Add matrix adaptors and addapted to the now rust features.

.gitignore

@@ -0,0 +1,2 @@
+*.swp
+doc

Makefile

@@ -1,5 +1,5 @@
 all:
-	rustpkg install
+	rust build src/nalgebra.rc --out-dir lib # rustpkg install
 
 doc:
 	rust doc src/nalgebra.rc --output-dir doc

src/adaptors/rotmat.rs

@@ -0,0 +1,112 @@
+use core::num::{One, Zero}; // , Trigonometric};
+use traits::workarounds::rlmul::{RMul, LMul};
+use traits::workarounds::trigonometric::Trigonometric;
+use traits::dim::Dim;
+use traits::inv::Inv;
+use traits::transpose::Transpose;
+use dim2::mat2::Mat2;
+use dim3::mat3::Mat3;
+use dim3::vec3::Vec3;
+
+// FIXME: use a newtype here?
+#[deriving(Eq)]
+pub struct Rotmat<M>
+{
+  priv submat: M
+}
+
+pub fn Rotmat2<T: Copy + Trigonometric + Neg<T>>(angle: T) -> Rotmat<Mat2<T>>
+{
+  let coa = Trigonometric::cos(angle);
+  let sia = Trigonometric::sin(angle);
+
+  Rotmat
+  { submat: Mat2(coa, -sia, sia, coa) }
+}
+
+pub fn Rotmat3<T: Copy + Trigonometric + Neg<T> + One + Sub<T, T> + Add<T, T> +
+                  Mul<T, T>>
+(axis: &Vec3<T>, angle: T) -> Rotmat<Mat3<T>>
+{
+  let _1        = One::one::<T>();
+  let ux        = axis.x;
+  let uy        = axis.y;
+  let uz        = axis.z;
+  let sqx       = ux * ux;
+  let sqy       = uy * uy;
+  let sqz       = uz * uz;
+  let cos       = Trigonometric::cos(angle);
+  let one_m_cos = _1 - cos;
+  let sin       = Trigonometric::sin(angle);
+
+  Rotmat {
+    submat: Mat3(
+      (sqx + (_1 - sqx) * cos),
+      (ux * uy * one_m_cos - uz * sin),
+      (ux * uz * one_m_cos + uy * sin),
+
+      (ux * uy * one_m_cos + uz * sin),
+      (sqy + (_1 - sqy) * cos),
+      (uy * uz * one_m_cos - ux * sin),
+
+      (ux * uz * one_m_cos - uy * sin),
+      (uy * uz * one_m_cos + ux * sin),
+      (sqz + (_1 - sqz) * cos))
+  }
+}
+
+impl<M: Dim> Dim for Rotmat<M>
+{
+  fn dim() -> uint
+  { Dim::dim::<M>() }
+}
+ 
+impl<M:Copy + One + Zero> One for Rotmat<M>
+{
+  fn one() -> Rotmat<M>
+  { Rotmat { submat: One::one() } }
+}
+
+impl<M:Copy + Mul<M, M>> Mul<Rotmat<M>, Rotmat<M>> for Rotmat<M>
+{
+  fn mul(&self, other: &Rotmat<M>) -> Rotmat<M>
+  { Rotmat { submat: self.submat.mul(&other.submat) } }
+}
+
+impl<V, M: RMul<V>> RMul<V> for Rotmat<M>
+{
+  fn rmul(&self, other: &V) -> V
+  { self.submat.rmul(other) }
+}
+
+impl<V, M: LMul<V>> LMul<V> for Rotmat<M>
+{
+  fn lmul(&self, other: &V) -> V
+  { self.submat.lmul(other) }
+}
+
+impl<M:Copy + Transpose>
+Inv for Rotmat<M>
+{
+  fn invert(&mut self)
+  { self.transpose() }
+
+  fn inverse(&self) -> Rotmat<M>
+  { self.transposed() }
+}
+
+impl<M:Copy + Transpose>
+Transpose for Rotmat<M>
+{
+  fn transposed(&self) -> Rotmat<M>
+  { Rotmat { submat: self.submat.transposed() } }
+
+  fn transpose(&mut self)
+  { self.submat.transpose() }
+}
+
+impl<M:ToStr> ToStr for Rotmat<M>
+{
+  fn to_str(&self) -> ~str
+  { ~"Rotmat {" + " submat: " + self.submat.to_str() + " }" }
+}

