Add tests and basis generation.

Makefile

@@ -1,7 +1,11 @@
+nalgebra_lib_path=lib
 all:
-	rust build src/nalgebra.rc --out-dir lib # rustpkg install
+	rust build src/nalgebra.rc --out-dir $(nalgebra_lib_path)
+
+test:
+	rust test src/nalgebra.rc
 
 doc:
-	rust doc src/nalgebra.rc --output-dir doc
+	rust test src/nalgebra.rc
 
-.PHONY:doc
+.PHONY:doc, test

src/dim1/vec1.rs

@@ -1,8 +1,10 @@
-use core::num::{Zero, Algebraic};
+use core::num::{Zero, One, Algebraic};
 use core::rand::{Rand, Rng, RngUtil};
 use std::cmp::FuzzyEq;
 use traits::dot::Dot;
 use traits::dim::Dim;
+use traits::basis::Basis;
+use traits::norm::Norm;
 
 #[deriving(Eq)]
 pub struct Vec1<T>
@@ -33,12 +35,28 @@ impl<T:Copy + Mul<T, T> + Add<T, T> + Algebraic> Dot<T> for Vec1<T>
 {
   fn dot(&self, other : &Vec1<T>) -> T
   { self.x * other.x } 
+}
 
+impl<T:Copy + Mul<T, T> + Add<T, T> + Quot<T, T> + Algebraic>
+Norm<T> for Vec1<T>
+{
   fn sqnorm(&self) -> T
   { self.dot(self) }
 
   fn norm(&self) -> T
   { self.sqnorm().sqrt() }
+
+  fn normalized(&self) -> Vec1<T>
+  { Vec1(self.x / self.norm()) }
+
+  fn normalize(&mut self) -> T
+  {
+    let l = self.norm();
+
+    self.x /= l;
+
+    l
+  }
 }
 
 impl<T:Copy + Neg<T>> Neg<Vec1<T>> for Vec1<T>
@@ -59,6 +77,15 @@ impl<T:Copy + Zero> Zero for Vec1<T>
   { self.x.is_zero() }
 }
 
+impl<T: Copy + One> Basis for Vec1<T>
+{
+  fn canonical_basis()     -> ~[Vec1<T>]
+  { ~[ Vec1(One::one()) ] } // FIXME: this should be static
+
+  fn orthogonal_subspace_basis(&self) -> ~[Vec1<T>]
+  { ~[] }
+}
+
 impl<T:FuzzyEq<T>> FuzzyEq<T> for Vec1<T>
 {
   fn fuzzy_eq(&self, other: &Vec1<T>) -> bool

src/dim2/vec2.rs

@@ -1,9 +1,11 @@
-use core::num::{Zero, Algebraic};
+use core::num::{Zero, One, Algebraic};
 use core::rand::{Rand, Rng, RngUtil};
 use std::cmp::FuzzyEq;
 use traits::dot::Dot;
 use traits::dim::Dim;
 use traits::cross::Cross;
+use traits::basis::Basis;
+use traits::norm::Norm;
 use dim1::vec1::Vec1;
 
 #[deriving(Eq)]
@@ -38,12 +40,33 @@ 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 } 
+}
 
+impl<T:Copy + Mul<T, T> + Add<T, T> + Quot<T, T> + Algebraic>
+Norm<T> for Vec2<T>
+{
   fn sqnorm(&self) -> T
   { self.dot(self) }
 
   fn norm(&self) -> T
   { self.sqnorm().sqrt() }
+
+  fn normalized(&self) -> Vec2<T>
+  {
+    let l = self.norm();
+
+    Vec2(self.x / l, self.y / l)
+  }
+
+  fn normalize(&mut self) -> T
+  {
+    let l = self.norm();
+
+    self.x /= l;
+    self.y /= l;
+
+    l
+  }
 }
 
 impl<T:Copy + Mul<T, T> + Sub<T, T>> Cross<Vec1<T>> for Vec2<T>
@@ -70,6 +93,19 @@ impl<T:Copy + Zero> Zero for Vec2<T>
   { self.x.is_zero() && self.y.is_zero() }
 }
 
