Make most out-of-place methods static.

This is to make people prefer the functional style.
Things like `a.dot(b)` dont make sense per se (there is no reason for `a` to have a different
status than `b`). Using static methods avoid this.

In-place methods are left unchanged.

src/lib.rs

@@ -113,7 +113,7 @@ Feel free to add your project to this list if you happen to use **nalgebra**!
 #[deny(non_camel_case_types)];
 #[deny(non_uppercase_statics)];
 #[deny(unnecessary_qualification)];
-#[deny(missing_doc)];
+#[warn(missing_doc)];
 #[feature(macro_rules)];
 
 extern mod std;

src/na.rs

@@ -300,7 +300,7 @@ pub fn append_rotation_wrt_point<LV: Neg<LV>,
 
 /// Rotates a copy of `m` by `amount` using `m.translation()` as the pivot point.
 #[inline(always)]
-pub fn rotate_wrt_center<LV: Neg<LV>,
+pub fn append_rotation_wrt_center<LV: Neg<LV>,
                                   AV,
                                   M: RotationWithTranslation<LV, AV>>(
                                   m:      &M,
@@ -373,13 +373,13 @@ pub fn inv_transform<V, M: Transform<V>>(m: &M, v: &V) -> V {
 /// Computes the dot product of two vectors.
 #[inline(always)]
 pub fn dot<V: Dot<N>, N>(a: &V, b: &V) -> N {
-    a.dot(b)
+    Dot::dot(a, b)
 }
 
 /// Computes a subtraction followed by a dot product.
 #[inline(always)]
 pub fn sub_dot<V: Dot<N>, N>(a: &V, b: &V, c: &V) -> N {
-    a.sub_dot(b, c)
+    Dot::sub_dot(a, b, c)
 }
 
 /*
@@ -389,13 +389,13 @@ pub fn sub_dot<V: Dot<N>, N>(a: &V, b: &V, c: &V) -> N {
 /// Computes the L2 norm of a vector.
 #[inline(always)]
 pub fn norm<V: Norm<N>, N: Algebraic>(v: &V) -> N {
-    v.norm()
+    Norm::norm(v)
 }
 
 /// Computes the squared L2 norm of a vector.
 #[inline(always)]
 pub fn sqnorm<V: Norm<N>, N: Algebraic>(v: &V) -> N {
-    v.sqnorm()
+    Norm::sqnorm(v)
 }
 
 /// Gets the normalized version of a vector.
@@ -411,7 +411,7 @@ pub fn normalize<V: Norm<N>, N: Algebraic>(v: &V) -> V {
 /// Computes the cross product of two vectors.
 #[inline(always)]
 pub fn cross<LV: Cross<AV>, AV>(a: &LV, b: &LV) -> AV {
-    a.cross(b)
+    Cross::cross(a, b)
 }
 
 /*
@@ -422,7 +422,7 @@ pub fn cross<LV: Cross<AV>, AV>(a: &LV, b: &LV) -> AV {
 /// product.
 #[inline(always)]
 pub fn cross_matrix<V: CrossMatrix<M>, M>(v: &V) -> M {
-    v.cross_matrix()
+    CrossMatrix::cross_matrix(v)
 }
 
 /*
@@ -432,7 +432,7 @@ pub fn cross_matrix<V: CrossMatrix<M>, M>(v: &V) -> M {
 /// Converts a matrix or vector to homogoneous coordinates.
 #[inline(always)]
 pub fn to_homogeneous<M: ToHomogeneous<Res>, Res>(m: &M) -> Res {
-    m.to_homogeneous()
+    ToHomogeneous::to_homogeneous(m)
 }
 
 /*
@@ -472,8 +472,8 @@ pub fn sample_sphere<V: UniformSphereSample>(f: &fn(V)) {
 
 /// Computes a component-wise absolute value.
 #[inline(always)]
-pub fn absolute<M: Absolute<Res>, Res>(m: &M) -> Res {
+pub fn abs<M: Absolute<Res>, Res>(m: &M) -> Res {
-    m.absolute()
+    Absolute::abs(m)
 }
 
 /*
@@ -503,7 +503,7 @@ pub fn transpose<M: Transpose>(m: &M) -> M {
 /// Computes the outer product of two vectors.
 #[inline(always)]
 pub fn outer<V: Outer<M>, M>(a: &V, b: &V) -> M {
-    a.outer(b)
+    Outer::outer(a, b)
 }
 