src/adaptors/transform.rs

@@ -0,0 +1,85 @@
+use core::num::{One, Zero};
+use traits::dim::Dim;
+use traits::inv::Inv;
+use traits::transpose::Transpose;
+use traits::workarounds::rlmul::{RMul, LMul};
+
+pub struct Transform<M, V>
+{
+  submat   : M,
+  subtrans : V
+}
+
+pub fn Transform<M: Copy, V: Copy>(mat: &M, trans: &V) -> Transform<M, V>
+{ Transform { submat: *mat, subtrans: *trans } }
+
+impl<M:Dim, V> Dim for Transform<M, V>
+{
+  fn dim() -> uint
+  { Dim::dim::<M>() }
+}
+
+impl<M:Copy + One, V:Copy + Zero> One for Transform<M, V>
+{
+  fn one() -> Transform<M, V>
+  { Transform { submat: One::one(), subtrans: Zero::zero() } }
+}
+
+impl<M:Copy + Zero, V:Copy + Zero> Zero for Transform<M, V>
+{
+  fn zero() -> Transform<M, V>
+  { Transform { submat: Zero::zero(), subtrans: Zero::zero() } }
+
+  fn is_zero(&self) -> bool
+  { self.submat.is_zero() && self.subtrans.is_zero() }
+}
+
+impl<M:Copy + RMul<V> + Mul<M, M>, V:Copy + Add<V, V>>
+Mul<Transform<M, V>, Transform<M, V>> for Transform<M, V>
+{
+  fn mul(&self, other: &Transform<M, V>) -> Transform<M, V>
+  {
+    Transform { submat: self.submat * other.submat,
+                subtrans: self.subtrans + self.submat.rmul(&other.subtrans) }
+  }
+}
+
+impl<M: RMul<V>, V> RMul<V> for Transform<M, V>
+{
+  fn rmul(&self, other: &V) -> V
+  { self.submat.rmul(other) }
+}
+
+impl<M: LMul<V>, V> LMul<V> for Transform<M, V>
+{
+  fn lmul(&self, other: &V) -> V
+  { self.submat.lmul(other) }
+}
+
+impl<M:Copy + Transpose + Inv + RMul<V>, V:Copy + Neg<V>>
+Inv for Transform<M, V>
+{
+  fn invert(&mut self)
+  {
+    self.submat.invert();
+    self.subtrans = self.submat.rmul(&-self.subtrans);
+  }
+
+  fn inverse(&self) -> Transform<M, V>
+  {
+    let mut res = *self;
+
+    res.invert();
+
+    res
+  }
+}
+
+impl<M:ToStr, V:ToStr> ToStr for Transform<M, V>
+{
+  fn to_str(&self) -> ~str
+  {
+    ~"Transform {" + " submat: "    + self.submat.to_str()    +
+                     " subtrans: "  + self.subtrans.to_str()  + " }"
+  }
+}

src/dim2/mat2.rs

@@ -2,6 +2,7 @@ use core::num::{One, Zero};
 use traits::dim::Dim;
 use traits::inv::Inv;
 use traits::transpose::Transpose;
+use traits::workarounds::rlmul::{RMul, LMul};
 use dim2::vec2::Vec2;
 
 #[deriving(Eq)]
@@ -45,11 +46,11 @@ impl<T:Copy + Zero> Zero for Mat2<T>
                 _0, _0)
   }
 
-  // fn is_zero(&self) -> bool
+  fn is_zero(&self) -> bool
-  // {
+  {
-  //   self.m11.is_zero() && self.m11.is_zero() && self.m12.is_zero()
+    self.m11.is_zero() && self.m12.is_zero() &&
-  //   && self.m21.is_zero() && self.m21.is_zero() && self.m22.is_zero()
+    self.m21.is_zero() && self.m22.is_zero()
-  // }
+  }
 }
 
 impl<T:Copy + Mul<T, T> + Add<T, T>> Mul<Mat2<T>, Mat2<T>> for Mat2<T>
@@ -64,31 +65,47 @@ impl<T:Copy + Mul<T, T> + Add<T, T>> Mul<Mat2<T>, Mat2<T>> for Mat2<T>
   }
 }
 
