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Add methods for computing decompositions.

This commit is contained in:
Sébastien Crozet 2017-08-13 19:52:46 +02:00 committed by Sébastien Crozet
parent aaa359f3b0
commit 00039c0a76
20 changed files with 242 additions and 100 deletions
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14
src/linalg/bidiagonal.rs
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@ -255,3 +255,17 @@ impl<N: Real, R: DimMin<C>, C: Dim> Bidiagonal<N, R, C>
// // res self.q_determinant()
// // }
// }
impl<N: Real, R: DimMin<C>, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S>
where DimMinimum<R, C>: DimSub<U1>,
DefaultAllocator: Allocator<N, R, C> +
Allocator<N, C> +
Allocator<N, R> +
Allocator<N, DimMinimum<R, C>> +
Allocator<N, DimDiff<DimMinimum<R, C>, U1>> {
/// Computes the bidiagonalization using householder reflections.
pub fn bidiagonalize(self) -> Bidiagonal<N, R, C> {
Bidiagonal::new(self.into_owned())
}
}

14
src/linalg/cholesky.rs
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@ -1,6 +1,6 @@
use alga::general::Real;
use core::{DefaultAllocator, MatrixN, MatrixMN, Matrix};
use core::{DefaultAllocator, MatrixN, MatrixMN, Matrix, SquareMatrix};
use constraint::{ShapeConstraint, SameNumberOfRows};
use storage::{Storage, StorageMut};
use allocator::Allocator;
@ -110,3 +110,15 @@ impl<N: Real, D: DimSub<Dynamic>> Cholesky<N, D>
res
}
}
impl<N: Real, D: DimSub<Dynamic>, S: Storage<N, D, D>> SquareMatrix<N, D, S>
where DefaultAllocator: Allocator<N, D, D> {
/// Attempts to compute the sholesky decomposition of this matrix.
///
/// Returns `None` if the input matrix is not definite-positive. The intput matrix is assumed
/// to be symmetric and only the lower-triangular part is read.
pub fn cholesky(self) -> Option<Cholesky<N, D>> {
Cholesky::new(self.into_owned())
}
}

15
src/linalg/full_piv_lu.rs
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@ -23,7 +23,9 @@ pub struct FullPivLU<N: Real, R: DimMin<C>, C: Dim>
impl<N: Real, R: DimMin<C>, C: Dim> FullPivLU<N, R, C>
where DefaultAllocator: Allocator<N, R, C> +
Allocator<(usize, usize), DimMinimum<R, C>> {
/// This computes the matrixces `P, L, U` such that `P * matrix = LU`.
/// Computes the LU decomposition with full-pivoting of `matrix`.
///
/// This effectively computes `P, L, U, Q` such that `P * matrix * Q = LU`.
pub fn new(mut matrix: MatrixMN<N, R, C>) -> Self {
let (nrows, ncols) = matrix.data.shape();
let min_nrows_ncols = nrows.min(ncols);
@ -203,3 +205,14 @@ impl<N: Real, D: DimMin<D, Output = D>> FullPivLU<N, D, D>
}
}
}
impl<N: Real, R: DimMin<C>, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S>
where DefaultAllocator: Allocator<N, R, C> +
Allocator<(usize, usize), DimMinimum<R, C>> {
/// Computes the LU decomposition with full-pivoting of `matrix`.
///
/// This effectively computes `P, L, U, Q` such that `P * matrix * Q = LU`.
pub fn full_piv_lu(self) -> FullPivLU<N, R, C> {
FullPivLU::new(self.into_owned())
}
}

13
src/linalg/hessenberg.rs
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@ -1,5 +1,5 @@
use alga::general::Real;
use core::{MatrixN, MatrixMN, VectorN, DefaultAllocator};
use core::{SquareMatrix, MatrixN, MatrixMN, VectorN, DefaultAllocator};
use dimension::{DimSub, DimDiff, Dynamic, U1};
use storage::Storage;
use allocator::Allocator;
@ -95,3 +95,14 @@ impl<N: Real, D: DimSub<U1>> Hessenberg<N, D>
&self.hess
}
}
impl<N: Real, D: DimSub<U1>, S: Storage<N, D, D>> SquareMatrix<N, D, S>
where DefaultAllocator: Allocator<N, D, D> +
Allocator<N, D> +
Allocator<N, DimDiff<D, U1>> {
/// Computes the Hessenberg decomposition of this matrix using householder reflections.
pub fn hessenberg(self) -> Hessenberg<N, D> {
Hessenberg::new(self.into_owned())
}
}

10
src/linalg/lu.rs
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@ -300,3 +300,13 @@ pub fn gauss_step_swap<N, R: Dim, C: Dim, S>(matrix: &mut Matrix<N, R, C, S>, di
down.column_mut(k).axpy(-pivot_row[k], &coeffs, N::one());
}
}
impl<N: Real, R: DimMin<C>, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S>
where DefaultAllocator: Allocator<N, R, C> +
Allocator<(usize, usize), DimMinimum<R, C>> {
/// Computes the LU decomposition with partial (row) pivoting of `matrix`.
pub fn lu(self) -> LU<N, R, C> {
LU::new(self.into_owned())
}
}

