMatrix<N, R1, C1, S1>
+where
+    N: Scalar + ClosedAdd + ClosedMul + Zero,
+    R1: Dim,
+    C1: Dim,
+    R2: Dim,
+    C2: Dim,
+    S1: CsStorage<N, R1, C1>,
+    S2: CsStorage<N, R2, C2>,
+    ShapeConstraint: AreMultipliable<R1, C1, R2, C2>,
+    DefaultAllocator: Allocator<usize, C2> + Allocator<usize, R1> + Allocator<N, R1>,
+{
+    type Output = CsMatrix<N, R1, C2>;
+
+    fn mul(self, rhs: &'b CsMatrix<N, R2, C2, S2>) -> Self::Output {
+        let (nrows1, ncols1) = self.data.shape();
+        let (nrows2, ncols2) = rhs.data.shape();
+        assert_eq!(
+            ncols1.value(),
+            nrows2.value(),
+            "Mismatched dimensions for matrix multiplication."
+        );
+
+        let mut res = CsMatrix::new_uninitialized_generic(nrows1, ncols2, self.len() + rhs.len());
+        let mut workspace = VectorN::<N, R1>::zeros_generic(nrows1, U1);
+        let mut nz = 0;
+
+        for j in 0..ncols2.value() {
+            res.data.p[j] = nz;
+            let new_size_bound = nz + nrows1.value();
+            res.data.i.resize(new_size_bound, 0);
+            res.data.vals.resize(new_size_bound, N::zero());
+
+            for (i, beta) in rhs.data.column_entries(j) {
+                for (k, val) in self.data.column_entries(i) {
+                    workspace[k] += val * beta;
+                }
+            }
+
+            for (i, val) in workspace.as_mut_slice().iter_mut().enumerate() {
+                if !val.is_zero() {
+                    res.data.i[nz] = i;
+                    res.data.vals[nz] = *val;
+                    *val = N::zero();
+                    nz += 1;
+                }
+            }
+        }
+
+        // NOTE: the following has a lower complexity, but is slower in many cases, likely because
+        // of branching inside of the inner loop.
+        //
+        // let mut res = CsMatrix::new_uninitialized_generic(nrows1, ncols2, self.len() + rhs.len());
+        // let mut timestamps = VectorN::zeros_generic(nrows1, U1);
+        // let mut workspace = unsafe { VectorN::new_uninitialized_generic(nrows1, U1) };
+        // let mut nz = 0;
+        //
+        // for j in 0..ncols2.value() {
+        //     res.data.p[j] = nz;
+        //     let new_size_bound = nz + nrows1.value();
+        //     res.data.i.resize(new_size_bound, 0);
+        //     res.data.vals.resize(new_size_bound, N::zero());
+        //
+        //     for (i, val) in rhs.data.column_entries(j) {
+        //         nz = self.scatter(
+        //             i,
+        //             val,
+        //             timestamps.as_mut_slice(),
+        //             j + 1,
+        //             workspace.as_mut_slice(),
+        //             nz,
+        //             &mut res,
+        //         );
+        //     }
+        //
+        //     // Keep the output sorted.
+        //     let range = res.data.p[j]..nz;
+        //     res.data.i[range.clone()].sort();
+        //
+        //     for p in range {
+        //         res.data.vals[p] = workspace[res.data.i[p]]
+        //     }
+        // }
+
+        res.data.i.truncate(nz);
+        res.data.i.shrink_to_fit();
+        res.data.vals.truncate(nz);
+        res.data.vals.shrink_to_fit();
+        res
+    }
+}
+
+impl<'a, 'b, N, R1, R2, C1, C2, S1, S2> Add<&'b CsMatrix<N, R2, C2, S2>>
+    for &'a CsMatrix<N, R1, C1, S1>
+where
+    N: Scalar + ClosedAdd + ClosedMul + One,
+    R1: Dim,
+    C1: Dim,
+    R2: Dim,
+    C2: Dim,
+    S1: CsStorage<N, R1, C1>,
+    S2: CsStorage<N, R2, C2>,
+    ShapeConstraint: DimEq<R1, R2> + DimEq<C1, C2>,
+    DefaultAllocator: Allocator<usize, C2> + Allocator<usize, R1> + Allocator<N, R1>,
+{
+    type Output = CsMatrix<N, R1, C2>;
+
+    fn add(self, rhs: &'b CsMatrix<N, R2, C2, S2>) -> Self::Output {
+        let (nrows1, ncols1) = self.data.shape();
+        let (nrows2, ncols2) = rhs.data.shape();
+        assert_eq!(
+            (nrows1.value(), ncols1.value()),
+            (nrows2.value(), ncols2.value()),
+            "Mismatched dimensions for matrix sum."
+        );
+
+        let mut res = CsMatrix::new_uninitialized_generic(nrows1, ncols2, self.len() + rhs.len());
+        let mut timestamps = VectorN::zeros_generic(nrows1, U1);
+        let mut workspace = unsafe { VectorN::new_uninitialized_generic(nrows1, U1) };
+        let mut nz = 0;
+
+        for j in 0..ncols2.value() {
+            res.data.p[j] = nz;
+
+            nz = self.scatter(
+                j,
+                N::one(),
+                timestamps.as_mut_slice(),
+                j + 1,
+                workspace.as_mut_slice(),
+                nz,
+                &mut res,
+            );
+
+            nz = rhs.scatter(
+                j,
+                N::one(),
+                timestamps.as_mut_slice(),
+                j + 1,
+                workspace.as_mut_slice(),
+                nz,
+                &mut res,
+            );
+
+            // Keep the output sorted.
+            let range = res.data.p[j]..nz;
+            res.data.i[range.clone()].sort();
+
+            for p in range {
+                res.data.vals[p] = workspace[res.data.i[p]]
+            }
+        }
+
+        res.data.i.truncate(nz);
+        res.data.i.shrink_to_fit();
+        res.data.vals.truncate(nz);
+        res.data.vals.shrink_to_fit();
+        res
+    }
+}
+
+impl<'a, 'b, N, R, C, S> Mul<N> for CsMatrix<N, R, C, S>
+where
+    N: Scalar + ClosedAdd + ClosedMul + Zero,
+    R: Dim,
+    C: Dim,
+    S: CsStorageMut<N, R, C>,
+{
+    type Output = Self;
+
+    fn mul(mut self, rhs: N) -> Self::Output {
+        for e in self.values_mut() {
+            *e *= rhs
+        }
+
+        self
+    }
+}