-// FIXME: implementation of multiple classes for the same struct fails
+impl<T:Copy + Add<T, T> + Mul<T, T>> RMul<Vec2<T>> for Mat2<T>
-// with "internal compiler error: Asked to compute kind of a type variable".
-//
-// impl<T:Copy + Mul<T, T> + Add<T, T>> Mul<Vec2<T>, Vec2<T>> for Mat2<T>
-// {
-//   fn mul(&self, v: &Vec2<T>) -> Vec2<T>
-//   { Vec2(self.m11 * v.x + self.m12 * v.y, self.m21 * v.x + self.m22 * v.y) }
-// }
-
-impl<T:Copy + Mul<T, T> + Add<T, T>> Mul<Mat2<T>, Vec2<T>> for Vec2<T>
 {
-  fn mul(&self, m: &Mat2<T>) -> Vec2<T>
+  fn rmul(&self, other: &Vec2<T>) -> Vec2<T>
-  { Vec2(self.x * m.m11 + self.y * m.m21, self.x * m.m12 + self.y * m.m22) }
+  {
+    Vec2(
+      self.m11 * other.x + self.m12 * other.y,
+      self.m21 * other.x + self.m22 * other.y
+    )
+  }
 }
 
-impl<T:Copy + Mul<T, T> + Div<T, T> + Sub<T, T> + Neg<T> + Eq + Zero>
+impl<T:Copy + Add<T, T> + Mul<T, T>> LMul<Vec2<T>> for Mat2<T>
+{
+  fn lmul(&self, other: &Vec2<T>) -> Vec2<T>
+  {
+    Vec2(
+      self.m11 * other.x + self.m21 * other.y,
+      self.m12 * other.x + self.m22 * other.y
+    )
+  }
+}
+
+impl<T:Copy + Mul<T, T> + Quot<T, T> + Sub<T, T> + Neg<T> + Eq + Zero>
 Inv for Mat2<T>
 {
-  fn inv(&self) -> Mat2<T>
+  fn inverse(&self) -> Mat2<T>
+  {
+    let mut res : Mat2<T> = *self;
+
+    res.invert();
+
+    res
+  }
+
+  fn invert(&mut self)
   {
     let det = self.m11 * self.m22 - self.m21 * self.m12;
 
     assert!(det != Zero::zero());
 
-    Mat2(self.m22 / det , -self.m12 / det,
+    *self = Mat2(self.m22 / det , -self.m12 / det,
                  -self.m21 / det, self.m11 / det)
   }
 }

src/dim2/rotmat2.rs

@@ -1,92 +0,0 @@
-use core::num::{One, Zero};
-use traits::workarounds::trigonometric::Trigonometric;
-use traits::dim::Dim;
-use dim2::mat2::Mat2;
-// use dim2::vec2::Vec2;
-
-// FIXME: using a newtype did not compile (due a compiler bug)
-// pub type Rotmat2<T> = (Mat2<T>)
-#[deriving(Eq)]
-pub struct Rotmat2<T>
-{
-  priv submat: Mat2<T>
-}
-
-pub fn Rotmat2<T:Copy + Trigonometric + Neg<T>>(angle: T) -> Rotmat2<T>
-{
-  let coa = angle.cos();
-  let sia = angle.sin();
-
-  Rotmat2
-  { submat: Mat2(coa, -sia, sia, coa) }
-}
-
-impl<T> Dim for Rotmat2<T>
-{
-  fn dim() -> uint
-  { 2 }
-}
- 
-impl<T:Copy + One + Zero> One for Rotmat2<T>
-{
-  fn one() -> Rotmat2<T>
-  { Rotmat2 { submat: One::one() } }
-}
-
-impl<T:Copy + Mul<T, T> + Add<T, T>> Mul<Rotmat2<T>, Rotmat2<T>> for Rotmat2<T>
-{
-  fn mul(&self, other: &Rotmat2<T>) -> Rotmat2<T>
-  { Rotmat2 { submat: self.submat.mul(&other.submat) } }
-}
-
-// FIXME: implementation of the same classes for the same struct fails
-// with "internal compiler error: Asked to compute kind of a type variable".
-//
-// impl<T:Copy + Mul<T, T> + Add<T, T>> Mul<Vec2<T>, Vec2<T>> for Rotmat2<T>
-// {
-//   fn mul(&self, v: &Vec2<T>) -> Vec2<T>
-//   { Vec2(self.m11 * v.x + self.m12 * v.y, self.m21 * v.x + self.m22 * v.y) }
-// }
-
-// FIXME: implementation of the same classes for the same struct (here Vec2<T>)
-// fails with "internal compiler error: Asked to compute kind of a type
-// variable".
-//
-// impl<T:Copy + Mul<T, T> + Add<T, T>> Mul<Rotmat2<T>, Vec2<T>> for Vec2<T>
-// {
-//   fn mul(&self, m: &Rotmat2<T>) -> Vec2<T>
-//   { self.mult(&m.submat) }
-// }
-
-/*
-impl<T:Copy + Mul<T, T> + Div<T, T> + Sub<T, T> + Neg<T> + Eq + Zero>
-Inv<T> for Rotmat2<T>
-{
-  fn inv(&self) -> Rotmat2<T>
-  {
-    // transpose
-    Rotmat2(
-      Mat2(
-        self.submat.m11, self.submat.m21,
-        self.submat.m12, self.submat.m22
-      )
-    )
-  }
-}
-*/
-
-/*
-impl<T:ToStr> ToStr for Rotmat2<T>
-{
-  fn to_str(&self) -> ~str
-  {
-    ~"Rotmat2 {"
-    + " m11: " + self.m11.to_str()
-    + " m12: " + self.m12.to_str()
-
-    + " m21: " + self.m21.to_str()
-    + " m22: " + self.m22.to_str()
-    + " }"
-  }
-}
-*/