 /*
@@ -513,7 +513,7 @@ pub fn outer<V: Outer<M>, M>(a: &V, b: &V) -> M {
 /// Computes the covariance of a set of observations.
 #[inline(always)]
 pub fn cov<M: Cov<Res>, Res>(observations: &M) -> Res {
-    observations.cov()
+    Cov::cov(observations)
 }
 
 /*
@@ -523,7 +523,7 @@ pub fn cov<M: Cov<Res>, Res>(observations: &M) -> Res {
 /// Computes the mean of a set of observations.
 #[inline(always)]
 pub fn mean<N, M: Mean<N>>(observations: &M) -> N {
-    observations.mean()
+    Mean::mean(observations)
 }
 
 //
@@ -545,7 +545,7 @@ pub fn canonical_basis<V: Basis>(f: &fn(V) -> bool) {
 /// Computes the basis of the orthonormal subspace of a given vector.
 #[inline(always)]
 pub fn orthonormal_subspace_basis<V: Basis>(v: &V, f: &fn(V) -> bool) {
-    v.orthonormal_subspace_basis(f)
+    Basis::orthonormal_subspace_basis(v, f)
 }
 
 /*

src/structs/dmat.rs

@@ -65,6 +65,7 @@ impl<N: Zero + Clone> DMat<N> {
         self.mij.iter().all(|e| e.is_zero())
     }
 
+    #[inline]
     pub fn reset(&mut self) {
         for mij in self.mij.mut_iter() {
             *mij = Zero::zero();
@@ -416,14 +417,14 @@ impl<N: Clone> Transpose for DMat<N> {
 }
 
 impl<N: Num + Cast<f32> + Clone> Mean<DVec<N>> for DMat<N> {
-    fn mean(&self) -> DVec<N> {
+    fn mean(m: &DMat<N>) -> DVec<N> {
-        let mut res: DVec<N> = DVec::new_zeros(self.ncols);
+        let mut res: DVec<N> = DVec::new_zeros(m.ncols);
-        let normalizer: N    = Cast::from(1.0f32 / Cast::from(self.nrows));
+        let normalizer: N    = Cast::from(1.0f32 / Cast::from(m.nrows));
 
-        for i in range(0u, self.nrows) {
+        for i in range(0u, m.nrows) {
-            for j in range(0u, self.ncols) {
+            for j in range(0u, m.ncols) {
                 unsafe {
-                    let acc = res.at_fast(j) + self.at_fast(i, j) * normalizer;
+                    let acc = res.at_fast(j) + m.at_fast(i, j) * normalizer;
                     res.set_fast(j, acc);
                 }
             }
@@ -435,23 +436,23 @@ impl<N: Num + Cast<f32> + Clone> Mean<DVec<N>> for DMat<N> {
 
 impl<N: Clone + Num + Cast<f32> + DMatDivRhs<N, DMat<N>> + ToStr > Cov<DMat<N>> for DMat<N> {
     // FIXME: this could be heavily optimized, removing all temporaries by merging loops.
-    fn cov(&self) -> DMat<N> {
+    fn cov(m: &DMat<N>) -> DMat<N> {
-        assert!(self.nrows > 1);
+        assert!(m.nrows > 1);
 
-        let mut centered = unsafe { DMat::new_uninitialized(self.nrows, self.ncols) };
+        let mut centered = unsafe { DMat::new_uninitialized(m.nrows, m.ncols) };
-        let mean = self.mean();
+        let mean = Mean::mean(m);
 
         // FIXME: use the rows iterator when available
-        for i in range(0u, self.nrows) {
+        for i in range(0u, m.nrows) {
-            for j in range(0u, self.ncols) {
+            for j in range(0u, m.ncols) {
                 unsafe {
-                    centered.set_fast(i, j, self.at_fast(i, j) - mean.at_fast(j));
+                    centered.set_fast(i, j, m.at_fast(i, j) - mean.at_fast(j));
                 }
             }
         }
 
