forked from M-Labs/nalgebra
846 lines
18 KiB
Rust
846 lines
18 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::{Rotation2, Rotation3, Isometry2, Isometry3, Similarity2, Similarity3, Vector3, Matrix1, Matrix2, Matrix3, Matrix4, Matrix5, Matrix6, DMatrix, DVector,
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Row, Column, Diagonal, Transpose, RowSlice, ColumnSlice, Shape};
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macro_rules! test_inverse_mat_impl(
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($t: ty) => (
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for _ in 0usize .. 10000 {
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let randmatrix : $t = random();
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match na::inverse(&randmatrix) {
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None => { },
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Some(i) => {
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assert!(na::approx_eq(&(i * randmatrix), &na::one()))
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}
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}
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}
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);
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);
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macro_rules! test_transpose_mat_impl(
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($t: ty) => (
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for _ in 0usize .. 10000 {
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let randmatrix : $t = random();
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assert!(na::transpose(&na::transpose(&randmatrix)) == randmatrix);
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}
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);
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);
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macro_rules! test_qr_impl(
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($t: ty) => (
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for _ in 0usize .. 10000 {
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let randmatrix : $t = random();
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let (q, r) = na::qr(&randmatrix);
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let recomp = q * r;
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assert!(na::approx_eq(&randmatrix, &recomp));
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}
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);
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);
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macro_rules! test_cholesky_impl(
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($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 randmatrix : $t = random();
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let mut diagmatrix : $t = Diagonal::from_diagonal(&na::diagonal(&randmatrix));
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diagmatrix = na::abs(&diagmatrix) + 1.0;
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randmatrix = randmatrix * diagmatrix * na::transpose(&randmatrix);
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let result = na::cholesky(&randmatrix);
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assert!(result.is_ok());
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let v = result.unwrap();
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let recomp = v * na::transpose(&v);
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assert!(na::approx_eq(&randmatrix, &recomp));
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}
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);
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);
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macro_rules! test_hessenberg_impl(
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($t: ty) => (
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for _ in 0usize .. 10000 {
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let randmatrix : $t = random();
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let (q, h) = na::hessenberg(&randmatrix);
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let recomp = q * h * na::transpose(&q);
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let (rows, cols) = h.shape();
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// Check if `h` has zero entries below the first subdiagonal
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if cols > 2 {
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for j in 0..(cols-2) {
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for i in (j+2)..rows {
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assert!(na::approx_eq(&h[(i,j)], &0.0f64));
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}
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}
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}
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assert!(na::approx_eq(&randmatrix, &recomp));
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}
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);
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);
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macro_rules! test_eigen_qr_impl(
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($t: ty) => {
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for _ in 0usize .. 10000 {
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let randmatrix : $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 randmatrix = na::transpose(&randmatrix) * randmatrix;
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let (eigenvectors, eigenvalues) = na::eigen_qr(&randmatrix, &1e-13, 100);
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let diagonal: $t = Diagonal::from_diagonal(&eigenvalues);
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let recomp = eigenvectors * diagonal * na::transpose(&eigenvectors);
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println!("eigenvalues: {:?}", eigenvalues);
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println!(" matrix: {:?}", randmatrix);
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println!("recomp: {:?}", recomp);
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assert!(na::approx_eq_eps(&randmatrix, &recomp, &1.0e-2));
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}
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for _ in 0usize .. 10000 {
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let randmatrix : $t = random();
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// Take only diagonal part
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let randmatrix: $t = Diagonal::from_diagonal(&randmatrix.diagonal());
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let (eigenvectors, eigenvalues) = na::eigen_qr(&randmatrix, &1e-13, 100);