src/dim2/vec2.rs

@@ -1,8 +1,7 @@
-use core::num::Zero;
+use core::num::{Zero, Algebraic};
 use traits::dot::Dot;
 use traits::dim::Dim;
 use traits::cross::Cross;
-use traits::workarounds::sqrt::Sqrt;
 
 #[deriving(Eq)]
 pub struct Vec2<T>
@@ -32,7 +31,7 @@ impl<T:Copy + Sub<T,T>> Sub<Vec2<T>, Vec2<T>> for Vec2<T>
   { Vec2(self.x - other.x, self.y - other.y) }
 }
 
-impl<T:Copy + Mul<T, T> + Add<T, T> + Sqrt> Dot<T> for Vec2<T>
+impl<T:Copy + Mul<T, T> + Add<T, T> + Algebraic> Dot<T> for Vec2<T>
 {
   fn dot(&self, other : &Vec2<T>) -> T
   { self.x * other.x + self.y * other.y } 
@@ -50,6 +49,12 @@ impl<T:Copy + Mul<T, T> + Sub<T, T>> Cross<T> for Vec2<T>
   { self.x * other.y - self.y * other.x }
 }
 
+impl<T:Copy + Neg<T>> Neg<Vec2<T>> for Vec2<T>
+{
+  fn neg(&self) -> Vec2<T>
+  { Vec2(-self.x, -self.y) }
+}
+
 impl<T:Copy + Zero> Zero for Vec2<T>
 {
   fn zero() -> Vec2<T>
@@ -57,6 +62,9 @@ impl<T:Copy + Zero> Zero for Vec2<T>
     let _0 = Zero::zero();
     Vec2(_0, _0)
   }
+
+  fn is_zero(&self) -> bool
+  { self.x.is_zero() && self.y.is_zero() }
 }
 
 impl<T:ToStr> ToStr for Vec2<T>

src/dim3/mat3.rs

@@ -1,8 +1,8 @@
 use core::num::{One, Zero};
-// use core::rand::{Rand, Rng};
 use traits::dim::Dim;
 use traits::inv::Inv;
 use traits::transpose::Transpose;
+use traits::workarounds::rlmul::{RMul, LMul};
 use dim3::vec3::Vec3;
 