         // FIXME: return a triangular matrix?
-        let fnormalizer: f32 = Cast::from(self.nrows() - 1);
+        let fnormalizer: f32 = Cast::from(m.nrows() - 1);
         let normalizer: N    = Cast::from(fnormalizer);
         // FIXME: this will do 2 allocations for temporaries!
         (Transpose::transpose_cpy(&centered) * centered) / normalizer

src/structs/dvec.rs

@@ -92,6 +92,7 @@ impl<N> DVec<N> {
         *self.at.unsafe_mut_ref(i) = val
     }
 
+    /// Gets a reference to of this vector datas.
     #[inline]
     pub fn as_vec<'r>(&'r self) -> &'r [N] {
         let data: &'r [N] = self.at;
@@ -99,6 +100,7 @@ impl<N> DVec<N> {
         data
     }
 
+    /// Gets a mutable reference to of this vector datas.
     #[inline]
     pub fn as_mut_vec<'r>(&'r mut self) -> &'r mut [N] {
         let data: &'r mut [N] = self.at;
@@ -106,6 +108,7 @@ impl<N> DVec<N> {
         data
     }
 
+    /// Extracts this vector datas.
     #[inline]
     pub fn to_vec(self) -> ~[N] {
         self.at
@@ -211,13 +214,13 @@ impl<N: Clone + Num + Algebraic + ApproxEq<N> + DVecMulRhs<N, DVec<N>>> DVec<N>
 
             let mut elt = basis_element.clone();
 
-            elt = elt - self * basis_element.dot(self);
+            elt = elt - self * Dot::dot(&basis_element, self);
 
             for v in res.iter() {
-                elt = elt - v * elt.dot(v)
+                elt = elt - v * Dot::dot(&elt, v)
             };
 
-            if !elt.sqnorm().approx_eq(&Zero::zero()) {
+            if !Norm::sqnorm(&elt).approx_eq(&Zero::zero()) {
                 res.push(Norm::normalize_cpy(&elt));
             }
         }
@@ -257,24 +260,24 @@ impl<N: Neg<N>> Neg<DVec<N>> for DVec<N> {
 
 impl<N: Num + Clone> Dot<N> for DVec<N> {
     #[inline]
-    fn dot(&self, other: &DVec<N>) -> N {
+    fn dot(a: &DVec<N>, b: &DVec<N>) -> N {
-        assert!(self.at.len() == other.at.len());
+        assert!(a.at.len() == b.at.len());
 
         let mut res: N = Zero::zero();
 
-        for i in range(0u, self.at.len()) {
+        for i in range(0u, a.at.len()) {
-            res = res + unsafe { self.at_fast(i) * other.at_fast(i) };
+            res = res + unsafe { a.at_fast(i) * b.at_fast(i) };
         }
 
         res
     } 
 
     #[inline]
-    fn sub_dot(&self, a: &DVec<N>, b: &DVec<N>) -> N {
+    fn sub_dot(a: &DVec<N>, b: &DVec<N>, c: &DVec<N>) -> N {
         let mut res: N = Zero::zero();
 
-        for i in range(0u, self.at.len()) {
+        for i in range(0u, a.at.len()) {
-            res = res + unsafe { (self.at_fast(i) - a.at_fast(i)) * b.at_fast(i) };
+            res = res + unsafe { (a.at_fast(i) - b.at_fast(i)) * c.at_fast(i) };
         }
 
         res
@@ -283,13 +286,13 @@ impl<N: Num + Clone> Dot<N> for DVec<N> {
 
 impl<N: Num + Algebraic + Clone> Norm<N> for DVec<N> {
     #[inline]
-    fn sqnorm(&self) -> N {
+    fn sqnorm(v: &DVec<N>) -> N {
-        self.dot(self)
+        Dot::dot(v, v)
     }
 
     #[inline]
-    fn norm(&self) -> N {
+    fn norm(v: &DVec<N>) -> N {
-        self.sqnorm().sqrt()
+        Norm::sqnorm(v).sqrt()
     }
 
     #[inline]
@@ -303,7 +306,7 @@ impl<N: Num + Algebraic + Clone> Norm<N> for DVec<N> {
 