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let diagonal: $t = Diagonal::from_diagonal(&eigenvalues);
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let recomp = eigenvectors * diagonal * na::transpose(&eigenvectors);
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println!("eigenvalues: {:?}", eigenvalues);
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println!(" matrix: {:?}", randmatrix);
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println!("recomp: {:?}", recomp);
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assert!(na::approx_eq_eps(&randmatrix, &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!(Matrix1<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!(Matrix2<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!(Matrix3<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!(Matrix4<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!(Matrix5<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!(Matrix6<f64>);
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}
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#[test]
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fn test_inverse_mat1() {
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test_inverse_mat_impl!(Matrix1<f64>);
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}
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#[test]
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fn test_inverse_mat2() {
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test_inverse_mat_impl!(Matrix2<f64>);
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}
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#[test]
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fn test_inverse_mat3() {
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test_inverse_mat_impl!(Matrix3<f64>);
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}
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#[test]
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fn test_inverse_mat4() {
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test_inverse_mat_impl!(Matrix4<f64>);
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}
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#[test]
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fn test_inverse_mat5() {
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test_inverse_mat_impl!(Matrix5<f64>);
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}
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#[test]
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fn test_inverse_mat6() {
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test_inverse_mat_impl!(Matrix6<f64>);
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}
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#[test]
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fn test_inverse_rot2() {
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test_inverse_mat_impl!(Rotation2<f64>);
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}
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#[test]
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fn test_inverse_rot3() {
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test_inverse_mat_impl!(Rotation3<f64>);
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}
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#[test]
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fn test_inverse_iso2() {
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test_inverse_mat_impl!(Isometry2<f64>);
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}
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#[test]
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fn test_inverse_iso3() {
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test_inverse_mat_impl!(Isometry3<f64>);
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}
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#[test]
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fn test_inverse_sim2() {
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test_inverse_mat_impl!(Similarity2<f64>);
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}
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#[test]
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fn test_inverse_sim3() {
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test_inverse_mat_impl!(Similarity3<f64>);
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}
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#[test]
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fn test_index_mat2() {
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let matrix: Matrix2<f64> = random();
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assert!(matrix[(0, 1)] == na::transpose(&matrix)[(1, 0)]);
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}
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#[test]
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fn test_mean_dmatrix() {
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let matrix = DMatrix::from_row_vector(
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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(&matrix), &DVector::from_slice(3, &[4.0f64, 5.0, 6.0])));
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}
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#[test]
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fn test_covariance_dmatrix() {
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let matrix = DMatrix::from_row_vector(
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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 = DMatrix::from_row_vector(
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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::covariance(&matrix), &expected));
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}
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#[test]
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fn test_transpose_dmatrix() {
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let matrix = DMatrix::from_row_vector(
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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(&matrix)) == matrix);
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}
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#[test]
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fn test_row_dmatrix() {
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let matrix = DMatrix::from_row_vector(
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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!(&DVector::from_slice(4, &[1u32, 2, 3, 4]), &matrix.row(0));
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assert_eq!(&DVector::from_slice(4, &[5u32, 6, 7, 8]), &matrix.row(1));
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assert_eq!(&DVector::from_slice(4, &[9u32, 10, 11, 12]), &matrix.row(2));
