Merge pull request #6 from vbarrielle/master

Implementation of QR factorizarion

src/lib.rs

@@ -119,6 +119,7 @@ extern crate test;
 pub mod na;
 mod structs;
 mod traits;
+mod linalg;
 
 // mod lower_triangular;
 // mod chol;

src/linalg/decompositions.rs

@@ -0,0 +1,58 @@
+use std::num::{Zero, Float};
+use na::DVec;
+use na::DMat;
+use traits::operations::Transpose;
+use traits::structure::ColSlice;
+use traits::geometry::Norm;
+use std::cmp::min;
+
+/// QR decomposition using Householder reflections
+/// # Arguments
+/// * `m` - matrix to decompose
+pub fn decomp_qr<N: Clone + Float>(m: &DMat<N>) -> (DMat<N>, DMat<N>) {
+    let rows = m.nrows();
+    let cols = m.ncols();
+    assert!(rows >= cols);
+    let mut q : DMat<N> = DMat::new_identity(rows);
+    let mut r = m.clone();
+
+    let subtract_reflection = |vec: DVec<N>| -> DMat<N> {
+        // FIXME: we don't handle the complex case here
+        let mut qk : DMat<N> = DMat::new_identity(rows);
+        let start = rows - vec.at.len();
+        for j in range(start, rows) {
+            for i in range(start, rows) {
+                unsafe {
+                    let vv = vec.at_fast(i - start) * vec.at_fast(j - start);
+                    let qkij = qk.at_fast(i, j);
+                    qk.set_fast(i, j, qkij - vv - vv);
+                }
+            }
+        }
+        qk
+    };
+
+    let iterations = min(rows - 1, cols);
+
+    for ite in range(0u, iterations) {
+        let mut v = r.col_slice(ite, ite, rows);
+        let alpha =
+            if unsafe { v.at_fast(ite) } >= Zero::zero() {
+                -Norm::norm(&v)
+            }
+            else {
+                Norm::norm(&v)
+            };
+        unsafe {
+            let x = v.at_fast(0);
+            v.set_fast(0, x - alpha);
+        }
+        let _ = v.normalize();
+        let qk = subtract_reflection(v);
+        r = qk * r;
+        q = q * Transpose::transpose_cpy(&qk);
+    }
+
+    (q, r)
+}
+

src/linalg/mod.rs

@@ -0,0 +1,4 @@
+
+pub use self::decompositions::decomp_qr;
+
+mod decompositions;

src/na.rs

@@ -39,7 +39,8 @@ pub use traits::{
     Transpose,
     UniformSphereSample,
     AnyVec,
-    VecExt
+    VecExt,
+    ColSlice, RowSlice
 };
 
 pub use structs::{
@@ -52,6 +53,10 @@ pub use structs::{
     Vec0, Vec1, Vec2, Vec3, Vec4, Vec5, Vec6
 };
 
+pub use linalg::{
+    decomp_qr
+};
+
 /// Traits to work around the language limitations related to operator overloading.
 ///
 /// The trait names are formed by:

src/structs/dmat.rs

@@ -9,7 +9,8 @@ use traits::operations::ApproxEq;
 use std::mem;
 use structs::dvec::{DVec, DVecMulRhs};
 use traits::operations::{Inv, Transpose, Mean, Cov};
-use traits::structure::Cast;
+use traits::structure::{Cast, ColSlice, RowSlice};
+use std::fmt::{Show, Formatter, Result};
 
 #[doc(hidden)]
 mod metal;
@@ -494,6 +495,39 @@ impl<N: Clone + Num + Cast<f32> + DMatDivRhs<N, DMat<N>> + ToStr > Cov<DMat<N>>
     }
 }
 
