846 lines
17 KiB
Rust
846 lines
17 KiB
Rust
extern crate nalgebra as na;
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extern crate rand;
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use rand::random;
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use na::{Rot2, Rot3, Iso2, Iso3, Sim2, Sim3, Vec3, Mat1, Mat2, Mat3, Mat4, Mat5, Mat6, DMat, DVec,
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Row, Col, Diag, Transpose, RowSlice, ColSlice, Shape};
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macro_rules! test_inv_mat_impl(
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($t: ty) => (
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for _ in 0usize .. 10000 {
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let randmat : $t = random();
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match na::inv(&randmat) {
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None => { },
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Some(i) => {
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assert!(na::approx_eq(&(i * randmat), &na::one()))
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}
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}
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}
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);
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);
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macro_rules! test_transpose_mat_impl(
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($t: ty) => (
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for _ in 0usize .. 10000 {
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let randmat : $t = random();
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assert!(na::transpose(&na::transpose(&randmat)) == randmat);
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}
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);
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);
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macro_rules! test_qr_impl(
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($t: ty) => (
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for _ in 0usize .. 10000 {
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let randmat : $t = random();
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let (q, r) = na::qr(&randmat);
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let recomp = q * r;
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assert!(na::approx_eq(&randmat, &recomp));
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}
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);
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);
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macro_rules! test_cholesky_impl(
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($t: ty) => (
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for _ in 0usize .. 10000 {
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// construct symmetric positive definite matrix
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let mut randmat : $t = random();
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let mut diagmat : $t = Diag::from_diag(&na::diag(&randmat));
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diagmat = na::abs(&diagmat) + 1.0;
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randmat = randmat * diagmat * na::transpose(&randmat);
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let result = na::cholesky(&randmat);
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assert!(result.is_ok());
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let v = result.unwrap();
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let recomp = v * na::transpose(&v);
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assert!(na::approx_eq(&randmat, &recomp));
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}
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);
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);
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macro_rules! test_hessenberg_impl(
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($t: ty) => (
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for _ in 0usize .. 10000 {
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let randmat : $t = random();
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let (q, h) = na::hessenberg(&randmat);
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let recomp = q * h * na::transpose(&q);
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let (rows, cols) = h.shape();
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// Check if `h` has zero entries below the first subdiagonal
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if cols > 2 {
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for j in 0..(cols-2) {
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for i in (j+2)..rows {
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assert!(na::approx_eq(&h[(i,j)], &0.0f64));
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}
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}
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}
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assert!(na::approx_eq(&randmat, &recomp));
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}
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);
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);
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macro_rules! test_eigen_qr_impl(
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($t: ty) => {
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for _ in 0usize .. 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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let (eigenvectors, eigenvalues) = na::eigen_qr(&randmat, &1e-13, 100);
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let diag: $t = Diag::from_diag(&eigenvalues);
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let recomp = eigenvectors * diag * na::transpose(&eigenvectors);
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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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assert!(na::approx_eq_eps(&randmat, &recomp, &1.0e-2));
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}
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for _ in 0usize .. 10000 {
