nalgebra/tests/linalg/lu.rs

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use na::Matrix3;
#[test]
#[rustfmt::skip]
fn 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.lu();
assert_eq!(lu.determinant(), 4.0);
let (p, l, u) = lu.unpack();
let mut lu = l * u;
p.inv_permute_rows(&mut lu);
assert!(relative_eq!(m, lu, epsilon = 1.0e-7));
}
#[test]
#[rustfmt::skip]
fn 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.lu();
assert_eq!(lu.determinant(), -4.0);
let (p, l, u) = lu.unpack();
let mut lu = l * u;
p.inv_permute_rows(&mut lu);
assert!(relative_eq!(m, lu, epsilon = 1.0e-7));
}
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#[cfg(feature = "proptest-support")]
mod proptest_tests {
macro_rules! gen_tests(
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($module: ident, $scalar: expr, $scalar_type: ty) => {
mod $module {
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use na::{DMatrix, Matrix4x3, DVector, Vector4};
#[allow(unused_imports)]
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use crate::core::helper::{RandScalar, RandComplex};
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use crate::proptest::*;
use proptest::{prop_assert, proptest};
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proptest! {
#[test]
fn lu(m in dmatrix_($scalar)) {
let lu = m.clone().lu();
let (p, l, u) = lu.unpack();
let mut lu = l * u;
p.inv_permute_rows(&mut lu);
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prop_assert!(relative_eq!(m, lu, epsilon = 1.0e-7))
}
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#[test]
fn lu_static_3_5(m in matrix3x5_($scalar)) {
let lu = m.lu();
let (p, l, u) = lu.unpack();
let mut lu = l * u;
p.inv_permute_rows(&mut lu);
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prop_assert!(relative_eq!(m, lu, epsilon = 1.0e-7))
}
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fn lu_static_5_3(m in matrix5x3_($scalar)) {
let lu = m.lu();
let (p, l, u) = lu.unpack();
let mut lu = l * u;
p.inv_permute_rows(&mut lu);
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prop_assert!(relative_eq!(m, lu, epsilon = 1.0e-7));
}
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#[test]
fn lu_static_square(m in matrix4_($scalar)) {
let lu = m.lu();
let (p, l, u) = lu.unpack();
let mut lu = l * u;
p.inv_permute_rows(&mut lu);
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prop_assert!(relative_eq!(m, lu, epsilon = 1.0e-7));
}
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#[test]
fn lu_solve(n in PROPTEST_MATRIX_DIM, nb in PROPTEST_MATRIX_DIM) {
let m = DMatrix::<$scalar_type>::new_random(n, n).map(|e| e.0);
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let lu = m.clone().lu();
let b1 = DVector::<$scalar_type>::new_random(n).map(|e| e.0);
let b2 = DMatrix::<$scalar_type>::new_random(n, nb).map(|e| e.0);
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let sol1 = lu.solve(&b1);
let sol2 = lu.solve(&b2);
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prop_assert!(sol1.is_none() || relative_eq!(&m * sol1.unwrap(), b1, epsilon = 1.0e-6));
prop_assert!(sol2.is_none() || relative_eq!(&m * sol2.unwrap(), b2, epsilon = 1.0e-6));
}
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#[test]
fn lu_solve_static(m in matrix4_($scalar)) {
let lu = m.lu();
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let b1 = Vector4::<$scalar_type>::new_random().map(|e| e.0);
let b2 = Matrix4x3::<$scalar_type>::new_random().map(|e| e.0);
let sol1 = lu.solve(&b1);
let sol2 = lu.solve(&b2);
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prop_assert!(sol1.is_none() || relative_eq!(&m * sol1.unwrap(), b1, epsilon = 1.0e-6));
prop_assert!(sol2.is_none() || relative_eq!(&m * sol2.unwrap(), b2, epsilon = 1.0e-6));
}
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#[test]
fn lu_inverse(n in PROPTEST_MATRIX_DIM) {
let m = DMatrix::<$scalar_type>::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(na::one());
u.fill_diagonal(na::one());
let m = l * u;
let m1 = m.clone().lu().try_inverse().unwrap();
let id1 = &m * &m1;
let id2 = &m1 * &m;
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prop_assert!(id1.is_identity(1.0e-5));
prop_assert!(id2.is_identity(1.0e-5));
}
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#[test]
fn lu_inverse_static(m in matrix4_($scalar)) {
let lu = m.lu();
if let Some(m1) = lu.try_inverse() {
let id1 = &m * &m1;
let id2 = &m1 * &m;
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prop_assert!(id1.is_identity(1.0e-5));
prop_assert!(id2.is_identity(1.0e-5));
}
}
}
}
}
);
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gen_tests!(complex, complex_f64(), RandComplex<f64>);
gen_tests!(f64, PROPTEST_F64, RandScalar<f64>);
}