11
src/linalg/qr.rs
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@ -228,3 +228,14 @@ impl<N: Real, D: DimMin<D, Output = D>> QR<N, D, D>
// res self.q_determinant()
// }
}
impl<N: Real, R: DimMin<C>, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S>
where DefaultAllocator: Allocator<N, R, C> +
Allocator<N, R> +
Allocator<N, DimMinimum<R, C>> {
/// Computes the QR decomposition of this matrix.
pub fn qr(self) -> QR<N, R, C> {
QR::new(self.into_owned())
}
}

22
src/linalg/schur.rs
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@ -35,7 +35,7 @@ impl<N: Real, D: Dim> RealSchur<N, D>
Self::try_new(m, N::default_epsilon(), 0).unwrap()
}
/// Computes the schur decomposition of a square matrix.
/// Attempts to compute the schur decomposition of a square matrix.
///
/// If only eigenvalues are needed, it is more efficient to call the matrix method
/// `.eigenvalues()` instead.
@ -444,6 +444,26 @@ impl<N: Real, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S>
Allocator<N, DimDiff<D, U1>> + // For Hessenberg.
Allocator<N, D, D> +
Allocator<N, D> {
/// Computes the schur decomposition of a square matrix.
pub fn real_schur(self) -> RealSchur<N, D> {
RealSchur::new(self.into_owned())
}
/// Attempts to compute the schur decomposition of a square matrix.
///
/// If only eigenvalues are needed, it is more efficient to call the matrix method
/// `.eigenvalues()` instead.
///
/// # Arguments
///
/// * `eps` − tolerence used to determine when a value converged to 0.
/// * `max_niter` − maximum total number of iterations performed by the algorithm. If this
/// number of iteration is exceeded, `None` is returned. If `niter == 0`, then the algorithm
/// continues indefinitely until convergence.
pub fn try_real_schur(self, eps: N, max_niter: usize) -> Option<RealSchur<N, D>> {
RealSchur::try_new(self.into_owned(), eps, max_niter)
}
/// Computes the eigenvalues of this matrix.
pub fn eigenvalues(&self) -> Option<VectorN<N, D>> {
assert!(self.is_square(), "Unable to compute eigenvalues of a non-square matrix.");

21
src/linalg/svd.rs
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@ -45,7 +45,7 @@ impl<N: Real, R: DimMin<C>, C: Dim> SVD<N, R, C>
Self::try_new(matrix, compute_u, compute_v, N::default_epsilon(), 0).unwrap()
}
/// Computes the Singular Value Decomposition of `matrix` using implicit shift.
/// Attempts to compute the Singular Value Decomposition of `matrix` using implicit shift.
///
/// # Arguments
///
@ -487,6 +487,25 @@ impl<N: Real, R: DimMin<C>, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S>
Allocator<N, DimMinimum<R, C>, C> +
Allocator<N, R, DimMinimum<R, C>> +
Allocator<N, DimMinimum<R, C>> {
/// Computes the Singular Value Decomposition using implicit shift.
pub fn svd(self, compute_u: bool, compute_v: bool) -> SVD<N, R, C> {
SVD::new(self.into_owned(), compute_u, compute_v)
}
/// Attempts to compute the Singular Value Decomposition of `matrix` using implicit shift.
///
/// # Arguments
///
/// * `compute_u` − set this to `true` to enable the computation of left-singular vectors.
/// * `compute_v` − set this to `true` to enable the computation of left-singular vectors.
/// * `eps` − tolerence used to determine when a value converged to 0.
/// * `max_niter` − maximum total number of iterations performed by the algorithm. If this
/// number of iteration is exceeded, `None` is returned. If `niter == 0`, then the algorithm
/// continues indefinitely until convergence.
pub fn try_svd(self, compute_u: bool, compute_v: bool, eps: N, max_niter: usize) -> Option<SVD<N, R, C>> {
SVD::try_new(self.into_owned(), compute_u, compute_v, eps, max_niter)
}
/// Computes the singular values of this matrix.
pub fn singular_values(&self) -> VectorN<N, DimMinimum<R, C>> {
SVD::new(self.clone_owned(), false, false).singular_values

23
src/linalg/symmetric_eigen.rs
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@ -267,6 +267,29 @@ impl<N: Real, D: DimSub<U1>, S: Storage<N, D, D>> SquareMatrix<N, D, S>
where DefaultAllocator: Allocator<N, D, D> +
Allocator<N, D> +
Allocator<N, DimDiff<D, U1>> {
/// Computes the eigendecomposition of this symmetric matrix.
///
/// Only the lower-triangular part (including the diagonal) of `m` are read.
pub fn symmetric_eigen(self) -> SymmetricEigen<N, D> {
SymmetricEigen::new(self.into_owned())
}
/// Computes the eigendecomposition of the given symmetric matrix with user-specified
/// convergence parameters.
///
/// Only the lower-triangular and diagonal parts of `m` are read.
///
/// # Arguments
///
/// * `eps` − tolerence used to determine when a value converged to 0.
/// * `max_niter` − maximum total number of iterations performed by the algorithm. If this
/// number of iteration is exceeded, `None` is returned. If `niter == 0`, then the algorithm
/// continues indefinitely until convergence.
pub fn try_symmetric_eigen(self, eps: N, max_niter: usize) -> Option<SymmetricEigen<N, D>> {
SymmetricEigen::try_new(self.into_owned(), eps, max_niter)
}
/// Computes the eigenvalues of this symmetric matrix.
///
/// Only the lower-triangular part of the matrix is read.