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let randmat : $t = random();
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// Take only diagonal part
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let randmat: $t = Diag::from_diag(&randmat.diag());
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let (eigenvectors, eigenvalues) = na::eigen_qr(&randmat, &1e-13, 100);
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let diag: $t = Diag::from_diag(&eigenvalues);
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let recomp = eigenvectors * diag * na::transpose(&eigenvectors);
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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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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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test_transpose_mat_impl!(Mat1<f64>);
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}
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#[test]
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fn test_transpose_mat2() {
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test_transpose_mat_impl!(Mat2<f64>);
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}
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#[test]
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fn test_transpose_mat3() {
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test_transpose_mat_impl!(Mat3<f64>);
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}
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#[test]
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fn test_transpose_mat4() {
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test_transpose_mat_impl!(Mat4<f64>);
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}
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#[test]
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fn test_transpose_mat5() {
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test_transpose_mat_impl!(Mat5<f64>);
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}
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#[test]
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fn test_transpose_mat6() {
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test_transpose_mat_impl!(Mat6<f64>);
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}
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#[test]
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fn test_inv_mat1() {
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test_inv_mat_impl!(Mat1<f64>);
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}
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#[test]
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fn test_inv_mat2() {
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test_inv_mat_impl!(Mat2<f64>);
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}
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#[test]
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fn test_inv_mat3() {
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test_inv_mat_impl!(Mat3<f64>);
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}
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#[test]
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fn test_inv_mat4() {
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test_inv_mat_impl!(Mat4<f64>);
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}
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#[test]
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fn test_inv_mat5() {
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test_inv_mat_impl!(Mat5<f64>);
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}
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#[test]
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fn test_inv_mat6() {
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test_inv_mat_impl!(Mat6<f64>);
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}
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#[test]
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fn test_inv_rot2() {
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test_inv_mat_impl!(Rot2<f64>);
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}
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#[test]
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fn test_inv_rot3() {
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test_inv_mat_impl!(Rot3<f64>);
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}
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#[test]
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fn test_inv_iso2() {
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test_inv_mat_impl!(Iso2<f64>);
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}
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#[test]
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fn test_inv_iso3() {
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test_inv_mat_impl!(Iso3<f64>);
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}
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#[test]
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fn test_inv_sim2() {
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test_inv_mat_impl!(Sim2<f64>);
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}
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#[test]
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fn test_inv_sim3() {
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test_inv_mat_impl!(Sim3<f64>);
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}
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#[test]
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fn test_index_mat2() {
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let mat: Mat2<f64> = random();
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assert!(mat[(0, 1)] == na::transpose(&mat)[(1, 0)]);
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}
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#[test]
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fn test_mean_dmat() {
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let mat = DMat::from_row_vec(
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3,
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3,
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&[
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1.0f64, 2.0, 3.0,
