473 lines
14 KiB
Rust
473 lines
14 KiB
Rust
use na::Matrix3;
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#[test]
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#[rustfmt::skip]
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fn full_piv_lu_simple() {
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let m = Matrix3::new(
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2.0, -1.0, 0.0,
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-1.0, 2.0, -1.0,
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0.0, -1.0, 2.0);
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let lu = m.full_piv_lu();
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assert_eq!(lu.determinant(), 4.0);
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let (p, l, u, q) = lu.unpack();
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let mut lu = l * u;
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p.inv_permute_rows(&mut lu);
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q.inv_permute_columns(&mut lu);
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assert!(relative_eq!(m, lu, epsilon = 1.0e-7));
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}
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#[test]
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#[rustfmt::skip]
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fn full_piv_lu_simple_with_pivot() {
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let m = Matrix3::new(0.0, -1.0, 2.0,
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-1.0, 2.0, -1.0,
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2.0, -1.0, 0.0);
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let lu = m.full_piv_lu();
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assert_eq!(lu.determinant(), -4.0);
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let (p, l, u, q) = lu.unpack();
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let mut lu = l * u;
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p.inv_permute_rows(&mut lu);
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q.inv_permute_columns(&mut lu);
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assert!(relative_eq!(m, lu, epsilon = 1.0e-7));
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}
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#[cfg(feature = "arbitrary")]
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mod proptest_tests {
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macro_rules! gen_tests(
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($module: ident, $scalar: expr, $scalar_type: ty) => {
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mod $module {
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use std::cmp;
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use num::One;
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use na::{DMatrix, Matrix4x3, DVector, Vector4};
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#[allow(unused_imports)]
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use crate::core::helper::{RandScalar, RandComplex};
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use crate::proptest::*;
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use proptest::{prop_assert, proptest};
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proptest! {
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#[test]
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fn full_piv_lu(m in dmatrix_($scalar)) {
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let lu = m.clone().full_piv_lu();
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let (p, l, u, q) = lu.unpack();
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let mut lu = l * u;
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p.inv_permute_rows(&mut lu);
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q.inv_permute_columns(&mut lu);
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prop_assert!(relative_eq!(m, lu, epsilon = 1.0e-7))
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}
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#[test]
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fn full_piv_lu_static_3_5(m in matrix3x5_($scalar)) {
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let lu = m.full_piv_lu();
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let (p, l, u, q) = lu.unpack();
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let mut lu = l * u;
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p.inv_permute_rows(&mut lu);
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q.inv_permute_columns(&mut lu);
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prop_assert!(relative_eq!(m, lu, epsilon = 1.0e-7))
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}
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#[test]
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fn full_piv_lu_static_5_3(m in matrix5x3_($scalar)) {
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let lu = m.full_piv_lu();
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let (p, l, u, q) = lu.unpack();
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let mut lu = l * u;
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p.inv_permute_rows(&mut lu);
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q.inv_permute_columns(&mut lu);
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prop_assert!(relative_eq!(m, lu, epsilon = 1.0e-7))
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}
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#[test]
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fn full_piv_lu_static_square(m in matrix4_($scalar)) {
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let lu = m.full_piv_lu();
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let (p, l, u, q) = lu.unpack();
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let mut lu = l * u;
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p.inv_permute_rows(&mut lu);
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q.inv_permute_columns(&mut lu);
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prop_assert!(relative_eq!(m, lu, epsilon = 1.0e-7))
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}
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#[test]
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fn full_piv_lu_solve(n in PROPTEST_MATRIX_DIM, nb in PROPTEST_MATRIX_DIM) {
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let m = DMatrix::<$scalar_type>::new_random(n, n).map(|e| e.0);
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let lu = m.clone().full_piv_lu();
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let b1 = DVector::<$scalar_type>::new_random(n).map(|e| e.0);
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let b2 = DMatrix::<$scalar_type>::new_random(n, nb).map(|e| e.0);
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let sol1 = lu.solve(&b1);
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let sol2 = lu.solve(&b2);
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prop_assert!(sol1.is_none() || relative_eq!(&m * sol1.unwrap(), b1, epsilon = 1.0e-6));
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prop_assert!(sol2.is_none() || relative_eq!(&m * sol2.unwrap(), b2, epsilon = 1.0e-6));
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}
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#[test]
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fn full_piv_lu_solve_static(m in matrix4_($scalar)) {
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let lu = m.full_piv_lu();
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let b1 = Vector4::<$scalar_type>::new_random().map(|e| e.0);
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let b2 = Matrix4x3::<$scalar_type>::new_random().map(|e| e.0);
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let sol1 = lu.solve(&b1);
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let sol2 = lu.solve(&b2);
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prop_assert!(sol1.is_none() || relative_eq!(&m * sol1.unwrap(), b1, epsilon = 1.0e-6));
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prop_assert!(sol2.is_none() || relative_eq!(&m * sol2.unwrap(), b2, epsilon = 1.0e-6));
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}
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#[test]
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fn full_piv_lu_inverse(n in PROPTEST_MATRIX_DIM) {
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let n = cmp::max(1, cmp::min(n, 15)); // To avoid slowing down the test too much.