14
src/linalg/symmetric_tridiagonal.rs
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@ -1,5 +1,5 @@
use alga::general::Real;
use core::{MatrixN, MatrixMN, VectorN, DefaultAllocator};
use core::{SquareMatrix, MatrixN, MatrixMN, VectorN, DefaultAllocator};
use dimension::{DimSub, DimDiff, U1};
use storage::Storage;
use allocator::Allocator;
@ -110,3 +110,15 @@ impl<N: Real, D: DimSub<U1>> SymmetricTridiagonal<N, D>
&q * self.tri * q.transpose()
}
}
impl<N: Real, D: DimSub<U1>, S: Storage<N, D, D>> SquareMatrix<N, D, S>
where DefaultAllocator: Allocator<N, D, D> +
Allocator<N, DimDiff<D, U1>> {
/// Computes the tridiagonalization of this symmetric matrix.
///
/// Only the lower-triangular and diagonal parts of `self` are read.
pub fn symmetric_tridiagonalize(self) -> SymmetricTridiagonal<N, D> {
SymmetricTridiagonal::new(self.into_owned())
}
}

12
tests/linalg/bidiagonal.rs
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@ -1,4 +1,4 @@
use na::{DMatrix, Matrix2, Matrix4, Matrix5x3, Matrix3x5, Bidiagonal};
use na::{DMatrix, Matrix2, Matrix4, Matrix5x3, Matrix3x5};
#[cfg(feature = "arbitrary")]
@ -8,7 +8,7 @@ quickcheck! {
return true;
}
let bidiagonal = Bidiagonal::new(m.clone());
let bidiagonal = m.clone().bidiagonalize();
let (u, d, v_t) = bidiagonal.unpack();
println!("{}{}{}", &u, &d, &v_t);
@ -18,7 +18,7 @@ quickcheck! {
}
fn bidiagonal_static_5_3(m: Matrix5x3<f64>) -> bool {
let bidiagonal = Bidiagonal::new(m);
let bidiagonal = m.bidiagonalize();
let (u, d, v_t) = bidiagonal.unpack();
println!("{}{}{}", &u, &d, &v_t);
@ -28,7 +28,7 @@ quickcheck! {
}
fn bidiagonal_static_3_5(m: Matrix3x5<f64>) -> bool {
let bidiagonal = Bidiagonal::new(m);
let bidiagonal = m.bidiagonalize();
let (u, d, v_t) = bidiagonal.unpack();
println!("{}{}{}", &u, &d, &v_t);
@ -38,7 +38,7 @@ quickcheck! {
}
fn bidiagonal_static_square(m: Matrix4<f64>) -> bool {
let bidiagonal = Bidiagonal::new(m);
let bidiagonal = m.bidiagonalize();
let (u, d, v_t) = bidiagonal.unpack();
println!("{}{}{}", &u, &d, &v_t);
@ -48,7 +48,7 @@ quickcheck! {
}
fn bidiagonal_static_square_2x2(m: Matrix2<f64>) -> bool {
let bidiagonal = Bidiagonal::new(m);
let bidiagonal = m.bidiagonalize();
let (u, d, v_t) = bidiagonal.unpack();
println!("{}{}{}", &u, &d, &v_t);

14
tests/linalg/cholesky.rs
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@ -1,5 +1,5 @@
use std::cmp;
use na::{DMatrix, Matrix4x3, DVector, Vector4, Cholesky};
use na::{DMatrix, Matrix4x3, DVector, Vector4};
use na::dimension::U4;
use na::debug::RandomSDP;
@ -11,14 +11,14 @@ quickcheck! {
// Put garbage on the upper triangle to make sure it is not read by the decomposition.
m.fill_upper_triangle(23.0, 1);
let l = Cholesky::new(m.clone()).unwrap().unpack();
let l = m.clone().cholesky().unwrap().unpack();
m.fill_upper_triangle_with_lower_triangle();
relative_eq!(m, &l * l.transpose(), epsilon = 1.0e-7)
}
fn cholesky_static(m: RandomSDP<f64, U4>) -> bool {
let m = m.unwrap();
let chol = Cholesky::new(m).unwrap();
let chol = m.cholesky().unwrap();
let l = chol.unpack();
if !relative_eq!(m, &l * l.transpose(), epsilon = 1.0e-7) {
@ -35,7 +35,7 @@ quickcheck! {
let n = m.nrows();
let nb = cmp::min(nb, 50); // To avoid slowing down the test too much.
let chol = Cholesky::new(m.clone()).unwrap();
let chol = m.clone().cholesky().unwrap();
let b1 = DVector::new_random(n);
let b2 = DMatrix::new_random(n, nb);
@ -48,7 +48,7 @@ quickcheck! {
fn cholesky_solve_static(m: RandomSDP<f64, U4>) -> bool {
let m = m.unwrap();
let chol = Cholesky::new(m).unwrap();
let chol = m.clone().cholesky().unwrap();
let b1 = Vector4::new_random();
let b2 = Matrix4x3::new_random();
@ -62,7 +62,7 @@ quickcheck! {
fn cholesky_inverse(m: RandomSDP<f64>) -> bool {
let m = m.unwrap();
let m1 = Cholesky::new(m.clone()).unwrap().inverse();
let m1 = m.clone().cholesky().unwrap().inverse();
let id1 = &m * &m1;
let id2 = &m1 * &m;
@ -71,7 +71,7 @@ quickcheck! {
fn cholesky_inverse_static(m: RandomSDP<f64, U4>) -> bool {
let m = m.unwrap();
let m1 = Cholesky::new(m.clone()).unwrap().inverse();
let m1 = m.clone().cholesky().unwrap().inverse();
let id1 = &m * &m1;
let id2 = &m1 * &m;