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4.0f64, 5.0, 6.0,
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7.0f64, 8.0, 9.0,
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]
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);
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assert!(na::approx_eq(&na::mean(&mat), &DVec::from_slice(3, &[4.0f64, 5.0, 6.0])));
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}
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#[test]
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fn test_cov_dmat() {
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let mat = DMat::from_row_vec(
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5,
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3,
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&[
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4.0f64, 2.0, 0.60,
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4.2f64, 2.1, 0.59,
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3.9f64, 2.0, 0.58,
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4.3f64, 2.1, 0.62,
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4.1f64, 2.2, 0.63
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]
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);
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let expected = DMat::from_row_vec(
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3,
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3,
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&[
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0.025f64, 0.0075, 0.00175,
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0.0075f64, 0.007, 0.00135,
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0.00175f64, 0.00135, 0.00043
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]
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);
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assert!(na::approx_eq(&na::cov(&mat), &expected));
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}
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#[test]
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fn test_transpose_dmat() {
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let mat = DMat::from_row_vec(
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8,
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4,
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&[
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1u32,2, 3, 4,
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5, 6, 7, 8,
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9, 10, 11, 12,
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13, 14, 15, 16,
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17, 18, 19, 20,
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21, 22, 23, 24,
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25, 26, 27, 28,
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29, 30, 31, 32
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]
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);
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assert!(na::transpose(&na::transpose(&mat)) == mat);
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}
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#[test]
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fn test_row_dmat() {
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let mat = DMat::from_row_vec(
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8,
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4,
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&[
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1u32,2, 3, 4,
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5, 6, 7, 8,
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9, 10, 11, 12,
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13, 14, 15, 16,
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17, 18, 19, 20,
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21, 22, 23, 24,
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25, 26, 27, 28,
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29, 30, 31, 32
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]
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);
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assert_eq!(&DVec::from_slice(4, &[1u32, 2, 3, 4]), &mat.row(0));
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assert_eq!(&DVec::from_slice(4, &[5u32, 6, 7, 8]), &mat.row(1));
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assert_eq!(&DVec::from_slice(4, &[9u32, 10, 11, 12]), &mat.row(2));
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assert_eq!(&DVec::from_slice(4, &[13u32, 14, 15, 16]), &mat.row(3));
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assert_eq!(&DVec::from_slice(4, &[17u32, 18, 19, 20]), &mat.row(4));
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assert_eq!(&DVec::from_slice(4, &[21u32, 22, 23, 24]), &mat.row(5));
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assert_eq!(&DVec::from_slice(4, &[25u32, 26, 27, 28]), &mat.row(6));
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assert_eq!(&DVec::from_slice(4, &[29u32, 30, 31, 32]), &mat.row(7));
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}
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#[test]
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fn test_row_slice_dmat() {
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let mat = DMat::from_row_vec(
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5,
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4,
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&[
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1u32,2, 3, 4,
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5, 6, 7, 8,
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9, 10, 11, 12,
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13, 14, 15, 16,
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17, 18, 19, 20,
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]
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);
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assert_eq!(&DVec::from_slice(4, &[1u32, 2, 3, 4]), &mat.row_slice(0, 0, 4));
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assert_eq!(&DVec::from_slice(2, &[1u32, 2]), &mat.row_slice(0, 0, 2));