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assert_eq!(&DVector::from_slice(4, &[13u32, 14, 15, 16]), &matrix.row(3));
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assert_eq!(&DVector::from_slice(4, &[17u32, 18, 19, 20]), &matrix.row(4));
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assert_eq!(&DVector::from_slice(4, &[21u32, 22, 23, 24]), &matrix.row(5));
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assert_eq!(&DVector::from_slice(4, &[25u32, 26, 27, 28]), &matrix.row(6));
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assert_eq!(&DVector::from_slice(4, &[29u32, 30, 31, 32]), &matrix.row(7));
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}
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#[test]
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fn test_row_slice_dmatrix() {
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let matrix = DMatrix::from_row_vector(
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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!(&DVector::from_slice(4, &[1u32, 2, 3, 4]), &matrix.row_slice(0, 0, 4));
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assert_eq!(&DVector::from_slice(2, &[1u32, 2]), &matrix.row_slice(0, 0, 2));
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assert_eq!(&DVector::from_slice(2, &[10u32, 11]), &matrix.row_slice(2, 1, 3));
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assert_eq!(&DVector::from_slice(2, &[19u32, 20]), &matrix.row_slice(4, 2, 4));
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}
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#[test]
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fn test_column_dmatrix() {
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let matrix = DMatrix::from_row_vector(
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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!(&DVector::from_slice(8, &[1u32, 5, 9, 13, 17, 21, 25, 29]), &matrix.column(0));
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assert_eq!(&DVector::from_slice(8, &[2u32, 6, 10, 14, 18, 22, 26, 30]), &matrix.column(1));
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assert_eq!(&DVector::from_slice(8, &[3u32, 7, 11, 15, 19, 23, 27, 31]), &matrix.column(2));
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assert_eq!(&DVector::from_slice(8, &[4u32, 8, 12, 16, 20, 24, 28, 32]), &matrix.column(3));
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}
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#[test]
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fn test_column_slice_dmatrix() {
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let matrix = DMatrix::from_row_vector(
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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!(&DVector::from_slice(8, &[1u32, 5, 9, 13, 17, 21, 25, 29]), &matrix.column_slice(0, 0, 8));
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assert_eq!(&DVector::from_slice(3, &[1u32, 5, 9]), &matrix.column_slice(0, 0, 3));
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assert_eq!(&DVector::from_slice(5, &[11u32, 15, 19, 23, 27]), &matrix.column_slice(2, 2, 7));
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assert_eq!(&DVector::from_slice(2, &[28u32, 32]), &matrix.column_slice(3, 6, 8));
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}
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#[test]
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fn test_dmat_from_vector() {
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let mat1 = DMatrix::from_row_vector(
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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 = DMatrix::from_column_vector(
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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 = DMatrix::from_row_vector(
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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 = DMatrix::from_row_vector(
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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 = DMatrix::from_row_vector(
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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 = DMatrix::from_row_vector(
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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 = DMatrix::from_row_vector(
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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 = DMatrix::from_row_vector(
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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 = DMatrix::from_row_vector(
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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 = DMatrix::from_row_vector(
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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 = DMatrix::from_row_vector(
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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 = DMatrix::from_row_vector(
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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 = DMatrix::from_row_vector(
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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 = DMatrix::from_row_vector(
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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_column() {
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let matrix = DMatrix::from_row_vector(
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3,
|
|
3,
|
|
&[
|
|
1.0, 2.0, 3.0,
|
|
4.0, 5.0, 6.0,
|
|
7.0, 8.0, 9.0,
|
|
]
|
|
);
|
|
|
|
assert!(matrix.column(1) == DVector::from_slice(3, &[2.0, 5.0, 8.0]));
|
|
}
|
|
|
|
#[test]
|
|
fn test_dmat_set_column() {
|
|
let mut matrix = DMatrix::from_row_vector(
|
|
3,
|
|
3,
|
|
&[
|
|
1.0, 2.0, 3.0,
|
|
4.0, 5.0, 6.0,
|
|
7.0, 8.0, 9.0,
|
|
]
|
|
);
|
|
|
|
matrix.set_column(1, DVector::from_slice(3, &[12.0, 15.0, 18.0]));
|
|
|
|
let expected = DMatrix::from_row_vector(
|
|
3,
|
|
3,
|
|
&[
|
|
1.0, 12.0, 3.0,
|
|
4.0, 15.0, 6.0,
|
|
7.0, 18.0, 9.0,
|
|
]
|
|
);
|
|
|
|
assert!(matrix == expected);
|
|
}
|
|
|
|
#[test]
|
|
fn test_dmat_row() {
|
|
let matrix = DMatrix::from_row_vector(
|
|
3,
|
|
3,
|
|
&[
|
|
1.0, 2.0, 3.0,
|
|
4.0, 5.0, 6.0,
|
|
7.0, 8.0, 9.0,
|
|
]
|
|
);
|
|
|
|
assert!(matrix.row(1) == DVector::from_slice(3, &[4.0, 5.0, 6.0]));
|
|
}
|
|
|
|
#[test]
|
|
fn test_dmat_set_row() {
|
|
let mut matrix = DMatrix::from_row_vector(
|
|
3,
|
|
3,
|
|
&[
|
|
1.0, 2.0, 3.0,
|
|
4.0, 5.0, 6.0,
|
|
7.0, 8.0, 9.0,
|
|
]
|
|
);
|
|
|
|
matrix.set_row(1, DVector::from_slice(3, &[14.0, 15.0, 16.0]));
|
|
|
|
let expected = DMatrix::from_row_vector(
|
|
3,
|
|
3,
|
|
&[
|
|
1.0, 2.0, 3.0,
|
|
14.0, 15.0, 16.0,
|
|
7.0, 8.0, 9.0,
|
|
]
|
|
);
|
|
|
|
assert!(matrix == expected);
|
|
}
|
|
|
|
/* FIXME: review qr decomposition to make it work with DMatrix.
