481 lines
14 KiB
Rust
481 lines
14 KiB
Rust
#![cfg_attr(rustfmt, rustfmt_skip)]
|
|
|
|
use na::Matrix3;
|
|
|
|
#[test]
|
|
fn full_piv_lu_simple() {
|
|
let m = Matrix3::new(
|
|
2.0, -1.0, 0.0,
|
|
-1.0, 2.0, -1.0,
|
|
0.0, -1.0, 2.0);
|
|
|
|
let lu = m.full_piv_lu();
|
|
assert_eq!(lu.determinant(), 4.0);
|
|
|
|
let (p, l, u, q) = lu.unpack();
|
|
|
|
let mut lu = l * u;
|
|
p.inv_permute_rows(&mut lu);
|
|
q.inv_permute_columns(&mut lu);
|
|
|
|
assert!(relative_eq!(m, lu, epsilon = 1.0e-7));
|
|
}
|
|
|
|
#[test]
|
|
fn full_piv_lu_simple_with_pivot() {
|
|
let m = Matrix3::new(
|
|
0.0, -1.0, 2.0,
|
|
-1.0, 2.0, -1.0,
|
|
2.0, -1.0, 0.0);
|
|
|
|
let lu = m.full_piv_lu();
|
|
assert_eq!(lu.determinant(), -4.0);
|
|
|
|
let (p, l, u, q) = lu.unpack();
|
|
|
|
let mut lu = l * u;
|
|
p.inv_permute_rows(&mut lu);
|
|
q.inv_permute_columns(&mut lu);
|
|
|
|
assert!(relative_eq!(m, lu, epsilon = 1.0e-7));
|
|
}
|
|
|
|
#[cfg(feature = "arbitrary")]
|
|
mod quickcheck_tests {
|
|
macro_rules! gen_tests(
|
|
($module: ident, $scalar: ty) => {
|
|
mod $module {
|
|
use std::cmp;
|
|
use num::One;
|
|
use na::{DMatrix, Matrix4, Matrix4x3, Matrix5x3, Matrix3x5, DVector, Vector4};
|
|
#[allow(unused_imports)]
|
|
use crate::core::helper::{RandScalar, RandComplex};
|
|
|
|
quickcheck! {
|
|
fn full_piv_lu(m: DMatrix<$scalar>) -> bool {
|
|
let mut m = m.map(|e| e.0);
|
|
if m.len() == 0 {
|
|
m = DMatrix::<$scalar>::new_random(1, 1).map(|e| e.0);
|
|
}
|
|
|
|
let lu = m.clone().full_piv_lu();
|
|
let (p, l, u, q) = lu.unpack();
|
|
let mut lu = l * u;
|
|
p.inv_permute_rows(&mut lu);
|
|
q.inv_permute_columns(&mut lu);
|
|
|
|
relative_eq!(m, lu, epsilon = 1.0e-7)
|
|
}
|
|
|
|
fn full_piv_lu_static_3_5(m: Matrix3x5<$scalar>) -> bool {
|
|
let m = m.map(|e| e.0);
|
|
let lu = m.full_piv_lu();
|
|
let (p, l, u, q) = lu.unpack();
|
|
let mut lu = l * u;
|
|
p.inv_permute_rows(&mut lu);
|
|
q.inv_permute_columns(&mut lu);
|
|
|
|
relative_eq!(m, lu, epsilon = 1.0e-7)
|
|
}
|
|
|
|
fn full_piv_lu_static_5_3(m: Matrix5x3<$scalar>) -> bool {
|
|
let m = m.map(|e| e.0);
|
|
let lu = m.full_piv_lu();
|
|
let (p, l, u, q) = lu.unpack();
|
|
let mut lu = l * u;
|
|
p.inv_permute_rows(&mut lu);
|
|
q.inv_permute_columns(&mut lu);
|
|
|
|
relative_eq!(m, lu, epsilon = 1.0e-7)
|
|
}
|
|
|
|
fn full_piv_lu_static_square(m: Matrix4<$scalar>) -> bool {
|
|
let m = m.map(|e| e.0);
|
|
let lu = m.full_piv_lu();
|
|
let (p, l, u, q) = lu.unpack();
|
|
let mut lu = l * u;
|
|
p.inv_permute_rows(&mut lu);
|
|
q.inv_permute_columns(&mut lu);
|
|
|
|
relative_eq!(m, lu, epsilon = 1.0e-7)
|
|
}
|
|
|
|
fn full_piv_lu_solve(n: usize, nb: usize) -> bool {
|
|
if n != 0 && nb != 0 {
|
|
let n = cmp::min(n, 50); // To avoid slowing down the test too much.
