Add the types: DVec1, .., DVec6.

They are stack-allocated, dynamically sized vectors with a maximum size.
This is useful for slicing small matrices, without allocation.

Cargo.toml

@@ -3,6 +3,6 @@ name    = "nalgebra"
 version = "0.1.0"
 authors = [ "Sébastien Crozet <developer@crozet.re>" ] # FIXME: add the contributors.
 
-[[lib]]
+[lib]
 name = "nalgebra"
 path = "src/lib.rs"

src/linalg/decompositions.rs

@@ -34,11 +34,12 @@ pub fn householder_matrix<N: Float,
 ///
 /// # Arguments
 /// * `m` - matrix to decompose
-pub fn decomp_qr<N: Float,
+pub fn qr<N: Float,
-                 V: Indexable<uint, N> + Norm<N>,
+          V: Indexable<uint, N> + Norm<N>,
-                 M: Clone + Eye + ColSlice<V> + Transpose
+          M: Clone + Eye + ColSlice<V> + Transpose
-                    + Indexable<(uint, uint), N> + Mul<M, M>>
+              + Indexable<(uint, uint), N> + Mul<M, M>>
-                 (m: &M) -> (M, M) {
+          (m: &M) 
+          -> (M, M) {
     let (rows, cols) = m.shape();
     assert!(rows >= cols);
     let mut q : M = Eye::new_identity(rows);
@@ -67,4 +68,3 @@ pub fn decomp_qr<N: Float,
 
     (q, r)
 }
-

src/linalg/mod.rs

@@ -1,4 +1,4 @@
 
-pub use self::decompositions::{decomp_qr, householder_matrix};
+pub use self::decompositions::{qr, eigen_qr, householder_matrix};
 
 mod decompositions;

src/na.rs

@@ -48,7 +48,8 @@ pub use traits::{
 
 pub use structs::{
     Identity,
-    DMat, DVec,
+    DMat,
+    DVec, DVec1, DVec2,  DVec3,  DVec4,  DVec5,  DVec6,
     Iso2, Iso3, Iso4,
     Mat1, Mat2, Mat3, Mat4,
     Mat5, Mat6,
@@ -57,7 +58,8 @@ pub use structs::{
 };
 
 pub use linalg::{
-    decomp_qr,
+    qr,
+    eigen_qr,
     householder_matrix
 };
 

src/structs/dmat.rs

@@ -245,7 +245,7 @@ impl<N: Clone> Indexable<(uint, uint), N> for DMat<N> {
     #[inline]
     unsafe fn unsafe_at(&self, rowcol: (uint,  uint)) -> N {
         let (row, col) = rowcol;
-        (*self.mij.as_slice().unsafe_ref(self.offset(row, col))).clone()
+        (*self.mij.as_slice().unsafe_get(self.offset(row, col))).clone()
     }
 
     #[inline]
@@ -524,7 +524,7 @@ impl<N: Clone> ColSlice<DVec<N>> for DMat<N> {
         // we can init from slice thanks to the matrix being column major
         let start= self.offset(row_start, col_id);
         let stop = self.offset(row_end, col_id);
-        let slice = DVec::from_vec(
+        let slice = DVec::from_slice(
             row_end - row_start, self.mij.slice(start, stop));
         slice
     }

src/structs/dvec.rs

@@ -11,97 +11,13 @@ use std::iter::FromIterator;
 use traits::geometry::{Dot, Norm};
 use traits::structure::{Iterable, IterableMut, Indexable};
 
-/// Vector with a dimension unknown at compile-time.
+/// Heap allocated, dynamically sized vector.
 #[deriving(Eq, PartialEq, Show, Clone)]
 pub struct DVec<N> {
     /// Components of the vector. Contains as much elements as the vector dimension.
     pub at: Vec<N>
 }
 
-double_dispatch_binop_decl_trait!(DVec, DVecMulRhs)
-double_dispatch_binop_decl_trait!(DVec, DVecDivRhs)
-double_dispatch_binop_decl_trait!(DVec, DVecAddRhs)
-double_dispatch_binop_decl_trait!(DVec, DVecSubRhs)
-
-mul_redispatch_impl!(DVec, DVecMulRhs)
-div_redispatch_impl!(DVec, DVecDivRhs)
-add_redispatch_impl!(DVec, DVecAddRhs)
-sub_redispatch_impl!(DVec, DVecSubRhs)
-
-impl<N: Zero + Clone> DVec<N> {
-    /// Builds a vector filled with zeros.
-    ///
-    /// # Arguments
-    /// * `dim` - The dimension of the vector.
-    #[inline]
-    pub fn new_zeros(dim: uint) -> DVec<N> {
-        DVec::from_elem(dim, Zero::zero())
-    }
-
-    /// Tests if all components of the vector are zeroes.
-    #[inline]
-    pub fn is_zero(&self) -> bool {
-        self.at.iter().all(|e| e.is_zero())
-    }
-}
-
-impl<N: Clone> Indexable<uint, N> for DVec<N> {
-
-    fn at(&self, i: uint) -> N {
-        assert!(i < self.at.len());
-        unsafe {
-            self.unsafe_at(i)
-        }
-    }
-
-    fn set(&mut self, i: uint, val: N) {
-        assert!(i < self.at.len());
-        unsafe {
-            self.unsafe_set(i, val);
-        }
-    }
-
-    fn swap(&mut self, i: uint, j: uint) {
-        assert!(i < self.at.len());
-        assert!(j < self.at.len());
-        self.at.as_mut_slice().swap(i, j);
-    }
-
-    fn shape(&self) -> uint {
-        self.at.len()
-    }
-
-    #[inline]
-    unsafe fn unsafe_at(&self, i: uint) -> N {
-        (*self.at.as_slice().unsafe_ref(i)).clone()
-    }
-
-    #[inline]
-    unsafe fn unsafe_set(&mut self, i: uint, val: N) {
-        *self.at.as_mut_slice().unsafe_mut_ref(i) = val
-    }
-
-}
-
-impl<N: One + Clone> DVec<N> {
-    /// Builds a vector filled with ones.
-    ///
-    /// # Arguments
-    /// * `dim` - The dimension of the vector.
-    #[inline]
-    pub fn new_ones(dim: uint) -> DVec<N> {
-        DVec::from_elem(dim, One::one())
-    }
-}
-
-impl<N: Rand> DVec<N> {
-    /// Builds a vector filled with random values.
-    #[inline]
-    pub fn new_random(dim: uint) -> DVec<N> {
-        DVec::from_fn(dim, |_| rand::random())
-    }
-}
-
 impl<N> DVec<N> {
     /// Creates an uninitialized vec.
     #[inline]
@@ -113,24 +29,6 @@ impl<N> DVec<N> {
             at: vec
         }
     }
-
-    /// Gets a reference to of this vector data.
-    #[inline]
-    pub fn as_vec<'r>(&'r self) -> &'r [N] {
-        self.at.as_slice()
-    }
-
-    /// Gets a mutable reference to of this vector data.
-    #[inline]
-    pub fn as_mut_vec<'r>(&'r mut self) -> &'r mut [N] {
-        self.at.as_mut_slice()
-    }
-
-    /// Extracts this vector data.
-    #[inline]
-    pub fn to_vec(self) -> Vec<N> {
-        self.at
-    }
 }
 
 impl<N: Clone> DVec<N> {
@@ -144,7 +42,7 @@ impl<N: Clone> DVec<N> {
     ///
     /// The vector must have at least `dim` elements.
     #[inline]
-    pub fn from_vec(dim: uint, vec: &[N]) -> DVec<N> {
+    pub fn from_slice(dim: uint, vec: &[N]) -> DVec<N> {
         assert!(dim <= vec.len());
 