+impl<T: Copy + One + Zero + Neg<T>> Basis for Vec2<T>
+{
+  fn canonical_basis()     -> ~[Vec2<T>]
+  {
+    // FIXME: this should be static
+    ~[ Vec2(One::one(), Zero::zero()),
+       Vec2(Zero::zero(), One::one()) ]
+  }
+
+  fn orthogonal_subspace_basis(&self) -> ~[Vec2<T>]
+  { ~[ Vec2(-self.y, self.x) ] }
+}
+
 impl<T:FuzzyEq<T>> FuzzyEq<T> for Vec2<T>
 {
   fn fuzzy_eq(&self, other: &Vec2<T>) -> bool

src/dim3/mat3.rs

@@ -128,7 +128,7 @@ Inv for Mat3<T>
               - self.m12 * minor_m21_m33
               + self.m13 * minor_m21_m32;
 
-    assert!(det.is_zero());
+    assert!(!det.is_zero());
 
     *self = Mat3(
       (minor_m22_m33  / det),

src/dim3/vec3.rs

@@ -1,9 +1,11 @@
-use core::num::{Zero, Algebraic};
+use core::num::{Zero, One, Algebraic, abs};
 use core::rand::{Rand, Rng, RngUtil};
 use std::cmp::FuzzyEq;
 use traits::dim::Dim;
 use traits::dot::Dot;
 use traits::cross::Cross;
+use traits::basis::Basis;
+use traits::norm::Norm;
 
 #[deriving(Eq)]
 pub struct Vec3<T>
@@ -44,12 +46,34 @@ 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 } 
+}
 
+impl<T:Copy + Mul<T, T> + Add<T, T> + Quot<T, T> + Algebraic>
+Norm<T> for Vec3<T>
+{
   fn sqnorm(&self) -> T
   { self.dot(self) }
 
   fn norm(&self) -> T
   { self.sqnorm().sqrt() }
+
+  fn normalized(&self) -> Vec3<T>
+  {
+    let l = self.norm();
+
+    Vec3(self.x / l, self.y / l, self.z / l)
+  }
+
+  fn normalize(&mut self) -> T
+  {
+    let l = self.norm();
+
+    self.x /= l;
+    self.y /= l;
+    self.z /= l;
+
+    l
+  }
 }
 
 impl<T:Copy + Mul<T, T> + Sub<T, T>> Cross<Vec3<T>> for Vec3<T>
@@ -76,6 +100,30 @@ impl<T:Copy + Zero> Zero for Vec3<T>
   { self.x.is_zero() && self.y.is_zero() && self.z.is_zero() }
 }
 
+impl<T: Copy + One + Zero + Neg<T> + Ord + Mul<T, T> + Sub<T, T> + Add<T, T> +
+        Quot<T, T> + Algebraic>
+Basis for Vec3<T>
+{
+  fn canonical_basis() -> ~[Vec3<T>]
+  {
+    // FIXME: this should be static
+    ~[ Vec3(One::one(), Zero::zero(), Zero::zero()),
+       Vec3(Zero::zero(), One::one(), Zero::zero()),
+       Vec3(Zero::zero(), Zero::zero(), One::one()) ]
+  }
+
+  fn orthogonal_subspace_basis(&self) -> ~[Vec3<T>]
+  {
+      let a = 
+        if (abs(self.x) > abs(self.y))
+        { Vec3(self.z, Zero::zero(), -self.x).normalized() }
+        else
+        { Vec3(Zero::zero(), -self.z, self.y).normalized() };
+
+      ~[ a, a.cross(self) ]
+  }
+}
+
 impl<T:FuzzyEq<T>> FuzzyEq<T> for Vec3<T>
 {
   fn fuzzy_eq(&self, other: &Vec3<T>) -> bool

src/nalgebra.rc

@@ -27,9 +27,12 @@ pub use traits::cross::Cross;
 pub use traits::dim::Dim;
 pub use traits::inv::Inv;
 pub use traits::transpose::Transpose;
+pub use traits::basis::Basis;
+pub use traits::norm::Norm;
 
 pub use traits::workarounds::rlmul::{RMul, LMul};
 pub use traits::workarounds::trigonometric::Trigonometric;
+pub use traits::workarounds::scalar_op::ScalarOp;
 
 mod dim2
 {
@@ -68,10 +71,19 @@ mod traits
   mod inv;
   mod transpose;
   mod dim;
+  mod basis;
+  mod norm;
 