|
|
let nb = cmp::min(nb, 50); // To avoid slowing down the test too much.
|
|
let m = DMatrix::<$scalar>::new_random(n, n).map(|e| e.0);
|
|
|
|
let lu = m.clone().full_piv_lu();
|
|
let b1 = DVector::<$scalar>::new_random(n).map(|e| e.0);
|
|
let b2 = DMatrix::<$scalar>::new_random(n, nb).map(|e| e.0);
|
|
|
|
let sol1 = lu.solve(&b1);
|
|
let sol2 = lu.solve(&b2);
|
|
|
|
return (sol1.is_none() || relative_eq!(&m * sol1.unwrap(), b1, epsilon = 1.0e-6)) &&
|
|
(sol2.is_none() || relative_eq!(&m * sol2.unwrap(), b2, epsilon = 1.0e-6))
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
fn full_piv_lu_solve_static(m: Matrix4<$scalar>) -> bool {
|
|
let m = m.map(|e| e.0);
|
|
let lu = m.full_piv_lu();
|
|
let b1 = Vector4::<$scalar>::new_random().map(|e| e.0);
|
|
let b2 = Matrix4x3::<$scalar>::new_random().map(|e| e.0);
|
|
|
|
let sol1 = lu.solve(&b1);
|
|
let sol2 = lu.solve(&b2);
|
|
|
|
return (sol1.is_none() || relative_eq!(&m * sol1.unwrap(), b1, epsilon = 1.0e-6)) &&
|
|
(sol2.is_none() || relative_eq!(&m * sol2.unwrap(), b2, epsilon = 1.0e-6))
|
|
}
|
|
|
|
fn full_piv_lu_inverse(n: usize) -> bool {
|
|
let n = cmp::max(1, cmp::min(n, 15)); // To avoid slowing down the test too much.
|
|
let m = DMatrix::<$scalar>::new_random(n, n).map(|e| e.0);
|
|
|
|
let mut l = m.lower_triangle();
|
|
let mut u = m.upper_triangle();
|
|
|
|
// Ensure the matrix is well conditioned for inversion.
|
|
l.fill_diagonal(One::one());
|
|
u.fill_diagonal(One::one());
|
|
let m = l * u;
|
|
|
|
let m1 = m.clone().full_piv_lu().try_inverse().unwrap();
|
|
let id1 = &m * &m1;
|
|
let id2 = &m1 * &m;
|
|
|
|
return id1.is_identity(1.0e-5) && id2.is_identity(1.0e-5);
|
|
}
|
|
|
|
fn full_piv_lu_inverse_static(m: Matrix4<$scalar>) -> bool {
|
|
let m = m.map(|e| e.0);
|
|
let lu = m.full_piv_lu();
|
|
|
|
if let Some(m1) = lu.try_inverse() {
|
|
let id1 = &m * &m1;
|
|
let id2 = &m1 * &m;
|
|
|
|
id1.is_identity(1.0e-5) && id2.is_identity(1.0e-5)
|
|
}
|
|
else {
|
|
true
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