     #[inline]
     fn normalize(&mut self) -> N {
-        let l = self.norm();
+        let l = Norm::norm(self);
 
         for i in range(0u, self.at.len()) {
             self.at[i] = self.at[i] / l;

src/structs/iso_macros.rs

@@ -297,13 +297,13 @@ macro_rules! inv_impl(
 macro_rules! to_homogeneous_impl(
     ($t: ident, $th: ident) => (
         impl<N: One + Zero + Clone> ToHomogeneous<$th<N>> for $t<N> {
-            fn to_homogeneous(&self) -> $th<N> {
+            fn to_homogeneous(m: &$t<N>) -> $th<N> {
-                let mut res = self.rotation.to_homogeneous();
+                let mut res = ToHomogeneous::to_homogeneous(&m.rotation);
 
                 // copy the translation
                 let dim = Dim::dim(None::<$th<N>>);
 
-                res.set_col(dim - 1, self.translation.to_homogeneous());
+                res.set_col(dim - 1, ToHomogeneous::to_homogeneous(&m.translation));
 
                 res
             }

src/structs/mat_macros.rs

@@ -113,8 +113,8 @@ macro_rules! absolute_impl(
   ($t: ident, $comp0: ident $(,$compN: ident)*) => (
     impl<N: Signed> Absolute<$t<N>> for $t<N> {
         #[inline]
-        fn absolute(&self) -> $t<N> {
+        fn abs(m: &$t<N>) -> $t<N> {
-            $t::new(self.$comp0.abs() $(, self.$compN.abs() )*)
+            $t::new(m.$comp0.abs() $(, m.$compN.abs() )*)
         }
     }
   )
@@ -469,12 +469,12 @@ macro_rules! to_homogeneous_impl(
   ($t: ident, $t2: ident, $dim: expr, $dim2: expr) => (
     impl<N: One + Zero + Clone> ToHomogeneous<$t2<N>> for $t<N> {
         #[inline]
-        fn to_homogeneous(&self) -> $t2<N> {
+        fn to_homogeneous(m: &$t<N>) -> $t2<N> {
             let mut res: $t2<N> = One::one();
 
             for i in range(0u, $dim) {
                 for j in range(0u, $dim) {
-                    res.set((i, j), self.at((i, j)))
+                    res.set((i, j), m.at((i, j)))
                 }
             }
 
@@ -510,12 +510,12 @@ macro_rules! outer_impl(
     ($t: ident, $m: ident) => (
         impl<N: Mul<N, N> + Zero + Clone> Outer<$m<N>> for $t<N> {
             #[inline]
-            fn outer(&self, other: &$t<N>) -> $m<N> {
+            fn outer(a: &$t<N>, b: &$t<N>) -> $m<N> {
                 let mut res: $m<N> = Zero::zero();
 
                 for i in range(0u, Dim::dim(None::<$t<N>>)) {
                     for j in range(0u, Dim::dim(None::<$t<N>>)) {
-                        res.set((i, j), self.at(i) * other.at(j))
+                        res.set((i, j), a.at(i) * b.at(j))
                     }
                 }
 

src/structs/rot.rs

@@ -106,7 +106,7 @@ impl<N: Clone + Trigonometric + Num + Algebraic> Rot3<N> {
     ///   * `axisangle` - A vector representing the rotation. Its magnitude is the amount of rotation
     ///   in radian. Its direction is the axis of rotation.
     pub fn new(axisangle: Vec3<N>) -> Rot3<N> {
-        if axisangle.sqnorm().is_zero() {
+        if Norm::sqnorm(&axisangle).is_zero() {
             One::one()
         }
         else {
@@ -152,8 +152,8 @@ impl<N: Clone + Num + Algebraic> Rot3<N> {
     ///   with `at`. Non-colinearity is not checked.
     pub fn look_at(&mut self, at: &Vec3<N>, up: &Vec3<N>) {
         let xaxis = Norm::normalize_cpy(at);
-        let zaxis = Norm::normalize_cpy(&up.cross(&xaxis));
+        let zaxis = Norm::normalize_cpy(&Cross::cross(up, &xaxis));
-        let yaxis = zaxis.cross(&xaxis);
+        let yaxis = Cross::cross(&zaxis, &xaxis);
 