14
tests/linalg/eigen.rs
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@ -1,13 +1,13 @@
use std::cmp;
use na::{DMatrix, Matrix2, Matrix3, Matrix4, SymmetricEigen};
use na::{DMatrix, Matrix2, Matrix3, Matrix4};
#[cfg(feature = "arbitrary")]
quickcheck! {
fn symmetric_eigen(n: usize) -> bool {
let n = cmp::max(1, cmp::min(n, 10));
let m = DMatrix::<f64>::new_random(n, n);
let eig = SymmetricEigen::new(m.clone());
let eig = m.clone().symmetric_eigen();
let recomp = eig.recompose();
println!("{}{}", m.lower_triangle(), recomp.lower_triangle());
@ -20,7 +20,7 @@ quickcheck! {
let mut m = DMatrix::<f64>::new_random(n, n);
m.row_mut(n / 2).fill(0.0);
m.column_mut(n / 2).fill(0.0);
let eig = SymmetricEigen::new(m.clone());
let eig = m.clone().symmetric_eigen();
let recomp = eig.recompose();
println!("{}{}", m.lower_triangle(), recomp.lower_triangle());
@ -29,7 +29,7 @@ quickcheck! {
}
fn symmetric_eigen_static_square_4x4(m: Matrix4<f64>) -> bool {
let eig = SymmetricEigen::new(m);
let eig = m.symmetric_eigen();
let recomp = eig.recompose();
println!("{}{}", m.lower_triangle(), recomp.lower_triangle());
@ -38,7 +38,7 @@ quickcheck! {
}
fn symmetric_eigen_static_square_3x3(m: Matrix3<f64>) -> bool {
let eig = SymmetricEigen::new(m);
let eig = m.symmetric_eigen();
let recomp = eig.recompose();
println!("{}{}", m.lower_triangle(), recomp.lower_triangle());
@ -47,7 +47,7 @@ quickcheck! {
}
fn symmetric_eigen_static_square_2x2(m: Matrix2<f64>) -> bool {
let eig = SymmetricEigen::new(m);
let eig = m.symmetric_eigen();
let recomp = eig.recompose();
println!("{}{}", m.lower_triangle(), recomp.lower_triangle());
@ -85,7 +85,7 @@ fn symmetric_eigen_singular_24x24() {
0.0, 0.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0]);
let eig = SymmetricEigen::new(m.clone());
let eig = m.clone().symmetric_eigen();
let recomp = eig.recompose();
assert!(relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5));

23
tests/linalg/full_piv_lu.rs
View File

@ -1,7 +1,6 @@
use std::cmp;
use na::{DMatrix, Matrix3, Matrix4, Matrix4x3, Matrix5x3, Matrix3x5,
DVector, Vector4,
FullPivLU};
DVector, Vector4};
#[test]
@ -11,7 +10,7 @@ fn full_piv_lu_simple() {
-1.0, 2.0, -1.0,
0.0, -1.0, 2.0);
let lu = FullPivLU::new(m);
let lu = m.full_piv_lu();
assert_eq!(lu.determinant(), 4.0);
let (p, l, u, q) = lu.unpack();
@ -30,7 +29,7 @@ fn full_piv_lu_simple_with_pivot() {
-1.0, 2.0, -1.0,
2.0, -1.0, 0.0);
let lu = FullPivLU::new(m);
let lu = m.full_piv_lu();
assert_eq!(lu.determinant(), -4.0);
let (p, l, u, q) = lu.unpack();
@ -50,7 +49,7 @@ quickcheck! {
m = DMatrix::new_random(1, 1);
}
let lu = FullPivLU::new(m.clone());
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);
@ -60,7 +59,7 @@ quickcheck! {
}
fn full_piv_lu_static_3_5(m: Matrix3x5<f64>) -> bool {
let lu = FullPivLU::new(m);
let lu = m.full_piv_lu();
let (p, l, u, q) = lu.unpack();
let mut lu = l * u;
p.inv_permute_rows(&mut lu);
@ -70,7 +69,7 @@ quickcheck! {
}
fn full_piv_lu_static_5_3(m: Matrix5x3<f64>) -> bool {
let lu = FullPivLU::new(m);
let lu = m.full_piv_lu();
let (p, l, u, q) = lu.unpack();
let mut lu = l * u;
p.inv_permute_rows(&mut lu);
@ -80,7 +79,7 @@ quickcheck! {
}
fn full_piv_lu_static_square(m: Matrix4<f64>) -> bool {
let lu = FullPivLU::new(m);
let lu = m.full_piv_lu();
let (p, l, u, q) = lu.unpack();
let mut lu = l * u;
p.inv_permute_rows(&mut lu);
@ -95,7 +94,7 @@ quickcheck! {
let nb = cmp::min(nb, 50); // To avoid slowing down the test too much.
let m = DMatrix::<f64>::new_random(n, n);
let lu = FullPivLU::new(m.clone());
let lu = m.clone().full_piv_lu();
let b1 = DVector::new_random(n);
let b2 = DMatrix::new_random(n, nb);
@ -110,7 +109,7 @@ quickcheck! {
}
fn full_piv_lu_solve_static(m: Matrix4<f64>) -> bool {
let lu = FullPivLU::new(m);
let lu = m.full_piv_lu();
let b1 = Vector4::new_random();
let b2 = Matrix4x3::new_random();
@ -133,7 +132,7 @@ quickcheck! {
u.fill_diagonal(1.0);
let m = l * u;
let m1 = FullPivLU::new(m.clone()).try_inverse().unwrap();
let m1 = m.clone().full_piv_lu().try_inverse().unwrap();
let id1 = &m * &m1;
let id2 = &m1 * &m;
@ -141,7 +140,7 @@ quickcheck! {
}
fn full_piv_lu_inverse_static(m: Matrix4<f64>) -> bool {
let lu = FullPivLU::new(m);
let lu = m.full_piv_lu();
if let Some(m1) = lu.try_inverse() {
let id1 = &m * &m1;