 #[deriving(Eq)]
@@ -51,11 +51,18 @@ impl<T:Copy + Zero> Zero for Mat3<T>
                 _0, _0, _0,
                 _0, _0, _0)
   }
+
+  fn is_zero(&self) -> bool
+  {
+    self.m11.is_zero() && self.m12.is_zero() && self.m13.is_zero() &&
+    self.m21.is_zero() && self.m22.is_zero() && self.m23.is_zero() &&
+    self.m31.is_zero() && self.m32.is_zero() && self.m33.is_zero()
+  }
 }
 
 impl<T:Copy + Mul<T, T> + Add<T, T>> Mul<Mat3<T>, Mat3<T>> for Mat3<T>
 {
-  fn mul(&self, other : &Mat3<T>) -> Mat3<T>
+  fn mul(&self, other: &Mat3<T>) -> Mat3<T>
   {
     Mat3(
       self.m11 * other.m11  + self.m12 * other.m21 + self.m13 * other.m31,
@@ -73,34 +80,44 @@ impl<T:Copy + Mul<T, T> + Add<T, T>> Mul<Mat3<T>, Mat3<T>> for Mat3<T>
   }
 }
 
-// FIXME: implementation of multiple classes for the same struct fails
+impl<T:Copy + Add<T, T> + Mul<T, T>> RMul<Vec3<T>> for Mat3<T>
-// with "internal compiler error: Asked to compute kind of a type variable".
-//
-// impl<T:Copy + Mul<T, T> + Add<T, T>> Mul<Vec3<T>, Vec3<T>> for Mat3<T>
-// {
-//   fn mul(&self, m : &Mat3<T>) -> Vec3<T>
-//   {
-//     Vec3(self.x * m.m11 + self.y * m.m21 + self.z * m.m31,
-//          self.x * m.m12 + self.y * m.m22 + self.z * m.m32,
-//          self.x * m.m13 + self.y * m.m23 + self.z * m.m33)
-//   }
-// }
-
-impl<T:Copy + Mul<T, T> + Add<T, T>> Mul<Mat3<T>, Vec3<T>> for Vec3<T>
 {
-  fn mul(&self, m : &Mat3<T>) -> Vec3<T>
+  fn rmul(&self, other: &Vec3<T>) -> Vec3<T>
   {
-    Vec3(self.x * m.m11 + self.y * m.m21 + self.z * m.m31,
+    Vec3(
-         self.x * m.m12 + self.y * m.m22 + self.z * m.m32,
+      self.m11 * other.x + self.m12 * other.y + self.m13 * other.z,
-         self.x * m.m13 + self.y * m.m23 + self.z * m.m33)
+      self.m21 * other.x + self.m22 * other.y + self.m33 * other.z,
+      self.m31 * other.x + self.m32 * other.y + self.m33 * other.z
+    )
   }
 }
 
-impl<T:Copy + Mul<T, T> + Div<T, T> + Sub<T, T> + Add<T, T> + Neg<T>
+impl<T:Copy + Add<T, T> + Mul<T, T>> LMul<Vec3<T>> for Mat3<T>
+{
+  fn lmul(&self, other: &Vec3<T>) -> Vec3<T>
+  {
+    Vec3(
+      self.m11 * other.x + self.m21 * other.y + self.m31 * other.z,
+      self.m12 * other.x + self.m22 * other.y + self.m32 * other.z,
+      self.m13 * other.x + self.m23 * other.y + self.m33 * other.z
+    )
+  }
+}
+
+impl<T:Copy + Mul<T, T> + Quot<T, T> + Sub<T, T> + Add<T, T> + Neg<T>
      + Eq + Zero>
 Inv for Mat3<T>
 {
-  fn inv(&self) -> Mat3<T>
+  fn inverse(&self) -> Mat3<T>
+  {
+    let mut res = *self;
+
+    res.invert();
+
+    res
+  }
+
+  fn invert(&mut self)
   {
     let minor_m22_m33 = self.m22 * self.m33 - self.m32 * self.m23;
     let minor_m21_m33 = self.m21 * self.m33 - self.m31 * self.m23;
@@ -112,7 +129,7 @@ Inv for Mat3<T>
 
     assert!(det != Zero::zero());
 
-    Mat3(
+    *self = Mat3(
       (minor_m22_m33  / det),
       ((self.m13 * self.m32 - self.m33 * self.m12) / det),
       ((self.m12 * self.m23 - self.m22 * self.m13) / det),

src/dim3/vec3.rs

@@ -1,8 +1,7 @@
-use core::num::Zero;
+use core::num::{Zero, Algebraic};
 use traits::dim::Dim;
 use traits::dot::Dot;
 use traits::cross::Cross;
-use traits::workarounds::sqrt::Sqrt;
 