         DVec {
@@ -161,27 +59,6 @@ impl<N> DVec<N> {
     }
 }
 
-impl<N> Collection for DVec<N> {
-    #[inline]
-    fn len(&self) -> uint {
-        self.at.len()
-    }
-}
-
-impl<N> Iterable<N> for DVec<N> {
-    #[inline]
-    fn iter<'l>(&'l self) -> Items<'l, N> {
-        self.at.iter()
-    }
-}
-
-impl<N> IterableMut<N> for DVec<N> {
-    #[inline]
-    fn mut_iter<'l>(&'l mut self) -> MutItems<'l, N> {
-        self.at.mut_iter()
-    }
-}
-
 impl<N> FromIterator<N> for DVec<N> {
     #[inline]
     fn from_iter<I: Iterator<N>>(mut param: I) -> DVec<N> {
@@ -195,258 +72,71 @@ impl<N> FromIterator<N> for DVec<N> {
     }
 }
 
-impl<N: Clone + Float + ApproxEq<N> + DVecMulRhs<N, DVec<N>>> DVec<N> {
-    /// Computes the canonical basis for the given dimension. A canonical basis is a set of
-    /// vectors, mutually orthogonal, with all its component equal to 0.0 except one which is equal
-    /// to 1.0.
-    pub fn canonical_basis_with_dim(dim: uint) -> Vec<DVec<N>> {
-        let mut res : Vec<DVec<N>> = Vec::new();
 
-        for i in range(0u, dim) {
+impl<N> Collection for DVec<N> {
-            let mut basis_element : DVec<N> = DVec::new_zeros(dim);
+    #[inline]
-
+    fn len(&self) -> uint {
-            *basis_element.at.get_mut(i) = One::one();
+        self.at.len()
-
-            res.push(basis_element);
-        }
-
-        res
-    }
-
-    /// Computes a basis of the space orthogonal to the vector. If the input vector is of dimension
-    /// `n`, this will return `n - 1` vectors.
-    pub fn orthogonal_subspace_basis(&self) -> Vec<DVec<N>> {
-        // compute the basis of the orthogonal subspace using Gram-Schmidt
-        // orthogonalization algorithm
-        let     dim                = self.at.len();
-        let mut res : Vec<DVec<N>> = Vec::new();
-
-        for i in range(0u, dim) {
-            let mut basis_element : DVec<N> = DVec::new_zeros(self.at.len());
-
-            *basis_element.at.get_mut(i) = One::one();
-
-            if res.len() == dim - 1 {
-                break;
-            }
-
-            let mut elt = basis_element.clone();
-
-            elt = elt - self * Dot::dot(&basis_element, self);
-
-            for v in res.iter() {
-                elt = elt - v * Dot::dot(&elt, v)
-            };
-
-            if !ApproxEq::approx_eq(&Norm::sqnorm(&elt), &Zero::zero()) {
-                res.push(Norm::normalize_cpy(&elt));
-            }
-        }
-
-        assert!(res.len() == dim - 1);
-
-        res
     }
 }
 
-impl<N: Add<N, N>> DVecAddRhs<N, DVec<N>> for DVec<N> {
+dvec_impl!(DVec, DVecMulRhs, DVecDivRhs, DVecAddRhs, DVecSubRhs)
-    #[inline]
+
-    fn binop(left: &DVec<N>, right: &DVec<N>) -> DVec<N> {
+/// Stack-allocated, dynamically sized vector with a maximum size of 1.
-        assert!(left.at.len() == right.at.len());
+pub struct DVec1<N> {
-        DVec {
+    at:  [N, ..1],
-            at: left.at.iter().zip(right.at.iter()).map(|(a, b)| *a + *b).collect()
+    dim: uint
-        }
-    }
 }
 
-impl<N: Sub<N, N>> DVecSubRhs<N, DVec<N>> for DVec<N> {
+small_dvec_impl!(DVec1, 1, DVec1MulRhs, DVec1DivRhs, DVec1AddRhs, DVec1SubRhs, 0)
-    #[inline]
+small_dvec_from_impl!(DVec1, 1, Zero::zero())
-    fn binop(left: &DVec<N>, right: &DVec<N>) -> DVec<N> {
+
-        assert!(left.at.len() == right.at.len());
+
-        DVec {
+/// Stack-allocated, dynamically sized vector with a maximum size of 2.
-            at: left.at.iter().zip(right.at.iter()).map(|(a, b)| *a - *b).collect()
+pub struct DVec2<N> {
-        }
+    at:  [N, ..2],
-    }
+    dim: uint
 }
 
-impl<N: Neg<N>> Neg<DVec<N>> for DVec<N> {
+small_dvec_impl!(DVec2, 2, DVec2MulRhs, DVec2DivRhs, DVec2AddRhs, DVec2SubRhs, 0, 1)
-    #[inline]
+small_dvec_from_impl!(DVec2, 2, Zero::zero(), Zero::zero())
-    fn neg(&self) -> DVec<N> {
+
-        DVec { at: self.at.iter().map(|a| -*a).collect() }
+
-    }
+/// Stack-allocated, dynamically sized vector with a maximum size of 3.
+pub struct DVec3<N> {
+    at:  [N, ..3],
+    dim: uint
 }
 
-impl<N: Num + Clone> Dot<N> for DVec<N> {
+small_dvec_impl!(DVec3, 3, DVec3MulRhs, DVec3DivRhs, DVec3AddRhs, DVec3SubRhs, 0, 1, 2)
-    #[inline]
+small_dvec_from_impl!(DVec3, 3, Zero::zero(), Zero::zero(), Zero::zero())
-    fn dot(a: &DVec<N>, b: &DVec<N>) -> N {
-        assert!(a.at.len() == b.at.len());
 
-        let mut res: N = Zero::zero();
 
-        for i in range(0u, a.at.len()) {
+/// Stack-allocated, dynamically sized vector with a maximum size of 4.
-            res = res + unsafe { a.unsafe_at(i) * b.unsafe_at(i) };
+pub struct DVec4<N> {
-        }
+    at:  [N, ..4],
-
+    dim: uint
-        res
-    }
-
-    #[inline]
-    fn sub_dot(a: &DVec<N>, b: &DVec<N>, c: &DVec<N>) -> N {
-        let mut res: N = Zero::zero();
-
-        for i in range(0u, a.at.len()) {
-            res = res + unsafe { (a.unsafe_at(i) - b.unsafe_at(i)) * c.unsafe_at(i) };
-        }
-
-        res
-    }
 }
 