10
tests/linalg/hessenberg.rs
View File

@ -1,12 +1,12 @@
use std::cmp;
use na::{DMatrix, Matrix2, Matrix4, Hessenberg};
use na::{DMatrix, Matrix2, Matrix4};
#[test]
fn hessenberg_simple() {
let m = Matrix2::new(1.0, 0.0,
1.0, 3.0);
let hess = Hessenberg::new(m);
let hess = m.hessenberg();
let (p, h) = hess.unpack();
assert!(relative_eq!(m, p * h * p.transpose(), epsilon = 1.0e-7))
}
@ -18,19 +18,19 @@ quickcheck! {
let n = cmp::max(1, cmp::min(n, 50));
let m = DMatrix::<f64>::new_random(n, n);
let hess = Hessenberg::new(m.clone());
let hess = m.clone().hessenberg();
let (p, h) = hess.unpack();
relative_eq!(m, &p * h * p.transpose(), epsilon = 1.0e-7)
}
fn hessenberg_static_mat2(m: Matrix2<f64>) -> bool {
let hess = Hessenberg::new(m);
let hess = m.hessenberg();
let (p, h) = hess.unpack();
relative_eq!(m, p * h * p.transpose(), epsilon = 1.0e-7)
}
fn hessenberg_static(m: Matrix4<f64>) -> bool {
let hess = Hessenberg::new(m);
let hess = m.hessenberg();
let (p, h) = hess.unpack();
relative_eq!(m, p * h * p.transpose(), epsilon = 1.0e-7)
}

23
tests/linalg/lu.rs
View File

@ -1,7 +1,6 @@
use std::cmp;
use na::{DMatrix, Matrix3, Matrix4, Matrix4x3, Matrix5x3, Matrix3x5,
DVector, Vector4,
LU};
DVector, Vector4};
#[test]
@ -11,7 +10,7 @@ fn lu_simple() {
-1.0, 2.0, -1.0,
0.0, -1.0, 2.0);
let lu = LU::new(m);
let lu = m.lu();
assert_eq!(lu.determinant(), 4.0);
let (p, l, u) = lu.unpack();
@ -29,7 +28,7 @@ fn lu_simple_with_pivot() {
-1.0, 2.0, -1.0,
2.0, -1.0, 0.0);
let lu = LU::new(m);
let lu = m.lu();
assert_eq!(lu.determinant(), -4.0);
let (p, l, u) = lu.unpack();
@ -48,7 +47,7 @@ quickcheck! {
m = DMatrix::new_random(1, 1);
}
let lu = LU::new(m.clone());
let lu = m.clone().lu();
let (p, l, u) = lu.unpack();
let mut lu = l * u;
p.inv_permute_rows(&mut lu);
@ -57,7 +56,7 @@ quickcheck! {
}
fn lu_static_3_5(m: Matrix3x5<f64>) -> bool {
let lu = LU::new(m);
let lu = m.lu();
let (p, l, u) = lu.unpack();
let mut lu = l * u;
p.inv_permute_rows(&mut lu);
@ -66,7 +65,7 @@ quickcheck! {
}
fn lu_static_5_3(m: Matrix5x3<f64>) -> bool {
let lu = LU::new(m);
let lu = m.lu();
let (p, l, u) = lu.unpack();
let mut lu = l * u;
p.inv_permute_rows(&mut lu);
@ -75,7 +74,7 @@ quickcheck! {
}
fn lu_static_square(m: Matrix4<f64>) -> bool {
let lu = LU::new(m);
let lu = m.lu();
let (p, l, u) = lu.unpack();
let mut lu = l * u;
p.inv_permute_rows(&mut lu);
@ -89,7 +88,7 @@ quickcheck! {
let nb = cmp::min(nb, 50); // To avoid slowing down the test too much.
let m = DMatrix::<f64>::new_random(n, n);
let lu = LU::new(m.clone());
let lu = m.clone().lu();
let b1 = DVector::new_random(n);
let b2 = DMatrix::new_random(n, nb);
@ -104,7 +103,7 @@ quickcheck! {
}
fn lu_solve_static(m: Matrix4<f64>) -> bool {
let lu = LU::new(m);
let lu = m.lu();
let b1 = Vector4::new_random();
let b2 = Matrix4x3::new_random();
@ -127,7 +126,7 @@ quickcheck! {
u.fill_diagonal(1.0);
let m = l * u;
let m1 = LU::new(m.clone()).try_inverse().unwrap();
let m1 = m.clone().lu().try_inverse().unwrap();
let id1 = &m * &m1;
let id2 = &m1 * &m;
@ -135,7 +134,7 @@ quickcheck! {
}
fn lu_inverse_static(m: Matrix4<f64>) -> bool {
let lu = LU::new(m);
let lu = m.lu();
if let Some(m1) = lu.try_inverse() {
let id1 = &m * &m1;