src/sparse/cs_matrix_solve.rs

@@ -0,0 +1,283 @@
+use allocator::Allocator;
+use constraint::{SameNumberOfRows, ShapeConstraint};
+use sparse::{CsMatrix, CsStorage, CsVector};
+use storage::{Storage, StorageMut};
+use {DefaultAllocator, Dim, Matrix, MatrixMN, Real, VectorN, U1};
+
+impl<N: Real, D: Dim, S: CsStorage<N, D, D>> CsMatrix<N, D, D, S> {
+    /// Solve a lower-triangular system with a dense right-hand-side.
+    pub fn solve_lower_triangular<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>,
+        ShapeConstraint: SameNumberOfRows<D, R2>,
+    {
+        let mut b = b.clone_owned();
+        if self.solve_lower_triangular_mut(&mut b) {
+            Some(b)
+        } else {
+            None
+        }
+    }
+
+    /// Solve a lower-triangular system with `self` transposed and a dense right-hand-side.
+    pub fn tr_solve_lower_triangular<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>,
+        ShapeConstraint: SameNumberOfRows<D, R2>,
+    {
+        let mut b = b.clone_owned();
+        if self.tr_solve_lower_triangular_mut(&mut b) {
+            Some(b)
+        } else {
+            None
+        }
+    }
+
+    /// Solve in-place a lower-triangular system with a dense right-hand-side.
+    pub fn solve_lower_triangular_mut<R2: Dim, C2: Dim, S2>(
+        &self,
+        b: &mut Matrix<N, R2, C2, S2>,
+    ) -> bool
+    where
+        S2: StorageMut<N, R2, C2>,
+        ShapeConstraint: SameNumberOfRows<D, R2>,
+    {
+        let (nrows, ncols) = self.data.shape();
+        assert_eq!(nrows.value(), ncols.value(), "The matrix must be square.");
+        assert_eq!(nrows.value(), b.len(), "Mismatched matrix dimensions.");
+
+        for j2 in 0..b.ncols() {
+            let mut b = b.column_mut(j2);
+
+            for j in 0..ncols.value() {
+                let mut column = self.data.column_entries(j);
+                let mut diag_found = false;
+
+                while let Some((i, val)) = column.next() {
+                    if i == j {
+                        if val.is_zero() {
+                            return false;
+                        }
+
+                        b[j] /= val;
+                        diag_found = true;
+                        break;
+                    }
+                }
+
+                if !diag_found {
+                    return false;
+                }
+
+                for (i, val) in column {
+                    b[i] -= b[j] * val;
+                }
+            }
+        }
+
+        true
+    }
+
+    /// Solve a lower-triangular system with `self` transposed and a dense right-hand-side.
+    pub fn tr_solve_lower_triangular_mut<R2: Dim, C2: Dim, S2>(
+        &self,
+        b: &mut Matrix<N, R2, C2, S2>,
+    ) -> bool
+    where
+        S2: StorageMut<N, R2, C2>,
+        ShapeConstraint: SameNumberOfRows<D, R2>,
+    {
+        let (nrows, ncols) = self.data.shape();
+        assert_eq!(nrows.value(), ncols.value(), "The matrix must be square.");
+        assert_eq!(nrows.value(), b.len(), "Mismatched matrix dimensions.");
+
+        for j2 in 0..b.ncols() {
+            let mut b = b.column_mut(j2);
+
+            for j in (0..ncols.value()).rev() {
+                let mut column = self.data.column_entries(j);
+                let mut diag = None;
+
+                while let Some((i, val)) = column.next() {
+                    if i == j {
+                        if val.is_zero() {
+                            return false;
+                        }
+
+                        diag = Some(val);
+                        break;
+                    }
+                }
+
+                if let Some(diag) = diag {
+                    for (i, val) in column {
+                        b[j] -= val * b[i];
+                    }
+
+                    b[j] /= diag;
+                } else {
+                    return false;
+                }
+            }
+        }
+
+        true
+    }
+
+    /// Solve a lower-triangular system with a sparse right-hand-side.
+    pub fn solve_lower_triangular_cs<D2: Dim, S2>(
+        &self,
+        b: &CsVector<N, D2, S2>,
+    ) -> Option<CsVector<N, D2>>
+    where
+        S2: CsStorage<N, D2>,
+        DefaultAllocator: Allocator<bool, D> + Allocator<N, D2> + Allocator<usize, D2>,
+        ShapeConstraint: SameNumberOfRows<D, D2>,
+    {
+        let mut reach = Vec::new();
+        // We don't compute a postordered reach here because it will be sorted after anyway.
+        self.lower_triangular_reach(b, &mut reach);
+        // We sort the reach so the result matrix has sorted indices.
+        reach.sort();
+        let mut workspace = unsafe { VectorN::new_uninitialized_generic(b.data.shape().0, U1) };
+
+        for i in reach.iter().cloned() {
+            workspace[i] = N::zero();
+        }
+
+        for (i, val) in b.data.column_entries(0) {
+            workspace[i] = val;
+        }
+
+        for j in reach.iter().cloned() {
+            let mut column = self.data.column_entries(j);
+            let mut diag_found = false;
+
+            while let Some((i, val)) = column.next() {
+                if i == j {
+                    if val.is_zero() {
+                        break;
+                    }
+
+                    workspace[j] /= val;
+                    diag_found = true;
+                    break;
+                }
+            }
+
+            if !diag_found {
+                return None;
+            }
+
+            for (i, val) in column {
+                workspace[i] -= workspace[j] * val;
+            }
+        }
+
+        // Copy the result into a sparse vector.
+        let mut result = CsVector::new_uninitialized_generic(b.data.shape().0, U1, reach.len());
+
+        for (i, val) in reach.iter().zip(result.data.vals.iter_mut()) {
+            *val = workspace[*i];
+        }
+
+        result.data.i = reach;
+        Some(result)
+    }
+
+    /*
+    // Computes the reachable, post-ordered, nodes from `b`.
+    fn lower_triangular_reach_postordered<D2: Dim, S2>(
+        &self,
+        b: &CsVector<N, D2, S2>,
+        xi: &mut Vec<usize>,
+    ) where
+        S2: CsStorage<N, D2>,
+        DefaultAllocator: Allocator<bool, D>,
+    {
+        let mut visited = VectorN::repeat_generic(self.data.shape().1, U1, false);
+        let mut stack = Vec::new();
+
+        for i in b.data.column_range(0) {
+            let row_index = b.data.row_index(i);
+
+            if !visited[row_index] {
+                let rng = self.data.column_range(row_index);
+                stack.push((row_index, rng));
+                self.lower_triangular_dfs(visited.as_mut_slice(), &mut stack, xi);
+            }
+        }
+    }
+
+    fn lower_triangular_dfs(
+        &self,
+        visited: &mut [bool],
+        stack: &mut Vec<(usize, Range<usize>)>,
+        xi: &mut Vec<usize>,
+    )
+    {
+        'recursion: while let Some((j, rng)) = stack.pop() {
+            visited[j] = true;
+
+            for i in rng.clone() {
+                let row_id = self.data.row_index(i);
+                if row_id > j && !visited[row_id] {
+                    stack.push((j, (i + 1)..rng.end));
+                    stack.push((row_id, self.data.column_range(row_id)));
+                    continue 'recursion;
+                }
+            }
+
+            xi.push(j)
+        }
+    }
+    */
+
+    // Computes the nodes reachable from `b` in an arbitrary order.
+    fn lower_triangular_reach<D2: Dim, S2>(&self, b: &CsVector<N, D2, S2>, xi: &mut Vec<usize>)
+    where
+        S2: CsStorage<N, D2>,
+        DefaultAllocator: Allocator<bool, D>,
+    {
+        let mut visited = VectorN::repeat_generic(self.data.shape().1, U1, false);
+        let mut stack = Vec::new();
+
+        for irow in b.data.column_row_indices(0) {
+            self.lower_triangular_bfs(irow, visited.as_mut_slice(), &mut stack, xi);
+        }
+    }
+
+    fn lower_triangular_bfs(
+        &self,
+        start: usize,
+        visited: &mut [bool],
+        stack: &mut Vec<usize>,
+        xi: &mut Vec<usize>,
+    )
+    {
+        if !visited[start] {
+            stack.clear();
+            stack.push(start);
+            xi.push(start);
+            visited[start] = true;
+
+            while let Some(j) = stack.pop() {
+                for irow in self.data.column_row_indices(j) {
+                    if irow > j && !visited[irow] {
+                        stack.push(irow);
+                        xi.push(irow);
+                        visited[irow] = true;
+                    }
+                }
+            }
+        }
+    }
+}

src/sparse/cs_utils.rs

@@ -0,0 +1,16 @@
+use allocator::Allocator;
+use {DefaultAllocator, Dim, VectorN};
+
+pub fn cumsum<D: Dim>(a: &mut VectorN<usize, D>, b: &mut VectorN<usize, D>) -> usize
+where DefaultAllocator: Allocator<usize, D> {
+    assert!(a.len() == b.len());
+    let mut sum = 0;
+
+    for i in 0..a.len() {
+        b[i] = sum;
+        sum += a[i];
+        a[i] = b[i];
+    }
+
+    sum
+}

src/sparse/mod.rs

@@ -0,0 +1,13 @@
+//! Sparse matrices.
+
+pub use self::cs_matrix::{
+    CsMatrix, CsStorage, CsStorageIter, CsStorageIterMut, CsStorageMut, CsVecStorage, CsVector,
+};
+pub use self::cs_matrix_cholesky::CsCholesky;
+
+mod cs_matrix;
+mod cs_matrix_cholesky;
+mod cs_matrix_conversion;
+mod cs_matrix_ops;
+mod cs_matrix_solve;
+pub(crate) mod cs_utils;

tests/core/matrix.rs

@@ -195,10 +195,10 @@ fn from_columns() {
 #[test]
 fn from_columns_dynamic() {
     let columns = &[
-        DVector::from_row_slice(3, &[11, 21, 31]),
+        DVector::from_row_slice(&[11, 21, 31]),
-        DVector::from_row_slice(3, &[12, 22, 32]),
+        DVector::from_row_slice(&[12, 22, 32]),
-        DVector::from_row_slice(3, &[13, 23, 33]),
+        DVector::from_row_slice(&[13, 23, 33]),
-        DVector::from_row_slice(3, &[14, 24, 34]),
+        DVector::from_row_slice(&[14, 24, 34]),
     ];
 
     let expected = DMatrix::from_row_slice(3, 4, &[11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33, 34]);
@@ -233,8 +233,8 @@ fn from_not_enough_columns() {
 #[should_panic]
 fn from_rows_with_different_dimensions() {
     let columns = &[
-        DVector::from_row_slice(3, &[11, 21, 31]),
+        DVector::from_row_slice(&[11, 21, 31]),
-        DVector::from_row_slice(3, &[12, 22, 32, 33]),
+        DVector::from_row_slice(&[12, 22, 32, 33]),
     ];
 
     let _ = DMatrix::from_columns(columns);
@@ -272,8 +272,8 @@ fn to_homogeneous() {
     let a = Vector3::new(1.0, 2.0, 3.0);
     let expected_a = Vector4::new(1.0, 2.0, 3.0, 0.0);
 
