use std::cmp; use na::{DMatrix, Matrix3, Matrix4, Matrix4x3, Matrix5x3, Matrix3x5, DVector, Vector4}; #[test] 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] 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)); } #[cfg(feature = "arbitrary")] quickcheck! { fn lu(m: DMatrix) -> bool { let mut m = m; if m.len() == 0 { m = DMatrix::new_random(1, 1); } let lu = m.clone().lu(); let (p, l, u) = lu.unpack(); let mut lu = l * u; p.inv_permute_rows(&mut lu); relative_eq!(m, lu, epsilon = 1.0e-7) } fn lu_static_3_5(m: Matrix3x5) -> bool { let lu = m.lu(); let (p, l, u) = lu.unpack(); let mut lu = l * u; p.inv_permute_rows(&mut lu); relative_eq!(m, lu, epsilon = 1.0e-7) } fn lu_static_5_3(m: Matrix5x3) -> bool { let lu = m.lu(); let (p, l, u) = lu.unpack(); let mut lu = l * u; p.inv_permute_rows(&mut lu); relative_eq!(m, lu, epsilon = 1.0e-7) } fn lu_static_square(m: Matrix4) -> bool { let lu = m.lu(); let (p, l, u) = lu.unpack(); let mut lu = l * u; p.inv_permute_rows(&mut lu); relative_eq!(m, lu, epsilon = 1.0e-7) } fn 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::::new_random(n, n); let lu = m.clone().lu(); let b1 = DVector::new_random(n); let b2 = DMatrix::new_random(n, nb); 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 lu_solve_static(m: Matrix4) -> bool { let lu = m.lu(); let b1 = Vector4::new_random(); let b2 = Matrix4x3::new_random(); 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 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::::new_random(n, n); let mut l = m.lower_triangle(); let mut u = m.upper_triangle(); // Ensure the matrix is well conditioned for inversion. l.fill_diagonal(1.0); u.fill_diagonal(1.0); let m = l * u; let m1 = m.clone().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 lu_inverse_static(m: Matrix4) -> bool { let lu = m.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 } } }