18
tests/linalg/qr.rs
View File

@ -1,11 +1,11 @@
use std::cmp;
use na::{DMatrix, Matrix4, Matrix4x3, Matrix5x3, Matrix3x5,
DVector, Vector4, QR};
DVector, Vector4};
#[cfg(feature = "arbitrary")]
quickcheck! {
fn qr(m: DMatrix<f64>) -> bool {
let qr = QR::new(m.clone());
let qr = m.clone().qr();
let q = qr.q();
let r = qr.r();
@ -14,7 +14,7 @@ quickcheck! {
}
fn qr_static_5_3(m: Matrix5x3<f64>) -> bool {
let qr = QR::new(m);
let qr = m.qr();
let q = qr.q();
let r = qr.r();
@ -23,7 +23,7 @@ quickcheck! {
}
fn qr_static_3_5(m: Matrix3x5<f64>) -> bool {
let qr = QR::new(m);
let qr = m.qr();
let q = qr.q();
let r = qr.r();
@ -32,7 +32,7 @@ quickcheck! {
}
fn qr_static_square(m: Matrix4<f64>) -> bool {
let qr = QR::new(m);
let qr = m.qr();
let q = qr.q();
let r = qr.r();
@ -48,7 +48,7 @@ quickcheck! {
let nb = cmp::min(nb, 50); // To avoid slowing down the test too much.
let m = DMatrix::<f64>::new_random(n, n);
let qr = QR::new(m.clone());
let qr = m.clone().qr();
let b1 = DVector::new_random(n);
let b2 = DMatrix::new_random(n, nb);
@ -65,7 +65,7 @@ quickcheck! {
}
fn qr_solve_static(m: Matrix4<f64>) -> bool {
let qr = QR::new(m);
let qr = m.qr();
let b1 = Vector4::new_random();
let b2 = Matrix4x3::new_random();
@ -85,7 +85,7 @@ quickcheck! {
let n = cmp::max(1, cmp::min(n, 15)); // To avoid slowing down the test too much.
let m = DMatrix::<f64>::new_random(n, n);
if let Some(m1) = QR::new(m.clone()).try_inverse() {
if let Some(m1) = m.clone().qr().try_inverse() {
let id1 = &m * &m1;
let id2 = &m1 * &m;
@ -97,7 +97,7 @@ quickcheck! {
}
fn qr_inverse_static(m: Matrix4<f64>) -> bool {
let qr = QR::new(m);
let qr = m.qr();
if let Some(m1) = qr.try_inverse() {
let id1 = &m * &m1;

20
tests/linalg/real_schur.rs
View File

@ -1,5 +1,5 @@
use std::cmp;
use na::{DMatrix, Matrix2, Matrix3, Matrix4, RealSchur};
use na::{DMatrix, Matrix2, Matrix3, Matrix4};
#[test]
@ -8,7 +8,7 @@ fn schur_simpl_mat3() {
-2.0, 1.0, 2.0,
4.0, 2.0, 5.0);
let schur = RealSchur::new(m);
let schur = m.real_schur();
let (vecs, vals) = schur.unpack();
assert!(relative_eq!(vecs * vals * vecs.transpose(), m, epsilon = 1.0e-7));
@ -20,7 +20,7 @@ quickcheck! {
let n = cmp::max(1, cmp::min(n, 10));
let m = DMatrix::<f64>::new_random(n, n);
let (vecs, vals) = RealSchur::new(m.clone()).unpack();
let (vecs, vals) = m.clone().real_schur().unpack();
if !relative_eq!(&vecs * &vals * vecs.transpose(), m, epsilon = 1.0e-7) {
println!("{:.5}{:.5}", m, &vecs * &vals * vecs.transpose());
@ -30,7 +30,7 @@ quickcheck! {
}
fn schur_static_mat2(m: Matrix2<f64>) -> bool {
let (vecs, vals) = RealSchur::new(m.clone()).unpack();
let (vecs, vals) = m.clone().real_schur().unpack();
let ok = relative_eq!(vecs * vals * vecs.transpose(), m, epsilon = 1.0e-7);
if !ok {
@ -41,7 +41,7 @@ quickcheck! {
}
fn schur_static_mat3(m: Matrix3<f64>) -> bool {
let (vecs, vals) = RealSchur::new(m.clone()).unpack();
let (vecs, vals) = m.clone().real_schur().unpack();
let ok = relative_eq!(vecs * vals * vecs.transpose(), m, epsilon = 1.0e-7);
if !ok {
@ -51,7 +51,7 @@ quickcheck! {
}
fn schur_static_mat4(m: Matrix4<f64>) -> bool {
let (vecs, vals) = RealSchur::new(m.clone()).unpack();
let (vecs, vals) = m.clone().real_schur().unpack();
let ok = relative_eq!(vecs * vals * vecs.transpose(), m, epsilon = 1.0e-7);
if !ok {
@ -69,7 +69,7 @@ fn schur_static_mat4_fail() {
-94.61793793643038, -18.64216213611094, 88.32376703241675, -99.30169870309795,
90.62661897246733, 96.74200696130146, 34.7421322611369, 84.86773307198098);
let (vecs, vals) = RealSchur::new(m.clone()).unpack();
let (vecs, vals) = m.clone().real_schur().unpack();
println!("{:.6}{:.6}", m, &vecs * &vals * vecs.transpose());
assert!(relative_eq!(vecs * vals * vecs.transpose(), m, epsilon = 1.0e-7))
}
@ -82,7 +82,7 @@ fn schur_static_mat4_fail2() {
27.932377940728202, 82.94220150938, -35.5898884705951, 67.56447552434219,
55.66754906908682, -42.14328890569226, -20.684709585152206, -87.9456949841046);
let (vecs, vals) = RealSchur::new(m.clone()).unpack();
let (vecs, vals) = m.clone().real_schur().unpack();
println!("{:.6}{:.6}", m, &vecs * &vals * vecs.transpose());
assert!(relative_eq!(vecs * vals * vecs.transpose(), m, epsilon = 1.0e-7))
}
@ -94,7 +94,7 @@ fn schur_static_mat3_fail() {
-7.525423104386547, -17.827350599642287, 11.297377444555849,
38.080736654870464, -84.27428302131528, -95.88198590331922);
let (vecs, vals) = RealSchur::new(m.clone()).unpack();
let (vecs, vals) = m.clone().real_schur().unpack();
println!("{:.6}{:.6}", m, &vecs * &vals * vecs.transpose());
assert!(relative_eq!(vecs * vals * vecs.transpose(), m, epsilon = 1.0e-7))
}
@ -128,7 +128,7 @@ fn schur_singular() {
0.0, 0.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0]);
let (vecs, vals) = RealSchur::new(m.clone()).unpack();
let (vecs, vals) = m.clone().real_schur().unpack();
println!("{:.6}{:.6}", m, &vecs * &vals * vecs.transpose());
assert!(relative_eq!(&vecs * vals * vecs.transpose(), m, epsilon = 1.0e-7))
}