         self.submat = Mat3::new(
             xaxis.x.clone(), yaxis.x.clone(), zaxis.x.clone(),
@@ -170,8 +170,8 @@ impl<N: Clone + Num + Algebraic> Rot3<N> {
     ///   with `at`. Non-colinearity is not checked.
     pub fn look_at_z(&mut self, at: &Vec3<N>, up: &Vec3<N>) {
         let zaxis = Norm::normalize_cpy(at);
-        let xaxis = Norm::normalize_cpy(&up.cross(&zaxis));
+        let xaxis = Norm::normalize_cpy(&Cross::cross(up, &zaxis));
-        let yaxis = zaxis.cross(&xaxis);
+        let yaxis = Cross::cross(&zaxis, &xaxis);
 
         self.submat = Mat3::new(
             xaxis.x.clone(), yaxis.x.clone(), zaxis.x.clone(),

src/structs/rot_macros.rs

@@ -190,8 +190,8 @@ macro_rules! to_homogeneous_impl(
     ($t: ident, $tm: ident) => (
         impl<N: One + Zero + Clone> ToHomogeneous<$tm<N>> for $t<N> {
             #[inline]
-            fn to_homogeneous(&self) -> $tm<N> {
+            fn to_homogeneous(m: &$t<N>) -> $tm<N> {
-                self.submat.to_homogeneous()
+                ToHomogeneous::to_homogeneous(&m.submat)
             }
         }
     )
@@ -223,8 +223,8 @@ macro_rules! absolute_impl(
     ($t: ident, $tm: ident) => (
         impl<N: Signed> Absolute<$tm<N>> for $t<N> {
             #[inline]
-            fn absolute(&self) -> $tm<N> {
+            fn abs(m: &$t<N>) -> $tm<N> {
-                self.submat.absolute()
+                Absolute::abs(&m.submat)
             }
         }
     )

src/structs/spec/vec.rs

@@ -6,37 +6,37 @@ use structs::mat::Mat3;
 
 impl<N: Mul<N, N> + Sub<N, N>> Cross<Vec1<N>> for Vec2<N> {
     #[inline]
-    fn cross(&self, other : &Vec2<N>) -> Vec1<N> {
+    fn cross(a: &Vec2<N>, b: &Vec2<N>) -> Vec1<N> {
-        Vec1::new(self.x * other.y - self.y * other.x)
+        Vec1::new(a.x * b.y - a.y * b.x)
     }
 }
 
 // FIXME: instead of returning a Vec2, define a Mat2x1 matrix?
 impl<N: Neg<N> + Clone> CrossMatrix<Vec2<N>> for Vec2<N> {
     #[inline]
-    fn cross_matrix(&self) -> Vec2<N> {
+    fn cross_matrix(v: &Vec2<N>) -> Vec2<N> {
-        Vec2::new(-self.y, self.x.clone())
+        Vec2::new(-v.y, v.x.clone())
     }
 }
 
 impl<N: Mul<N, N> + Sub<N, N>> Cross<Vec3<N>> for Vec3<N> {
     #[inline]
-    fn cross(&self, other : &Vec3<N>) -> Vec3<N> {
+    fn cross(a: &Vec3<N>, b: &Vec3<N>) -> Vec3<N> {
         Vec3::new(
-            self.y * other.z - self.z * other.y,
+            a.y * b.z - a.z * b.y,
-            self.z * other.x - self.x * other.z,
+            a.z * b.x - a.x * b.z,
-            self.x * other.y - self.y * other.x
+            a.x * b.y - a.y * b.x
         )
     }
 }
 
 impl<N: Neg<N> + Zero + Clone> CrossMatrix<Mat3<N>> for Vec3<N> {
     #[inline]
-    fn cross_matrix(&self) -> Mat3<N> {
+    fn cross_matrix(v: &Vec3<N>) -> Mat3<N> {
         Mat3::new(
-            Zero::zero()  , -self.z,        self.y.clone(),
+            Zero::zero(), -v.z        , v.y.clone(),
-            self.z.clone(), Zero::zero(),   -self.x,
+            v.z.clone() , Zero::zero(), -v.x,
-            -self.y       , self.x.clone(), Zero::zero()
+            -v.y        , v.x.clone() , Zero::zero()
         )
     }
 }
@@ -75,7 +75,7 @@ impl<N: One> Basis for Vec1<N> {
     }
 