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assert_eq!(&DVec::from_slice(2, &[10u32, 11]), &mat.row_slice(2, 1, 3));
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assert_eq!(&DVec::from_slice(2, &[19u32, 20]), &mat.row_slice(4, 2, 4));
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}
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#[test]
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fn test_col_dmat() {
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let mat = DMat::from_row_vec(
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8,
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4,
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&[
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1u32,2, 3, 4,
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5, 6, 7, 8,
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9, 10, 11, 12,
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13, 14, 15, 16,
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17, 18, 19, 20,
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21, 22, 23, 24,
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25, 26, 27, 28,
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29, 30, 31, 32
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]
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);
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assert_eq!(&DVec::from_slice(8, &[1u32, 5, 9, 13, 17, 21, 25, 29]), &mat.col(0));
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assert_eq!(&DVec::from_slice(8, &[2u32, 6, 10, 14, 18, 22, 26, 30]), &mat.col(1));
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assert_eq!(&DVec::from_slice(8, &[3u32, 7, 11, 15, 19, 23, 27, 31]), &mat.col(2));
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assert_eq!(&DVec::from_slice(8, &[4u32, 8, 12, 16, 20, 24, 28, 32]), &mat.col(3));
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}
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#[test]
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fn test_col_slice_dmat() {
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let mat = DMat::from_row_vec(
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8,
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4,
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&[
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1u32,2, 3, 4,
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5, 6, 7, 8,
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9, 10, 11, 12,
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13, 14, 15, 16,
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17, 18, 19, 20,
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21, 22, 23, 24,
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25, 26, 27, 28,
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29, 30, 31, 32
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]
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);
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assert_eq!(&DVec::from_slice(8, &[1u32, 5, 9, 13, 17, 21, 25, 29]), &mat.col_slice(0, 0, 8));
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assert_eq!(&DVec::from_slice(3, &[1u32, 5, 9]), &mat.col_slice(0, 0, 3));
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assert_eq!(&DVec::from_slice(5, &[11u32, 15, 19, 23, 27]), &mat.col_slice(2, 2, 7));
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assert_eq!(&DVec::from_slice(2, &[28u32, 32]), &mat.col_slice(3, 6, 8));
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}
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#[test]
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fn test_dmat_from_vec() {
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let mat1 = DMat::from_row_vec(
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8,
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4,
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&[
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1i32, 2, 3, 4,
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5, 6, 7, 8,
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9, 10, 11, 12,
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13, 14, 15, 16,
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17, 18, 19, 20,
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21, 22, 23, 24,
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25, 26, 27, 28,
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29, 30, 31, 32
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]
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);
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let mat2 = DMat::from_col_vec(
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8,
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4,
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&[
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1i32, 5, 9, 13, 17, 21, 25, 29,
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2i32, 6, 10, 14, 18, 22, 26, 30,
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3i32, 7, 11, 15, 19, 23, 27, 31,
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4i32, 8, 12, 16, 20, 24, 28, 32
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]
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);
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println!("mat1: {:?}, mat2: {:?}", mat1, mat2);
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assert!(mat1 == mat2);
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}
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#[test]
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fn test_dmat_addition() {
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let mat1 = DMat::from_row_vec(
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2,
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2,
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&[
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1.0, 2.0,
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3.0, 4.0
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]
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);
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let mat2 = DMat::from_row_vec(
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2,
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2,
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&[
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10.0, 20.0,