43
tests/linalg/svd.rs
View File

@ -1,15 +1,14 @@
use std::cmp;
use na::{DMatrix, Matrix2, Matrix3, Matrix4, Matrix6, Matrix5x2, Matrix5x3, Matrix2x5, Matrix3x5,
DVector,
SVD};
DVector};
#[cfg(feature = "arbitrary")]
quickcheck! {
fn svd(m: DMatrix<f64>) -> bool {
if m.len() > 0 {
let svd = SVD::new(m.clone(), true, true);
let svd = m.clone().svd(true, true);
let recomp_m = svd.clone().recompose();
let (u, s, v_t) = (svd.u.unwrap(), svd.singular_values, svd.v_t.unwrap());
let ds = DMatrix::from_diagonal(&s);
@ -26,7 +25,7 @@ quickcheck! {
}
fn svd_static_5_3(m: Matrix5x3<f64>) -> bool {
let svd = SVD::new(m, true, true);
let svd = m.svd(true, true);
let (u, s, v_t) = (svd.u.unwrap(), svd.singular_values, svd.v_t.unwrap());
let ds = Matrix3::from_diagonal(&s);
@ -37,7 +36,7 @@ quickcheck! {
}
fn svd_static_5_2(m: Matrix5x2<f64>) -> bool {
let svd = SVD::new(m, true, true);
let svd = m.svd(true, true);
let (u, s, v_t) = (svd.u.unwrap(), svd.singular_values, svd.v_t.unwrap());
let ds = Matrix2::from_diagonal(&s);
@ -48,7 +47,7 @@ quickcheck! {
}
fn svd_static_3_5(m: Matrix3x5<f64>) -> bool {
let svd = SVD::new(m, true, true);
let svd = m.svd(true, true);
let (u, s, v_t) = (svd.u.unwrap(), svd.singular_values, svd.v_t.unwrap());
let ds = Matrix3::from_diagonal(&s);
@ -58,7 +57,7 @@ quickcheck! {
}
fn svd_static_2_5(m: Matrix2x5<f64>) -> bool {
let svd = SVD::new(m, true, true);
let svd = m.svd(true, true);
let (u, s, v_t) = (svd.u.unwrap(), svd.singular_values, svd.v_t.unwrap());
let ds = Matrix2::from_diagonal(&s);
@ -67,7 +66,7 @@ quickcheck! {
}
fn svd_static_square(m: Matrix4<f64>) -> bool {
let svd = SVD::new(m, true, true);
let svd = m.svd(true, true);
let (u, s, v_t) = (svd.u.unwrap(), svd.singular_values, svd.v_t.unwrap());
let ds = Matrix4::from_diagonal(&s);
@ -78,7 +77,7 @@ quickcheck! {
}
fn svd_static_square_2x2(m: Matrix2<f64>) -> bool {
let svd = SVD::new(m, true, true);
let svd = m.svd(true, true);
let (u, s, v_t) = (svd.u.unwrap(), svd.singular_values, svd.v_t.unwrap());
let ds = Matrix2::from_diagonal(&s);
@ -90,7 +89,7 @@ quickcheck! {
fn svd_pseudo_inverse(m: DMatrix<f64>) -> bool {
if m.len() > 0 {
let svd = SVD::new(m.clone(), true, true);
let svd = m.clone().svd(true, true);
let pinv = svd.pseudo_inverse(1.0e-10);
if m.nrows() > m.ncols() {
@ -112,7 +111,7 @@ quickcheck! {
let nb = cmp::min(nb, 10);
let m = DMatrix::<f64>::new_random(n, n);
let svd = SVD::new(m.clone(), true, true);
let svd = m.clone().svd(true, true);
if svd.rank(1.0e-7) == n {
let b1 = DVector::new_random(n);
@ -169,7 +168,7 @@ fn svd_singular() {
0.0, 0.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0]);
let svd = SVD::new(m.clone(), true, true);
let svd = m.clone().svd(true, true);
let (u, s, v_t) = (svd.u.unwrap(), svd.singular_values, svd.v_t.unwrap());
let ds = DMatrix::from_diagonal(&s);
@ -212,7 +211,7 @@ fn svd_singular_vertical() {
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0]);
let svd = SVD::new(m.clone(), true, true);
let svd = m.clone().svd(true, true);
let (u, s, v_t) = (svd.u.unwrap(), svd.singular_values, svd.v_t.unwrap());
let ds = DMatrix::from_diagonal(&s);
@ -249,7 +248,7 @@ fn svd_singular_horizontal() {
0.0, 0.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]);
let svd = SVD::new(m.clone(), true, true);
