QR decomposition depends less on DMat internals
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@ -119,6 +119,7 @@ extern crate test;
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pub mod na;
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pub mod na;
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mod structs;
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mod structs;
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mod traits;
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mod traits;
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mod linalg;
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// mod lower_triangular;
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// mod lower_triangular;
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// mod chol;
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// mod chol;
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@ -0,0 +1,58 @@
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use std::num::{Zero, Float};
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use na::DVec;
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use na::DMat;
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use traits::operations::{Transpose, ColSlice};
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use traits::geometry::Norm;
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use std::cmp::min;
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/// QR decomposition using Householder reflections
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/// # Arguments
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/// * `m` matrix to decompose
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pub fn decomp_qr<N: Clone + Num + Float>(m: &DMat<N>) -> (DMat<N>, DMat<N>) {
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let rows = m.nrows();
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let cols = m.ncols();
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assert!(rows >= cols);
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let mut q : DMat<N> = DMat::new_identity(rows);
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let mut r = m.clone();
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let subtract_reflection = |vec: DVec<N>| -> DMat<N> {
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// FIXME: we don't handle the complex case here
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let mut qk : DMat<N> = DMat::new_identity(rows);
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let start = rows - vec.at.len();
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for j in range(start, rows) {
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for i in range(start, rows) {
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unsafe {
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let vv = vec.at_fast(i-start)*vec.at_fast(j-start);
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let qkij = qk.at_fast(i,j);
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qk.set_fast(i, j, qkij - vv - vv);
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}
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}
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}
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qk
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};
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let iterations = min(rows-1, cols);
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for ite in range(0u, iterations) {
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let mut v = r.col_slice(ite, ite, rows);
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//let mut v = r.col_slice<DVec<N>>(ite, rows-ite, rows);
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let alpha =
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if unsafe { v.at_fast(ite) } >= Zero::zero() {
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-Norm::norm(&v)
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}
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else {
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Norm::norm(&v)
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};
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unsafe {
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let x = v.at_fast(0);
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v.set_fast(0, x - alpha);
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}
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let _ = v.normalize();
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let qk = subtract_reflection(v);
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r = qk * r;
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q = q * Transpose::transpose_cpy(&qk);
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}
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(q, r)
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}
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@ -0,0 +1,4 @@
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pub use self::decompositions::decomp_qr;
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mod decompositions;
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@ -39,12 +39,12 @@ pub use traits::{
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Transpose,
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Transpose,
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UniformSphereSample,
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UniformSphereSample,
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AnyVec,
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AnyVec,
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VecExt
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VecExt,
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ColSlice, RowSlice
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};
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};
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pub use structs::{
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pub use structs::{
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Identity,
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Identity,
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decomp_qr,
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DMat, DVec,
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DMat, DVec,
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Iso2, Iso3, Iso4,
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Iso2, Iso3, Iso4,
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Mat1, Mat2, Mat3, Mat4,
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Mat1, Mat2, Mat3, Mat4,
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@ -53,6 +53,10 @@ pub use structs::{
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Vec0, Vec1, Vec2, Vec3, Vec4, Vec5, Vec6
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Vec0, Vec1, Vec2, Vec3, Vec4, Vec5, Vec6
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};
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};
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pub use linalg::{
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decomp_qr
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};
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/// Traits to work around the language limitations related to operator overloading.
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/// Traits to work around the language limitations related to operator overloading.
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///
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///
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/// The trait names are formed by:
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/// The trait names are formed by:
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@ -4,14 +4,12 @@
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use rand::Rand;
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use rand::Rand;
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use rand;
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use rand;
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use std::num::{One, Zero, Float};
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use std::num::{One, Zero};
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use traits::operations::ApproxEq;
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use traits::operations::ApproxEq;
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use std::mem;
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use std::mem;
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use structs::dvec::{DVec, DVecMulRhs};
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use structs::dvec::{DVec, DVecMulRhs};
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use traits::operations::{Inv, Transpose, Mean, Cov};
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use traits::operations::{Inv, Transpose, Mean, Cov, ColSlice, RowSlice};
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use traits::structure::Cast;
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use traits::structure::Cast;
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use traits::geometry::Norm;
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use std::cmp::min;
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use std::fmt::{Show, Formatter, Result};
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use std::fmt::{Show, Formatter, Result};
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#[doc(hidden)]
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#[doc(hidden)]
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@ -497,61 +495,38 @@ impl<N: Clone + Num + Cast<f32> + DMatDivRhs<N, DMat<N>> + ToStr > Cov<DMat<N>>
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}
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}
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}
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}
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impl<N: Clone> ColSlice<DVec<N>> for DMat<N> {
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fn col_slice(&self, col_id :uint, row_start: uint, row_end: uint) -> DVec<N> {
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assert!(col_id < self.ncols);
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assert!(row_start < row_end);
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assert!(row_end <= self.nrows);
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// we can init from slice thanks to the matrix being column major
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let start= self.offset(row_start, col_id);
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let stop = self.offset(row_end, col_id);
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let slice = DVec::from_vec(
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row_end - row_start, self.mij.slice(start, stop));
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slice
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}
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}
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/// QR decomposition using Householder reflections