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30.0, 40.0
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]
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);
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let res = DMat::from_row_vec(
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2,
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2,
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&[
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11.0, 22.0,
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33.0, 44.0
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]
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);
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assert!((mat1 + mat2) == res);
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}
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#[test]
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fn test_dmat_multiplication() {
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let mat1 = DMat::from_row_vec(
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2,
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2,
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&[
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1.0, 2.0,
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3.0, 4.0
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]
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);
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let mat2 = DMat::from_row_vec(
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2,
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2,
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&[
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10.0, 20.0,
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30.0, 40.0
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]
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);
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let res = DMat::from_row_vec(
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2,
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2,
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&[
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70.0, 100.0,
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150.0, 220.0
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]
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);
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assert!((mat1 * mat2) == res);
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}
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// Tests multiplication of rectangular (non-square) matrices.
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#[test]
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fn test_dmat_multiplication_rect() {
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let mat1 = DMat::from_row_vec(
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1,
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2,
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&[
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1.0, 2.0,
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]
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);
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let mat2 = DMat::from_row_vec(
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2,
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3,
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&[
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3.0, 4.0, 5.0,
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6.0, 7.0, 8.0,
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]
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);
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let res = DMat::from_row_vec(
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1,
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3,
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&[
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15.0, 18.0, 21.0,
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]
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);
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assert!((mat1.clone() * mat2.clone()) == res);
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assert!((&mat1 * mat2.clone()) == res);
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assert!((mat1.clone() * &mat2) == res);
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assert!((&mat1 * &mat2) == res);
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}
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#[test]
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fn test_dmat_subtraction() {
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let mat1 = DMat::from_row_vec(
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2,
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2,
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&[
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1.0, 2.0,
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3.0, 4.0
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]
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);
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let mat2 = DMat::from_row_vec(
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2,
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2,
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&[
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10.0, 20.0,
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30.0, 40.0
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]
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);
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let res = DMat::from_row_vec(
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2,
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2,
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&[
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-09.0, -18.0,
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-27.0, -36.0
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]
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);
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assert!((mat1 - mat2) == res);
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}
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#[test]
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fn test_dmat_col() {