-impl<N: Float + Clone> Norm<N> for DVec<N> {
+small_dvec_impl!(DVec4, 4, DVec4MulRhs, DVec4DivRhs, DVec4AddRhs, DVec4SubRhs, 0, 1, 2, 3)
-    #[inline]
+small_dvec_from_impl!(DVec4, 4, Zero::zero(), Zero::zero(), Zero::zero(), Zero::zero())
-    fn sqnorm(v: &DVec<N>) -> N {
-        Dot::dot(v, v)
-    }
 
-    #[inline]
-    fn norm(v: &DVec<N>) -> N {
-        Norm::sqnorm(v).sqrt()
-    }
 
-    #[inline]
+/// Stack-allocated, dynamically sized vector with a maximum size of 5.
-    fn normalize_cpy(v: &DVec<N>) -> DVec<N> {
+pub struct DVec5<N> {
-        let mut res : DVec<N> = v.clone();
+    at:  [N, ..5],
-
+    dim: uint
-        let _ = res.normalize();
-
-        res
-    }
-
-    #[inline]
-    fn normalize(&mut self) -> N {
-        let l = Norm::norm(self);
-
-        for i in range(0u, self.at.len()) {
-            *self.at.get_mut(i) = self.at[i] / l;
-        }
-
-        l
-    }
 }
 
-impl<N: ApproxEq<N>> ApproxEq<N> for DVec<N> {
+small_dvec_impl!(DVec5, 5, DVec5MulRhs, DVec5DivRhs, DVec5AddRhs, DVec5SubRhs, 0, 1, 2, 3, 4)
-    #[inline]
+small_dvec_from_impl!(DVec5, 5, Zero::zero(), Zero::zero(), Zero::zero(), Zero::zero(), Zero::zero())
-    fn approx_epsilon(_: Option<DVec<N>>) -> N {
-        ApproxEq::approx_epsilon(None::<N>)
-    }
 
-    #[inline]
-    fn approx_eq(a: &DVec<N>, b: &DVec<N>) -> bool {
-        let mut zip = a.at.iter().zip(b.at.iter());
 
-        zip.all(|(a, b)| ApproxEq::approx_eq(a, b))
+/// Stack-allocated, dynamically sized vector with a maximum size of 6.
-    }
+pub struct DVec6<N> {
-
+    at:  [N, ..6],
-    #[inline]
+    dim: uint
-    fn approx_eq_eps(a: &DVec<N>, b: &DVec<N>, epsilon: &N) -> bool {
-        let mut zip = a.at.iter().zip(b.at.iter());
-
-        zip.all(|(a, b)| ApproxEq::approx_eq_eps(a, b, epsilon))
-    }
 }
 
-macro_rules! scalar_mul_impl (
+small_dvec_impl!(DVec6, 6, DVec6MulRhs, DVec6DivRhs, DVec6AddRhs, DVec6SubRhs, 0, 1, 2, 3, 4, 5)
-    ($n: ident) => (
+small_dvec_from_impl!(DVec6, 6, Zero::zero(), Zero::zero(), Zero::zero(), Zero::zero(), Zero::zero(), Zero::zero())
-        impl DVecMulRhs<$n, DVec<$n>> for $n {
-            #[inline]
-            fn binop(left: &DVec<$n>, right: &$n) -> DVec<$n> {
-                DVec { at: left.at.iter().map(|a| a * *right).collect() }
-            }
-        }
-    )
-)
-
-macro_rules! scalar_div_impl (
-    ($n: ident) => (
-        impl DVecDivRhs<$n, DVec<$n>> for $n {
-            #[inline]
-            fn binop(left: &DVec<$n>, right: &$n) -> DVec<$n> {
-                DVec { at: left.at.iter().map(|a| a / *right).collect() }
-            }
-        }
-    )
-)
-
-macro_rules! scalar_add_impl (
-    ($n: ident) => (
-        impl DVecAddRhs<$n, DVec<$n>> for $n {
-            #[inline]
-            fn binop(left: &DVec<$n>, right: &$n) -> DVec<$n> {
-                DVec { at: left.at.iter().map(|a| a + *right).collect() }
-            }
-        }
-    )
-)
-
-macro_rules! scalar_sub_impl (
-    ($n: ident) => (
-        impl DVecSubRhs<$n, DVec<$n>> for $n {
-            #[inline]
-            fn binop(left: &DVec<$n>, right: &$n) -> DVec<$n> {
-                DVec { at: left.at.iter().map(|a| a - *right).collect() }
-            }
-        }
-    )
-)
-
-scalar_mul_impl!(f64)
-scalar_mul_impl!(f32)
-scalar_mul_impl!(u64)
-scalar_mul_impl!(u32)
-scalar_mul_impl!(u16)
-scalar_mul_impl!(u8)
-scalar_mul_impl!(i64)
-scalar_mul_impl!(i32)
-scalar_mul_impl!(i16)
-scalar_mul_impl!(i8)
-scalar_mul_impl!(uint)
-scalar_mul_impl!(int)
-
-scalar_div_impl!(f64)
-scalar_div_impl!(f32)
-scalar_div_impl!(u64)
-scalar_div_impl!(u32)
-scalar_div_impl!(u16)
-scalar_div_impl!(u8)
-scalar_div_impl!(i64)
-scalar_div_impl!(i32)
-scalar_div_impl!(i16)
-scalar_div_impl!(i8)
-scalar_div_impl!(uint)
-scalar_div_impl!(int)
-
-scalar_add_impl!(f64)
-scalar_add_impl!(f32)
-scalar_add_impl!(u64)
-scalar_add_impl!(u32)
-scalar_add_impl!(u16)
-scalar_add_impl!(u8)
-scalar_add_impl!(i64)
-scalar_add_impl!(i32)
-scalar_add_impl!(i16)
-scalar_add_impl!(i8)
-scalar_add_impl!(uint)
-scalar_add_impl!(int)
-
-scalar_sub_impl!(f64)
-scalar_sub_impl!(f32)
-scalar_sub_impl!(u64)
-scalar_sub_impl!(u32)
-scalar_sub_impl!(u16)
-scalar_sub_impl!(u8)
-scalar_sub_impl!(i64)
-scalar_sub_impl!(i32)
-scalar_sub_impl!(i16)
-scalar_sub_impl!(i8)
-scalar_sub_impl!(uint)
-scalar_sub_impl!(int)

