Merge pull request #6 from vbarrielle/master

Implementation of QR factorizarion
This commit is contained in:
Sébastien Crozet 2014-05-10 18:45:09 +02:00
commit 43a6c96d33
9 changed files with 152 additions and 3 deletions

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

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@ -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)
}

4
src/linalg/mod.rs Normal file
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@ -0,0 +1,4 @@
pub use self::decompositions::decomp_qr;
mod decompositions;

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

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@ -9,7 +9,8 @@ use traits::operations::ApproxEq;
use std::mem; use std::mem;
use structs::dvec::{DVec, DVecMulRhs}; use structs::dvec::{DVec, DVecMulRhs};
use traits::operations::{Inv, Transpose, Mean, Cov}; 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)] #[doc(hidden)]
mod metal; 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> { impl<N: ApproxEq<N>> ApproxEq<N> for DMat<N> {
#[inline] #[inline]
fn approx_epsilon(_: Option<DMat<N>>) -> N { 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 ( macro_rules! scalar_mul_impl (
($n: ident) => ( ($n: ident) => (
impl DMatMulRhs<$n, DMat<$n>> for $n { impl DMatMulRhs<$n, DMat<$n>> for $n {

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@ -2,6 +2,7 @@ use std::num::{Float, abs};
use rand::random; use rand::random;
use na::{Vec1, Vec3, Mat1, Mat2, Mat3, Mat4, Mat5, Mat6, Rot3, DMat, DVec, Indexable}; use na::{Vec1, Vec3, Mat1, Mat2, Mat3, Mat4, Mat5, Mat6, Rot3, DMat, DVec, Indexable};
use na; use na;
use na::decomp_qr;
macro_rules! test_inv_mat_impl( macro_rules! test_inv_mat_impl(
($t: ty) => ( ($t: ty) => (
@ -206,3 +207,23 @@ fn test_dmat_from_vec() {
assert!(mat1 == mat2); 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));
}

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

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

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@ -91,6 +91,18 @@ pub trait Col<C> {
// a lot of operations. // 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. /// Trait of objects having a spacial dimension known at compile time.
pub trait Dim { pub trait Dim {
/// The dimension of the object. /// The dimension of the object.