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let mat = DMat::from_row_vec(
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3,
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3,
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&[
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|
1.0, 2.0, 3.0,
|
|
4.0, 5.0, 6.0,
|
|
7.0, 8.0, 9.0,
|
|
]
|
|
);
|
|
|
|
assert!(mat.col(1) == DVec::from_slice(3, &[2.0, 5.0, 8.0]));
|
|
}
|
|
|
|
#[test]
|
|
fn test_dmat_set_col() {
|
|
let mut mat = DMat::from_row_vec(
|
|
3,
|
|
3,
|
|
&[
|
|
1.0, 2.0, 3.0,
|
|
4.0, 5.0, 6.0,
|
|
7.0, 8.0, 9.0,
|
|
]
|
|
);
|
|
|
|
mat.set_col(1, DVec::from_slice(3, &[12.0, 15.0, 18.0]));
|
|
|
|
let expected = DMat::from_row_vec(
|
|
3,
|
|
3,
|
|
&[
|
|
1.0, 12.0, 3.0,
|
|
4.0, 15.0, 6.0,
|
|
7.0, 18.0, 9.0,
|
|
]
|
|
);
|
|
|
|
assert!(mat == expected);
|
|
}
|
|
|
|
#[test]
|
|
fn test_dmat_row() {
|
|
let mat = DMat::from_row_vec(
|
|
3,
|
|
3,
|
|
&[
|
|
1.0, 2.0, 3.0,
|
|
4.0, 5.0, 6.0,
|
|
7.0, 8.0, 9.0,
|
|
]
|
|
);
|
|
|
|
assert!(mat.row(1) == DVec::from_slice(3, &[4.0, 5.0, 6.0]));
|
|
}
|
|
|
|
#[test]
|
|
fn test_dmat_set_row() {
|
|
let mut mat = DMat::from_row_vec(
|
|
3,
|
|
3,
|
|
&[
|
|
1.0, 2.0, 3.0,
|
|
4.0, 5.0, 6.0,
|
|
7.0, 8.0, 9.0,
|
|
]
|
|
);
|
|
|
|
mat.set_row(1, DVec::from_slice(3, &[14.0, 15.0, 16.0]));
|
|
|
|
let expected = DMat::from_row_vec(
|
|
3,
|
|
3,
|
|
&[
|
|
1.0, 2.0, 3.0,
|
|
14.0, 15.0, 16.0,
|
|
7.0, 8.0, 9.0,
|
|
]
|
|
);
|
|
|
|
assert!(mat == expected);
|
|
}
|
|
|
|
/* FIXME: review qr decomposition to make it work with DMat.
|
|
#[test]
|
|
fn test_qr() {
|
|
for _ in 0usize .. 10 {
|
|
let dim1: usize = random();
|
|
let dim2: usize = random();
|
|
let rows = min(40, max(dim1, dim2));
|
|
let cols = min(40, min(dim1, dim2));
|
|
let randmat: DMat<f64> = DMat::new_random(rows, cols);
|
|
let (q, r) = na::qr(&randmat);
|
|
let recomp = q * r;
|
|
|
|
assert!(na::approx_eq(&randmat, &recomp));
|
|
}
|
|
}
|
|
*/
|
|
|
|
#[test]
|
|
fn test_qr_mat1() {
|
|
test_qr_impl!(Mat1<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_qr_mat2() {
|
|
test_qr_impl!(Mat2<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_qr_mat3() {
|
|
test_qr_impl!(Mat3<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_qr_mat4() {
|
|
test_qr_impl!(Mat4<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_qr_mat5() {
|
|
test_qr_impl!(Mat5<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_qr_mat6() {
|
|
test_qr_impl!(Mat6<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_eigen_qr_mat1() {
|
|
test_eigen_qr_impl!(Mat1<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_eigen_qr_mat2() {
|
|
test_eigen_qr_impl!(Mat2<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_eigen_qr_mat3() {
|
|
test_eigen_qr_impl!(Mat3<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_eigen_qr_mat4() {
|
|
test_eigen_qr_impl!(Mat4<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_eigen_qr_mat5() {
|
|
test_eigen_qr_impl!(Mat5<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_eigen_qr_mat6() {
|
|
test_eigen_qr_impl!(Mat6<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_from_fn() {
|
|
let actual: DMat<usize> = DMat::from_fn(3, 4, |i, j| 10 * i + j);
|
|
let expected: DMat<usize> = DMat::from_row_vec(3, 4,
|
|
&[ 0_0, 0_1, 0_2, 0_3,
|
|
1_0, 1_1, 1_2, 1_3,
|
|
2_0, 2_1, 2_2, 2_3 ]);
|
|
|
|
assert_eq!(actual, expected);
|
|
}
|
|
|
|
#[test]
|
|
fn test_row_3() {
|
|
let mat = Mat3::new(0.0f32, 1.0, 2.0,
|
|
3.0, 4.0, 5.0,
|
|
6.0, 7.0, 8.0);
|
|
let second_row = mat.row(1);
|
|
let second_col = mat.col(1);
|
|
|
|
assert!(second_row == Vec3::new(3.0, 4.0, 5.0));
|
|
assert!(second_col == Vec3::new(1.0, 4.0, 7.0));
|
|
}
|
|
|
|
#[test]
|
|
fn test_cholesky_const() {
|
|
|
|
let a : Mat3<f64> = Mat3::<f64>::new(1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 1.0, 2.0, 3.0);
|
|
let g : Mat3<f64> = Mat3::<f64>::new(1.0, 0.0, 0.0, 1.0, 1.0, 0.0, 1.0, 1.0, 1.0);
|
|
|
|
let result = na::cholesky(&a);
|
|
|
|
assert!(result.is_ok());
|
|
|
|
let v = result.unwrap();
|
|
assert!(na::approx_eq(&v, &g));
|
|
|
|
let recomp = v * na::transpose(&v);
|
|
assert!(na::approx_eq(&recomp, &a));
|
|
}
|
|
|
|
#[test]
|
|
fn test_cholesky_not_spd() {
|
|
|
|
let a : Mat3<f64> = Mat3::<f64>::new(1.0, 2.0, 3.0, 3.0, 2.0, 1.0, 1.0, 1.0, 1.0);
|
|
|
|
let result = na::cholesky(&a);
|
|
|
|
assert!(result.is_err());
|
|
}
|
|
|
|
#[test]
|
|
fn test_cholesky_not_symmetric() {
|
|
|
|
let a : Mat2<f64> = Mat2::<f64>::new(1.0, 1.0, -1.0, 1.0);
|
|
|
|
let result = na::cholesky(&a);
|
|
|
|
assert!(result.is_err());
|
|
}
|
|
|
|
#[test]
|
|
fn test_cholesky_mat1() {
|
|
test_cholesky_impl!(Mat1<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_cholesky_mat2() {
|
|
test_cholesky_impl!(Mat2<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_cholesky_mat3() {
|
|
test_cholesky_impl!(Mat3<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_cholesky_mat4() {
|
|
test_cholesky_impl!(Mat4<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_cholesky_mat5() {
|
|
test_cholesky_impl!(Mat5<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_cholesky_mat6() {
|
|
test_cholesky_impl!(Mat6<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_hessenberg_mat1() {
|
|
test_hessenberg_impl!(Mat1<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_hessenberg_mat2() {
|
|
test_hessenberg_impl!(Mat2<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_hessenberg_mat3() {
|
|
test_hessenberg_impl!(Mat3<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_hessenberg_mat4() {
|
|
test_hessenberg_impl!(Mat4<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_hessenberg_mat5() {
|
|
test_hessenberg_impl!(Mat5<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_hessenberg_mat6() {
|
|
test_hessenberg_impl!(Mat6<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_transpose_square_mat() {
|
|
let col_major_mat = &[0, 1, 2, 3,
|
|
0, 1, 2, 3,
|
|
0, 1, 2, 3,
|
|
0, 1, 2, 3];
|
|
let num_rows = 4;
|
|
let num_cols = 4;
|
|
let mut mat = DMat::from_col_vec(num_rows, num_cols, col_major_mat);
|
|
mat.transpose_mut();
|
|
for i in 0..num_rows {
|
|
assert_eq!(&[0, 1, 2, 3], &mat.row_slice(i, 0, num_cols)[..]);
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn test_outer_dvec() {
|
|
let vec = DVec::from_slice(5, &[ 1.0, 2.0, 3.0, 4.0, 5.0 ]);
|
|
let row = DMat::from_row_vec(1, 5, &vec[..]);
|
|
|
|
assert_eq!(row.transpose() * row, na::outer(&vec, &vec))
|
|
}
|