);
|
|
|
|
gen_tests!(complex, RandComplex<f64>);
|
|
gen_tests!(f64, RandScalar<f64>);
|
|
}
|
|
|
|
|
|
/*
|
|
#[test]
|
|
fn swap_rows() {
|
|
let mut m = Matrix5x3::new(
|
|
11.0, 12.0, 13.0,
|
|
21.0, 22.0, 23.0,
|
|
31.0, 32.0, 33.0,
|
|
41.0, 42.0, 43.0,
|
|
51.0, 52.0, 53.0);
|
|
|
|
let expected = Matrix5x3::new(
|
|
11.0, 12.0, 13.0,
|
|
41.0, 42.0, 43.0,
|
|
31.0, 32.0, 33.0,
|
|
21.0, 22.0, 23.0,
|
|
51.0, 52.0, 53.0);
|
|
|
|
m.swap_rows(1, 3);
|
|
|
|
assert_eq!(m, expected);
|
|
}
|
|
|
|
#[test]
|
|
fn swap_columns() {
|
|
let mut m = Matrix3x5::new(
|
|
11.0, 12.0, 13.0, 14.0, 15.0,
|
|
21.0, 22.0, 23.0, 24.0, 25.0,
|
|
31.0, 32.0, 33.0, 34.0, 35.0);
|
|
|
|
let expected = Matrix3x5::new(
|
|
11.0, 14.0, 13.0, 12.0, 15.0,
|
|
21.0, 24.0, 23.0, 22.0, 25.0,
|
|
31.0, 34.0, 33.0, 32.0, 35.0);
|
|
|
|
m.swap_columns(1, 3);
|
|
|
|
assert_eq!(m, expected);
|
|
}
|
|
|
|
#[test]
|
|
fn remove_columns() {
|
|
let m = Matrix3x5::new(
|
|
11, 12, 13, 14, 15,
|
|
21, 22, 23, 24, 25,
|
|
31, 32, 33, 34, 35);
|
|
|
|
let expected1 = Matrix3x4::new(
|
|
12, 13, 14, 15,
|
|
22, 23, 24, 25,
|
|
32, 33, 34, 35);
|
|
|
|
let expected2 = Matrix3x4::new(
|
|
11, 12, 13, 14,
|
|
21, 22, 23, 24,
|
|
31, 32, 33, 34);
|
|
|
|
let expected3 = Matrix3x4::new(
|
|
11, 12, 14, 15,
|
|
21, 22, 24, 25,
|
|
31, 32, 34, 35);
|
|
|
|
assert_eq!(m.remove_column(0), expected1);
|
|
assert_eq!(m.remove_column(4), expected2);
|
|
assert_eq!(m.remove_column(2), expected3);
|
|
|
|
let expected1 = Matrix3::new(
|
|
13, 14, 15,
|
|
23, 24, 25,
|
|
33, 34, 35);
|
|
|
|
let expected2 = Matrix3::new(
|
|
11, 12, 13,
|
|
21, 22, 23,
|
|
31, 32, 33);
|
|
|
|
let expected3 = Matrix3::new(
|
|
11, 12, 15,
|
|
21, 22, 25,
|
|
31, 32, 35);
|
|
|
|
assert_eq!(m.remove_fixed_columns::<U2>(0), expected1);
|
|
assert_eq!(m.remove_fixed_columns::<U2>(3), expected2);
|
|
assert_eq!(m.remove_fixed_columns::<U2>(2), expected3);
|
|
|
|
// The following is just to verify that the return type dimensions is correctly inferred.