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let m = DMatrix::<$scalar_type>::new_random(n, n).map(|e| e.0);
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let mut l = m.lower_triangle();
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let mut u = m.upper_triangle();
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// Ensure the matrix is well conditioned for inversion.
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l.fill_diagonal(One::one());
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u.fill_diagonal(One::one());
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let m = l * u;
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let m1 = m.clone().full_piv_lu().try_inverse().unwrap();
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let id1 = &m * &m1;
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let id2 = &m1 * &m;
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prop_assert!(id1.is_identity(1.0e-5));
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prop_assert!(id2.is_identity(1.0e-5));
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}
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#[test]
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fn full_piv_lu_inverse_static(m in matrix4_($scalar)) {
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let lu = m.full_piv_lu();
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if let Some(m1) = lu.try_inverse() {
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let id1 = &m * &m1;
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let id2 = &m1 * &m;
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prop_assert!(id1.is_identity(1.0e-5));
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prop_assert!(id2.is_identity(1.0e-5));
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}
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}
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}
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}
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}
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);
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gen_tests!(complex, complex_f64(), RandComplex<f64>);
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gen_tests!(f64, PROPTEST_F64, RandScalar<f64>);
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}
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/*
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#[test]
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fn swap_rows() {
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let mut m = Matrix5x3::new(
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11.0, 12.0, 13.0,
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21.0, 22.0, 23.0,
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31.0, 32.0, 33.0,
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41.0, 42.0, 43.0,
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51.0, 52.0, 53.0);
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let expected = Matrix5x3::new(
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11.0, 12.0, 13.0,
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41.0, 42.0, 43.0,
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31.0, 32.0, 33.0,
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21.0, 22.0, 23.0,
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51.0, 52.0, 53.0);
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m.swap_rows(1, 3);
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assert_eq!(m, expected);
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}
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#[test]
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fn swap_columns() {
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let mut m = Matrix3x5::new(
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11.0, 12.0, 13.0, 14.0, 15.0,
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21.0, 22.0, 23.0, 24.0, 25.0,
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31.0, 32.0, 33.0, 34.0, 35.0);
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let expected = Matrix3x5::new(
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11.0, 14.0, 13.0, 12.0, 15.0,
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21.0, 24.0, 23.0, 22.0, 25.0,
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31.0, 34.0, 33.0, 32.0, 35.0);
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m.swap_columns(1, 3);
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assert_eq!(m, expected);
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}
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#[test]
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fn remove_columns() {
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let m = Matrix3x5::new(
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11, 12, 13, 14, 15,
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21, 22, 23, 24, 25,
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31, 32, 33, 34, 35);
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let expected1 = Matrix3x4::new(
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12, 13, 14, 15,
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22, 23, 24, 25,
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32, 33, 34, 35);
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let expected2 = Matrix3x4::new(
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11, 12, 13, 14,
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21, 22, 23, 24,
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31, 32, 33, 34);
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let expected3 = Matrix3x4::new(
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11, 12, 14, 15,
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21, 22, 24, 25,
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31, 32, 34, 35);
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assert_eq!(m.remove_column(0), expected1);
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assert_eq!(m.remove_column(4), expected2);
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assert_eq!(m.remove_column(2), expected3);
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let expected1 = Matrix3::new(
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13, 14, 15,
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23, 24, 25,
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33, 34, 35);
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let expected2 = Matrix3::new(
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11, 12, 13,
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21, 22, 23,
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31, 32, 33);
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let expected3 = Matrix3::new(
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11, 12, 15,
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21, 22, 25,
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31, 32, 35);
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assert_eq!(m.remove_fixed_columns::<U2>(0), expected1);
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assert_eq!(m.remove_fixed_columns::<U2>(3), expected2);
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assert_eq!(m.remove_fixed_columns::<U2>(2), expected3);
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// The following is just to verify that the return type dimensions is correctly inferred.