src/structs/dvec_macros.rs

@@ -0,0 +1,502 @@
+#![macro_escape]
+
+macro_rules! dvec_impl(
+    ($dvec: ident, $mul: ident, $div: ident, $add: ident, $sub: ident) => (
+        double_dispatch_binop_decl_trait!($dvec, $mul)
+        double_dispatch_binop_decl_trait!($dvec, $div)
+        double_dispatch_binop_decl_trait!($dvec, $add)
+        double_dispatch_binop_decl_trait!($dvec, $sub)
+
+        mul_redispatch_impl!($dvec, $mul)
+        div_redispatch_impl!($dvec, $div)
+        add_redispatch_impl!($dvec, $add)
+        sub_redispatch_impl!($dvec, $sub)
+
+        impl<N: Zero + Clone> $dvec<N> {
+            /// Builds a vector filled with zeros.
+            ///
+            /// # Arguments
+            /// * `dim` - The dimension of the vector.
+            #[inline]
+            pub fn new_zeros(dim: uint) -> $dvec<N> {
+                $dvec::from_elem(dim, Zero::zero())
+            }
+
+            /// Tests if all components of the vector are zeroes.
+            #[inline]
+            pub fn is_zero(&self) -> bool {
+                self.as_slice().iter().all(|e| e.is_zero())
+            }
+        }
+
+        impl<N> $dvec<N> {
+            /// Slices this vector.
+            #[inline]
+            pub fn as_slice<'a>(&'a self) -> &'a [N] {
+                self.at.slice_to(self.len())
+            }
+
+            /// Mutably slices this vector.
+            #[inline]
+            pub fn as_mut_slice<'a>(&'a mut self) -> &'a mut [N] {
+                let len = self.len();
+                self.at.mut_slice_to(len)
+            }
+        }
+
+        impl<N: Clone> Indexable<uint, N> for $dvec<N> {
+            #[inline]
+            fn at(&self, i: uint) -> N {
+                assert!(i < self.len());
+                unsafe {
+                    self.unsafe_at(i)
+                }
+            }
+
+            #[inline]
+            fn set(&mut self, i: uint, val: N) {
+                assert!(i < self.len());
+                unsafe {
+                    self.unsafe_set(i, val);
+                }
+            }
+
+            #[inline]
+            fn swap(&mut self, i: uint, j: uint) {
+                assert!(i < self.len());
+                assert!(j < self.len());
+                self.as_mut_slice().swap(i, j);
+            }
+
+            #[inline]
+            fn shape(&self) -> uint {
+                self.len()
+            }
+
+            #[inline]
+            unsafe fn unsafe_at(&self, i: uint) -> N {
+                (*self.at.as_slice().unsafe_get(i)).clone()
+            }
+
+            #[inline]
+            unsafe fn unsafe_set(&mut self, i: uint, val: N) {
+                *self.at.as_mut_slice().unsafe_mut_ref(i) = val
+            }
+
+        }
+
+        impl<N: One + Zero + Clone> $dvec<N> {
+            /// Builds a vector filled with ones.
+            ///
+            /// # Arguments
+            /// * `dim` - The dimension of the vector.
+            #[inline]
+            pub fn new_ones(dim: uint) -> $dvec<N> {
+                $dvec::from_elem(dim, One::one())
+            }
+        }
+
+        impl<N: Rand + Zero> $dvec<N> {
+            /// Builds a vector filled with random values.
+            #[inline]
+            pub fn new_random(dim: uint) -> $dvec<N> {
+                $dvec::from_fn(dim, |_| rand::random())
+            }
+        }
+
+        impl<N> Iterable<N> for $dvec<N> {
+            #[inline]
+            fn iter<'l>(&'l self) -> Items<'l, N> {
+                self.as_slice().iter()
+            }
+        }
+
+        impl<N> IterableMut<N> for $dvec<N> {
+            #[inline]
+            fn mut_iter<'l>(&'l mut self) -> MutItems<'l, N> {
+                self.as_mut_slice().mut_iter()
+            }
+        }
+
+        impl<N: Clone + Float + ApproxEq<N> + $mul<N, $dvec<N>>> $dvec<N> {
+            /// Computes the canonical basis for the given dimension. A canonical basis is a set of
+            /// vectors, mutually orthogonal, with all its component equal to 0.0 except one which is equal
+            /// to 1.0.
+            pub fn canonical_basis_with_dim(dim: uint) -> Vec<$dvec<N>> {
+                let mut res : Vec<$dvec<N>> = Vec::new();
+
+                for i in range(0u, dim) {
+                    let mut basis_element : $dvec<N> = $dvec::new_zeros(dim);
+
+                    basis_element.set(i, One::one());
+
+                    res.push(basis_element);
+                }
+
+                res
+            }
+
+            /// Computes a basis of the space orthogonal to the vector. If the input vector is of dimension
+            /// `n`, this will return `n - 1` vectors.
+            pub fn orthogonal_subspace_basis(&self) -> Vec<$dvec<N>> {
+                // compute the basis of the orthogonal subspace using Gram-Schmidt
+                // orthogonalization algorithm
+                let     dim                 = self.len();
+                let mut res : Vec<$dvec<N>> = Vec::new();
+
+                for i in range(0u, dim) {
+                    let mut basis_element : $dvec<N> = $dvec::new_zeros(self.len());
+
+                    basis_element.set(i, One::one());
+
+                    if res.len() == dim - 1 {
+                        break;
+                    }
+
+                    let mut elt = basis_element.clone();
+
+                    elt = elt - self * Dot::dot(&basis_element, self);
+
+                    for v in res.iter() {
+                        elt = elt - v * Dot::dot(&elt, v)
+                    };
+
+                    if !ApproxEq::approx_eq(&Norm::sqnorm(&elt), &Zero::zero()) {
+                        res.push(Norm::normalize_cpy(&elt));
+                    }
+                }
+
+                assert!(res.len() == dim - 1);
+
+                res
+            }
+        }
+
+        impl<N: Add<N, N> + Zero> $add<N, $dvec<N>> for $dvec<N> {
+            #[inline]
+            fn binop(left: &$dvec<N>, right: &$dvec<N>) -> $dvec<N> {
+                assert!(left.len() == right.len());
+                FromIterator::from_iter(left.as_slice().iter().zip(right.as_slice().iter()).map(|(a, b)| *a + *b))
+            }
+        }
+
+        impl<N: Sub<N, N> + Zero> $sub<N, $dvec<N>> for $dvec<N> {
+            #[inline]
+            fn binop(left: &$dvec<N>, right: &$dvec<N>) -> $dvec<N> {
+                assert!(left.len() == right.len());
+                FromIterator::from_iter(left.as_slice().iter().zip(right.as_slice().iter()).map(|(a, b)| *a - *b))
+            }
+        }
+
+        impl<N: Neg<N> + Zero> Neg<$dvec<N>> for $dvec<N> {
+            #[inline]
+            fn neg(&self) -> $dvec<N> {
+                FromIterator::from_iter(self.as_slice().iter().map(|a| -*a))
+            }
+        }
+
+        impl<N: Num + Clone> Dot<N> for $dvec<N> {
+            #[inline]
+            fn dot(a: &$dvec<N>, b: &$dvec<N>) -> N {
+                assert!(a.len() == b.len());
+
+                let mut res: N = Zero::zero();
+
+                for i in range(0u, a.len()) {
+                    res = res + unsafe { a.unsafe_at(i) * b.unsafe_at(i) };
+                }
+
+                res
+            }
+
+            #[inline]
+            fn sub_dot(a: &$dvec<N>, b: &$dvec<N>, c: &$dvec<N>) -> N {
+                let mut res: N = Zero::zero();
+
+                for i in range(0u, a.len()) {
+                    res = res + unsafe { (a.unsafe_at(i) - b.unsafe_at(i)) * c.unsafe_at(i) };
+                }
+
+                res
+            }
+        }
+
+        impl<N: Float + Clone> Norm<N> for $dvec<N> {
+            #[inline]
+            fn sqnorm(v: &$dvec<N>) -> N {
+                Dot::dot(v, v)
+            }
+
+            #[inline]
+            fn norm(v: &$dvec<N>) -> N {
+                Norm::sqnorm(v).sqrt()
+            }
+
+            #[inline]
+            fn normalize_cpy(v: &$dvec<N>) -> $dvec<N> {
+                let mut res : $dvec<N> = v.clone();
+
+                let _ = res.normalize();
+
+                res
+            }
+
+            #[inline]
+            fn normalize(&mut self) -> N {
+                let l = Norm::norm(self);
+
+                for n in self.as_mut_slice().mut_iter() {