 #[deriving(Eq)]
 pub struct Vec3<T>
@@ -33,7 +32,13 @@ impl<T:Copy + Sub<T,T>> Sub<Vec3<T>, Vec3<T>> for Vec3<T>
   { Vec3(self.x - other.x, self.y - other.y, self.z - other.z) }
 }
 
-impl<T:Copy + Mul<T, T> + Add<T, T> + Sqrt> Dot<T> for Vec3<T>
+impl<T:Copy + Neg<T>> Neg<Vec3<T>> for Vec3<T>
+{
+  fn neg(&self) -> Vec3<T>
+  { Vec3(-self.x, -self.y, -self.z) }
+}
+
+impl<T:Copy + Mul<T, T> + Add<T, T> + Algebraic> Dot<T> for Vec3<T>
 {
   fn dot(&self, other : &Vec3<T>) -> T
   { self.x * other.x + self.y * other.y + self.z * other.z } 
@@ -64,6 +69,9 @@ impl<T:Copy + Zero> Zero for Vec3<T>
     let _0 = Zero::zero();
     Vec3(_0, _0, _0)
   }
+
+  fn is_zero(&self) -> bool
+  { self.x.is_zero() && self.y.is_zero() && self.z.is_zero() }
 }
 
 impl<T:ToStr> ToStr for Vec3<T>

src/nalgebra.rc

@@ -12,26 +12,26 @@ pub use dim3::mat3::Mat3;
 
 pub use dim2::vec2::Vec2;
 pub use dim2::mat2::Mat2;
-pub use dim2::rotmat2::Rotmat2;
 
 pub use ndim::nvec::NVec;
 pub use ndim::nmat::NMat;
 
+pub use adaptors::rotmat::Rotmat;
+pub use adaptors::transform::Transform;
+
 pub use traits::dot::Dot;
 pub use traits::cross::Cross;
 pub use traits::dim::Dim;
-
-pub use traits::workarounds::sqrt::Sqrt;
-pub use traits::workarounds::trigonometric::Trigonometric;
-
 pub use traits::inv::Inv;
 pub use traits::transpose::Transpose;
 
+pub use traits::workarounds::rlmul::{RMul, LMul};
+pub use traits::workarounds::trigonometric::Trigonometric;
+
 mod dim2
 {
   mod vec2;
   mod mat2;
-  mod rotmat2;
 }
 
 mod dim3
@@ -46,6 +46,12 @@ mod ndim
   mod nmat;
 }
 
+mod adaptors
+{
+  mod rotmat;
+  mod transform;
+}
+
 mod traits
 {
   mod dot;
@@ -56,7 +62,7 @@ mod traits
 
   mod workarounds
   {
-    mod sqrt;
+    mod rlmul;
     mod trigonometric;
   }
 }

src/ndim/nmat.rs

@@ -1,9 +1,10 @@
 use core::num::{One, Zero};
-use core::vec::{from_elem, swap};
+use core::vec::{from_elem, swap, all};
 use traits::dim::Dim;
 use traits::inv::Inv;
 use traits::transpose::Transpose;
-// use ndim::nvec::NVec;
+use traits::workarounds::rlmul::{RMul, LMul};
+use ndim::nvec::NVec;
 
 // D is a phantom type parameter, used only as a dimensional token.
 // Its allows use to encode the vector dimension at the type-level.
@@ -15,6 +16,12 @@ pub struct NMat<D, T>
   mij: ~[T]
 }
 
+impl<D, T: Clone> Clone for NMat<D, T>
+{
+  fn clone(&self) -> NMat<D, T>
+  { NMat{ mij: self.mij.clone() } }
+}
+
 impl<D: Dim, T: Copy> NMat<D, T>
 {
   fn offset(i: uint, j: uint) -> uint
@@ -59,6 +66,9 @@ impl<D: Dim, T:Copy + Zero> Zero for NMat<D, T>
 
     NMat{ mij: from_elem(dim * dim, Zero::zero()) }
   }
+
+  fn is_zero(&self) -> bool
+  { all(self.mij, |e| e.is_zero()) }
 }
 
 impl<D: Dim, T:Copy + Mul<T, T> + Add<T, T> + Zero>
@@ -86,13 +96,59 @@ Mul<NMat<D, T>, NMat<D, T>> for NMat<D, T>
   }
 }
 