   mod workarounds
   {
     mod rlmul;
     mod trigonometric;
+    mod scalar_op;
   }
 }
+
+mod tests
+{
+  mod mat;
+  mod vec;
+}

src/ndim/nvec.rs

@@ -1,9 +1,12 @@
-use core::vec::{map_zip, from_elem, map, all, all2};
+use core::num::{Zero, One, Algebraic};
 use core::rand::{Rand, Rng, RngUtil};
-use core::num::{Zero, Algebraic};
+use core::vec::{map_zip, from_elem, map, all, all2};
 use std::cmp::FuzzyEq;
 use traits::dim::Dim;
 use traits::dot::Dot;
+use traits::norm::Norm;
+use traits::basis::Basis;
+use traits::workarounds::scalar_op::ScalarOp;
 
 // D is a phantom parameter, used only as a dimensional token.
 // Its allows use to encode the vector dimension at the type-level.
@@ -24,25 +27,31 @@ impl<D: Dim, T> Dim for NVec<D, T>
   { Dim::dim::<D>() }
 }
 
-impl<D, T:Copy + Add<T,T>> Add<NVec<D, T>, NVec<D, T>> for NVec<D, T>
+impl<D, T: Clone> Clone for NVec<D, T>
+{
+  fn clone(&self) -> NVec<D, T>
+  { NVec{ at: self.at.clone() } }
+}
+
+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: 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>
+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: map_zip(self.at, other.at, | a, b | *a - *b) } }
 }
 
-impl<D, T:Copy + Neg<T>> Neg<NVec<D, 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>
+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
@@ -54,23 +63,142 @@ Dot<T> for NVec<D, T>
 
     res
   } 
+}
 
+impl<D: Dim, T: Copy + Mul<T, T> + Quot<T, T> + Add<T, T> + Sub<T, T>>
+ScalarOp<T> for NVec<D, T>
+{
+  fn scalar_mul(&self, s: &T) -> NVec<D, T>
+  { NVec { at: map(self.at, |a| a * *s) } }
+
+  fn scalar_div(&self, s: &T) -> NVec<D, T>
+  { NVec { at: map(self.at, |a| a / *s) } }
+
+  fn scalar_add(&self, s: &T) -> NVec<D, T>
+  { NVec { at: map(self.at, |a| a + *s) } }
+
+  fn scalar_sub(&self, s: &T) -> NVec<D, T>
+  { NVec { at: map(self.at, |a| a - *s) } }
+
+  fn scalar_mul_inplace(&mut self, s: &T)
+  {
+    for uint::range(0u, Dim::dim::<D>()) |i|
+    { self.at[i] *= *s; }
+  }
+
+  fn scalar_div_inplace(&mut self, s: &T)
+  {
+    for uint::range(0u, Dim::dim::<D>()) |i|
+    { self.at[i] /= *s; }
+  }
+
+  fn scalar_add_inplace(&mut self, s: &T)
+  {
+    for uint::range(0u, Dim::dim::<D>()) |i|
+    { self.at[i] += *s; }
+  }
+
+  fn scalar_sub_inplace(&mut self, s: &T)
+  {
+    for uint::range(0u, Dim::dim::<D>()) |i|
+    { self.at[i] -= *s; }
+  }
+}
+
+impl<D: Dim, T: Copy + Mul<T, T> + Add<T, T> + Quot<T, T> + Algebraic + Zero +
+                Clone>
+Norm<T> for NVec<D, T>
+{
   fn sqnorm(&self) -> T
   { self.dot(self) }
 