+                    *n = *n / l;
+                }
+
+                l
+            }
+        }
+
+        impl<N: ApproxEq<N>> ApproxEq<N> for $dvec<N> {
+            #[inline]
+            fn approx_epsilon(_: Option<$dvec<N>>) -> N {
+                ApproxEq::approx_epsilon(None::<N>)
+            }
+
+            #[inline]
+            fn approx_eq(a: &$dvec<N>, b: &$dvec<N>) -> bool {
+                let mut zip = a.as_slice().iter().zip(b.as_slice().iter());
+
+                zip.all(|(a, b)| ApproxEq::approx_eq(a, b))
+            }
+
+            #[inline]
+            fn approx_eq_eps(a: &$dvec<N>, b: &$dvec<N>, epsilon: &N) -> bool {
+                let mut zip = a.as_slice().iter().zip(b.as_slice().iter());
+
+                zip.all(|(a, b)| ApproxEq::approx_eq_eps(a, b, epsilon))
+            }
+        }
+
+        dvec_scalar_mul_impl!($dvec, f64, $mul)
+        dvec_scalar_mul_impl!($dvec, f32, $mul)
+        dvec_scalar_mul_impl!($dvec, u64, $mul)
+        dvec_scalar_mul_impl!($dvec, u32, $mul)
+        dvec_scalar_mul_impl!($dvec, u16, $mul)
+        dvec_scalar_mul_impl!($dvec, u8, $mul)
+        dvec_scalar_mul_impl!($dvec, i64, $mul)
+        dvec_scalar_mul_impl!($dvec, i32, $mul)
+        dvec_scalar_mul_impl!($dvec, i16, $mul)
+        dvec_scalar_mul_impl!($dvec, i8, $mul)
+        dvec_scalar_mul_impl!($dvec, uint, $mul)
+        dvec_scalar_mul_impl!($dvec, int, $mul)
+
+        dvec_scalar_div_impl!($dvec, f64, $div)
+        dvec_scalar_div_impl!($dvec, f32, $div)
+        dvec_scalar_div_impl!($dvec, u64, $div)
+        dvec_scalar_div_impl!($dvec, u32, $div)
+        dvec_scalar_div_impl!($dvec, u16, $div)
+        dvec_scalar_div_impl!($dvec, u8, $div)
+        dvec_scalar_div_impl!($dvec, i64, $div)
+        dvec_scalar_div_impl!($dvec, i32, $div)
+        dvec_scalar_div_impl!($dvec, i16, $div)
+        dvec_scalar_div_impl!($dvec, i8, $div)
+        dvec_scalar_div_impl!($dvec, uint, $div)
+        dvec_scalar_div_impl!($dvec, int, $div)
+
+        dvec_scalar_add_impl!($dvec, f64, $add)
+        dvec_scalar_add_impl!($dvec, f32, $add)
+        dvec_scalar_add_impl!($dvec, u64, $add)
+        dvec_scalar_add_impl!($dvec, u32, $add)
+        dvec_scalar_add_impl!($dvec, u16, $add)
+        dvec_scalar_add_impl!($dvec, u8, $add)
+        dvec_scalar_add_impl!($dvec, i64, $add)
+        dvec_scalar_add_impl!($dvec, i32, $add)
+        dvec_scalar_add_impl!($dvec, i16, $add)
+        dvec_scalar_add_impl!($dvec, i8, $add)
+        dvec_scalar_add_impl!($dvec, uint, $add)
+        dvec_scalar_add_impl!($dvec, int, $add)
+
+        dvec_scalar_sub_impl!($dvec, f64, $sub)
+        dvec_scalar_sub_impl!($dvec, f32, $sub)
+        dvec_scalar_sub_impl!($dvec, u64, $sub)
+        dvec_scalar_sub_impl!($dvec, u32, $sub)
+        dvec_scalar_sub_impl!($dvec, u16, $sub)
+        dvec_scalar_sub_impl!($dvec, u8, $sub)
+        dvec_scalar_sub_impl!($dvec, i64, $sub)
+        dvec_scalar_sub_impl!($dvec, i32, $sub)
+        dvec_scalar_sub_impl!($dvec, i16, $sub)
+        dvec_scalar_sub_impl!($dvec, i8, $sub)
+        dvec_scalar_sub_impl!($dvec, uint, $sub)
+        dvec_scalar_sub_impl!($dvec, int, $sub)
+    )
+)
+
+macro_rules! dvec_scalar_mul_impl (
+    ($dvec: ident, $n: ident, $mul: ident) => (
+        impl $mul<$n, $dvec<$n>> for $n {
+            #[inline]
+            fn binop(left: &$dvec<$n>, right: &$n) -> $dvec<$n> {
+                FromIterator::from_iter(left.as_slice().iter().map(|a| a * *right))
+            }
+        }
+    )
+)
+
+macro_rules! dvec_scalar_div_impl (
+    ($dvec: ident, $n: ident, $div: ident) => (
+        impl $div<$n, $dvec<$n>> for $n {
+            #[inline]
+            fn binop(left: &$dvec<$n>, right: &$n) -> $dvec<$n> {
+                FromIterator::from_iter(left.as_slice().iter().map(|a| a / *right))
+            }
+        }
+    )
+)
+
+macro_rules! dvec_scalar_add_impl (
+    ($dvec: ident, $n: ident, $add: ident) => (
+        impl $add<$n, $dvec<$n>> for $n {
+            #[inline]
+            fn binop(left: &$dvec<$n>, right: &$n) -> $dvec<$n> {
+                FromIterator::from_iter(left.as_slice().iter().map(|a| a + *right))
+            }
+        }
+    )
+)
+
+macro_rules! dvec_scalar_sub_impl (
+    ($dvec: ident, $n: ident, $sub: ident) => (
+        impl $sub<$n, $dvec<$n>> for $n {
+            #[inline]
+            fn binop(left: &$dvec<$n>, right: &$n) -> $dvec<$n> {
+                FromIterator::from_iter(left.as_slice().iter().map(|a| a - *right))
+            }
+        }
+    )
+)
+
+macro_rules! small_dvec_impl (
+    ($dvec: ident, $dim: expr, $mul: ident, $div: ident, $add: ident, $sub: ident $(,$idx: expr)*) => (
+        impl<N> Collection for $dvec<N> {
+            #[inline]
+            fn len(&self) -> uint {
+                self.dim
+            }
+        }
+
+        impl<N: PartialEq> PartialEq for $dvec<N> {
+            #[inline]
+            fn eq(&self, other: &$dvec<N>) -> bool {
+                if self.len() != other.len() {
+                    return false; // FIXME: fail instead?
+                }
+
+                for (a, b) in self.as_slice().iter().zip(other.as_slice().iter()) {
+                    if *a != *b {
+                        return false;
+                    }
+                }
+
+                true
+            }
+        }
+
+        impl<N: Clone> Clone for $dvec<N> {
+            fn clone(&self) -> $dvec<N> {
+                let at: [N, ..$dim] = [ $( self.at[$idx].clone(), )* ];
+
+                $dvec {
+                    at:  at,
+                    dim: self.dim
+                }
+            }
+        }
+
+        dvec_impl!($dvec, $mul, $div, $add, $sub)
+    )
+)
+
+macro_rules! small_dvec_from_impl (
+    ($dvec: ident, $dim: expr $(,$zeros: expr)*) => (
+        impl<N: Clone + Zero> $dvec<N> {
+            /// Builds a vector filled with a constant.
+            #[inline]
+            pub fn from_elem(dim: uint, elem: N) -> $dvec<N> {
+                assert!(dim <= $dim);
+
+                let mut at: [N, ..$dim] = [ $( $zeros, )* ];
+
+                for n in at.mut_slice_to(dim).mut_iter() {
+                    *n = elem.clone();
+                }
+
+                $dvec {
+                    at:  at,
+                    dim: dim
+                }
+            }
+        }
+
+        impl<N: Clone + Zero> $dvec<N> {
+            /// Builds a vector filled with the components provided by a vector.
+            ///
+            /// The vector must have at least `dim` elements.
+            #[inline]
+            pub fn from_slice(dim: uint, vec: &[N]) -> $dvec<N> {
+                assert!(dim <= vec.len() && dim <= $dim);
+
+                // FIXME: not safe.
+                let mut at: [N, ..$dim] = [ $( $zeros, )* ];
+
+                for (curr, other) in vec.iter().zip(at.mut_iter()) {
+                    *other = curr.clone();
+                }
+
+                $dvec {
+                    at:  at,
+                    dim: dim
+                }
+            }
+        }
+
+        impl<N: Zero> $dvec<N> {
+            /// Builds a vector filled with the result of a function.
+            #[inline(always)]
+            pub fn from_fn(dim: uint, f: |uint| -> N) -> $dvec<N> {
+                assert!(dim <= $dim);
+
+                let mut at: [N, ..$dim] = [ $( $zeros, )* ];
+
+                for i in range(0, dim) {
+                    at[i] = f(i);
+                }
+
+                $dvec {
+                    at:  at,
+                    dim: dim
+                }
+            }
+        }
+
+        impl<N: Zero> FromIterator<N> for $dvec<N> {
+            #[inline]
+            fn from_iter<I: Iterator<N>>(mut param: I) -> $dvec<N> {
+                let mut at: [N, ..$dim] = [ $( $zeros, )* ];
+
+                let mut dim = 0;
+
+                for n in param {
+                    if dim == $dim {
+                        break;
+                    }
+
+                    at[dim] = n;
+
+                    dim = dim + 1;
+                }
+
+                $dvec {
+                    at:  at,
+                    dim: dim
+                }
+            }
+        }
+    )
+)