-    let b = DVector::from_row_slice(3, &[1.0, 2.0, 3.0]);
+    let b = DVector::from_row_slice(&[1.0, 2.0, 3.0]);
-    let expected_b = DVector::from_row_slice(4, &[1.0, 2.0, 3.0, 0.0]);
+    let expected_b = DVector::from_row_slice(&[1.0, 2.0, 3.0, 0.0]);
 
     let c = Matrix2::new(1.0, 2.0, 3.0, 4.0);
     let expected_c = Matrix3::new(1.0, 2.0, 0.0, 3.0, 4.0, 0.0, 0.0, 0.0, 1.0);
@@ -287,6 +287,18 @@ fn to_homogeneous() {
     assert_eq!(d.to_homogeneous(), expected_d);
 }
 
+#[test]
+fn push() {
+    let a = Vector3::new(1.0, 2.0, 3.0);
+    let expected_a = Vector4::new(1.0, 2.0, 3.0, 4.0);
+
+    let b = DVector::from_row_slice(&[1.0, 2.0, 3.0]);
+    let expected_b = DVector::from_row_slice(&[1.0, 2.0, 3.0, 4.0]);
+
+    assert_eq!(a.push(4.0), expected_a);
+    assert_eq!(b.push(4.0), expected_b);
+}
+
 #[test]
 fn simple_add() {
     let a = Matrix2x3::new(1.0, 2.0, 3.0, 4.0, 5.0, 6.0);

tests/geometry/isometry.rs

@@ -25,27 +25,35 @@ quickcheck!(
         let viewmatrix = Isometry3::look_at_rh(&eye, &target, &up);
 
         let origin = Point3::origin();
-        relative_eq!(viewmatrix * eye, origin, epsilon = 1.0e-7) &&
+        relative_eq!(viewmatrix * eye, origin, epsilon = 1.0e-7)
-        relative_eq!((viewmatrix * (target - eye)).normalize(), -Vector3::z(), epsilon = 1.0e-7)
+            && relative_eq!(
+                (viewmatrix * (target - eye)).normalize(),
+                -Vector3::z(),
+                epsilon = 1.0e-7
+            )
     }
 
     fn observer_frame_3(eye: Point3<f64>, target: Point3<f64>, up: Vector3<f64>) -> bool {
-        let observer = Isometry3::new_observer_frame(&eye, &target, &up);
+        let observer = Isometry3::face_towards(&eye, &target, &up);
 
         let origin = Point3::origin();
-        relative_eq!(observer * origin, eye, epsilon = 1.0e-7) &&
+        relative_eq!(observer * origin, eye, epsilon = 1.0e-7)
-        relative_eq!(observer * Vector3::z(), (target - eye).normalize(), epsilon = 1.0e-7)
+            && relative_eq!(
+                observer * Vector3::z(),
+                (target - eye).normalize(),
+                epsilon = 1.0e-7
+            )
     }
 
     fn inverse_is_identity(i: Isometry3<f64>, p: Point3<f64>, v: Vector3<f64>) -> bool {
         let ii = i.inverse();
 
-        relative_eq!(i  * ii, Isometry3::identity(), epsilon = 1.0e-7) &&
+        relative_eq!(i * ii, Isometry3::identity(), epsilon = 1.0e-7)
-        relative_eq!(ii *  i, Isometry3::identity(), epsilon = 1.0e-7) &&
+            && relative_eq!(ii * i, Isometry3::identity(), epsilon = 1.0e-7)
-        relative_eq!((i  * ii) * p, p, epsilon = 1.0e-7) &&
+            && relative_eq!((i * ii) * p, p, epsilon = 1.0e-7)
-        relative_eq!((ii * i)  * p, p, epsilon = 1.0e-7) &&
+            && relative_eq!((ii * i) * p, p, epsilon = 1.0e-7)
-        relative_eq!((i  * ii) * v, v, epsilon = 1.0e-7) &&
+            && relative_eq!((i * ii) * v, v, epsilon = 1.0e-7)
-        relative_eq!((ii * i)  * v, v, epsilon = 1.0e-7)
+            && relative_eq!((ii * i) * v, v, epsilon = 1.0e-7)
     }
 
     fn inverse_is_parts_inversion(t: Translation3<f64>, r: UnitQuaternion<f64>) -> bool {
@@ -54,14 +62,29 @@ quickcheck!(
     }
 
     fn multiply_equals_alga_transform(i: Isometry3<f64>, v: Vector3<f64>, p: Point3<f64>) -> bool {
-        i * v == i.transform_vector(&v) &&
+        i * v == i.transform_vector(&v)
-        i * p == i.transform_point(&p)  &&
+            && i * p == i.transform_point(&p)
-        relative_eq!(i.inverse() * v, i.inverse_transform_vector(&v), epsilon = 1.0e-7) &&
+            && relative_eq!(
-        relative_eq!(i.inverse() * p, i.inverse_transform_point(&p), epsilon = 1.0e-7)
+                i.inverse() * v,
+                i.inverse_transform_vector(&v),
+                epsilon = 1.0e-7
+            )
+            && relative_eq!(
+                i.inverse() * p,
+                i.inverse_transform_point(&p),
+                epsilon = 1.0e-7
+            )
     }
 
-    fn composition2(i: Isometry2<f64>,    uc: UnitComplex<f64>, r: Rotation2<f64>,
+    fn composition2(
-                    t: Translation2<f64>, v:  Vector2<f64>,     p: Point2<f64>) -> bool {
+        i: Isometry2<f64>,
+        uc: UnitComplex<f64>,
+        r: Rotation2<f64>,
+        t: Translation2<f64>,
+        v: Vector2<f64>,
+        p: Point2<f64>,
+    ) -> bool
+    {
         // (rotation × translation) * point = rotation × (translation * point)
         relative_eq!((uc * t) * v, uc * v, epsilon = 1.0e-7)       &&
         relative_eq!((r  * t) * v, r  * v, epsilon = 1.0e-7)       &&
@@ -91,8 +114,15 @@ quickcheck!(
         relative_eq!((i * t) * p, i * (t * p), epsilon = 1.0e-7)
     }
 
-    fn composition3(i: Isometry3<f64>,    uq: UnitQuaternion<f64>, r: Rotation3<f64>,
+    fn composition3(
-                    t: Translation3<f64>, v:  Vector3<f64>,        p: Point3<f64>) -> bool {
+        i: Isometry3<f64>,
+        uq: UnitQuaternion<f64>,
+        r: Rotation3<f64>,
+        t: Translation3<f64>,
+        v: Vector3<f64>,
+        p: Point3<f64>,
+    ) -> bool
+    {
         // (rotation × translation) * point = rotation × (translation * point)
         relative_eq!((uq * t) * v, uq * v, epsilon = 1.0e-7)       &&
         relative_eq!((r  * t) * v, r  * v, epsilon = 1.0e-7)       &&
@@ -122,11 +152,18 @@ quickcheck!(
         relative_eq!((i * t) * p, i * (t * p), epsilon = 1.0e-7)
     }
 
-    fn all_op_exist(i: Isometry3<f64>, uq: UnitQuaternion<f64>, t: Translation3<f64>,
+    fn all_op_exist(
-                    v: Vector3<f64>, p: Point3<f64>, r: Rotation3<f64>) -> bool {
+        i: Isometry3<f64>,
-        let iMi  = i * i;
+        uq: UnitQuaternion<f64>,
+        t: Translation3<f64>,
+        v: Vector3<f64>,
+        p: Point3<f64>,
+        r: Rotation3<f64>,
+    ) -> bool
+    {
+        let iMi = i * i;
         let iMuq = i * uq;
-        let iDi  = i / i;
+        let iDi = i / i;
         let iDuq = i / uq;
 
         let iMp = i * p;
@@ -135,13 +172,13 @@ quickcheck!(
         let iMt = i * t;
         let tMi = t * i;
 
-        let tMr  = t * r;
+        let tMr = t * r;
         let tMuq = t * uq;
 
         let uqMi = uq * i;
         let uqDi = uq / i;
 
-        let rMt  = r * t;
+        let rMt = r * t;
         let uqMt = uq * t;
 
         let mut iMt1 = i;
@@ -174,75 +211,57 @@ quickcheck!(
         iDuq1 /= uq;
         iDuq2 /= &uq;
 