|
|
#[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 randmatrix: DMatrix<f64> = DMatrix::new_random(rows, cols);
|
|
let (q, r) = na::qr(&randmatrix);
|
|
let recomp = q * r;
|
|
|
|
assert!(na::approx_eq(&randmatrix, &recomp));
|
|
}
|
|
}
|
|
*/
|
|
|
|
#[test]
|
|
fn test_qr_mat1() {
|
|
test_qr_impl!(Matrix1<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_qr_mat2() {
|
|
test_qr_impl!(Matrix2<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_qr_mat3() {
|
|
test_qr_impl!(Matrix3<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_qr_mat4() {
|
|
test_qr_impl!(Matrix4<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_qr_mat5() {
|
|
test_qr_impl!(Matrix5<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_qr_mat6() {
|
|
test_qr_impl!(Matrix6<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_eigen_qr_mat1() {
|
|
test_eigen_qr_impl!(Matrix1<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_eigen_qr_mat2() {
|
|
test_eigen_qr_impl!(Matrix2<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_eigen_qr_mat3() {
|
|
test_eigen_qr_impl!(Matrix3<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_eigen_qr_mat4() {
|
|
test_eigen_qr_impl!(Matrix4<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_eigen_qr_mat5() {
|
|
test_eigen_qr_impl!(Matrix5<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_eigen_qr_mat6() {
|
|
test_eigen_qr_impl!(Matrix6<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_from_fn() {
|
|
let actual: DMatrix<usize> = DMatrix::from_fn(3, 4, |i, j| 10 * i + j);
|
|
let expected: DMatrix<usize> = DMatrix::from_row_vector(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 matrix = Matrix3::new(0.0f32, 1.0, 2.0,
|
|
3.0, 4.0, 5.0,
|
|
6.0, 7.0, 8.0);
|
|
let second_row = matrix.row(1);
|
|
let second_col = matrix.column(1);
|
|
|
|
assert!(second_row == Vector3::new(3.0, 4.0, 5.0));
|
|
assert!(second_col == Vector3::new(1.0, 4.0, 7.0));
|
|
}
|
|
|
|
#[test]
|
|
fn test_cholesky_const() {
|
|
|
|
let a : Matrix3<f64> = Matrix3::<f64>::new(1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 1.0, 2.0, 3.0);
|
|
let g : Matrix3<f64> = Matrix3::<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 : Matrix3<f64> = Matrix3::<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 : Matrix2<f64> = Matrix2::<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!(Matrix1<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_cholesky_mat2() {
|
|
test_cholesky_impl!(Matrix2<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_cholesky_mat3() {
|
|
test_cholesky_impl!(Matrix3<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_cholesky_mat4() {
|
|
test_cholesky_impl!(Matrix4<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_cholesky_mat5() {
|
|
test_cholesky_impl!(Matrix5<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_cholesky_mat6() {
|
|
test_cholesky_impl!(Matrix6<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_hessenberg_mat1() {
|
|
test_hessenberg_impl!(Matrix1<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_hessenberg_mat2() {
|
|
test_hessenberg_impl!(Matrix2<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_hessenberg_mat3() {
|
|
test_hessenberg_impl!(Matrix3<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_hessenberg_mat4() {
|
|
test_hessenberg_impl!(Matrix4<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_hessenberg_mat5() {
|
|
test_hessenberg_impl!(Matrix5<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_hessenberg_mat6() {
|
|
test_hessenberg_impl!(Matrix6<f64>);
|
|
}
|
|
|
|
#[test]
|
|
fn test_transpose_square_matrix() {
|
|
let column_major_matrix = &[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 matrix = DMatrix::from_column_vector(num_rows, num_cols, column_major_matrix);
|
|
matrix.transpose_mut();
|
|
for i in 0..num_rows {
|
|
assert_eq!(&[0, 1, 2, 3], &matrix.row_slice(i, 0, num_cols)[..]);
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn test_outer_dvector() {
|
|
let vector = DVector::from_slice(5, &[ 1.0, 2.0, 3.0, 4.0, 5.0 ]);
|
|
let row = DMatrix::from_row_vector(1, 5, &vector[..]);
|
|
|
|
assert_eq!(row.transpose() * row, na::outer(&vector, &vector))
|
|
}
|