   fn norm(&self) -> T
   { self.sqnorm().sqrt() }
+
+  fn normalized(&self) -> NVec<D, T>
+  {
+    let mut res : NVec<D, T> = self.clone();
+
+    res.normalize();
+
+    res
+  }
+
+  fn normalize(&mut self) -> T
+  {
+    let l = self.norm();
+
+    for uint::range(0u, Dim::dim::<D>()) |i|
+    { self.at[i] /= l; }
+
+    l
+  }
+}
+
+impl<D: Dim,
+     T: Copy + One + Zero + Neg<T> + Ord + Mul<T, T> + Sub<T, T> + Add<T, T> +
+        Quot<T, T> + Algebraic + Clone + FuzzyEq<T>>
+Basis for NVec<D, T>
+{
+  fn canonical_basis() -> ~[NVec<D, T>]
+  {
+    let     dim = Dim::dim::<D>();
+    let mut res : ~[NVec<D, T>] = ~[];
+
+    for uint::range(0u, dim) |i|
+    {
+      let mut basis_element : NVec<D, T> = Zero::zero();
+
+      basis_element.at[i] = One::one();
+
+      res.push(basis_element);
+    }
+
+    res
+  }
+
+  fn orthogonal_subspace_basis(&self) -> ~[NVec<D, T>]
+  {
+    // compute the basis of the orthogonal subspace using Gram-Schmidt
+    // orthogonalization algorithm
+    let     dim = Dim::dim::<D>();
+    let mut res : ~[NVec<D, T>] = ~[];
+
+    for uint::range(0u, dim) |i|
+    {
+      let mut basis_element : NVec<D, T> = Zero::zero();
+
+      basis_element.at[i] = One::one();
+
+      if (res.len() == dim - 1)
+      { break; }
+
+      let mut elt = basis_element.clone();
+
+      elt -= self.scalar_mul(&basis_element.dot(self));
+
+      for res.each |v|
+      { elt -= v.scalar_mul(&elt.dot(v)) };
+
+      if (!elt.sqnorm().fuzzy_eq(&Zero::zero()))
+      { res.push(elt.normalized()); }
+    }
+
+    assert!(res.len() == dim - 1);
+
+    res
+  }
 }
 
 // FIXME: I dont really know how te generalize the cross product int
 // n-dimensions…
-// impl<T:Copy + Mul<T, T> + Sub<T, T>> Cross<T> for NVec<D, T>
+// impl<T: Copy + Mul<T, T> + Sub<T, T>> Cross<T> for NVec<D, T>
 // {
 //   fn cross(&self, other: &NVec<D, T>) -> T
 //   { self.x * other.y - self.y * other.x }
 // }
 
-impl<D: Dim, T:Copy + Zero> Zero for NVec<D, T>
+impl<D: Dim, T: Copy + Zero> Zero for NVec<D, T>
 {
   fn zero() -> NVec<D, T>
   {
@@ -85,7 +213,7 @@ impl<D: Dim, T:Copy + Zero> Zero for NVec<D, T>
   }
 }
 
-impl<D, T:FuzzyEq<T>> FuzzyEq<T> for NVec<D, T>
+impl<D, T: FuzzyEq<T>> FuzzyEq<T> for NVec<D, T>
 {
   fn fuzzy_eq(&self, other: &NVec<D, T>) -> bool
   { all2(self.at, other.at, |a, b| a.fuzzy_eq(b)) }
@@ -108,7 +236,7 @@ impl<D: Dim, T: Rand + Zero + Copy> Rand for NVec<D, T>
   }
 }
 
-impl<D: Dim, T:ToStr> ToStr for NVec<D, T>
+impl<D: Dim, T: ToStr> ToStr for NVec<D, T>
 {
   fn to_str(&self) -> ~str
   { ~"Vec" + Dim::dim::<D>().to_str() + self.at.to_str() }

src/tests/mat.rs

@@ -0,0 +1,63 @@
+#[test]
+use core::num::{One};
+#[test]
+use core::rand::{random};
+#[test]
+use std::cmp::FuzzyEq;
+// #[test]
+// use ndim::nmat::NMat;
+#[test]
+use dim1::mat1::Mat1;
+#[test]
+use dim2::mat2::Mat2;
+#[test]
+use dim3::mat3::Mat3;
+// #[test]
+// use traits::dim::d7;
+
+// FIXME: this one fails with an ICE: node_id_to_type: no type for node [...]
+// #[test]
+// fn test_inv_nmat()
+// {
+//   let randmat : NMat<d7, f64> = random();
+// 
+//   assert!((randmat.inverse() * randmat).fuzzy_eq(&One::one()));
+// }
+
+#[test]
+fn test_inv_mat1()
+{
+  for uint::range(0u, 10000u) |_|
+  {
+    let randmat : Mat1<f64> = random();
+
+    assert!((randmat.inverse() * randmat).fuzzy_eq(&One::one()));
+  }
+}
+
+#[test]
+fn test_inv_mat2()
+{
+  for uint::range(0u, 10000u) |_|
+  {
+    let randmat : Mat2<f64> = random();
+
+    assert!((randmat.inverse() * randmat).fuzzy_eq(&One::one()));
+  }
+}
+
+#[test]
+fn test_inv_mat3()
+{
+  for uint::range(0u, 10000u) |_|
+  {
+    let randmat : Mat3<f64> = random();
+
+    assert!((randmat.inverse() * randmat).fuzzy_eq(&One::one()));
+  }
+}
+
+#[test]
+fn test_rot2()
+{
+}

