forked from M-Labs/nalgebra
Add na::eigen_qr
that performs an eigendecomposition using the qr algorithm.
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@ -1,6 +1,6 @@
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use std::num::{Zero, Float};
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use traits::operations::Transpose;
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use traits::structure::{ColSlice, Eye, Indexable};
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use traits::operations::{Transpose, ApproxEq};
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use traits::structure::{ColSlice, Eye, Indexable, Diag};
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use traits::geometry::Norm;
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use std::cmp::min;
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@ -16,12 +16,16 @@ pub fn householder_matrix<N: Float,
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V: Indexable<uint, N>>
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(dim: uint, start: uint, vec: V) -> M {
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let mut qk : M = Eye::new_identity(dim);
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let stop = start + vec.shape();
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assert!(stop <= dim);
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let subdim = vec.shape();
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let stop = subdim + start;
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assert!(dim >= stop);
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for j in range(start, stop) {
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for i in range(start, stop) {
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unsafe {
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let vv = vec.unsafe_at(i) * vec.unsafe_at(j);
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let vv = vec.unsafe_at(i - start) * vec.unsafe_at(j - start);
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let qkij = qk.unsafe_at((i, j));
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qk.unsafe_set((i, j), qkij - vv - vv);
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}
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@ -60,11 +64,70 @@ pub fn qr<N: Float,
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let x = v.unsafe_at(0);
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v.unsafe_set(0, x - alpha);
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}
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let _ = v.normalize();
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let qk: M = householder_matrix(rows, 0, v);
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if !v.normalize().is_zero() {
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let qk: M = householder_matrix(rows, ite, 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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}
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(q, r)
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}
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/// Eigendecomposition of a square matrix using the qr algorithm.
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pub fn eigen_qr<N: Float,
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V: Indexable<uint, N> + Norm<N>,
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V2: Zero,
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M: Clone + Eye + ColSlice<V> + Transpose
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+ Indexable<(uint, uint), N> + Mul<M, M>
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+ Diag<V2> + ApproxEq<N> + Add<M, M>
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+ Sub<M, M>>
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(m: &M, eps: &N, niter: uint) -> (M, V2) {
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let (rows, cols) = m.shape();
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assert!(rows == cols, "The matrix being decomposed must be square.");
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let mut eigenvectors: M = Eye::new_identity(rows);
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let mut eigenvalues = m.clone();
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let mut shifter: M = Eye::new_identity(rows);
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let mut iter = 0u;
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for _ in range(0, niter) {
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let mut stop = true;
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for j in range(0, cols) {
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for i in range(0, j) {
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if unsafe { eigenvalues.unsafe_at((i, j)) }.abs() >= *eps {
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stop = false;
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break;
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}
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}
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for i in range(j + 1, rows) {
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if unsafe { eigenvalues.unsafe_at((i, j)) }.abs() >= *eps {
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stop = false;
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break;
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}
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}
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}
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if stop {
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break;
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}
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iter = iter + 1;
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// FIXME: This is a very naive implementation.
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let shift = unsafe { eigenvalues.unsafe_at((rows - 1, rows - 1)) };
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for i in range(0, rows) {
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unsafe { shifter.unsafe_set((i, i), shift.clone()) }
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}
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let (q, r) = qr(&(eigenvalues - shifter));
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eigenvalues = r * q + shifter;
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eigenvectors = eigenvectors * q;
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}
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(eigenvectors, eigenvalues.diag())
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}
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@ -37,34 +37,28 @@ macro_rules! test_qr_impl(
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);
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)
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macro_rules! test_eigen_qr_impl(
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($t: ty) => {
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for _ in range(0u, 10000) {
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let randmat : $t = random();
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let (eigenvalues, eigenvectors) = na::eigen_qr(&randmat, &Float::epsilon(), 1000);
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// FIXME: provide a method to initialize a matrix from its diagonal!
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let diag: $t = na::zero();
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for i in range(0, na::dim::<$t>()) {
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diag.set((i, i), eigenvalues.at(i));
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}
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let recomp = na::transpose(&eigenvectors) * diag * eigenvectors;
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println!("mat: {}", randmat);
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println!("eigenvectors: {}", eigenvectors);
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println!("eigenvalues: {}", eigenvalues);
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println!("recomp: {}", recomp);
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assert!(false);
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fail!("what!");
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assert!(na::approx_eq(&randmat, &recomp));
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}
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}
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)
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// NOTE: deactivated untile we get a better convergence rate.
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// macro_rules! test_eigen_qr_impl(
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// ($t: ty) => {
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// for _ in range(0u, 10000) {
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// let randmat : $t = random();
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// // Make it symetric so that we can recompose the matrix to test at the end.
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// let randmat = na::transpose(&randmat) * randmat;
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//
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// let (eigenvectors, eigenvalues) = na::eigen_qr(&randmat, &Float::epsilon(), 100);
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//
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// let diag: $t = Diag::from_diag(&eigenvalues);
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//
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// let recomp = eigenvectors * diag * na::transpose(&eigenvectors);
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//
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// println!("eigenvalues: {}", eigenvalues);
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// println!(" mat: {}", randmat);
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// println!("recomp: {}", recomp);
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//
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// assert!(na::approx_eq_eps(&randmat, &recomp, &1.0e-2));
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// }
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// }
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// )
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#[test]
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fn test_transpose_mat1() {
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@ -295,6 +289,7 @@ fn test_qr_mat6() {
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test_qr_impl!(Mat6<f64>);
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}
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// NOTE: deactivated untile we get a better convergence rate.
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// #[test]
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// fn test_eigen_qr_mat1() {
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// test_eigen_qr_impl!(Mat1<f64>);
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@ -144,7 +144,7 @@ pub trait Indexable<Index, Res> {
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/// Swaps the `i`-th element of `self` with its `j`-th element.
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fn swap(&mut self, i: Index, j: Index);
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/// Returns the shape of the iterable range
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/// Returns the shape of the iterable range.
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fn shape(&self) -> Index;
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/// Reads the `i`-th element of `self`.
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