let svd = m.clone().svd(true, true);
let (u, s, v_t) = (svd.u.unwrap(), svd.singular_values, svd.v_t.unwrap());
let ds = DMatrix::from_diagonal(&s);
@ -261,22 +260,22 @@ fn svd_singular_horizontal() {
#[test]
fn svd_zeros() {
let m = DMatrix::from_element(10, 10, 0.0);
let svd = SVD::new(m.clone(), true, true);
let svd = m.clone().svd(true, true);
assert_eq!(m, svd.recompose());
}
#[test]
fn svd_identity() {
let m = DMatrix::<f64>::identity(10, 10);
let svd = SVD::new(m.clone(), true, true);
let svd = m.clone().svd(true, true);
assert_eq!(m, svd.recompose());
let m = DMatrix::<f64>::identity(10, 15);
let svd = SVD::new(m.clone(), true, true);
let svd = m.clone().svd(true, true);
assert_eq!(m, svd.recompose());
let m = DMatrix::<f64>::identity(15, 10);
let svd = SVD::new(m.clone(), true, true);
let svd = m.clone().svd(true, true);
assert_eq!(m, svd.recompose());
}
@ -293,7 +292,7 @@ fn svd_with_delimited_subproblem() {
m[(7,7)] = 14.0; m[(3,8)] = 13.0;
m[(8,8)] = 16.0; m[(3,9)] = 17.0;
m[(9,9)] = 18.0;
let svd = SVD::new(m.clone(), true, true);
let svd = m.clone().svd(true, true);
assert!(relative_eq!(m, svd.recompose(), epsilon = 1.0e-7));
// Rectangular versions.
@ -308,10 +307,10 @@ fn svd_with_delimited_subproblem() {
m[(7,7)] = 14.0; m[(3,8)] = 13.0;
m[(8,8)] = 16.0; m[(3,9)] = 17.0;
m[(9,9)] = 18.0;
let svd = SVD::new(m.clone(), true, true);
let svd = m.clone().svd(true, true);
assert!(relative_eq!(m, svd.recompose(), epsilon = 1.0e-7));
let svd = SVD::new(m.transpose(), true, true);
let svd = m.transpose().svd(true, true);
assert!(relative_eq!(m.transpose(), svd.recompose(), epsilon = 1.0e-7));
}
@ -324,7 +323,7 @@ fn svd_fail() {
0.07311092531259344, 0.5579247949052946, 0.14518764691585773, 0.03502980663114896, 0.7991329455957719, 0.4929930019965745,
0.12293810556077789, 0.6617084679545999, 0.9002240700227326, 0.027153062135304884, 0.3630189466989524, 0.18207502727558866,
0.843196731466686, 0.08951878746549924, 0.7533450877576973, 0.009558876499740077, 0.9429679490873482, 0.9355764454129878);
let svd = SVD::new(m.clone(), true, true);
let svd = m.clone().svd(true, true);
println!("Singular values: {}", svd.singular_values);
println!("u: {:.5}", svd.u.unwrap());
println!("v: {:.5}", svd.v_t.unwrap());

8
tests/linalg/tridiagonal.rs
View File

@ -1,6 +1,6 @@
use std::cmp;
use na::{DMatrix, Matrix2, Matrix4, SymmetricTridiagonal};
use na::{DMatrix, Matrix2, Matrix4};
#[cfg(feature = "arbitrary")]
@ -8,7 +8,7 @@ quickcheck! {
fn symm_tridiagonal(n: usize) -> bool {
let n = cmp::max(1, cmp::min(n, 50));
let m = DMatrix::<f64>::new_random(n, n);
let tri = SymmetricTridiagonal::new(m.clone());
let tri = m.clone().symmetric_tridiagonalize();
let recomp = tri.recompose();
println!("{}{}", m.lower_triangle(), recomp.lower_triangle());
@ -17,7 +17,7 @@ quickcheck! {
}
fn symm_tridiagonal_static_square(m: Matrix4<f64>) -> bool {
let tri = SymmetricTridiagonal::new(m);
let tri = m.symmetric_tridiagonalize();
println!("{}{}", tri.internal_tri(), tri.off_diagonal());
let recomp = tri.recompose();
@ -27,7 +27,7 @@ quickcheck! {
}
fn symm_tridiagonal_static_square_2x2(m: Matrix2<f64>) -> bool {
let tri = SymmetricTridiagonal::new(m);
let tri = m.symmetric_tridiagonalize();
let recomp = tri.recompose();
relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-7)