+impl<N: Clone> ColSlice<DVec<N>> for DMat<N> {
+    fn col_slice(&self, col_id :uint, row_start: uint, row_end: uint) -> DVec<N> {
+        assert!(col_id < self.ncols);
+        assert!(row_start < row_end);
+        assert!(row_end <= self.nrows);
+        // 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(
+            row_end - row_start, self.mij.slice(start, stop));
+        slice
+    }
+}
+
+impl<N: Clone> RowSlice<DVec<N>> for DMat<N> {
+    fn row_slice(&self, row_id :uint, col_start: uint, col_end: uint) -> DVec<N> {
+        assert!(row_id < self.nrows);
+        assert!(col_start < col_end);
+        assert!(col_end <= self.ncols);
+        let mut slice : DVec<N> = unsafe {
+            DVec::new_uninitialized(self.nrows)
+        };
+        let mut slice_idx = 0u;
+        for col_id in range(col_start, col_end) {
+            unsafe {
+                slice.set_fast(slice_idx, self.at_fast(row_id, col_id));
+            }
+            slice_idx += 1;
+        }
+        slice
+    }
+}
+
 impl<N: ApproxEq<N>> ApproxEq<N> for DMat<N> {
     #[inline]
     fn approx_epsilon(_: Option<DMat<N>>) -> N {
@@ -515,6 +549,18 @@ impl<N: ApproxEq<N>> ApproxEq<N> for DMat<N> {
     }
 }
 
+impl<N: Show + Clone> Show for DMat<N> {
+    fn fmt(&self, form:&mut Formatter) -> Result {
+        for i in range(0u, self.nrows()) {
+            for j in range(0u, self.ncols()) {
+                let _ = write!(form.buf, "{} ", self.at(i, j));
+            }
+            let _ = write!(form.buf, "\n");
+        }
+        write!(form.buf, "\n")
+    }
+}
+
 macro_rules! scalar_mul_impl (
     ($n: ident) => (
         impl DMatMulRhs<$n, DMat<$n>> for $n {

src/tests/mat.rs

@@ -2,6 +2,7 @@ use std::num::{Float, abs};
 use rand::random;
 use na::{Vec1, Vec3, Mat1, Mat2, Mat3, Mat4, Mat5, Mat6, Rot3, DMat, DVec, Indexable};
 use na;
+use na::decomp_qr;
 
 macro_rules! test_inv_mat_impl(
   ($t: ty) => (
@@ -206,3 +207,23 @@ fn test_dmat_from_vec() {
 
     assert!(mat1 == mat2);
 }
+
+#[test]
+fn test_decomp_qr() {
+    let mat = DMat::from_row_vec(
+        5,
+        3,
+        [
+            4.0, 2.0, 0.60,
+            4.2, 2.1, 0.59,
+            3.9, 2.0, 0.58,
+            4.3, 2.1, 0.62,
+            4.1, 2.2, 0.63
+        ]
+    );
+
+    let (q, r) = decomp_qr(&mat);
+    let mat_ = q * r;
+
+    assert!(na::approx_eq(&mat_,  &mat));
+}

src/traits/mod.rs

@@ -5,7 +5,8 @@ pub use self::geometry::{AbsoluteRotate, Cross, CrossMatrix, Dot, FromHomogeneou
                          Transform, Transformation, Translate, Translation, UniformSphereSample};
 
 pub use self::structure::{FloatVec, FloatVecExt, Basis, Cast, Col, Dim, Indexable,
-                          Iterable, IterableMut, Mat, Row, AnyVec, VecExt};
+                          Iterable, IterableMut, Mat, Row, AnyVec, VecExt,
+                          ColSlice, RowSlice};
 
 pub use self::operations::{Absolute, ApproxEq, Cov, Inv, LMul, Mean, Outer, PartialOrd, RMul,
                            ScalarAdd, ScalarSub, Transpose};

src/traits/operations.rs

@@ -244,6 +244,7 @@ pub trait Mean<N> {
     fn mean(&Self) -> N;
 }
 
+
 // /// Cholesky decomposition.
 // pub trait Chol {
 //     /// Performs the cholesky decomposition on `self`. The resulting upper-triangular matrix is

src/traits/structure.rs

@@ -91,6 +91,18 @@ pub trait Col<C> {
     // a lot of operations.
 }
 
+/// Trait to access part of a column of a matrix
+pub trait ColSlice<C> {
+    /// Returns a view to a slice of a column of a matrix.
+    fn col_slice(&self, col_id: uint, row_start: uint, row_end: uint) -> C;
+}
+
+/// Trait to access part of a row of a matrix
+pub trait RowSlice<R> {
+    /// Returns a view to a slice of a row of a matrix.
+    fn row_slice(&self, row_id: uint, col_start: uint, col_end: uint) -> R;
+}
+
 /// Trait of objects having a spacial dimension known at compile time.
 pub trait Dim {
     /// The dimension of the object.