|
|
let computed: Matrix<_, U3, Dynamic, _> = m.remove_columns(3, 2);
|
|
assert!(computed.eq(&expected2));
|
|
}
|
|
|
|
|
|
#[test]
|
|
fn remove_rows() {
|
|
let m = Matrix5x3::new(
|
|
11, 12, 13,
|
|
21, 22, 23,
|
|
31, 32, 33,
|
|
41, 42, 43,
|
|
51, 52, 53);
|
|
|
|
let expected1 = Matrix4x3::new(
|
|
21, 22, 23,
|
|
31, 32, 33,
|
|
41, 42, 43,
|
|
51, 52, 53);
|
|
|
|
let expected2 = Matrix4x3::new(
|
|
11, 12, 13,
|
|
21, 22, 23,
|
|
31, 32, 33,
|
|
41, 42, 43);
|
|
|
|
let expected3 = Matrix4x3::new(
|
|
11, 12, 13,
|
|
21, 22, 23,
|
|
41, 42, 43,
|
|
51, 52, 53);
|
|
|
|
assert_eq!(m.remove_row(0), expected1);
|
|
assert_eq!(m.remove_row(4), expected2);
|
|
assert_eq!(m.remove_row(2), expected3);
|
|
|
|
let expected1 = Matrix3::new(
|
|
31, 32, 33,
|
|
41, 42, 43,
|
|
51, 52, 53);
|
|
|
|
let expected2 = Matrix3::new(
|
|
11, 12, 13,
|
|
21, 22, 23,
|
|
31, 32, 33);
|
|
|
|
let expected3 = Matrix3::new(
|
|
11, 12, 13,
|
|
21, 22, 23,
|
|
51, 52, 53);
|
|
|
|
assert_eq!(m.remove_fixed_rows::<U2>(0), expected1);
|
|
assert_eq!(m.remove_fixed_rows::<U2>(3), expected2);
|
|
assert_eq!(m.remove_fixed_rows::<U2>(2), expected3);
|
|
|
|
// The following is just to verify that the return type dimensions is correctly inferred.
|
|
let computed: Matrix<_, Dynamic, U3, _> = m.remove_rows(3, 2);
|
|
assert!(computed.eq(&expected2));
|
|
}
|
|
|
|
|
|
#[test]
|
|
fn insert_columns() {
|
|
let m = Matrix5x3::new(
|
|
11, 12, 13,
|
|
21, 22, 23,
|
|
31, 32, 33,
|
|
41, 42, 43,
|
|
51, 52, 53);
|
|
|
|
let expected1 = Matrix5x4::new(
|
|
0, 11, 12, 13,
|
|
0, 21, 22, 23,
|
|
0, 31, 32, 33,
|
|
0, 41, 42, 43,
|
|
0, 51, 52, 53);
|
|
|
|
let expected2 = Matrix5x4::new(
|
|
11, 12, 13, 0,
|
|
21, 22, 23, 0,
|
|
31, 32, 33, 0,
|
|
41, 42, 43, 0,
|
|
51, 52, 53, 0);
|
|
|
|
let expected3 = Matrix5x4::new(
|
|
11, 12, 0, 13,
|
|
21, 22, 0, 23,
|
|
31, 32, 0, 33,
|
|
41, 42, 0, 43,
|
|
51, 52, 0, 53);
|
|
|
|
assert_eq!(m.insert_column(0, 0), expected1);
|
|
assert_eq!(m.insert_column(3, 0), expected2);
|
|
assert_eq!(m.insert_column(2, 0), expected3);
|
|
|
|
let expected1 = Matrix5::new(
|
|
0, 0, 11, 12, 13,
|
|
0, 0, 21, 22, 23,
|
|
0, 0, 31, 32, 33,
|
|
0, 0, 41, 42, 43,
|
|
0, 0, 51, 52, 53);
|
|
|
|
let expected2 = Matrix5::new(
|
|
11, 12, 13, 0, 0,
|
|
21, 22, 23, 0, 0,
|
|
31, 32, 33, 0, 0,
|
|
41, 42, 43, 0, 0,
|
|
51, 52, 53, 0, 0);
|
|
|
|
let expected3 = Matrix5::new(
|
|
11, 12, 0, 0, 13,
|
|
21, 22, 0, 0, 23,
|
|
31, 32, 0, 0, 33,
|
|
41, 42, 0, 0, 43,
|
|
51, 52, 0, 0, 53);
|
|
|
|
assert_eq!(m.insert_fixed_columns::<U2>(0, 0), expected1);
|
|
assert_eq!(m.insert_fixed_columns::<U2>(3, 0), expected2);
|
|
assert_eq!(m.insert_fixed_columns::<U2>(2, 0), expected3);
|
|
|
|
// The following is just to verify that the return type dimensions is correctly inferred.
