76 lines
2.4 KiB
Rust
76 lines
2.4 KiB
Rust
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use crate::unit_tests::cholesky::positive_definite;
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use nalgebra_sparse::factorization::LeftLookingLUFactorization;
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use matrixcompare::{assert_matrix_eq, prop_assert_matrix_eq};
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use proptest::prelude::*;
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use crate::common::value_strategy;
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use nalgebra::proptest::matrix;
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use nalgebra_sparse::CscMatrix;
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proptest! {
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// Note that positive definite matrices are guaranteed to be invertible.
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// That's why they're used here, but it's not necessary for a matrix to be pd to be
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// invertible.
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#[test]
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fn lu_for_positive_def_matrices(
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matrix in positive_definite()
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) {
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let lu = LeftLookingLUFactorization::new(&matrix);
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let l = lu.l();
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prop_assert!(l.triplet_iter().all(|(i, j, _)| j <= i));
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let u = lu.u();
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prop_assert!(u.triplet_iter().all(|(i, j, _)| j >= i));
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prop_assert_matrix_eq!(l * u, matrix, comp = abs, tol = 1e-7);
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}
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#[test]
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fn lu_solve_correct_for_positive_def_matrices(
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(matrix, b) in positive_definite()
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.prop_flat_map(|csc| {
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let rhs = matrix(value_strategy::<f64>(), csc.nrows(), 1);
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(Just(csc), rhs)
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})
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) {
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let lu = LeftLookingLUFactorization::new(&matrix);
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let l = lu.l();
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prop_assert!(l.triplet_iter().all(|(i, j, _)| j <= i));
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let mut x_l = b.clone_owned();
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l.dense_lower_triangular_solve(b.as_slice(), x_l.as_mut_slice(), true);
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prop_assert_matrix_eq!(l * x_l, b, comp=abs, tol=1e-12);
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let u = lu.u();
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prop_assert!(u.triplet_iter().all(|(i, j, _)| j >= i));
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let mut x_u = b.clone_owned();
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u.dense_upper_triangular_solve(b.as_slice(), x_u.as_mut_slice());
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prop_assert_matrix_eq!(u * x_u, b, comp = abs, tol = 1e-7);
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let x = lu.solve(b.as_slice());
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prop_assert_matrix_eq!(&matrix * &x, b, comp=abs, tol=1e-12);
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}
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}
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#[test]
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fn minimized_lu() {
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let major_offsets = vec![0, 1, 3, 4, 5, 8];
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let minor_indices = vec![0, 1, 4, 2, 3, 1, 2, 4];
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let values = vec![1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 3.0, 1.0];
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assert_eq!(minor_indices.len(), values.len());
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let mat = CscMatrix::try_from_unsorted_csc_data(5, 5, major_offsets, minor_indices, values);
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let mat = mat.unwrap();
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let lu = LeftLookingLUFactorization::new(&mat);
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let l = lu.l();
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assert!(l.triplet_iter().all(|(i, j, _)| j <= i));
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let u = lu.u();
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assert!(u.triplet_iter().all(|(i, j, _)| j >= i));
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assert_matrix_eq!(l * u, mat, comp = abs, tol = 1e-7);
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}
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