-        iMt == iMt1 &&
+        iMt == iMt1
-        iMt == iMt2 &&
+            && iMt == iMt2
-
+            && iMi == iMi1
-        iMi == iMi1 &&
+            && iMi == iMi2
-        iMi == iMi2 &&
+            && iMuq == iMuq1
-
+            && iMuq == iMuq2
-        iMuq == iMuq1 &&
+            && iDi == iDi1
-        iMuq == iMuq2 &&
+            && iDi == iDi2
-
+            && iDuq == iDuq1
-        iDi == iDi1 &&
+            && iDuq == iDuq2
-        iDi == iDi2 &&
+            && iMi == &i * &i
-
+            && iMi == i * &i
-        iDuq == iDuq1 &&
+            && iMi == &i * i
-        iDuq == iDuq2 &&
+            && iMuq == &i * &uq
-
+            && iMuq == i * &uq
-        iMi == &i * &i &&
+            && iMuq == &i * uq
-        iMi ==  i * &i &&
+            && iDi == &i / &i
-        iMi == &i *  i &&
+            && iDi == i / &i
-
+            && iDi == &i / i
-        iMuq == &i * &uq &&
+            && iDuq == &i / &uq
-        iMuq ==  i * &uq &&
+            && iDuq == i / &uq
-        iMuq == &i *  uq &&
+            && iDuq == &i / uq
-
+            && iMp == &i * &p
-        iDi == &i / &i &&
+            && iMp == i * &p
-        iDi ==  i / &i &&
+            && iMp == &i * p
-        iDi == &i /  i &&
+            && iMv == &i * &v
-
+            && iMv == i * &v
-        iDuq == &i / &uq &&
+            && iMv == &i * v
-        iDuq ==  i / &uq &&
+            && iMt == &i * &t
-        iDuq == &i /  uq &&
+            && iMt == i * &t
-
+            && iMt == &i * t
-        iMp == &i * &p &&
+            && tMi == &t * &i
-        iMp ==  i * &p &&
+            && tMi == t * &i
-        iMp == &i *  p &&
+            && tMi == &t * i
-
+            && tMr == &t * &r
-        iMv == &i * &v &&
+            && tMr == t * &r
-        iMv ==  i * &v &&
+            && tMr == &t * r
-        iMv == &i *  v &&
+            && tMuq == &t * &uq
-
+            && tMuq == t * &uq
-        iMt == &i * &t &&
+            && tMuq == &t * uq
-        iMt ==  i * &t &&
+            && uqMi == &uq * &i
-        iMt == &i *  t &&
+            && uqMi == uq * &i
-
+            && uqMi == &uq * i
-        tMi == &t * &i &&
+            && uqDi == &uq / &i
-        tMi ==  t * &i &&
+            && uqDi == uq / &i
-        tMi == &t *  i &&
+            && uqDi == &uq / i
-
+            && rMt == &r * &t
-        tMr == &t * &r  &&
+            && rMt == r * &t
-        tMr ==  t * &r  &&
+            && rMt == &r * t
-        tMr == &t *  r  &&
+            && uqMt == &uq * &t
-
+            && uqMt == uq * &t
-        tMuq == &t * &uq &&
+            && uqMt == &uq * t
-        tMuq ==  t * &uq &&
-        tMuq == &t *  uq &&
-
-        uqMi == &uq * &i &&
-        uqMi ==  uq * &i &&
-        uqMi == &uq *  i &&
-
-        uqDi == &uq / &i &&
-        uqDi ==  uq / &i &&
-        uqDi == &uq /  i &&
-
-        rMt == &r * &t &&
-        rMt ==  r * &t &&
-        rMt == &r *  t &&
-
-        uqMt == &uq * &t &&
-        uqMt ==  uq * &t &&
-        uqMt == &uq *  t
     }
 );

tests/geometry/similarity.rs

@@ -8,33 +8,57 @@ quickcheck!(
     fn inverse_is_identity(i: Similarity3<f64>, p: Point3<f64>, v: Vector3<f64>) -> bool {
         let ii = i.inverse();
 
-        relative_eq!(i  * ii, Similarity3::identity(), epsilon = 1.0e-7) &&
+        relative_eq!(i * ii, Similarity3::identity(), epsilon = 1.0e-7)
-        relative_eq!(ii *  i, Similarity3::identity(), epsilon = 1.0e-7) &&
+            && relative_eq!(ii * i, Similarity3::identity(), epsilon = 1.0e-7)
-        relative_eq!((i  * ii) * p, p, epsilon = 1.0e-7) &&
+            && relative_eq!((i * ii) * p, p, epsilon = 1.0e-7)
-        relative_eq!((ii * i)  * p, p, epsilon = 1.0e-7) &&
+            && relative_eq!((ii * i) * p, p, epsilon = 1.0e-7)
-        relative_eq!((i  * ii) * v, v, epsilon = 1.0e-7) &&
+            && relative_eq!((i * ii) * v, v, epsilon = 1.0e-7)
-        relative_eq!((ii * i)  * v, v, epsilon = 1.0e-7)
+            && relative_eq!((ii * i) * v, v, epsilon = 1.0e-7)
     }
 
-    fn inverse_is_parts_inversion(t: Translation3<f64>, r: UnitQuaternion<f64>, scaling: f64) -> bool {
+    fn inverse_is_parts_inversion(
+        t: Translation3<f64>,
+        r: UnitQuaternion<f64>,
+        scaling: f64,
+    ) -> bool
+    {
         if relative_eq!(scaling, 0.0) {
             true
-        }
+        } else {
-        else {
             let s = Similarity3::from_isometry(t * r, scaling);
             s.inverse() == Similarity3::from_scaling(1.0 / scaling) * r.inverse() * t.inverse()
         }
     }
 
-    fn multiply_equals_alga_transform(s: Similarity3<f64>, v: Vector3<f64>, p: Point3<f64>) -> bool {
+    fn multiply_equals_alga_transform(
-        s * v == s.transform_vector(&v) &&
+        s: Similarity3<f64>,
-        s * p == s.transform_point(&p)  &&
+        v: Vector3<f64>,
-        relative_eq!(s.inverse() * v, s.inverse_transform_vector(&v), epsilon = 1.0e-7) &&
+        p: Point3<f64>,
-        relative_eq!(s.inverse() * p, s.inverse_transform_point(&p), epsilon = 1.0e-7)
+    ) -> bool
+    {
+        s * v == s.transform_vector(&v)
+            && s * p == s.transform_point(&p)
+            && relative_eq!(
+                s.inverse() * v,
+                s.inverse_transform_vector(&v),
+                epsilon = 1.0e-7
+            )
+            && relative_eq!(
+                s.inverse() * p,
+                s.inverse_transform_point(&p),
+                epsilon = 1.0e-7
+            )
     }
 
-    fn composition(i: Isometry3<f64>, uq: UnitQuaternion<f64>,
+    fn composition(
-                   t: Translation3<f64>, v: Vector3<f64>, p: Point3<f64>, scaling: f64) -> bool {
+        i: Isometry3<f64>,
+        uq: UnitQuaternion<f64>,
+        t: Translation3<f64>,
+        v: Vector3<f64>,
+        p: Point3<f64>,
+        scaling: f64,
+    ) -> bool
+    {
         if relative_eq!(scaling, 0.0) {
             return true;
         }
@@ -122,11 +146,18 @@ quickcheck!(
         relative_eq!((s * i * t) * p, scaling * (i * (t * p)), epsilon = 1.0e-7)
     }
 
-    fn all_op_exist(s: Similarity3<f64>, i: Isometry3<f64>, uq: UnitQuaternion<f64>,
+    fn all_op_exist(
-                    t: Translation3<f64>, v: Vector3<f64>, p: Point3<f64>) -> bool {
+        s: Similarity3<f64>,
-        let sMs  = s * s;
+        i: Isometry3<f64>,
+        uq: UnitQuaternion<f64>,
+        t: Translation3<f64>,
+        v: Vector3<f64>,
+        p: Point3<f64>,
+    ) -> bool
+    {
+        let sMs = s * s;
         let sMuq = s * uq;
-        let sDs  = s / s;
+        let sDs = s / s;
         let sDuq = s / uq;
 
         let sMp = s * p;
@@ -186,81 +217,61 @@ quickcheck!(
         sDi1 /= i;
         sDi2 /= &i;
 