src/structs/mat.rs

@@ -6,9 +6,9 @@ use std::mem;
 use std::num::{One, Zero};
 use traits::operations::ApproxEq;
 use std::slice::{Items, MutItems};
-use structs::vec::{Vec1, Vec2, Vec3, Vec4, Vec5, Vec6, Vec1MulRhs, Vec4MulRhs,
+use structs::vec::{Vec1, Vec2, Vec3, Vec4, Vec5, Vec6,
-                   Vec5MulRhs, Vec6MulRhs};
+                   Vec1MulRhs, Vec4MulRhs, Vec5MulRhs, Vec6MulRhs};
-use structs::dvec::DVec;
+use structs::dvec::{DVec1, DVec2, DVec3, DVec4, DVec5, DVec6};
 
 use traits::structure::{Cast, Row, Col, Iterable, IterableMut, Dim, Indexable,
                         Eye, ColSlice, RowSlice};
@@ -118,8 +118,8 @@ transpose_impl!(Mat1, 1)
 approx_eq_impl!(Mat1)
 row_impl!(Mat1, Vec1, 1)
 col_impl!(Mat1, Vec1, 1)
-col_slice_impl!(Mat1, Vec1, 1)
+col_slice_impl!(Mat1, Vec1, DVec1, 1)
-row_slice_impl!(Mat1, Vec1, 1)
+row_slice_impl!(Mat1, Vec1, DVec1, 1)
 to_homogeneous_impl!(Mat1, Mat2, 1, 2)
 from_homogeneous_impl!(Mat1, Mat2, 1, 2)
 outer_impl!(Vec1, Mat1)
@@ -219,8 +219,8 @@ transpose_impl!(Mat2, 2)
 approx_eq_impl!(Mat2)
 row_impl!(Mat2, Vec2, 2)
 col_impl!(Mat2, Vec2, 2)
-col_slice_impl!(Mat2, Vec2, 2)
+col_slice_impl!(Mat2, Vec2, DVec2, 2)
-row_slice_impl!(Mat2, Vec2, 2)
+row_slice_impl!(Mat2, Vec2, DVec2, 2)
 to_homogeneous_impl!(Mat2, Mat3, 2, 3)
 from_homogeneous_impl!(Mat2, Mat3, 2, 3)
 outer_impl!(Vec2, Mat2)
@@ -334,8 +334,8 @@ transpose_impl!(Mat3, 3)
 approx_eq_impl!(Mat3)
 // (specialized) row_impl!(Mat3, Vec3, 3)
 // (specialized) col_impl!(Mat3, Vec3, 3)
-col_slice_impl!(Mat3, Vec3, 3)
+col_slice_impl!(Mat3, Vec3, DVec3, 3)
-row_slice_impl!(Mat3, Vec3, 3)
+row_slice_impl!(Mat3, Vec3, DVec3, 3)
 to_homogeneous_impl!(Mat3, Mat4, 3, 4)
 from_homogeneous_impl!(Mat3, Mat4, 3, 4)
 outer_impl!(Vec3, Mat3)
@@ -501,8 +501,8 @@ transpose_impl!(Mat4, 4)
 approx_eq_impl!(Mat4)
 row_impl!(Mat4, Vec4, 4)
 col_impl!(Mat4, Vec4, 4)
-col_slice_impl!(Mat4, Vec4, 4)
+col_slice_impl!(Mat4, Vec4, DVec4, 4)
-row_slice_impl!(Mat4, Vec4, 4)
+row_slice_impl!(Mat4, Vec4, DVec4, 4)
 to_homogeneous_impl!(Mat4, Mat5, 4, 5)
 from_homogeneous_impl!(Mat4, Mat5, 4, 5)
 outer_impl!(Vec4, Mat4)
@@ -684,8 +684,8 @@ transpose_impl!(Mat5, 5)
 approx_eq_impl!(Mat5)
 row_impl!(Mat5, Vec5, 5)
 col_impl!(Mat5, Vec5, 5)
-col_slice_impl!(Mat5, Vec5, 5)
+col_slice_impl!(Mat5, Vec5, DVec5, 5)
-row_slice_impl!(Mat5, Vec5, 5)
+row_slice_impl!(Mat5, Vec5, DVec5, 5)
 to_homogeneous_impl!(Mat5, Mat6, 5, 6)
 from_homogeneous_impl!(Mat5, Mat6, 5, 6)
 outer_impl!(Vec5, Mat5)
@@ -919,6 +919,6 @@ transpose_impl!(Mat6, 6)
 approx_eq_impl!(Mat6)
 row_impl!(Mat6, Vec6, 6)
 col_impl!(Mat6, Vec6, 6)
-col_slice_impl!(Mat6, Vec6, 6)
+col_slice_impl!(Mat6, Vec6, DVec6, 6)
-row_slice_impl!(Mat6, Vec6, 6)
+row_slice_impl!(Mat6, Vec6, DVec6, 6)
 outer_impl!(Vec6, Mat6)