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let computed: Matrix<_, U3, Dyn, _> = m.remove_columns(3, 2);
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assert!(computed.eq(&expected2));
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}
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#[test]
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fn remove_rows() {
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let m = Matrix5x3::new(
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11, 12, 13,
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21, 22, 23,
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31, 32, 33,
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41, 42, 43,
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51, 52, 53);
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let expected1 = Matrix4x3::new(
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21, 22, 23,
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31, 32, 33,
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41, 42, 43,
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51, 52, 53);
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let expected2 = Matrix4x3::new(
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11, 12, 13,
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21, 22, 23,
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31, 32, 33,
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41, 42, 43);
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let expected3 = Matrix4x3::new(
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11, 12, 13,
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21, 22, 23,
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41, 42, 43,
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51, 52, 53);
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assert_eq!(m.remove_row(0), expected1);
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assert_eq!(m.remove_row(4), expected2);
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assert_eq!(m.remove_row(2), expected3);
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let expected1 = Matrix3::new(
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31, 32, 33,
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41, 42, 43,
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51, 52, 53);
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let expected2 = Matrix3::new(
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11, 12, 13,
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21, 22, 23,
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31, 32, 33);
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let expected3 = Matrix3::new(
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11, 12, 13,
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21, 22, 23,
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51, 52, 53);
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assert_eq!(m.remove_fixed_rows::<U2>(0), expected1);
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assert_eq!(m.remove_fixed_rows::<U2>(3), expected2);
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assert_eq!(m.remove_fixed_rows::<U2>(2), expected3);
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// The following is just to verify that the return type dimensions is correctly inferred.
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let computed: Matrix<_, Dyn, U3, _> = m.remove_rows(3, 2);
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assert!(computed.eq(&expected2));
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}
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#[test]
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fn insert_columns() {
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let m = Matrix5x3::new(
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11, 12, 13,
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21, 22, 23,
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31, 32, 33,
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41, 42, 43,
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51, 52, 53);
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let expected1 = Matrix5x4::new(
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0, 11, 12, 13,
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0, 21, 22, 23,
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0, 31, 32, 33,
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0, 41, 42, 43,
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0, 51, 52, 53);
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let expected2 = Matrix5x4::new(
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11, 12, 13, 0,
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21, 22, 23, 0,
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31, 32, 33, 0,
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41, 42, 43, 0,
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51, 52, 53, 0);
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let expected3 = Matrix5x4::new(
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11, 12, 0, 13,
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21, 22, 0, 23,
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31, 32, 0, 33,
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41, 42, 0, 43,
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51, 52, 0, 53);
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assert_eq!(m.insert_column(0, 0), expected1);
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assert_eq!(m.insert_column(3, 0), expected2);
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assert_eq!(m.insert_column(2, 0), expected3);
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let expected1 = Matrix5::new(
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0, 0, 11, 12, 13,
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0, 0, 21, 22, 23,
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0, 0, 31, 32, 33,
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0, 0, 41, 42, 43,
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0, 0, 51, 52, 53);
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let expected2 = Matrix5::new(
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11, 12, 13, 0, 0,
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21, 22, 23, 0, 0,
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31, 32, 33, 0, 0,
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41, 42, 43, 0, 0,
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51, 52, 53, 0, 0);
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let expected3 = Matrix5::new(
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11, 12, 0, 0, 13,
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21, 22, 0, 0, 23,
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31, 32, 0, 0, 33,
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41, 42, 0, 0, 43,
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51, 52, 0, 0, 53);
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assert_eq!(m.insert_fixed_columns::<U2>(0, 0), expected1);
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assert_eq!(m.insert_fixed_columns::<U2>(3, 0), expected2);
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assert_eq!(m.insert_fixed_columns::<U2>(2, 0), expected3);
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// The following is just to verify that the return type dimensions is correctly inferred.