-        sMt == sMt1 &&
+        sMt == sMt1
-        sMt == sMt2 &&
+            && sMt == sMt2
-
+            && sMs == sMs1
-        sMs == sMs1 &&
+            && sMs == sMs2
-        sMs == sMs2 &&
+            && sMuq == sMuq1
-
+            && sMuq == sMuq2
-        sMuq == sMuq1 &&
+            && sMi == sMi1
-        sMuq == sMuq2 &&
+            && sMi == sMi2
-
+            && sDs == sDs1
-        sMi == sMi1 &&
+            && sDs == sDs2
-        sMi == sMi2 &&
+            && sDuq == sDuq1
-
+            && sDuq == sDuq2
-        sDs == sDs1 &&
+            && sDi == sDi1
-        sDs == sDs2 &&
+            && sDi == sDi2
-
+            && sMs == &s * &s
-        sDuq == sDuq1 &&
+            && sMs == s * &s
-        sDuq == sDuq2 &&
+            && sMs == &s * s
-
+            && sMuq == &s * &uq
-        sDi == sDi1 &&
+            && sMuq == s * &uq
-        sDi == sDi2 &&
+            && sMuq == &s * uq
-
+            && sDs == &s / &s
-        sMs == &s * &s &&
+            && sDs == s / &s
-        sMs ==  s * &s &&
+            && sDs == &s / s
-        sMs == &s *  s &&
+            && sDuq == &s / &uq
-
+            && sDuq == s / &uq
-        sMuq == &s * &uq &&
+            && sDuq == &s / uq
-        sMuq ==  s * &uq &&
+            && sMp == &s * &p
-        sMuq == &s *  uq &&
+            && sMp == s * &p
-
+            && sMp == &s * p
-        sDs == &s / &s &&
+            && sMv == &s * &v
-        sDs ==  s / &s &&
+            && sMv == s * &v
-        sDs == &s /  s &&
+            && sMv == &s * v
-
+            && sMt == &s * &t
-        sDuq == &s / &uq &&
+            && sMt == s * &t
-        sDuq ==  s / &uq &&
+            && sMt == &s * t
-        sDuq == &s /  uq &&
+            && tMs == &t * &s
-
+            && tMs == t * &s
-        sMp == &s * &p &&
+            && tMs == &t * s
-        sMp ==  s * &p &&
+            && uqMs == &uq * &s
-        sMp == &s *  p &&
+            && uqMs == uq * &s
-
+            && uqMs == &uq * s
-        sMv == &s * &v &&
+            && uqDs == &uq / &s
-        sMv ==  s * &v &&
+            && uqDs == uq / &s
-        sMv == &s *  v &&
+            && uqDs == &uq / s
-
+            && sMi == &s * &i
-        sMt == &s * &t &&
+            && sMi == s * &i
-        sMt ==  s * &t &&
+            && sMi == &s * i
-        sMt == &s *  t &&
+            && sDi == &s / &i
-
+            && sDi == s / &i
-        tMs == &t * &s &&
+            && sDi == &s / i
-        tMs ==  t * &s &&
+            && iMs == &i * &s
-        tMs == &t *  s &&
+            && iMs == i * &s
-
+            && iMs == &i * s
-        uqMs == &uq * &s &&
+            && iDs == &i / &s
-        uqMs ==  uq * &s &&
+            && iDs == i / &s
-        uqMs == &uq *  s &&
+            && iDs == &i / s
-
-        uqDs == &uq / &s &&
-        uqDs ==  uq / &s &&
-        uqDs == &uq /  s &&
-
-        sMi == &s * &i &&
-        sMi ==  s * &i &&
-        sMi == &s *  i &&
-
-        sDi == &s / &i &&
-        sDi ==  s / &i &&
-        sDi == &s /  i &&
-
-        iMs == &i * &s &&
-        iMs ==  i * &s &&
-        iMs == &i *  s &&
-
-        iDs == &i / &s &&
-        iDs ==  i / &s &&
-        iDs == &i /  s
     }
 );

tests/geometry/unit_complex.rs

@@ -4,19 +4,17 @@
 use na::{Point2, Rotation2, Unit, UnitComplex, Vector2};
 
 quickcheck!(
-
     /*
      *
      * From/to rotation matrix.
      *
      */
     fn unit_complex_rotation_conversion(c: UnitComplex<f64>) -> bool {
-        let r  = c.to_rotation_matrix();
+        let r = c.to_rotation_matrix();
         let cc = UnitComplex::from_rotation_matrix(&r);
         let rr = cc.to_rotation_matrix();
 
-        relative_eq!(c, cc, epsilon = 1.0e-7) &&
+        relative_eq!(c, cc, epsilon = 1.0e-7) && relative_eq!(r, rr, epsilon = 1.0e-7)
-        relative_eq!(r, rr, epsilon = 1.0e-7)
     }
 
     /*
@@ -25,19 +23,18 @@ quickcheck!(
      *
      */
     fn unit_complex_transformation(c: UnitComplex<f64>, v: Vector2<f64>, p: Point2<f64>) -> bool {
-        let r  = c.to_rotation_matrix();
+        let r = c.to_rotation_matrix();
         let rv = r * v;
         let rp = r * p;
 
-        relative_eq!( c *  v, rv, epsilon = 1.0e-7) &&
+        relative_eq!(c * v, rv, epsilon = 1.0e-7)
-        relative_eq!( c * &v, rv, epsilon = 1.0e-7) &&
+            && relative_eq!(c * &v, rv, epsilon = 1.0e-7)
-        relative_eq!(&c *  v, rv, epsilon = 1.0e-7) &&
+            && relative_eq!(&c * v, rv, epsilon = 1.0e-7)
-        relative_eq!(&c * &v, rv, epsilon = 1.0e-7) &&
+            && relative_eq!(&c * &v, rv, epsilon = 1.0e-7)
-
+            && relative_eq!(c * p, rp, epsilon = 1.0e-7)
-        relative_eq!( c *  p, rp, epsilon = 1.0e-7) &&
+            && relative_eq!(c * &p, rp, epsilon = 1.0e-7)
-        relative_eq!( c * &p, rp, epsilon = 1.0e-7) &&
+            && relative_eq!(&c * p, rp, epsilon = 1.0e-7)
-        relative_eq!(&c *  p, rp, epsilon = 1.0e-7) &&
+            && relative_eq!(&c * &p, rp, epsilon = 1.0e-7)
-        relative_eq!(&c * &p, rp, epsilon = 1.0e-7)
     }
 
     /*
@@ -47,15 +44,14 @@ quickcheck!(
      */
     fn unit_complex_inv(c: UnitComplex<f64>) -> bool {
         let iq = c.inverse();
-        relative_eq!(&iq * &c, UnitComplex::identity(), epsilon = 1.0e-7) &&
+        relative_eq!(&iq * &c, UnitComplex::identity(), epsilon = 1.0e-7)
-        relative_eq!( iq * &c, UnitComplex::identity(), epsilon = 1.0e-7) &&
+            && relative_eq!(iq * &c, UnitComplex::identity(), epsilon = 1.0e-7)
-        relative_eq!(&iq *  c, UnitComplex::identity(), epsilon = 1.0e-7) &&
+            && relative_eq!(&iq * c, UnitComplex::identity(), epsilon = 1.0e-7)
-        relative_eq!( iq *  c, UnitComplex::identity(), epsilon = 1.0e-7) &&
+            && relative_eq!(iq * c, UnitComplex::identity(), epsilon = 1.0e-7)
-
+            && relative_eq!(&c * &iq, UnitComplex::identity(), epsilon = 1.0e-7)
-        relative_eq!(&c * &iq, UnitComplex::identity(), epsilon = 1.0e-7) &&
+            && relative_eq!(c * &iq, UnitComplex::identity(), epsilon = 1.0e-7)
-        relative_eq!( c * &iq, UnitComplex::identity(), epsilon = 1.0e-7) &&
+            && relative_eq!(&c * iq, UnitComplex::identity(), epsilon = 1.0e-7)
-        relative_eq!(&c *  iq, UnitComplex::identity(), epsilon = 1.0e-7) &&
+            && relative_eq!(c * iq, UnitComplex::identity(), epsilon = 1.0e-7)
-        relative_eq!( c *  iq, UnitComplex::identity(), epsilon = 1.0e-7)
     }
 
     /*
@@ -66,25 +62,30 @@ quickcheck!(
     fn unit_complex_mul_vector(c: UnitComplex<f64>, v: Vector2<f64>, p: Point2<f64>) -> bool {
         let r = c.to_rotation_matrix();
 
-        relative_eq!(c * v, r * v, epsilon = 1.0e-7) &&
+        relative_eq!(c * v, r * v, epsilon = 1.0e-7) && relative_eq!(c * p, r * p, epsilon = 1.0e-7)
-        relative_eq!(c * p, r * p, epsilon = 1.0e-7)
     }
 
     // Test that all operators (incl. all combinations of references) work.
     // See the top comment on `geometry/quaternion_ops.rs` for details on which operations are
     // supported.
-    fn all_op_exist(uc: UnitComplex<f64>, v: Vector2<f64>, p: Point2<f64>, r: Rotation2<f64>) -> bool {
+    fn all_op_exist(
+        uc: UnitComplex<f64>,
+        v: Vector2<f64>,
+        p: Point2<f64>,
+        r: Rotation2<f64>,
+    ) -> bool
+    {
         let uv = Unit::new_normalize(v);
 
         let ucMuc = uc * uc;
-        let ucMr  = uc * r;
+        let ucMr = uc * r;
-        let rMuc  = r  * uc;
+        let rMuc = r * uc;
         let ucDuc = uc / uc;
-        let ucDr  = uc / r;
+        let ucDr = uc / r;
-        let rDuc  = r / uc;
+        let rDuc = r / uc;
 
-        let ucMp  = uc * p;
+        let ucMp = uc * p;
-        let ucMv  = uc * v;
+        let ucMv = uc * v;
         let ucMuv = uc * uv;
 
         let mut ucMuc1 = uc;
@@ -111,52 +112,40 @@ quickcheck!(
         ucDr1 /= r;
         ucDr2 /= &r;
 