src/tests/vec.rs

@@ -0,0 +1,212 @@
+#[test]
+use core::num::{Zero, One};
+#[test]
+use core::rand::{random};
+#[test]
+use core::vec::{all, all2};
+#[test]
+use std::cmp::FuzzyEq;
+#[test]
+use dim3::vec3::Vec3;
+#[test]
+use dim2::vec2::Vec2;
+#[test]
+use dim1::vec1::Vec1;
+#[test]
+use ndim::nvec::NVec;
+#[test]
+use traits::dim::d7;
+#[test]
+use traits::basis::Basis;
+
+#[test]
+fn test_cross_vec3()
+{
+  for uint::range(0u, 10000u) |_|
+  {
+    let v1 : Vec3<f64> = random();
+    let v2 : Vec3<f64> = random();
+    let v3 : Vec3<f64> = v1.cross(&v2);
+
+    assert!(v3.dot(&v2).fuzzy_eq(&Zero::zero()));
+    assert!(v3.dot(&v1).fuzzy_eq(&Zero::zero()));
+  }
+}
+
+#[test]
+fn test_dot_nvec()
+{
+  for uint::range(0u, 10000u) |_|
+  {
+    let v1 : NVec<d7, f64> = random();
+    let v2 : NVec<d7, f64> = random();
+
+    assert!(v1.dot(&v2).fuzzy_eq(&v2.dot(&v1)));
+  }
+}
+
+#[test]
+fn test_commut_dot_vec3()
+{
+  for uint::range(0u, 10000u) |_|
+  {
+    let v1 : Vec3<f64> = random();
+    let v2 : Vec3<f64> = random();
+
+    assert!(v1.dot(&v2).fuzzy_eq(&v2.dot(&v1)));
+  }
+}
+
+#[test]
+fn test_commut_dot_vec2()
+{
+  for uint::range(0u, 10000u) |_|
+  {
+    let v1 : Vec2<f64> = random();
+    let v2 : Vec2<f64> = random();
+
+    assert!(v1.dot(&v2).fuzzy_eq(&v2.dot(&v1)));
+  }
+}
+
+#[test]
+fn test_commut_dot_vec1()
+{
+  for uint::range(0u, 10000u) |_|
+  {
+    let v1 : Vec1<f64> = random();
+    let v2 : Vec1<f64> = random();
+
+    assert!(v1.dot(&v2).fuzzy_eq(&v2.dot(&v1)));
+  }
+}
+
+#[test]
+fn test_basis_vec1()
+{
+  for uint::range(0u, 10000u) |_|
+  {
+    let basis = Basis::canonical_basis::<Vec1<f64>>();
+
+    // check vectors form an ortogonal basis
+    assert!(all2(basis, basis, |e1, e2| e1 == e2 || e1.dot(e2).fuzzy_eq(&Zero::zero())));
+    // check vectors form an orthonormal basis
+    assert!(all(basis, |e| e.norm().fuzzy_eq(&One::one())));
+  }
+}
+
+#[test]
+fn test_basis_vec2()
+{
+  for uint::range(0u, 10000u) |_|
+  {
+    let basis = Basis::canonical_basis::<Vec2<f64>>();
+
+    // check vectors form an ortogonal basis
+    assert!(all2(basis, basis, |e1, e2| e1 == e2 || e1.dot(e2).fuzzy_eq(&Zero::zero())));
+    // check vectors form an orthonormal basis
+    assert!(all(basis, |e| e.norm().fuzzy_eq(&One::one())));
+  }
+}
+
+#[test]
+fn test_basis_vec3()
+{
+  for uint::range(0u, 10000u) |_|
+  {
+    let basis = Basis::canonical_basis::<Vec3<f64>>();
+
+    // check vectors form an ortogonal basis
+    assert!(all2(basis, basis, |e1, e2| e1 == e2 || e1.dot(e2).fuzzy_eq(&Zero::zero())));
+    // check vectors form an orthonormal basis
+    assert!(all(basis, |e| e.norm().fuzzy_eq(&One::one())));
+  }
+}
+
+#[test]
+fn test_basis_nvec()
+{
+  for uint::range(0u, 10000u) |_|
+  {
+    let basis = Basis::canonical_basis::<NVec<d7, f64>>();
+
