693 lines
15 KiB
Rust
693 lines
15 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::{Vec1, Vec3, Mat1, Mat2, Mat3, Mat4, Mat5, Mat6, Rot2, Rot3, Persp3, PerspMat3, Ortho3,
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OrthoMat3, DMat, DVec, Row, Col, BaseFloat, Diag};
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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 : $t = random();
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match na::inv(&randmat) {
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None => { },
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Some(i) => assert!(na::approx_eq(&(i * randmat), &na::one()))
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}
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}
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);
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);
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macro_rules! test_transpose_mat_impl(
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($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 : $t = Diag::from_diag(&na::diag(&randmat));
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diagmat = na::abs(&diagmat) + 1.0;
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randmat = randmat * diagmat * na::transpose(&randmat);
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let result = na::cholesky(&randmat);
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match result {
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Ok(v) => {
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let recomp = v * na::transpose(&v);
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assert!(na::approx_eq(&randmat, &recomp));
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},
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Err(_) => assert!(false),
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}
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}
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);
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);
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// NOTE: deactivated untile we get a better convergence rate.
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// macro_rules! test_eigen_qr_impl(
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// ($t: ty) => {
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// for _ in (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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//
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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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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_rotation2() {
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for _ in (0usize .. 10000) {
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let randmat: na::Rot2<f64> = na::one();
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let ang = Vec1::new(na::abs(&random::<f64>()) % <f64 as BaseFloat>::pi());
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assert!(na::approx_eq(&na::rotation(&na::append_rotation(&randmat, &ang)), &ang));
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}
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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_inv_rotation3() {
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for _ in (0usize .. 10000) {
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let randmat: Rot3<f64> = na::one();
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let dir: Vec3<f64> = random();
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let ang = na::normalize(&dir) * (na::abs(&random::<f64>()) % <f64 as BaseFloat>::pi());
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let rot = na::append_rotation(&randmat, &ang);
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assert!(na::approx_eq(&(na::transpose(&rot) * rot), &na::one()));
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}
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}
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#[test]
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fn test_rot3_rotation_between() {
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let r1: Rot3<f64> = random();
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let r2: Rot3<f64> = random();
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let delta = na::rotation_between(&r1, &r2);
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assert!(na::approx_eq(&(delta * r1), &r2))
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}
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#[test]
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fn test_rot3_angle_between() {
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let r1: Rot3<f64> = random();
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let r2: Rot3<f64> = random();
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let delta = na::rotation_between(&r1, &r2);
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let delta_angle = na::angle_between(&r1, &r2);
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assert!(na::approx_eq(&na::norm(&na::rotation(&delta)), &delta_angle))
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}
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#[test]
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fn test_rot2_rotation_between() {
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let r1: Rot2<f64> = random();
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let r2: Rot2<f64> = random();
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let delta = na::rotation_between(&r1, &r2);
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assert!(na::approx_eq(&(delta * r1), &r2))
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}
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#[test]
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fn test_rot2_angle_between() {
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let r1: Rot2<f64> = random();
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let r2: Rot2<f64> = random();
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let delta = na::rotation_between(&r1, &r2);
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let delta_angle = na::angle_between(&r1, &r2);
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assert!(na::approx_eq(&na::norm(&na::rotation(&delta)), &delta_angle))
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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_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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/* FIXME: review qr decomposition to make it work with DMat.
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#[test]
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fn test_qr() {
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for _ in (0usize .. 10) {
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let dim1: usize = random();
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let dim2: usize = random();
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let rows = min(40, max(dim1, dim2));
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let cols = min(40, min(dim1, dim2));
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let randmat: DMat<f64> = DMat::new_random(rows, cols);
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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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#[test]
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fn test_qr_mat1() {
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test_qr_impl!(Mat1<f64>);
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}
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#[test]