-        ucMuc1 == ucMuc  &&
+        ucMuc1 == ucMuc
-        ucMuc1 == ucMuc2 &&
+            && ucMuc1 == ucMuc2
-
+            && ucMr1 == ucMr
-        ucMr1  == ucMr   &&
+            && ucMr1 == ucMr2
-        ucMr1  == ucMr2  &&
+            && ucDuc1 == ucDuc
-
+            && ucDuc1 == ucDuc2
-        ucDuc1 == ucDuc  &&
+            && ucDr1 == ucDr
-        ucDuc1 == ucDuc2 &&
+            && ucDr1 == ucDr2
-
+            && ucMuc == &uc * &uc
-        ucDr1  == ucDr   &&
+            && ucMuc == uc * &uc
-        ucDr1  == ucDr2  &&
+            && ucMuc == &uc * uc
-
+            && ucMr == &uc * &r
-        ucMuc == &uc * &uc &&
+            && ucMr == uc * &r
-        ucMuc ==  uc * &uc &&
+            && ucMr == &uc * r
-        ucMuc == &uc *  uc &&
+            && rMuc == &r * &uc
-
+            && rMuc == r * &uc
-        ucMr == &uc * &r &&
+            && rMuc == &r * uc
-        ucMr ==  uc * &r &&
+            && ucDuc == &uc / &uc
-        ucMr == &uc *  r &&
+            && ucDuc == uc / &uc
-
+            && ucDuc == &uc / uc
-        rMuc == &r * &uc &&
+            && ucDr == &uc / &r
-        rMuc ==  r * &uc &&
+            && ucDr == uc / &r
-        rMuc == &r *  uc &&
+            && ucDr == &uc / r
-
+            && rDuc == &r / &uc
-        ucDuc == &uc / &uc &&
+            && rDuc == r / &uc
-        ucDuc ==  uc / &uc &&
+            && rDuc == &r / uc
-        ucDuc == &uc /  uc &&
+            && ucMp == &uc * &p
-
+            && ucMp == uc * &p
-        ucDr == &uc / &r &&
+            && ucMp == &uc * p
-        ucDr ==  uc / &r &&
+            && ucMv == &uc * &v
-        ucDr == &uc /  r &&
+            && ucMv == uc * &v
-
+            && ucMv == &uc * v
-        rDuc == &r / &uc &&
+            && ucMuv == &uc * &uv
-        rDuc ==  r / &uc &&
+            && ucMuv == uc * &uv
-        rDuc == &r /  uc &&
+            && ucMuv == &uc * uv
-
-        ucMp == &uc * &p &&
-        ucMp ==  uc * &p &&
-        ucMp == &uc *  p &&
-
-        ucMv == &uc * &v &&
-        ucMv ==  uc * &v &&
-        ucMv == &uc *  v &&
-
-        ucMuv == &uc * &uv &&
-        ucMuv ==  uc * &uv &&
-        ucMuv == &uc *  uv
     }
 );

tests/lib.rs

@@ -16,3 +16,5 @@ extern crate serde_json;
 mod core;
 mod geometry;
 mod linalg;
+#[cfg(feature = "sparse")]
+mod sparse;

tests/linalg/eigen.rs

@@ -104,3 +104,89 @@ fn symmetric_eigen_singular_24x24() {
         epsilon = 1.0e-5
     ));
 }
+
+//  #[cfg(feature = "arbitrary")]
+//  quickcheck! {
+// FIXME: full eigendecomposition is not implemented yet because of its complexity when some
+// eigenvalues have multiplicity > 1.
+//
+//    /*
+//     * NOTE: for the following tests, we use only upper-triangular matrices.
+//     * Thes ensures the schur decomposition will work, and allows use to test the eigenvector
+//     * computation.
+//     */
+//    fn eigen(n: usize) -> bool {
+//        let n = cmp::max(1, cmp::min(n, 10));
+//        let m = DMatrix::<f64>::new_random(n, n).upper_triangle();
+//
+//        let eig = RealEigen::new(m.clone()).unwrap();
+//        verify_eigenvectors(m, eig)
+//    }
+//
+//    fn eigen_with_adjascent_duplicate_diagonals(n: usize) -> bool {
+//        let n = cmp::max(1, cmp::min(n, 10));
+//        let mut m = DMatrix::<f64>::new_random(n, n).upper_triangle();
+//
+//        // Suplicate some adjascent diagonal elements.
+//        for i in 0 .. n / 2 {
+//            m[(i * 2 + 1, i * 2 + 1)] = m[(i * 2, i * 2)];
+//        }
+//
+//        let eig = RealEigen::new(m.clone()).unwrap();
+//        verify_eigenvectors(m, eig)
+//    }
+//
+//    fn eigen_with_nonadjascent_duplicate_diagonals(n: usize) -> bool {
+//        let n = cmp::max(3, cmp::min(n, 10));
+//        let mut m = DMatrix::<f64>::new_random(n, n).upper_triangle();
+//
+//        // Suplicate some diagonal elements.
+//        for i in n / 2 .. n {
+//            m[(i, i)] = m[(i - n / 2, i - n / 2)];
+//        }
+//
+//        let eig = RealEigen::new(m.clone()).unwrap();
+//        verify_eigenvectors(m, eig)
+//    }
+//
+//    fn eigen_static_square_4x4(m: Matrix4<f64>) -> bool {
+//        let m = m.upper_triangle();
+//        let eig = RealEigen::new(m.clone()).unwrap();
+//        verify_eigenvectors(m, eig)
+//    }
+//
+//    fn eigen_static_square_3x3(m: Matrix3<f64>) -> bool {
+//        let m = m.upper_triangle();
+//        let eig = RealEigen::new(m.clone()).unwrap();
+//        verify_eigenvectors(m, eig)
+//    }
+//
+//    fn eigen_static_square_2x2(m: Matrix2<f64>) -> bool {
+//        let m = m.upper_triangle();
+//        println!("{}", m);
+//        let eig = RealEigen::new(m.clone()).unwrap();
+//        verify_eigenvectors(m, eig)
+//    }
+//  }
+//
+// fn verify_eigenvectors<D: Dim>(m: MatrixN<f64, D>, mut eig: RealEigen<f64, D>) -> bool
+//     where DefaultAllocator: Allocator<f64, D, D>   +
+//                             Allocator<f64, D>      +
+//                             Allocator<usize, D, D> +
+//                             Allocator<usize, D>,
+//           MatrixN<f64, D>: Display,
+//           VectorN<f64, D>: Display {
+//     let mv = &m * &eig.eigenvectors;
+//
+//     println!("eigenvalues: {}eigenvectors: {}", eig.eigenvalues, eig.eigenvectors);
+//
+//     let dim = m.nrows();
+//     for i in 0 .. dim {
+//         let mut col = eig.eigenvectors.column_mut(i);
+//         col *= eig.eigenvalues[i];
+//     }
+//
+//     println!("{}{:.5}{:.5}", m, mv, eig.eigenvectors);
+//
+//     relative_eq!(eig.eigenvectors, mv, epsilon = 1.0e-5)
+// }

tests/linalg/svd.rs

@@ -3,8 +3,10 @@ use na::{DMatrix, Matrix6};
 
 #[cfg(feature = "arbitrary")]
 mod quickcheck_tests {
+    use na::{
+        DMatrix, DVector, Matrix2, Matrix2x5, Matrix3, Matrix3x5, Matrix4, Matrix5x2, Matrix5x3,
+    };
     use std::cmp;
-    use na::{DMatrix, Matrix2, Matrix3, Matrix4, Matrix5x2, Matrix5x3, Matrix2x5, Matrix3x5, DVector};
 
     quickcheck! {
         fn svd(m: DMatrix<f64>) -> bool {
@@ -258,7 +260,6 @@ fn svd_singular_horizontal() {
     assert!(relative_eq!(m, &u * ds * &v_t, epsilon = 1.0e-5));
 }
 
-
 #[test]
 fn svd_zeros() {
     let m = DMatrix::from_element(10, 10, 0.0);

tests/sparse/cs_cholesky.rs

@@ -0,0 +1,75 @@
+#![cfg_attr(rustfmt, rustfmt_skip)]
+
+use na::{CsMatrix, CsVector, CsCholesky, Cholesky, Matrix5, Vector5};
+
+#[test]
+fn cs_cholesky() {
+    let mut a = Matrix5::new(
+        40.0, 0.0, 0.0, 0.0, 0.0,
+        2.0, 60.0, 0.0, 0.0, 0.0,
+        1.0, 0.0, 11.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 50.0, 0.0,
+        1.0, 0.0, 0.0, 4.0, 10.0
+    );
+    a.fill_upper_triangle_with_lower_triangle();
+    test_cholesky(a);
+
+    let a = Matrix5::from_diagonal(&Vector5::new(40.0, 60.0, 11.0, 50.0, 10.0));
+    test_cholesky(a);
+
+    let mut a = Matrix5::new(
+        40.0, 0.0, 0.0, 0.0, 0.0,
+        2.0, 60.0, 0.0, 0.0, 0.0,
+        1.0, 0.0, 11.0, 0.0, 0.0,
+        1.0, 0.0, 0.0, 50.0, 0.0,
+        0.0, 0.0, 0.0, 4.0, 10.0
+    );
+    a.fill_upper_triangle_with_lower_triangle();
+    test_cholesky(a);
+
+    let mut a = Matrix5::new(
+        2.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 2.0, 0.0, 0.0, 0.0,
+        1.0, 1.0, 2.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 2.0, 0.0,
+        1.0, 1.0, 0.0, 0.0, 2.0
+    );
+    a.fill_upper_triangle_with_lower_triangle();
+    // Test ::new, left_looking, and up_looking implementations.
+    test_cholesky(a);
+}
+
+fn test_cholesky(a: Matrix5<f32>) {
+    // Test ::new
+    test_cholesky_variant(a, 0);
+    // Test up-looking
+    test_cholesky_variant(a, 1);
+    // Test left-looking
+    test_cholesky_variant(a, 2);
+}
+
+fn test_cholesky_variant(a: Matrix5<f32>, option: usize) {
+    let cs_a: CsMatrix<_, _, _> = a.into();
+
+    let chol_a = Cholesky::new(a).unwrap();
+    let mut chol_cs_a;
+
+    match option {
+        0 => chol_cs_a = CsCholesky::new(&cs_a),
+        1 => {
+            chol_cs_a = CsCholesky::new_symbolic(&cs_a);
+            chol_cs_a.decompose_up_looking(cs_a.data.values());
+        }
+        _ => {
+            chol_cs_a = CsCholesky::new_symbolic(&cs_a);
+            chol_cs_a.decompose_left_looking(cs_a.data.values());
+        }
+    };
+
+    let l = chol_a.l();
+    let cs_l = chol_cs_a.unwrap_l().unwrap();
+    assert!(cs_l.is_sorted());
+
+    let cs_l_mat: Matrix5<_> = cs_l.into();
+    assert_relative_eq!(l, cs_l_mat);
+}