|
|
let computed: Matrix<_, U5, Dynamic, _> = m.insert_columns(3, 2, 0);
|
|
assert!(computed.eq(&expected2));
|
|
}
|
|
|
|
|
|
#[test]
|
|
fn insert_rows() {
|
|
let m = Matrix3x5::new(
|
|
11, 12, 13, 14, 15,
|
|
21, 22, 23, 24, 25,
|
|
31, 32, 33, 34, 35);
|
|
|
|
let expected1 = Matrix4x5::new(
|
|
0, 0, 0, 0, 0,
|
|
11, 12, 13, 14, 15,
|
|
21, 22, 23, 24, 25,
|
|
31, 32, 33, 34, 35);
|
|
|
|
let expected2 = Matrix4x5::new(
|
|
11, 12, 13, 14, 15,
|
|
21, 22, 23, 24, 25,
|
|
31, 32, 33, 34, 35,
|
|
0, 0, 0, 0, 0);
|
|
|
|
let expected3 = Matrix4x5::new(
|
|
11, 12, 13, 14, 15,
|
|
21, 22, 23, 24, 25,
|
|
0, 0, 0, 0, 0,
|
|
31, 32, 33, 34, 35);
|
|
|
|
assert_eq!(m.insert_row(0, 0), expected1);
|
|
assert_eq!(m.insert_row(3, 0), expected2);
|
|
assert_eq!(m.insert_row(2, 0), expected3);
|
|
|
|
let expected1 = Matrix5::new(
|
|
0, 0, 0, 0, 0,
|
|
0, 0, 0, 0, 0,
|
|
11, 12, 13, 14, 15,
|
|
21, 22, 23, 24, 25,
|
|
31, 32, 33, 34, 35);
|
|
|
|
let expected2 = Matrix5::new(
|
|
11, 12, 13, 14, 15,
|
|
21, 22, 23, 24, 25,
|
|
31, 32, 33, 34, 35,
|
|
0, 0, 0, 0, 0,
|
|
0, 0, 0, 0, 0);
|
|
|
|
let expected3 = Matrix5::new(
|
|
11, 12, 13, 14, 15,
|
|
21, 22, 23, 24, 25,
|
|
0, 0, 0, 0, 0,
|
|
0, 0, 0, 0, 0,
|
|
31, 32, 33, 34, 35);
|
|
|
|
assert_eq!(m.insert_fixed_rows::<U2>(0, 0), expected1);
|
|
assert_eq!(m.insert_fixed_rows::<U2>(3, 0), expected2);
|
|
assert_eq!(m.insert_fixed_rows::<U2>(2, 0), expected3);
|
|
|
|
// The following is just to verify that the return type dimensions is correctly inferred.
|
|
let computed: Matrix<_, Dynamic, U5, _> = m.insert_rows(3, 2, 0);
|
|
assert!(computed.eq(&expected2));
|
|
}
|
|
|
|
#[test]
|
|
fn resize() {
|
|
let m = Matrix3x5::new(
|
|
11, 12, 13, 14, 15,
|
|
21, 22, 23, 24, 25,
|
|
31, 32, 33, 34, 35);
|
|
|
|
let add_add = DMatrix::from_row_slice(5, 6, &[
|
|
11, 12, 13, 14, 15, 42,
|
|
21, 22, 23, 24, 25, 42,
|
|
31, 32, 33, 34, 35, 42,
|
|
42, 42, 42, 42, 42, 42,
|
|
42, 42, 42, 42, 42, 42]);
|
|
|
|
let del_del = DMatrix::from_row_slice(1, 2, &[11, 12]);
|
|
|
|
let add_del = DMatrix::from_row_slice(5, 2, &[
|
|
11, 12,
|
|
21, 22,
|
|
31, 32,
|
|
42, 42,
|
|
42, 42]);
|
|
|
|
let del_add = DMatrix::from_row_slice(1, 8, &[
|
|
11, 12, 13, 14, 15, 42, 42, 42]);
|
|
|
|
assert_eq!(del_del, m.resize(1, 2, 42));
|
|
assert_eq!(add_add, m.resize(5, 6, 42));
|
|
assert_eq!(add_del, m.resize(5, 2, 42));
|
|
assert_eq!(del_add, m.resize(1, 8, 42));
|
|
}
|
|
*/
|