+    // check vectors form an ortogonal basis
+    assert!(all2(basis, basis, |e1, e2| e1 == e2 || e1.dot(e2).fuzzy_eq(&Zero::zero())));
+    // check vectors form an orthonormal basis
+    assert!(all(basis, |e| e.norm().fuzzy_eq(&One::one())));
+  }
+}
+
+#[test]
+fn test_subspace_basis_vec1()
+{
+  for uint::range(0u, 10000u) |_|
+  {
+    let v : Vec1<f64> = random();
+    let v1 = v.normalized();
+    let subbasis = v1.orthogonal_subspace_basis();
+
+    // check vectors are orthogonal to v1
+    assert!(all(subbasis, |e| v1.dot(e).fuzzy_eq(&Zero::zero())));
+    // check vectors form an ortogonal basis
+    assert!(all2(subbasis, subbasis, |e1, e2| e1 == e2 || e1.dot(e2).fuzzy_eq(&Zero::zero())));
+    // check vectors form an orthonormal basis
+    assert!(all(subbasis, |e| e.norm().fuzzy_eq(&One::one())));
+  }
+}
+
+#[test]
+fn test_subspace_basis_vec2()
+{
+  for uint::range(0u, 10000u) |_|
+  {
+    let v : Vec2<f64> = random();
+    let v1 = v.normalized();
+    let subbasis = v1.orthogonal_subspace_basis();
+
+    // check vectors are orthogonal to v1
+    assert!(all(subbasis, |e| v1.dot(e).fuzzy_eq(&Zero::zero())));
+    // check vectors form an ortogonal basis
+    assert!(all2(subbasis, subbasis, |e1, e2| e1 == e2 || e1.dot(e2).fuzzy_eq(&Zero::zero())));
+    // check vectors form an orthonormal basis
+    assert!(all(subbasis, |e| e.norm().fuzzy_eq(&One::one())));
+  }
+}
+
+#[test]
+fn test_subspace_basis_vec3()
+{
+  for uint::range(0u, 10000u) |_|
+  {
+    let v : Vec3<f64> = random();
+    let v1 = v.normalized();
+    let subbasis = v1.orthogonal_subspace_basis();
+
+    // check vectors are orthogonal to v1
+    assert!(all(subbasis, |e| v1.dot(e).fuzzy_eq(&Zero::zero())));
+    // check vectors form an ortogonal basis
+    assert!(all2(subbasis, subbasis, |e1, e2| e1 == e2 || e1.dot(e2).fuzzy_eq(&Zero::zero())));
+    // check vectors form an orthonormal basis
+    assert!(all(subbasis, |e| e.norm().fuzzy_eq(&One::one())));
+  }
+}
+
+// ICE
+//
+// #[test]
+// fn test_subspace_basis_vecn()
+// {
+//   for uint::range(0u, 10000u) |_|
+//   {
+//     let v : NVec<d7, f64> = random();
+//     let v1 = v.normalized();
+//     let subbasis = v1.orthogonal_subspace_basis();
+// 
+//     // check vectors are orthogonal to v1
+//     assert!(all(subbasis, |e| v1.dot(e).fuzzy_eq(&Zero::zero())));
+//     // check vectors form an ortogonal basis
+//     assert!(all2(subbasis, subbasis, |e1, e2| e1 == e2 || e1.dot(e2).fuzzy_eq(&Zero::zero())));
+//     // check vectors form an orthonormal basis
+//     assert!(all(subbasis, |e| e.norm().fuzzy_eq(&One::one())));
+//   }
+// }

src/traits/basis.rs

@@ -0,0 +1,5 @@
+pub trait Basis
+{
+  fn canonical_basis()                -> ~[Self]; // FIXME: is it the right pointer?
+  fn orthogonal_subspace_basis(&self) -> ~[Self];
+}