tests/sparse/cs_construction.rs

@@ -0,0 +1 @@
+

tests/sparse/cs_conversion.rs

@@ -0,0 +1,89 @@
+use na::{CsMatrix, DMatrix, Matrix4x5};
+
+#[test]
+fn cs_from_to_matrix() {
+    #[cfg_attr(rustfmt, rustfmt_skip)]
+    let m = Matrix4x5::new(
+        5.0, 6.0, 0.0, 8.0, 15.0,
+        9.0, 10.0, 11.0, 12.0, 0.0,
+        0.0, 0.0, 13.0, 0.0, 0.0,
+        0.0, 1.0, 4.0, 0.0, 14.0,
+    );
+
+    let cs: CsMatrix<_, _, _> = m.into();
+    assert!(cs.is_sorted());
+
+    let m2: Matrix4x5<_> = cs.into();
+    assert_eq!(m2, m);
+}
+
+#[test]
+fn cs_matrix_from_triplet() {
+    let mut irows = vec![0, 0, 0, 0, 1, 1, 1, 1, 2, 3, 3, 3];
+    let mut icols = vec![0, 1, 3, 4, 0, 1, 2, 3, 2, 1, 2, 4];
+    let mut vals = vec![
+        5.0, 6.0, 8.0, 15.0, 9.0, 10.0, 11.0, 12.0, 13.0, 1.0, 4.0, 14.0,
+    ];
+
+    #[cfg_attr(rustfmt, rustfmt_skip)]
+    let expected = DMatrix::from_row_slice(4, 5, &[
+        5.0, 6.0, 0.0, 8.0, 15.0,
+        9.0, 10.0, 11.0, 12.0, 0.0,
+        0.0, 0.0, 13.0, 0.0, 0.0,
+        0.0, 1.0, 4.0, 0.0, 14.0,
+    ]);
+    let cs_expected = CsMatrix::from_parts(
+        4,
+        5,
+        vec![0, 2, 5, 8, 10],
+        vec![0, 1, 0, 1, 3, 1, 2, 3, 0, 1, 0, 3],
+        vec![
+            5.0, 9.0, 6.0, 10.0, 1.0, 11.0, 13.0, 4.0, 8.0, 12.0, 15.0, 14.0,
+        ],
+    );
+
+    let cs_mat = CsMatrix::from_triplet(4, 5, &irows, &icols, &vals);
+    println!("Mat from triplet: {:?}", cs_mat);
+    assert!(cs_mat.is_sorted());
+    assert_eq!(cs_mat, cs_expected);
+
+    let m: DMatrix<_> = cs_mat.into();
+    assert_eq!(m, expected);
+
+    /*
+     * Try again with some permutations.
+     */
+    let permutations = [(2, 5), (0, 4), (8, 10), (1, 11)];
+
+    for (i, j) in &permutations {
+        irows.swap(*i, *j);
+        icols.swap(*i, *j);
+        vals.swap(*i, *j);
+    }
+
+    let cs_mat = CsMatrix::from_triplet(4, 5, &irows, &icols, &vals);
+    println!("Mat from triplet: {:?}", cs_mat);
+    assert!(cs_mat.is_sorted());
+    assert_eq!(cs_mat, cs_expected);
+
+    let m: DMatrix<_> = cs_mat.into();
+    assert_eq!(m, expected);
+
+    /*
+     * Try again, duplicating all entries.
+     */
+    let mut ir = irows.clone();
+    let mut ic = icols.clone();
+    let mut va = vals.clone();
+    irows.append(&mut ir);
+    icols.append(&mut ic);
+    vals.append(&mut va);
+
+    let cs_mat = CsMatrix::from_triplet(4, 5, &irows, &icols, &vals);
+    println!("Mat from triplet: {:?}", cs_mat);
+    assert!(cs_mat.is_sorted());
+    assert_eq!(cs_mat, cs_expected * 2.0);
+
+    let m: DMatrix<_> = cs_mat.into();
+    assert_eq!(m, expected * 2.0);
+}

tests/sparse/cs_matrix.rs

@@ -0,0 +1,22 @@
+#![cfg_attr(rustfmt, rustfmt_skip)]
+
+use na::{Matrix4x5, Matrix5x4, CsMatrix};
+
+#[test]
+fn cs_transpose() {
+    let m = Matrix4x5::new(
+        4.0, 1.0, 4.0, 0.0, 9.0,
+        5.0, 6.0, 0.0, 8.0, 10.0,
+        9.0, 10.0, 11.0, 12.0, 0.0,
+        0.0, 0.0, 1.0, 0.0, 10.0
+    );
+
+    let cs: CsMatrix<_, _, _> = m.into();
+    assert!(cs.is_sorted());
+
+    let cs_transposed = cs.transpose();
+    assert!(cs_transposed.is_sorted());
+
+    let cs_transposed_mat: Matrix5x4<_> = cs_transposed.into();
+    assert_eq!(cs_transposed_mat, m.transpose())
+}

tests/sparse/cs_matrix_market.rs

@@ -0,0 +1,55 @@
+#![cfg_attr(rustfmt, rustfmt_skip)]
+
+
+use na::io;
+use na::DMatrix;
+
+#[test]
+fn cs_matrix_market() {
+    let file_str = r#"
+  %%MatrixMarket matrix coordinate real general
+%=================================================================================
+%
+% This ASCII file represents a sparse MxN matrix with L
+% nonzeros in the following Matrix Market format:
+%
+% +----------------------------------------------+
+% |%%MatrixMarket matrix coordinate real general | <--- header line
+% |%                                             | <--+
+% |% comments                                    |    |-- 0 or more comment lines
+% |%                                             | <--+
+% |    M  N  L                                   | <--- rows, columns, entries
+% |    I1  J1  A(I1, J1)                         | <--+
+% |    I2  J2  A(I2, J2)                         |    |
+% |    I3  J3  A(I3, J3)                         |    |-- L lines
+% |        . . .                                 |    |
+% |    IL JL  A(IL, JL)                          | <--+
+% +----------------------------------------------+
+%
+% Indices are 1-based, i.e. A(1,1) is the first element.
+%
+%=================================================================================
+  5  5  8
+    1     1   1.000e+00
+    2     2   1.050e+01
+    3     3   1.500e-02
+    1     4   6.000e+00
+    4     2   2.505e+02
+    4     4  -2.800e+02
+    4     5   3.332e+01
+    5     5   1.200e+01
+"#;
+
+    let cs_mat = io::cs_matrix_from_matrix_market_str(file_str).unwrap();
+    println!("CS mat: {:?}", cs_mat);
+    let mat: DMatrix<_> = cs_mat.into();
+    let expected = DMatrix::from_row_slice(5, 5, &[
+        1.0, 0.0,   0.0,   6.0,    0.0,
+        0.0, 10.5,  0.0,   0.0,    0.0,
+        0.0, 0.0,   0.015, 0.0,    0.0,
+        0.0, 250.5, 0.0,   -280.0, 33.32,
+        0.0, 0.0,   0.0,   0.0,    12.0,
+    ]);
+
+    assert_eq!(mat, expected);
+}