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fn test_qr_mat2() {
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test_qr_impl!(Mat2<f64>);
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}
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#[test]
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fn test_qr_mat3() {
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test_qr_impl!(Mat3<f64>);
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}
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#[test]
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fn test_qr_mat4() {
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test_qr_impl!(Mat4<f64>);
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}
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#[test]
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fn test_qr_mat5() {
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test_qr_impl!(Mat5<f64>);
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}
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#[test]
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fn test_qr_mat6() {
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test_qr_impl!(Mat6<f64>);
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}
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// NOTE: deactivated until 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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// }
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//
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// #[test]
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// fn test_eigen_qr_mat2() {
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// test_eigen_qr_impl!(Mat2<f64>);
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// }
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//
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// #[test]
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// fn test_eigen_qr_mat3() {
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// test_eigen_qr_impl!(Mat3<f64>);
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// }
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//
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// #[test]
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// fn test_eigen_qr_mat4() {
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// test_eigen_qr_impl!(Mat4<f64>);
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// }
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//
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// #[test]
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// fn test_eigen_qr_mat5() {
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// test_eigen_qr_impl!(Mat5<f64>);
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// }
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//
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// #[test]
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// fn test_eigen_qr_mat6() {
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// test_eigen_qr_impl!(Mat6<f64>);
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// }
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#[test]
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fn test_from_fn() {
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let actual: DMat<usize> = DMat::from_fn(3, 4, |i, j| 10 * i + j);
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let expected: DMat<usize> = DMat::from_row_vec(3, 4,
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&[ 0_0, 0_1, 0_2, 0_3,
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1_0, 1_1, 1_2, 1_3,
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2_0, 2_1, 2_2, 2_3 ]);
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assert_eq!(actual, expected);
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}
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#[test]
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fn test_row_3() {
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let mat = Mat3::new(0.0f32, 1.0, 2.0,
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3.0, 4.0, 5.0,
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6.0, 7.0, 8.0);
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let second_row = mat.row(1);
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let second_col = mat.col(1);
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assert!(second_row == Vec3::new(3.0, 4.0, 5.0));
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assert!(second_col == Vec3::new(1.0, 4.0, 7.0));
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}
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#[test]
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fn test_persp() {
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let mut p = Persp3::new(42.0f64, 0.5, 1.5, 10.0);
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let mut pm = PerspMat3::new(42.0f64, 0.5, 1.5, 10.0);
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assert!(p.to_mat() == pm.to_mat());
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assert!(p.aspect() == 42.0);
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assert!(p.fov() == 0.5);
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assert!(p.znear() == 1.5);
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assert!(p.zfar() == 10.0);
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assert!(na::approx_eq(&pm.aspect(), &42.0));
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assert!(na::approx_eq(&pm.fov(), &0.5));
|
|
assert!(na::approx_eq(&pm.znear(), &1.5));
|
|
assert!(na::approx_eq(&pm.zfar(), &10.0));
|
|
|
|
p.set_fov(0.1);
|
|
pm.set_fov(0.1);
|
|
assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
|
|
|
|
p.set_znear(24.0);
|
|
pm.set_znear(24.0);
|
|
assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
|
|
|
|
p.set_zfar(61.0);
|
|
pm.set_zfar(61.0);
|
|
assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
|
|
|
|
p.set_aspect(23.0);
|
|
pm.set_aspect(23.0);
|
|
assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
|
|
|
|
assert!(p.aspect() == 23.0);
|
|
assert!(p.fov() == 0.1);
|
|
assert!(p.znear() == 24.0);
|
|
assert!(p.zfar() == 61.0);
|
|
assert!(na::approx_eq(&pm.aspect(), &23.0));
|
|
assert!(na::approx_eq(&pm.fov(), &0.1));
|
|
assert!(na::approx_eq(&pm.znear(), &24.0));
|
|
assert!(na::approx_eq(&pm.zfar(), &61.0));
|
|
}
|
|
|
|
#[test]
|
|
fn test_ortho() {
|
|
let mut p = Ortho3::new(42.0f64, 0.5, 1.5, 10.0);
|
|
let mut pm = OrthoMat3::new(42.0f64, 0.5, 1.5, 10.0);
|
|
assert!(p.to_mat() == pm.to_mat());
|
|
assert!(p.width() == 42.0);
|
|
assert!(p.height() == 0.5);
|
|
assert!(p.znear() == 1.5);
|
|
assert!(p.zfar() == 10.0);
|
|
assert!(na::approx_eq(&pm.width(), &42.0));
|
|
assert!(na::approx_eq(&pm.height(), &0.5));
|
|
assert!(na::approx_eq(&pm.znear(), &1.5));
|
|
assert!(na::approx_eq(&pm.zfar(), &10.0));
|
|
|
|
p.set_width(0.1);
|
|
pm.set_width(0.1);
|
|
assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
|
|
|
|
p.set_znear(24.0);
|
|
pm.set_znear(24.0);
|
|
assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
|
|
|
|
p.set_zfar(61.0);
|
|
pm.set_zfar(61.0);
|
|
assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
|
|
|
|
p.set_height(23.0);
|
|
pm.set_height(23.0);
|
|
assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
|
|
|
|
assert!(p.height() == 23.0);
|
|
assert!(p.width() == 0.1);
|
|
assert!(p.znear() == 24.0);
|
|
assert!(p.zfar() == 61.0);
|
|
assert!(na::approx_eq(&pm.height(), &23.0));
|
|
assert!(na::approx_eq(&pm.width(), &0.1));
|
|
assert!(na::approx_eq(&pm.znear(), &24.0));
|
|
assert!(na::approx_eq(&pm.zfar(), &61.0));
|
|
}
|
|
|
|
#[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>);
|
|
} |