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impl<N: Clone> RowSlice<DVec<N>> for DMat<N> {
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/// # Arguments
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fn row_slice(&self, row_id :uint, col_start: uint, col_end: uint) -> DVec<N> {
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/// * `m` matrix to decompose
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assert!(row_id < self.nrows);
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pub fn decomp_qr<N: Clone + Num + Float + Show>(m: &DMat<N>) -> (DMat<N>, DMat<N>) {
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assert!(col_start < col_end);
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let rows = m.nrows();
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assert!(col_end <= self.ncols);
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let cols = m.ncols();
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let mut slice : DVec<N> = unsafe {
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assert!(rows >= cols);
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DVec::new_uninitialized(self.nrows)
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let mut q : DMat<N> = DMat::new_identity(rows);
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let mut r = m.clone();
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let subtract_reflection = |vec: DVec<N>| -> DMat<N> {
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// FIXME: we don't handle the complex case here
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let mut qk : DMat<N> = DMat::new_identity(rows);
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let start = rows - vec.at.len();
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for j in range(start, rows) {
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for i in range(start, rows) {
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unsafe {
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let vv = vec.at_fast(i-start)*vec.at_fast(j-start);
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let qkij = qk.at_fast(i,j);
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qk.set_fast(i, j, qkij - vv - vv);
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}
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}
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}
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qk
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};
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let iterations = min(rows-1, cols);
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for ite in range(0u, iterations) {
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// we get the ite-th column truncated from its first ite elements,
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// this is fast thanks to the matrix being column major
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let start= m.offset(ite, ite);
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let stop = m.offset(rows, ite);
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let mut v = DVec::from_vec(rows - ite, r.mij.slice(start, stop));
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let alpha =
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if unsafe { v.at_fast(ite) } >= Zero::zero() {
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-Norm::norm(&v)
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}
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else {
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Norm::norm(&v)
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};
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};
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let mut slice_idx = 0u;
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for col_id in range(col_start, col_end) {
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unsafe {
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unsafe {
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let x = v.at_fast(0);
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slice.set_fast(slice_idx, self.at_fast(row_id, col_id));
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v.set_fast(0, x - alpha);
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}
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}
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let _ = v.normalize();
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slice_idx += 1;
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let qk = subtract_reflection(v);
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}
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r = qk * r;
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slice
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q = q * Transpose::transpose_cpy(&qk);
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}
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}
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(q, r)
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}
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}
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impl<N: ApproxEq<N>> ApproxEq<N> for DMat<N> {
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impl<N: ApproxEq<N>> ApproxEq<N> for DMat<N> {
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#[inline]
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#[inline]
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@ -578,9 +553,9 @@ impl<N: Show + Clone> Show for DMat<N> {
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fn fmt(&self, form:&mut Formatter) -> Result {
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fn fmt(&self, form:&mut Formatter) -> Result {
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for i in range(0u, self.nrows()) {
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for i in range(0u, self.nrows()) {
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for j in range(0u, self.ncols()) {
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for j in range(0u, self.ncols()) {
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write!(form.buf, "{} ", self.at(i, j));
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let _ = write!(form.buf, "{} ", self.at(i, j));
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}
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}
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write!(form.buf, "\n");
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let _ = write!(form.buf, "\n");
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}
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}
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write!(form.buf, "\n")
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write!(form.buf, "\n")
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}
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}
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@ -1,7 +1,6 @@
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//! Data structures and implementations.
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//! Data structures and implementations.
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pub use self::dmat::DMat;
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pub use self::dmat::DMat;
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pub use self::dmat::decomp_qr;
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pub use self::dvec::DVec;
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pub use self::dvec::DVec;
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pub use self::vec::{Vec0, Vec1, Vec2, Vec3, Vec4, Vec5, Vec6};
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pub use self::vec::{Vec0, Vec1, Vec2, Vec3, Vec4, Vec5, Vec6};
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pub use self::mat::{Identity, Mat1, Mat2, Mat3, Mat4, Mat5, Mat6};
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pub use self::mat::{Identity, Mat1, Mat2, Mat3, Mat4, Mat5, Mat6};
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@ -8,7 +8,7 @@ pub use self::structure::{FloatVec, FloatVecExt, Basis, Cast, Col, Dim, Indexabl
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Iterable, IterableMut, Mat, Row, AnyVec, VecExt};
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Iterable, IterableMut, Mat, Row, AnyVec, VecExt};
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pub use self::operations::{Absolute, ApproxEq, Cov, Inv, LMul, Mean, Outer, PartialOrd, RMul,
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pub use self::operations::{Absolute, ApproxEq, Cov, Inv, LMul, Mean, Outer, PartialOrd, RMul,
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ScalarAdd, ScalarSub, Transpose};
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ScalarAdd, ScalarSub, Transpose, ColSlice, RowSlice};
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pub use self::operations::{PartialOrdering, PartialLess, PartialEqual, PartialGreater, NotComparable};
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pub use self::operations::{PartialOrdering, PartialLess, PartialEqual, PartialGreater, NotComparable};
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pub mod geometry;
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pub mod geometry;
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@ -244,6 +244,18 @@ pub trait Mean<N> {
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fn mean(&Self) -> N;
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fn mean(&Self) -> N;
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}
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}
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/// Trait for objects that support column slicing
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pub trait ColSlice<VecLike> {
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/// Returns a view to a slice of a column of a matrix.
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fn col_slice(&self, col_id :uint, row_start: uint, row_end: uint) -> VecLike;
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}
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/// Trait for objects that support column slicing
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pub trait RowSlice<VecLike> {
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/// Returns a view to a slice of a row of a matrix.
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fn row_slice(&self, row_id :uint, col_start: uint, col_end: uint) -> VecLike;
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}
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// /// Cholesky decomposition.
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// /// Cholesky decomposition.
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// pub trait Chol {
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// pub trait Chol {
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// /// Performs the cholesky decomposition on `self`. The resulting upper-triangular matrix is
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// /// Performs the cholesky decomposition on `self`. The resulting upper-triangular matrix is
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