tests/sparse/cs_ops.rs

@@ -0,0 +1,72 @@
+#![cfg_attr(rustfmt, rustfmt_skip)]
+
+
+use na::{Matrix3x4, Matrix4x5, Matrix3x5, CsMatrix, Vector5, CsVector};
+
+#[test]
+fn axpy_cs() {
+    let mut v1 = Vector5::new(1.0, 2.0, 3.0, 4.0, 5.0);
+    let v2 = Vector5::new(10.0, 0.0, 30.0, 0.0, 50.0);
+    let expected = 5.0 * v2 + 10.0 * v1;
+
+    let cs: CsVector<_, _> = v2.into();
+    v1.axpy_cs(5.0, &cs, 10.0);
+
+    assert!(cs.is_sorted());
+    assert_eq!(v1, expected)
+}
+
+
+#[test]
+fn cs_mat_mul() {
+    let m1 = Matrix3x4::new(
+        0.0, 1.0, 4.0, 0.0,
+        5.0, 6.0, 0.0, 8.0,
+        9.0, 10.0, 11.0, 12.0,
+    );
+
+    let m2 = Matrix4x5::new(
+        5.0, 6.0, 0.0, 8.0, 15.0,
+        9.0, 10.0, 11.0, 12.0, 0.0,
+        0.0, 0.0, 13.0, 0.0, 0.0,
+        0.0, 1.0, 4.0, 0.0, 14.0,
+    );
+
+    let sm1: CsMatrix<_, _, _> = m1.into();
+    let sm2: CsMatrix<_, _, _> = m2.into();
+
+    let mul = &sm1 * &sm2;
+
+    assert!(sm1.is_sorted());
+    assert!(sm2.is_sorted());
+    assert!(mul.is_sorted());
+    assert_eq!(Matrix3x5::from(mul), m1 * m2);
+}
+
+
+#[test]
+fn cs_mat_add() {
+    let m1 = Matrix4x5::new(
+        4.0, 1.0, 4.0, 0.0, 0.0,
+        5.0, 6.0, 0.0, 8.0, 0.0,
+        9.0, 10.0, 11.0, 12.0, 0.0,
+        0.0, 0.0, 1.0, 0.0, 10.0
+    );
+
+    let m2 = Matrix4x5::new(
+        0.0, 1.0, 4.0, 0.0, 14.0,
+        5.0, 6.0, 0.0, 8.0, 15.0,
+        9.0, 10.0, 11.0, 12.0, 0.0,
+        0.0, 0.0, 13.0, 0.0, 0.0,
+    );
+
+    let sm1: CsMatrix<_, _, _> = m1.into();
+    let sm2: CsMatrix<_, _, _> = m2.into();
+
+    let sum = &sm1 + &sm2;
+
+    assert!(sm1.is_sorted());
+    assert!(sm2.is_sorted());
+    assert!(sum.is_sorted());
+    assert_eq!(Matrix4x5::from(sum), m1 + m2);
+}

tests/sparse/cs_solve.rs

@@ -0,0 +1,106 @@
+#![cfg_attr(rustfmt, rustfmt_skip)]
+
+use na::{CsMatrix, CsVector, Matrix5, Vector5};
+
+
+#[test]
+fn cs_lower_triangular_solve() {
+    let a = Matrix5::new(
+        4.0, 1.0,  4.0,  0.0,  9.0,
+        5.0, 6.0,  0.0,  8.0,  10.0,
+        9.0, 10.0, 11.0, 12.0, 0.0,
+        0.0, -8.0, 3.0,  5.0,  9.0,
+        0.0, 0.0,  1.0,  0.0,  -10.0
+    );
+    let b = Vector5::new(1.0, 2.0, 3.0, 4.0, 5.0);
+
+    let cs_a: CsMatrix<_, _, _> = a.into();
+
+    assert_eq!(cs_a.solve_lower_triangular(&b), a.solve_lower_triangular(&b));
+}
+
+#[test]
+fn cs_tr_lower_triangular_solve() {
+    let a = Matrix5::new(
+        4.0, 1.0,  4.0,  0.0,  9.0,
+        5.0, 6.0,  0.0,  8.0,  10.0,
+        9.0, 10.0, 11.0, 12.0, 0.0,
+        0.0, -8.0, 3.0,  5.0,  9.0,
+        0.0, 0.0,  1.0,  0.0,  -10.0
+    );
+    let b = Vector5::new(1.0, 2.0, 3.0, 4.0, 5.0);
+
+    let cs_a: CsMatrix<_, _, _> = a.into();
+
+    assert!(cs_a.tr_solve_lower_triangular(&b).is_some());
+    assert_eq!(cs_a.tr_solve_lower_triangular(&b), a.tr_solve_lower_triangular(&b));
+
+    // Singular case.
+    let a = Matrix5::new(
+        4.0, 1.0,  4.0, 0.0,  9.0,
+        5.0, 6.0,  0.0, 8.0,  10.0,
+        9.0, 10.0, 0.0, 12.0, 0.0,
+        0.0, -8.0, 3.0, 5.0,  9.0,
+        0.0, 0.0,  1.0, 0.0,  -10.0
+    );
+    let cs_a: CsMatrix<_, _, _> = a.into();
+
+    assert!(cs_a.tr_solve_lower_triangular(&b).is_none());
+}
+
+
+#[test]
+fn cs_lower_triangular_solve_cs() {
+    let a = Matrix5::new(
+        4.0, 1.0,  4.0,  0.0,  9.0,
+        5.0, 6.0,  0.0,  8.0,  10.0,
+        9.0, 10.0, 11.0, 12.0, 0.0,
+        0.0, -8.0, 3.0,  5.0,  9.0,
+        0.0, 0.0,  1.0,  0.0,  -10.0
+    );
+    let b1 = Vector5::zeros();
+    let b2 = Vector5::new(1.0, 2.0, 3.0, 4.0, 5.0);
+    let b3 = Vector5::new(1.0, 0.0, 0.0, 4.0, 0.0);
+    let b4 = Vector5::new(0.0, 1.0, 0.0, 4.0, 5.0);
+    let b5 = Vector5::x();
+    let b6 = Vector5::y();
+    let b7 = Vector5::z();
+    let b8 = Vector5::w();
+    let b9 = Vector5::a();
+
+    let cs_a: CsMatrix<_, _, _> = a.into();
+    let cs_b1: CsVector<_, _> = Vector5::zeros().into();
+    let cs_b2: CsVector<_, _> = Vector5::new(1.0, 2.0, 3.0, 4.0, 5.0).into();
+    let cs_b3: CsVector<_, _> = Vector5::new(1.0, 0.0, 0.0, 4.0, 0.0).into();
+    let cs_b4: CsVector<_, _> = Vector5::new(0.0, 1.0, 0.0, 4.0, 5.0).into();
+    let cs_b5: CsVector<_, _> = Vector5::x().into();
+    let cs_b6: CsVector<_, _> = Vector5::y().into();
+    let cs_b7: CsVector<_, _> = Vector5::z().into();
+    let cs_b8: CsVector<_, _> = Vector5::w().into();
+    let cs_b9: CsVector<_, _> = Vector5::a().into();
+
+    assert_eq!(cs_a.solve_lower_triangular_cs(&cs_b1).map(|v| { assert!(v.is_sorted()); v.into() }), a.solve_lower_triangular(&b1));
+    assert_eq!(cs_a.solve_lower_triangular_cs(&cs_b5).map(|v| { assert!(v.is_sorted()); v.into() }), a.solve_lower_triangular(&b5));
+    assert_eq!(cs_a.solve_lower_triangular_cs(&cs_b6).map(|v| { assert!(v.is_sorted()); v.into() }), a.solve_lower_triangular(&b6));
+    assert_eq!(cs_a.solve_lower_triangular_cs(&cs_b7).map(|v| { assert!(v.is_sorted()); v.into() }), a.solve_lower_triangular(&b7));
+    assert_eq!(cs_a.solve_lower_triangular_cs(&cs_b8).map(|v| { assert!(v.is_sorted()); v.into() }), a.solve_lower_triangular(&b8));
+    assert_eq!(cs_a.solve_lower_triangular_cs(&cs_b9).map(|v| { assert!(v.is_sorted()); v.into() }), a.solve_lower_triangular(&b9));
+    assert_eq!(cs_a.solve_lower_triangular_cs(&cs_b2).map(|v| { assert!(v.is_sorted()); v.into() }), a.solve_lower_triangular(&b2));
+    assert_eq!(cs_a.solve_lower_triangular_cs(&cs_b3).map(|v| { assert!(v.is_sorted()); v.into() }), a.solve_lower_triangular(&b3));
+    assert_eq!(cs_a.solve_lower_triangular_cs(&cs_b4).map(|v| { assert!(v.is_sorted()); v.into() }), a.solve_lower_triangular(&b4));
+
+
+    // Singular case.
+    let a = Matrix5::new(
+        4.0, 1.0,  4.0, 0.0,  9.0,
+        5.0, 0.0,  0.0, 8.0,  10.0,
+        9.0, 10.0, 0.0, 12.0, 0.0,
+        0.0, -8.0, 3.0, 5.0,  9.0,
+        0.0, 0.0,  1.0, 0.0,  -10.0
+    );
+    let cs_a: CsMatrix<_, _, _> = a.into();
+
+    assert!(cs_a.solve_lower_triangular_cs(&cs_b2).is_none());
+    assert!(cs_a.solve_lower_triangular_cs(&cs_b3).is_none());
+    assert!(cs_a.solve_lower_triangular_cs(&cs_b4).is_none());
+}