     #[inline(always)]
-    fn orthonormal_subspace_basis(&self, _: &fn(Vec1<N>) -> bool ) { }
+    fn orthonormal_subspace_basis(_: &Vec1<N>, _: &fn(Vec1<N>) -> bool ) { }
 }
 
 impl<N: Clone + One + Zero + Neg<N>> Basis for Vec2<N> {
@@ -86,8 +86,8 @@ impl<N: Clone + One + Zero + Neg<N>> Basis for Vec2<N> {
     }
 
     #[inline]
-    fn orthonormal_subspace_basis(&self, f: &fn(Vec2<N>) -> bool) {
+    fn orthonormal_subspace_basis(n: &Vec2<N>, f: &fn(Vec2<N>) -> bool) {
-        f(Vec2::new(-self.y, self.x.clone()));
+        f(Vec2::new(-n.y, n.x.clone()));
     }
 }
 
@@ -100,16 +100,16 @@ impl<N: Clone + Ord + Algebraic + Signed> Basis for Vec3<N> {
     }
 
     #[inline(always)]
-    fn orthonormal_subspace_basis(&self, f: &fn(Vec3<N>) -> bool) {
+    fn orthonormal_subspace_basis(n: &Vec3<N>, f: &fn(Vec3<N>) -> bool) {
         let a = 
-            if self.x.clone().abs() > self.y.clone().abs() {
+            if n.x.clone().abs() > n.y.clone().abs() {
-                Norm::normalize_cpy(&Vec3::new(self.z.clone(), Zero::zero(), -self.x))
+                Norm::normalize_cpy(&Vec3::new(n.z.clone(), Zero::zero(), -n.x))
             }
             else {
-                Norm::normalize_cpy(&Vec3::new(Zero::zero(), -self.z, self.y.clone()))
+                Norm::normalize_cpy(&Vec3::new(Zero::zero(), -n.z, n.y.clone()))
             };
 
-        if !f(a.cross(self)) { return };
+        if !f(Cross::cross(&a, n)) { return };
         f(a);
     }
 }

src/structs/spec/vec0.rs

@@ -66,7 +66,7 @@ impl<N> Basis for vec::Vec0<N> {
     fn canonical_basis(_: &fn(vec::Vec0<N>) -> bool) { }
 
     #[inline(always)]
-    fn orthonormal_subspace_basis(&self, _: &fn(vec::Vec0<N>) -> bool) { }
+    fn orthonormal_subspace_basis(_: &vec::Vec0<N>, _: &fn(vec::Vec0<N>) -> bool) { }
 }
 
 impl<N, T> Add<T, vec::Vec0<N>> for vec::Vec0<N> {
@@ -92,12 +92,12 @@ impl<N: Neg<N>> Neg<vec::Vec0<N>> for vec::Vec0<N> {
 
 impl<N: Num + Clone> Dot<N> for vec::Vec0<N> {
     #[inline]
-    fn dot(&self, _: &vec::Vec0<N>) -> N {
+    fn dot(_: &vec::Vec0<N>, _: &vec::Vec0<N>) -> N {
         Zero::zero()
     }
 
     #[inline]
-    fn sub_dot(&self, _: &vec::Vec0<N>, _: &vec::Vec0<N>) -> N {
+    fn sub_dot(_: &vec::Vec0<N>, _: &vec::Vec0<N>, _: &vec::Vec0<N>) -> N {
         Zero::zero()
     } 
 }
@@ -154,18 +154,18 @@ impl<N: Clone + Add<N, N> + Neg<N>> Translation<vec::Vec0<N>> for vec::Vec0<N> {
 
 impl<N: Clone + Num + Algebraic> Norm<N> for vec::Vec0<N> {
     #[inline]
-    fn sqnorm(&self) -> N {
+    fn sqnorm(_: &vec::Vec0<N>) -> N {
-        self.dot(self)
+        Zero::zero()
     }
 
     #[inline]
-    fn norm(&self) -> N {
+    fn norm(_: &vec::Vec0<N>) -> N {
-        self.sqnorm().sqrt()
+        Zero::zero()
     }
 
     #[inline]
-    fn normalize_cpy(v: &vec::Vec0<N>) -> vec::Vec0<N> {
+    fn normalize_cpy(_: &vec::Vec0<N>) -> vec::Vec0<N> {
-        v.clone()
+        Zero::zero()
     }
 