+impl<D: Dim, T:Copy + Add<T, T> + Mul<T, T> + Zero>
+RMul<NVec<D, T>> for NMat<D, T>
+{
+  fn rmul(&self, other: &NVec<D, T>) -> NVec<D, T>
+  {
+    let     dim              = Dim::dim::<D>();
+    let mut res : NVec<D, T> = Zero::zero();
+
+    for uint::range(0u, dim) |i|
+    {
+      for uint::range(0u, dim) |j|
+      { res.at[i] = res.at[i] + other.at[j] * self[(i, j)]; }
+    }
+
+    res
+  }
+}
+
+impl<D: Dim, T:Copy + Add<T, T> + Mul<T, T> + Zero>
+LMul<NVec<D, T>> for NMat<D, T>
+{
+  fn lmul(&self, other: &NVec<D, T>) -> NVec<D, T>
+  {
+    let     dim              = Dim::dim::<D>();
+    let mut res : NVec<D, T> = Zero::zero();
+
+    for uint::range(0u, dim) |i|
+    {
+      for uint::range(0u, dim) |j|
+      { res.at[i] = res.at[i] + other.at[j] * self[(j, i)]; }
+    }
+
+    res
+  }
+}
+
 impl<D: Dim,
-     T: Copy + Mul<T, T> + Div<T, T> + Sub<T, T> + Neg<T> + Eq + One + Zero>
+     T: Clone + Copy + Eq + One + Zero +
+        Mul<T, T> + Quot<T, T> + Sub<T, T> + Neg<T>
+     >
 Inv for NMat<D, T>
 {
-  fn inv(&self) -> NMat<D, T>
+  fn inverse(&self) -> NMat<D, T>
+  {
+    let mut res : NMat<D, T> = self.clone();
+
+    res.invert();
+
+    res
+  }
+
+  fn invert(&mut self)
   {
-    let mut cpy = copy *self;
     let     dim = Dim::dim::<D>();
     let mut res = One::one::<NMat<D, T>>();
     let     _0T = Zero::zero::<T>();
@@ -111,7 +167,7 @@ Inv for NMat<D, T>
 
       while (n0 != dim)
       {
-        if (cpy[(n0, k)] != _0T)
+        if (self[(n0, k)] != _0T)
         { break; }
 
         n0 += 1;
@@ -124,7 +180,7 @@ Inv for NMat<D, T>
       {
         for uint::range(0u, dim) |j|
         {
-          swap(cpy.mij,
+          swap(self.mij,
                NMat::offset::<D, T>(n0, j),
                NMat::offset::<D, T>(k, j));
           swap(res.mij,
@@ -133,11 +189,11 @@ Inv for NMat<D, T>
         }
       }
 
-      let pivot = cpy[(k, k)];
+      let pivot = self[(k, k)];
 
       for uint::range(k, dim) |j|
       {
-        cpy.set(k, j, &(cpy[(k, j)] / pivot));
+        self.set(k, j, &(self[(k, j)] / pivot));
         res.set(k, j, &(res[(k, j)] / pivot));
       }
 
@@ -145,18 +201,16 @@ Inv for NMat<D, T>
       {
         if (l != k)
         {
-          let normalizer = cpy[(l, k)] / pivot;
+          let normalizer = self[(l, k)] / pivot;
 
           for uint::range(k, dim) |j|
           {
-            cpy.set(k, j, &(cpy[(l, j)] - cpy[(k, j)] * normalizer));
+            self.set(k, j, &(self[(l, j)] - self[(k, j)] * normalizer));
             res.set(k, j, &(res[(l, j)] - res[(k, j)] * normalizer));
           }
         }
       }
     }
-
-    res
   }
 }
 

src/ndim/nvec.rs

@@ -1,8 +1,7 @@
-use core::vec::{map2, from_elem};
+use core::vec::{map_zip, from_elem, map, all};
-use core::num::Zero;
+use core::num::{Zero, Algebraic};
 use traits::dim::Dim;
 use traits::dot::Dot;
-use traits::workarounds::sqrt::Sqrt;
 