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let computed: Matrix<_, U5, Dyn, _> = m.insert_columns(3, 2, 0);
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assert!(computed.eq(&expected2));
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}
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#[test]
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fn insert_rows() {
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let m = Matrix3x5::new(
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11, 12, 13, 14, 15,
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21, 22, 23, 24, 25,
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31, 32, 33, 34, 35);
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let expected1 = Matrix4x5::new(
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0, 0, 0, 0, 0,
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11, 12, 13, 14, 15,
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21, 22, 23, 24, 25,
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31, 32, 33, 34, 35);
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let expected2 = Matrix4x5::new(
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11, 12, 13, 14, 15,
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21, 22, 23, 24, 25,
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31, 32, 33, 34, 35,
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0, 0, 0, 0, 0);
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let expected3 = Matrix4x5::new(
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11, 12, 13, 14, 15,
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21, 22, 23, 24, 25,
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0, 0, 0, 0, 0,
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31, 32, 33, 34, 35);
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assert_eq!(m.insert_row(0, 0), expected1);
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assert_eq!(m.insert_row(3, 0), expected2);
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assert_eq!(m.insert_row(2, 0), expected3);
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let expected1 = Matrix5::new(
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0, 0, 0, 0, 0,
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0, 0, 0, 0, 0,
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11, 12, 13, 14, 15,
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21, 22, 23, 24, 25,
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31, 32, 33, 34, 35);
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let expected2 = Matrix5::new(
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11, 12, 13, 14, 15,
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21, 22, 23, 24, 25,
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31, 32, 33, 34, 35,
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0, 0, 0, 0, 0,
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0, 0, 0, 0, 0);
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let expected3 = Matrix5::new(
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11, 12, 13, 14, 15,
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21, 22, 23, 24, 25,
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0, 0, 0, 0, 0,
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0, 0, 0, 0, 0,
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31, 32, 33, 34, 35);
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assert_eq!(m.insert_fixed_rows::<2>(0, 0), expected1);
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assert_eq!(m.insert_fixed_rows::<2>(3, 0), expected2);
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assert_eq!(m.insert_fixed_rows::<2>(2, 0), expected3);
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// The following is just to verify that the return type dimensions is correctly inferred.
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let computed: Matrix<_, Dyn, U5, _> = m.insert_rows(3, 2, 0);
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assert!(computed.eq(&expected2));
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}
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#[test]
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fn resize() {
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let m = Matrix3x5::new(
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11, 12, 13, 14, 15,
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21, 22, 23, 24, 25,
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31, 32, 33, 34, 35);
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let add_add = DMatrix::from_row_slice(5, 6, &[
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11, 12, 13, 14, 15, 42,
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21, 22, 23, 24, 25, 42,
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31, 32, 33, 34, 35, 42,
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42, 42, 42, 42, 42, 42,
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42, 42, 42, 42, 42, 42]);
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let del_del = DMatrix::from_row_slice(1, 2, &[11, 12]);
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let add_del = DMatrix::from_row_slice(5, 2, &[
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11, 12,
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21, 22,
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31, 32,
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42, 42,
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42, 42]);
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let del_add = DMatrix::from_row_slice(1, 8, &[
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11, 12, 13, 14, 15, 42, 42, 42]);
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assert_eq!(del_del, m.resize(1, 2, 42));
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assert_eq!(add_add, m.resize(5, 6, 42));
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assert_eq!(add_del, m.resize(5, 2, 42));
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assert_eq!(del_add, m.resize(1, 8, 42));
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}
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*/
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