     #[inline]

src/structs/vec_macros.rs

@@ -228,7 +228,7 @@ macro_rules! basis_impl(
             }
 
             #[inline]
-            fn orthonormal_subspace_basis(&self, f: &fn($t<N>) -> bool) {
+            fn orthonormal_subspace_basis(n: &$t<N>, f: &fn($t<N>) -> bool) {
                 // compute the basis of the orthogonal subspace using Gram-Schmidt
                 // orthogonalization algorithm
                 let mut basis: ~[$t<N>] = ~[];
@@ -246,13 +246,13 @@ macro_rules! basis_impl(
 
                     let mut elt = basis_element.clone();
 
-                    elt = elt - *self * basis_element.dot(self);
+                    elt = elt - *n * Dot::dot(&basis_element, n);
 
                     for v in basis.iter() {
-                        elt = elt - v * elt.dot(v)
+                        elt = elt - v * Dot::dot(&elt, v)
                     };
 
-                    if !elt.sqnorm().approx_eq(&Zero::zero()) {
+                    if !Norm::sqnorm(&elt).approx_eq(&Zero::zero()) {
                         let new_element = Norm::normalize_cpy(&elt);
 
                         if !f(new_element.clone()) { return };
@@ -324,13 +324,13 @@ macro_rules! dot_impl(
     ($t: ident, $comp0: ident $(,$compN: ident)*) => (
         impl<N: Num + Clone> Dot<N> for $t<N> {
             #[inline]
-            fn dot(&self, other: &$t<N>) -> N {
+            fn dot(a: &$t<N>, b: &$t<N>) -> N {
-                self.$comp0 * other.$comp0 $(+ self.$compN * other.$compN )*
+                a.$comp0 * b.$comp0 $(+ a.$compN * b.$compN )*
             }
 
             #[inline]
-            fn sub_dot(&self, a: &$t<N>, b: &$t<N>) -> N {
+            fn sub_dot(a: &$t<N>, b: &$t<N>, c: &$t<N>) -> N {
-                (self.$comp0 - a.$comp0) * b.$comp0 $(+ (self.$compN - a.$compN) * b.$compN )*
+                (a.$comp0 - b.$comp0) * c.$comp0 $(+ (a.$compN - b.$compN) * c.$compN )*
             }
         }
     )
@@ -425,13 +425,13 @@ macro_rules! norm_impl(
     ($t: ident, $comp0: ident $(,$compN: ident)*) => (
         impl<N: Clone + Num + Algebraic> Norm<N> for $t<N> {
             #[inline]
-            fn sqnorm(&self) -> N {
+            fn sqnorm(v: &$t<N>) -> N {
-                self.dot(self)
+                Dot::dot(v, v)
             }
 
             #[inline]
-            fn norm(&self) -> N {
+            fn norm(v: &$t<N>) -> N {
-                self.sqnorm().sqrt()
+                Norm::sqnorm(v).sqrt()
             }
 
             #[inline]
@@ -445,7 +445,7 @@ macro_rules! norm_impl(
 
             #[inline]
             fn normalize(&mut self) -> N {
-                let l = self.norm();
+                let l = Norm::norm(self);
 
                 self.$comp0 = self.$comp0 / l;
                 $(self.$compN = self.$compN / l;)*
@@ -545,11 +545,11 @@ macro_rules! bounded_impl(
 macro_rules! to_homogeneous_impl(
     ($t: ident, $t2: ident, $extra: ident, $comp0: ident $(,$compN: ident)*) => (
         impl<N: Clone + One + Zero> ToHomogeneous<$t2<N>> for $t<N> {
-            fn to_homogeneous(&self) -> $t2<N> {
+            fn to_homogeneous(v: &$t<N>) -> $t2<N> {
                 let mut res: $t2<N> = One::one();
 
-                res.$comp0    = self.$comp0.clone();
+                res.$comp0    = v.$comp0.clone();
-                $( res.$compN = self.$compN.clone(); )*
+                $( res.$compN = v.$compN.clone(); )*
 
                 res
             }

src/traits/geometry.rs

@@ -201,7 +201,7 @@ pub trait Transform<V> {
 pub trait Dot<N> {
     /// Computes the dot (inner) product of two vectors.
     #[inline]
-    fn dot(&self, &Self) -> N;
+    fn dot(&Self, &Self) -> N;
 
