Add a `Det` trait to compute the determinant + implement it for `Mat{1,2,3}`.

src/na.rs

@@ -15,6 +15,7 @@ pub use traits::{
     Cov,
     Cross,
     CrossMatrix,
+    Det,
     Dim,
     Dot,
     FromHomogeneous,
@@ -580,6 +581,15 @@ pub fn normalize<V: Norm<N>, N: Float>(v: &V) -> V {
     Norm::normalize_cpy(v)
 }
 
+/*
+ * Det<N>
+ */
+/// Computes the determinant of a square matrix.
+#[inline(always)]
+pub fn det<M: Det<N>, N>(m: &M) -> N {
+    Det::det(m)
+}
+
 /*
  * Cross<V>
  */

src/structs/dvec.rs

@@ -327,7 +327,7 @@ impl<N: Float + Clone> Norm<N> for DVec<N> {
         let l = Norm::norm(self);
 
         for i in range(0u, self.at.len()) {
-            *self.at.get_mut(i) = *self.at.get(i) / l;
+            *self.at.get_mut(i) = self.at[i] / l;
         }
 
         l

src/structs/spec/mat.rs

@@ -1,12 +1,11 @@
 use std::num::{Zero, One};
 use structs::vec::{Vec2, Vec3, Vec2MulRhs, Vec3MulRhs};
 use structs::mat::{Mat1, Mat2, Mat3, Mat3MulRhs, Mat2MulRhs};
-use traits::operations::Inv;
+use traits::operations::{Inv, Det};
 use traits::structure::{Row, Col};
 
 // some specializations:
-impl<N: Num + Clone>
+impl<N: Num + Clone> Inv for Mat1<N> {
-Inv for Mat1<N> {
     #[inline]
     fn inv_cpy(m: &Mat1<N>) -> Option<Mat1<N>> {
         let mut res = m.clone();
@@ -26,14 +25,14 @@ Inv for Mat1<N> {
         }
         else {
             let _1: N = One::one();
-            self.m11 = _1 / self.m11;
+
+            self.m11 = _1 / Det::det(self);
             true
         }
     }
 }
 
-impl<N: Num + Clone>
+impl<N: Num + Clone> Inv for Mat2<N> {
-Inv for Mat2<N> {
     #[inline]
     fn inv_cpy(m: &Mat2<N>) -> Option<Mat2<N>> {
         let mut res = m.clone();
@@ -48,7 +47,7 @@ Inv for Mat2<N> {
 
     #[inline]
     fn inv(&mut self) -> bool {
-        let det = self.m11 * self.m22 - self.m21 * self.m12;
+        let det = Det::det(self);
 
         if det.is_zero() {
             false
@@ -63,8 +62,7 @@ Inv for Mat2<N> {
     }
 }
 
-impl<N: Num + Clone>
+impl<N: Num + Clone> Inv for Mat3<N> {
-Inv for Mat3<N> {
     #[inline]
     fn inv_cpy(m: &Mat3<N>) -> Option<Mat3<N>> {
         let mut res = m.clone();
@@ -83,9 +81,7 @@ Inv for Mat3<N> {
         let minor_m11_m23 = self.m21 * self.m33 - self.m31 * self.m23;
         let minor_m11_m22 = self.m21 * self.m32 - self.m31 * self.m22;
 
-        let det = self.m11 * minor_m12_m23
+        let det = self.m11 * minor_m12_m23 - self.m12 * minor_m11_m23 + self.m13 * minor_m11_m22;
-                  - self.m12 * minor_m11_m23
-                  + self.m13 * minor_m11_m22;
 
         if det.is_zero() {
             false
@@ -110,6 +106,31 @@ Inv for Mat3<N> {
     }
 }
 
+impl<N: Num + Clone> Det<N> for Mat1<N> {
+    #[inline]
+    fn det(m: &Mat1<N>) -> N {
+        m.m11.clone()
+    }
+}
+
+impl<N: Num> Det<N> for Mat2<N> {
+    #[inline]
+    fn det(m: &Mat2<N>) -> N {
+        m.m11 * m.m22 - m.m21 * m.m12
+    }
+}
+
+impl<N: Num> Det<N> for Mat3<N> {
+    #[inline]
+    fn det(m: &Mat3<N>) -> N {
+        let minor_m12_m23 = m.m22 * m.m33 - m.m32 * m.m23;
+        let minor_m11_m23 = m.m21 * m.m33 - m.m31 * m.m23;
+        let minor_m11_m22 = m.m21 * m.m32 - m.m31 * m.m22;
+
+        m.m11 * minor_m12_m23 - m.m12 * minor_m11_m23 + m.m13 * minor_m11_m22
+    }
+}
+
 impl<N: Clone> Row<Vec3<N>> for Mat3<N> {
     #[inline]
     fn nrows(&self) -> uint {

src/traits/mod.rs

@@ -8,7 +8,7 @@ pub use self::structure::{FloatVec, FloatVecExt, Basis, Cast, Col, Dim, Indexabl
                           Iterable, IterableMut, Mat, Row, AnyVec, VecExt,
                           ColSlice, RowSlice, Eye};
 
-pub use self::operations::{Absolute, ApproxEq, Cov, Inv, LMul, Mean, Outer, PartialOrd, RMul,
+pub use self::operations::{Absolute, ApproxEq, Cov, Det, Inv, LMul, Mean, Outer, PartialOrd, RMul,
                            ScalarAdd, ScalarSub, ScalarMul, ScalarDiv, Transpose};
 pub use self::operations::{PartialOrdering, PartialLess, PartialEqual, PartialGreater, NotComparable};
 

src/traits/operations.rs

@@ -196,13 +196,19 @@ pub trait Absolute<A> {
 
 /// Trait of objects having an inverse. Typically used to implement matrix inverse.
 pub trait Inv {
-    /// Returns the inverse of `self`.
+    /// Returns the inverse of `m`.
     fn inv_cpy(m: &Self) -> Option<Self>;
 
     /// In-place version of `inverse`.
     fn inv(&mut self) -> bool;
 }
 
+/// Trait of objects having a determinant. Typically used by square matrices.
+pub trait Det<N> {
+    /// Returns the determinant of `m`.
+    fn det(m: &Self) -> N;
+}
+
 /// Trait of objects which can be transposed.
 pub trait Transpose {
     /// Computes the transpose of a matrix.
@@ -214,19 +220,19 @@ pub trait Transpose {
 
 /// Traits of objects having an outer product.
 pub trait Outer<M> {
-    /// Computes the outer product: `self * other`
+    /// Computes the outer product: `a * b`
     fn outer(a: &Self, b: &Self) -> M;
 }
 
 /// Trait for computing the covariance of a set of data.
 pub trait Cov<M> {
-    /// Computes the covariance of the obsevations stored by `self`:
+    /// Computes the covariance of the obsevations stored by `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(m: &Self) -> M;
 
-    /// Computes the covariance of the obsevations stored by `self`:
+    /// Computes the covariance of the obsevations stored by `m`:
     ///
     ///   * For matrices, observations are stored in its rows.
     ///   * For vectors, observations are stored in its components (thus are 1-dimensional).
@@ -237,11 +243,11 @@ pub trait Cov<M> {
 
 /// Trait for computing the covariance of a set of data.
 pub trait Mean<N> {
-    /// Computes the mean of the observations stored by `self`.
+    /// Computes the mean of the observations stored by `v`.
     /// 
     ///   * 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(v: &Self) -> N;
 }