src/structs/mat_macros.rs

@@ -226,20 +226,12 @@ macro_rules! indexable_impl(
 )
 
 macro_rules! col_slice_impl(
-    ($t: ident, $tv: ident, $dim: expr) => (
+    ($t: ident, $tv: ident, $slice: ident, $dim: expr) => (
-        impl<N: Clone + Zero> ColSlice<DVec<N>> for $t<N> {
+        impl<N: Clone + Zero> ColSlice<$slice<N>> for $t<N> {
-            fn col_slice(& self, cid: uint, rstart: uint, rend: uint) -> DVec<N> {
+            fn col_slice(&self, cid: uint, rstart: uint, rend: uint) -> $slice<N> {
-                assert!(cid < $dim);
-                assert!(rstart < rend);
-                assert!(rend <= $dim);
                 let col = self.col(cid);
-                let res  = DVec::from_vec(
+
-                    rend - rstart,
+                $slice::from_slice(rend - rstart, col.as_slice().slice(rstart, rend))
-                    unsafe {
-                        mem::transmute::<&$tv<N>, & [N, ..$dim]>
-                        (&col).slice(rstart, rend)
-                    });
-                res
             }
         }
     )
@@ -275,20 +267,12 @@ macro_rules! row_impl(
 )
 
 macro_rules! row_slice_impl(
-    ($t: ident, $tv: ident, $dim: expr) => (
+    ($t: ident, $tv: ident, $slice: ident, $dim: expr) => (
-        impl<N: Clone + Zero> RowSlice<DVec<N>> for $t<N> {
+        impl<N: Clone + Zero> RowSlice<$slice<N>> for $t<N> {
-            fn row_slice(& self, rid: uint, cstart: uint, cend: uint) -> DVec<N> {
+            fn row_slice(&self, rid: uint, cstart: uint, cend: uint) -> $slice<N> {
-                assert!(rid < $dim);
-                assert!(cstart < cend);
-                assert!(cend <= $dim);
                 let row = self.row(rid);
-                let res  = DVec::from_vec(
+
-                    cend - cstart,
+                $slice::from_slice(cend - cstart, row.as_slice().slice(cstart, cend))
-                    unsafe {
-                        mem::transmute::<&$tv<N>, & [N, ..$dim]>
-                        (&row).slice(cstart, cend)
-                    });
-                res
             }
         }
     )

src/structs/mod.rs

@@ -1,7 +1,7 @@
 //! Data structures and implementations.
 
 pub use self::dmat::DMat;
-pub use self::dvec::DVec;
+pub use self::dvec::{DVec, DVec1, DVec2, DVec3, DVec4, DVec5, DVec6};
 pub use self::vec::{Vec0, Vec1, Vec2, Vec3, Vec4, Vec5, Vec6};
 pub use self::mat::{Identity, Mat1, Mat2, Mat3, Mat4, Mat5, Mat6};
 pub use self::rot::{Rot2, Rot3, Rot4};
@@ -18,6 +18,7 @@ pub use self::mat::{Mat1MulRhs, Mat2MulRhs, Mat3MulRhs, Mat4MulRhs, Mat5MulRhs,
 
 mod metal;
 mod dmat;
+mod dvec_macros;
 mod dvec;
 mod vec_macros;
 mod vec;

src/structs/vec.rs

@@ -38,6 +38,7 @@ new_impl!(Vec1, x)
 ord_impl!(Vec1, x)
 vec_axis_impl!(Vec1, x)
 vec_cast_impl!(Vec1, Vec1Cast, x)
+as_slice_impl!(Vec1, 1)
 indexable_impl!(Vec1, 1)
 at_fast_impl!(Vec1, 1)
 new_repeat_impl!(Vec1, val, x)
@@ -135,6 +136,7 @@ new_impl!(Vec2, x, y)
 ord_impl!(Vec2, x, y)
 vec_axis_impl!(Vec2, x, y)
 vec_cast_impl!(Vec2, Vec2Cast, x, y)
+as_slice_impl!(Vec2, 2)
 indexable_impl!(Vec2, 2)
 at_fast_impl!(Vec2, 2)
 new_repeat_impl!(Vec2, val, x, y)
@@ -234,6 +236,7 @@ new_impl!(Vec3, x, y, z)
 ord_impl!(Vec3, x, y, z)
 vec_axis_impl!(Vec3, x, y, z)
 vec_cast_impl!(Vec3, Vec3Cast, x, y, z)
+as_slice_impl!(Vec3, 3)
 indexable_impl!(Vec3, 3)
 at_fast_impl!(Vec3, 3)
 new_repeat_impl!(Vec3, val, x, y, z)
@@ -339,6 +342,7 @@ new_impl!(Vec4, x, y, z, w)
 ord_impl!(Vec4, x, y, z, w)
 vec_axis_impl!(Vec4, x, y, z, w)
 vec_cast_impl!(Vec4, Vec4Cast, x, y, z, w)
+as_slice_impl!(Vec4, 4)
 indexable_impl!(Vec4, 4)
 at_fast_impl!(Vec4, 4)
 new_repeat_impl!(Vec4, val, x, y, z, w)
@@ -442,6 +446,7 @@ new_impl!(Vec5, x, y, z, w, a)
 ord_impl!(Vec5, x, y, z, w, a)
 vec_axis_impl!(Vec5, x, y, z, w, a)
 vec_cast_impl!(Vec5, Vec5Cast, x, y, z, w, a)
+as_slice_impl!(Vec5, 5)
 indexable_impl!(Vec5, 5)
 at_fast_impl!(Vec5, 5)
 new_repeat_impl!(Vec5, val, x, y, z, w, a)
@@ -547,6 +552,7 @@ new_impl!(Vec6, x, y, z, w, a, b)
 ord_impl!(Vec6, x, y, z, w, a, b)
 vec_axis_impl!(Vec6, x, y, z, w, a, b)
 vec_cast_impl!(Vec6, Vec6Cast, x, y, z, w, a, b)
+as_slice_impl!(Vec6, 6)
 indexable_impl!(Vec6, 6)
 at_fast_impl!(Vec6, 6)
 new_repeat_impl!(Vec6, val, x, y, z, w, a, b)

src/structs/vec_macros.rs

@@ -15,6 +15,26 @@ macro_rules! new_impl(
     )
 )
 