 // D is a phantom parameter, used only as a dimensional token.
 // Its allows use to encode the vector dimension at the type-level.
@@ -26,16 +25,23 @@ impl<D: Dim, T> Dim for NVec<D, T>
 impl<D, T:Copy + Add<T,T>> Add<NVec<D, T>, NVec<D, T>> for NVec<D, T>
 {
   fn add(&self, other: &NVec<D, T>) -> NVec<D, T>
-  { NVec { at: map2(self.at, other.at, | a, b | { *a + *b }) } }
+  { NVec { at: map_zip(self.at, other.at, | a, b | { *a + *b }) } }
 }
 
 impl<D, T:Copy + Sub<T,T>> Sub<NVec<D, T>, NVec<D, T>> for NVec<D, T>
 {
   fn sub(&self, other: &NVec<D, T>) -> NVec<D, T>
-  { NVec { at: map2(self.at, other.at, | a, b | *a - *b) } }
+  { NVec { at: map_zip(self.at, other.at, | a, b | *a - *b) } }
 }
 
-impl<D: Dim, T:Copy + Mul<T, T> + Add<T, T> + Sqrt + Zero> Dot<T> for NVec<D, T>
+impl<D, T:Copy + Neg<T>> Neg<NVec<D, T>> for NVec<D, T>
+{
+  fn neg(&self) -> NVec<D, T>
+  { NVec { at: map(self.at, |a| -a) } }
+}
+
+impl<D: Dim, T:Copy + Mul<T, T> + Add<T, T> + Algebraic + Zero>
+Dot<T> for NVec<D, T>
 {
   fn dot(&self, other: &NVec<D, T>) -> T
   {
@@ -70,6 +76,11 @@ impl<D: Dim, T:Copy + Zero> Zero for NVec<D, T>
 
     NVec { at: from_elem(Dim::dim::<D>(), _0) }
   }
+
+  fn is_zero(&self) -> bool
+  {
+    all(self.at, |e| e.is_zero())
+  }
 }
 
 impl<D: Dim, T:ToStr> ToStr for NVec<D, T>

src/traits/inv.rs

@@ -1,4 +1,5 @@
 pub trait Inv
 {
-  fn inv(&self) -> Self;
+  fn inverse(&self) -> Self;
+  fn invert(&mut self);
 }

src/traits/workarounds/README

@@ -0,0 +1,4 @@
+This packages contains everything done because current (stable) compiler either
+bugs or miss features.
+Therefore, keep in mind anything in there will be inevitably removed some days.
+So dont rely on them too much.

src/traits/workarounds/rlmul.rs

@@ -0,0 +1,18 @@
+/** This is a workaround of the fact we cannot implement the same trait
+ * (with different type parameters) twice for the same type:
+ * ~~~
+ * trait Mul<V, V> for M
+ * trait Mul<V2, V2> for M
+ * ~~~
+ */
+pub trait RMul<V>
+{
+  /// Computes self * v
+  fn rmul(&self, v : &V) -> V;
+}
+
+pub trait LMul<V>
+{
+  /// Computes v * self
+  fn lmul(&self, &V) -> V;
+}

src/traits/workarounds/sqrt.rs

@@ -1,17 +0,0 @@
-// FIXME: this does not seem to exist already
-// but it will surely be added someday.
-
-pub trait Sqrt
-{
-  fn sqrt(&self) -> Self;
-}
-
-impl Sqrt for f64
-{
-  fn sqrt(&self) -> f64 { f64::sqrt(*self) }
-}
-
-impl Sqrt for f32
-{
-  fn sqrt(&self) -> f32 { f32::sqrt(*self) }
-}

src/traits/workarounds/trigonometric.rs

@@ -1,5 +1,19 @@
+// Trigonometric is available in core, but compilation fails with internal
+// error.
+
+use core::f64::{cos, sin};
+
 pub trait Trigonometric
 {
-  fn sin(&self) -> Self;
+  fn cos(Self) -> Self;
-  fn cos(&self) -> Self;
+  fn sin(Self) -> Self;
+}
+
+impl Trigonometric for f64
+{
+  fn cos(a: f64) -> f64
+  { cos(a) }
+
+  fn sin(a: f64) -> f64
+  { sin(a) }
 }