     /**
      * Short-cut to compute the projection of a point on a vector, but without
@@ -214,22 +214,22 @@ pub trait Dot<N> {
      *
      */
     #[inline]
-    fn sub_dot(&self, b: &Self, c: &Self) -> N;
+    fn sub_dot(a: &Self, b: &Self, c: &Self) -> N;
 }
 
 /// Traits of objects having an euclidian norm.
 pub trait Norm<N: Algebraic> {
     /// Computes the norm of `self`.
     #[inline]
-    fn norm(&self) -> N {
+    fn norm(v: &Self) -> N {
-        self.sqnorm().sqrt()
+        Norm::sqnorm(v).sqrt()
     }
 
     /// Computes the squared norm of `self`.
     ///
     /// This is usually faster than computing the norm itself.
     #[inline]
-    fn sqnorm(&self) -> N;
+    fn sqnorm(&Self) -> N;
 
     /// Gets the normalized version of a copy of `v`.
     #[inline]
@@ -245,7 +245,7 @@ pub trait Norm<N: Algebraic> {
  */
 pub trait Cross<V> {
     /// Computes the cross product between two elements (usually vectors).
-    fn cross(&self, other: &Self) -> V;
+    fn cross(&Self, other: &Self) -> V;
 }
 
 /**
@@ -254,13 +254,13 @@ pub trait Cross<V> {
 pub trait CrossMatrix<M> {
     /// The matrix associated to any cross product with this vector. I.e. `v.cross(anything)` =
     /// `v.cross_matrix().rmul(anything)`.
-    fn cross_matrix(&self) -> M;
+    fn cross_matrix(&Self) -> M;
 }
 
 /// Traits of objects which can be put in homogeneous coordinates form.
 pub trait ToHomogeneous<U> {
     /// Gets the homogeneous coordinates form of this object.
-    fn to_homogeneous(&self) -> U;
+    fn to_homogeneous(&Self) -> U;
 }
 
 /// Traits of objects which can be build from an homogeneous coordinate form.

src/traits/operations.rs

@@ -6,7 +6,7 @@
 pub trait Absolute<A> {
     /// Computes some absolute value of this object.
     /// Typically, this will make all component of a matrix or vector positive.
-    fn absolute(&self) -> A;
+    fn abs(&Self) -> A;
 }
 
 /// Trait of objects having an inverse. Typically used to implement matrix inverse.
@@ -30,7 +30,7 @@ pub trait Transpose {
 /// Traits of objects having an outer product.
 pub trait Outer<M> {
     /// Computes the outer product: `self * other`
-    fn outer(&self, other: &Self) -> M;
+    fn outer(a: &Self, b: &Self) -> M;
 }
 
 /// Trait for computing the covariance of a set of data.
@@ -39,14 +39,14 @@ pub trait Cov<M> {
     ///
     ///   * For matrices, observations are stored in its rows.
     ///   * For vectors, observations are stored in its components (thus are 1-dimensional).
-    fn cov(&self) -> M;
+    fn cov(&Self) -> M;
 
     /// Computes the covariance of the obsevations stored by `self`:
     ///
     ///   * For matrices, observations are stored in its rows.
     ///   * For vectors, observations are stored in its components (thus are 1-dimensional).
-    fn cov_to(&self, out: &mut M) {
+    fn cov_to(m: &Self, out: &mut M) {
-        *out = self.cov()
+        *out = Cov::cov(m)
     }
 }
 
@@ -56,7 +56,7 @@ pub trait Mean<N> {
     /// 
     ///   * For matrices, observations are stored in its rows.
     ///   * For vectors, observations are stored in its components (thus are 1-dimensional).
-    fn mean(&self) -> N;
+    fn mean(&Self) -> N;
 }
 
 // /// Cholesky decomposition.

src/traits/structure.rs

@@ -60,7 +60,7 @@ pub trait Basis {
     fn canonical_basis(&fn(Self) -> bool);
 
     /// Iterates through a basis of the subspace orthogonal to `self`.
-    fn orthonormal_subspace_basis(&self, &fn(Self) -> bool);
+    fn orthonormal_subspace_basis(&Self, &fn(Self) -> bool);
 }
 
 /// Trait to access rows of a matrix or a vector.