+macro_rules! as_slice_impl(
+    ($t: ident, $dim: expr) => (
+        impl<N> $t<N> {
+            /// Slices this vector.
+            pub fn as_slice<'a>(&'a self) -> &'a [N] {
+                unsafe {
+                    mem::transmute::<&$t<N>, &[N, ..$dim]>(self).as_slice()
+                }
+            }
+
+            /// Mutably slices this vector.
+            pub fn as_mut_slice<'a>(&'a mut self) -> &'a mut [N] {
+                unsafe {
+                    mem::transmute::<&mut $t<N>, &mut [N, ..$dim]>(self).as_mut_slice()
+                }
+            }
+        }
+    )
+)
+
 macro_rules! at_fast_impl(
     ($t: ident, $dim: expr) => (
         impl<N: Clone> $t<N> {

src/tests/mat.rs

@@ -2,7 +2,6 @@ use std::num::{Float, abs};
 use std::rand::random;
 use na::{Vec1, Vec3, Mat1, Mat2, Mat3, Mat4, Mat5, Mat6, Rot3, DMat, DVec, Indexable};
 use na;
-use na::decomp_qr;
 use std::cmp::{min, max};
 
 macro_rules! test_inv_mat_impl(
@@ -25,12 +24,12 @@ macro_rules! test_transpose_mat_impl(
   );
 )
 
-macro_rules! test_decomp_qr_impl(
+macro_rules! test_qr_impl(
   ($t: ty) => (
     for _ in range(0u, 10000) {
       let randmat : $t = random();
 
-      let (q, r) = decomp_qr(&randmat);
+      let (q, r) = na::qr(&randmat);
       let recomp = q * r;
 
       assert!(na::approx_eq(&randmat,  &recomp));
@@ -38,6 +37,35 @@ macro_rules! test_decomp_qr_impl(
   );
 )
 
+macro_rules! test_eigen_qr_impl(
+    ($t: ty) => {
+        for _ in range(0u, 10000) {
+            let randmat : $t = random();
+
+            let (eigenvalues, eigenvectors) = na::eigen_qr(&randmat, &Float::epsilon(), 1000);
+
+            // FIXME: provide a method to initialize a matrix from its diagonal!
+            let diag: $t = na::zero();
+
+            for i in range(0, na::dim::<$t>()) {
+                diag.set((i, i), eigenvalues.at(i));
+            }
+
+            let recomp = na::transpose(&eigenvectors) * diag * eigenvectors;
+
+            println!("mat: {}", randmat);
+            println!("eigenvectors: {}", eigenvectors);
+            println!("eigenvalues: {}", eigenvalues);
+            println!("recomp: {}", recomp);
+
+            assert!(false);
+            fail!("what!");
+
+            assert!(na::approx_eq(&randmat,  &recomp));
+        }
+    }
+)
+
 #[test]
 fn test_transpose_mat1() {
     test_transpose_mat_impl!(Mat1<f64>);
@@ -139,7 +167,7 @@ fn test_mean_dmat() {
         ]
     );
 
-    assert!(na::approx_eq(&na::mean(&mat), &DVec::from_vec(3, [4.0f64, 5.0, 6.0])));
+    assert!(na::approx_eq(&na::mean(&mat), &DVec::from_slice(3, [4.0f64, 5.0, 6.0])));
 }
 
 #[test]
@@ -223,14 +251,14 @@ fn test_dmat_from_vec() {
 }
 
 #[test]
-fn test_decomp_qr() {
+fn test_qr() {
     for _ in range(0u, 10) {
         let dim1: uint = random();
         let dim2: uint = random();
         let rows = min(40, max(dim1, dim2));
         let cols = min(40, min(dim1, dim2));
         let randmat: DMat<f64> = DMat::new_random(rows, cols);
-        let (q, r) = decomp_qr(&randmat);
+        let (q, r) = na::qr(&randmat);
         let recomp = q * r;
 
         assert!(na::approx_eq(&randmat,  &recomp));
@@ -238,40 +266,68 @@ fn test_decomp_qr() {
 }
 
 #[test]
-fn test_decomp_qr_mat1() {
+fn test_qr_mat1() {
-    test_decomp_qr_impl!(Mat1<f64>);
+    test_qr_impl!(Mat1<f64>);
 }
 
 #[test]
-fn test_decomp_qr_mat2() {
+fn test_qr_mat2() {
-    test_decomp_qr_impl!(Mat2<f64>);
+    test_qr_impl!(Mat2<f64>);
 }
 
 #[test]
-fn test_decomp_qr_mat3() {
+fn test_qr_mat3() {
-    test_decomp_qr_impl!(Mat3<f64>);
+    test_qr_impl!(Mat3<f64>);
 }
 
 #[test]
-fn test_decomp_qr_mat4() {
+fn test_qr_mat4() {
-    test_decomp_qr_impl!(Mat4<f64>);
+    test_qr_impl!(Mat4<f64>);
 }
 
 #[test]
-fn test_decomp_qr_mat5() {
+fn test_qr_mat5() {
-    test_decomp_qr_impl!(Mat5<f64>);
+    test_qr_impl!(Mat5<f64>);
 }
 
 #[test]
-fn test_decomp_qr_mat6() {
+fn test_qr_mat6() {
-    test_decomp_qr_impl!(Mat6<f64>);
+    test_qr_impl!(Mat6<f64>);
 }
 
+// #[test]
+// fn test_eigen_qr_mat1() {
+//     test_eigen_qr_impl!(Mat1<f64>);
+// }
+// 
+// #[test]
+// fn test_eigen_qr_mat2() {
+//     test_eigen_qr_impl!(Mat2<f64>);
+// }
+// 
+// #[test]
+// fn test_eigen_qr_mat3() {
+//     test_eigen_qr_impl!(Mat3<f64>);
+// }
+// 
+// #[test]
+// fn test_eigen_qr_mat4() {
+//     test_eigen_qr_impl!(Mat4<f64>);
+// }
+// 
+// #[test]
+// fn test_eigen_qr_mat5() {
+//     test_eigen_qr_impl!(Mat5<f64>);
+// }
+// 
+// #[test]
+// fn test_eigen_qr_mat6() {
+//     test_eigen_qr_impl!(Mat6<f64>);
+// }
 
 #[test]
 fn test_from_fn() {
-    let actual: DMat<uint> = DMat::from_fn( 3, 4, 
+    let actual: DMat<uint> = DMat::from_fn(3, 4, |i, j| 10 * i + j);
-                                           |i,j| 10*i + j);
     let expected: DMat<uint> = DMat::from_row_vec(3, 4, 
                                                   [0_0, 0_1, 0_2, 0_3,
                                                    1_0, 1_1, 1_2, 1_3,