src/traits/dim.rs

@@ -1,5 +1,4 @@
-pub trait Dim
-{
+pub trait Dim {
   /// The dimension of the object.
   fn dim() -> uint;
 }
@@ -8,20 +7,44 @@ pub trait Dim
 // object at the type-level.
 /// Dimensional token for 0-dimensions. Dimensional tokens are the preferred
 /// way to specify at the type level the dimension of n-dimensional objects.
+#[deriving(Eq)]
 pub struct d0;
+
 /// Dimensional token for 1-dimension. Dimensional tokens are the preferred
 /// way to specify at the type level the dimension of n-dimensional objects.
+#[deriving(Eq)]
 pub struct d1;
+
 /// Dimensional token for 2-dimensions. Dimensional tokens are the preferred
 /// way to specify at the type level the dimension of n-dimensional objects.
+#[deriving(Eq)]
 pub struct d2;
+
 /// Dimensional token for 3-dimensions. Dimensional tokens are the preferred
 /// way to specify at the type level the dimension of n-dimensional objects.
+#[deriving(Eq)]
 pub struct d3;
+
 /// Dimensional token for 4-dimensions. Dimensional tokens are the preferred
 /// way to specify at the type level the dimension of n-dimensional objects.
+#[deriving(Eq)]
 pub struct d4;
 
+/// Dimensional token for 5-dimensions. Dimensional tokens are the preferred
+/// way to specify at the type level the dimension of n-dimensional objects.
+#[deriving(Eq)]
+pub struct d5;
+
+/// Dimensional token for 6-dimensions. Dimensional tokens are the preferred
+/// way to specify at the type level the dimension of n-dimensional objects.
+#[deriving(Eq)]
+pub struct d6;
+
+/// Dimensional token for 7-dimensions. Dimensional tokens are the preferred
+/// way to specify at the type level the dimension of n-dimensional objects.
+#[deriving(Eq)]
+pub struct d7;
+
 impl Dim for d0
 { fn dim() -> uint { 0 } }
 
@@ -36,3 +59,12 @@ impl Dim for d3
 
 impl Dim for d4
 { fn dim() -> uint { 4 } }
+
+impl Dim for d5
+{ fn dim() -> uint { 5 } }
+
+impl Dim for d6
+{ fn dim() -> uint { 6 } }
+
+impl Dim for d7
+{ fn dim() -> uint { 7 } }

src/traits/dot.rs

@@ -2,13 +2,4 @@ pub trait Dot<T>
 {
   /// Computes the dot (inner) product of two objects.
   fn dot(&self, &Self) -> T;
-  /// Computes the norm a an object.
-  fn norm(&self)       -> T;
-  /**
-   * Computes the squared norm of an object.
-   * 
-   * Computes the squared norm of an object. Computation of the squared norm
-   * is usually faster than the norm itself.
-   */
-  fn sqnorm(&self)     -> T; // { self.dot(self); }
 }

src/traits/norm.rs

@@ -0,0 +1,19 @@
+pub trait Norm<T>
+{
+  /// Computes the norm a an object.
+  fn norm(&self)       -> T;
+
+  /**
+   * Computes the squared norm of an object.
+   * 
+   * Computes the squared norm of an object. Computation of the squared norm
+   * is usually faster than the norm itself.
+   */
+  fn sqnorm(&self)     -> T;
+
+  /// Returns the normalized version of the argument.
+  fn normalized(&self) -> Self;
+
+  /// Inplace version of `normalized`.
+  fn normalize(&mut self)  -> T;
+}

src/traits/workarounds/scalar_op.rs

@@ -0,0 +1,12 @@
+pub trait ScalarOp<T>
+{
+  fn scalar_mul(&self, &T) -> Self;
+  fn scalar_div(&self, &T) -> Self;
+  fn scalar_add(&self, &T) -> Self;
+  fn scalar_sub(&self, &T) -> Self;
+
+  fn scalar_mul_inplace(&mut self, &T);
+  fn scalar_div_inplace(&mut self, &T);
+  fn scalar_add_inplace(&mut self, &T);
+  fn scalar_sub_inplace(&mut self, &T);
+}