93 lines
2.8 KiB
Rust
93 lines
2.8 KiB
Rust
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#![cfg_attr(rustfmt, rustfmt_skip)]
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use crate::common::{value_strategy, PROPTEST_MATRIX_DIM, PROPTEST_MAX_NNZ};
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use nalgebra_sparse::csc::CscMatrix;
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use nalgebra_sparse::factorization::{CscCholesky};
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use nalgebra_sparse::proptest::csc;
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use nalgebra::{Matrix5, Vector5, Cholesky, DMatrix};
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use proptest::prelude::*;
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use matrixcompare::assert_matrix_eq;
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fn positive_definite() -> impl Strategy<Value=CscMatrix<f64>> {
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let csc_f64 = csc(value_strategy::<f64>(),
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PROPTEST_MATRIX_DIM,
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PROPTEST_MATRIX_DIM,
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PROPTEST_MAX_NNZ);
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csc_f64
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.prop_map(|x| {
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// Add a small multiple of the identity to ensure positive definiteness
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x.transpose() * &x + CscMatrix::identity(x.ncols())
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})
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}
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proptest! {
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#[test]
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fn cholesky_correct_for_positive_definite_matrices(
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matrix in positive_definite()
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) {
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let cholesky = CscCholesky::factor(&matrix).unwrap();
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let l = cholesky.take_l();
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let matrix_reconstructed = &l * l.transpose();
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// TODO: Use matrixcompare instead
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let diff = DMatrix::from(&(matrix_reconstructed - matrix));
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prop_assert!(diff.abs().max() < 1e-8);
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// TODO: Check that L is in fact lower triangular
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}
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}
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// This is a test ported from nalgebra's "sparse" module, for the original CsCholesky impl
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#[test]
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fn cs_cholesky() {
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let mut a = Matrix5::new(
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40.0, 0.0, 0.0, 0.0, 0.0,
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2.0, 60.0, 0.0, 0.0, 0.0,
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1.0, 0.0, 11.0, 0.0, 0.0,
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0.0, 0.0, 0.0, 50.0, 0.0,
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1.0, 0.0, 0.0, 4.0, 10.0
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);
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a.fill_upper_triangle_with_lower_triangle();
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test_cholesky(a);
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let a = Matrix5::from_diagonal(&Vector5::new(40.0, 60.0, 11.0, 50.0, 10.0));
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test_cholesky(a);
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let mut a = Matrix5::new(
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40.0, 0.0, 0.0, 0.0, 0.0,
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2.0, 60.0, 0.0, 0.0, 0.0,
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1.0, 0.0, 11.0, 0.0, 0.0,
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1.0, 0.0, 0.0, 50.0, 0.0,
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0.0, 0.0, 0.0, 4.0, 10.0
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);
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a.fill_upper_triangle_with_lower_triangle();
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test_cholesky(a);
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let mut a = Matrix5::new(
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2.0, 0.0, 0.0, 0.0, 0.0,
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0.0, 2.0, 0.0, 0.0, 0.0,
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1.0, 1.0, 2.0, 0.0, 0.0,
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0.0, 0.0, 0.0, 2.0, 0.0,
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1.0, 1.0, 0.0, 0.0, 2.0
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);
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a.fill_upper_triangle_with_lower_triangle();
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// Test crate::new, left_looking, and up_looking implementations.
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test_cholesky(a);
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}
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fn test_cholesky(a: Matrix5<f64>) {
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// TODO: Test "refactor"
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let cs_a = CscMatrix::from(&a);
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let chol_a = Cholesky::new(a).unwrap();
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let chol_cs_a = CscCholesky::factor(&cs_a).unwrap();
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let l = chol_a.l();
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let cs_l = chol_cs_a.take_l();
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let l = DMatrix::from_iterator(l.nrows(), l.ncols(), l.iter().cloned());
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let cs_l_mat = DMatrix::from(&cs_l);
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assert_matrix_eq!(l, cs_l_mat, comp = abs, tol = 1e-12);
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}
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