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nalgebra/tests/linalg/svd.rs

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Add rustfmt.toml and run it.
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#![cfg_attr(rustfmt, rustfmt_skip)]
Restructure test modules to avoid warnings These warnings occurred only when running the test suite with no features. Lots of uses had to be rescoped into newly created modules to make it easier to separate these issues.
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use na::{DMatrix, Matrix6};
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#[cfg(feature = "arbitrary")]
Restructure test modules to avoid warnings These warnings occurred only when running the test suite with no features. Lots of uses had to be rescoped into newly created modules to make it easier to separate these issues.
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mod quickcheck_tests {
Cleanup warnings and rename Schur -> RealSchur
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macro_rules! gen_tests(
($module: ident, $scalar: ty) => {
mod $module {
use na::{
DMatrix, DVector, Matrix2, Matrix2x5, Matrix3, Matrix3x5, Matrix4, Matrix5x2, Matrix5x3,
Complex
};
use std::cmp;
#[allow(unused_imports)]
2018 edition.
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use crate::core::helper::{RandScalar, RandComplex};
Cleanup warnings and rename Schur -> RealSchur
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quickcheck! {
fn svd(m: DMatrix<$scalar>) -> bool {
let m = m.map(|e| e.0);
if m.len() > 0 {
let svd = m.clone().svd(true, true);
let recomp_m = svd.clone().recompose().unwrap();
let (u, s, v_t) = (svd.u.unwrap(), svd.singular_values, svd.v_t.unwrap());
let ds = DMatrix::from_diagonal(&s.map(|e| Complex::from_real(e)));
s.iter().all(|e| *e >= 0.0) &&
relative_eq!(&u * ds * &v_t, recomp_m, epsilon = 1.0e-5) &&
relative_eq!(m, recomp_m, epsilon = 1.0e-5)
}
else {
true
}
}
fn svd_static_5_3(m: Matrix5x3<$scalar>) -> bool {
let m = m.map(|e| e.0);
let svd = m.svd(true, true);
let (u, s, v_t) = (svd.u.unwrap(), svd.singular_values, svd.v_t.unwrap());
let ds = Matrix3::from_diagonal(&s.map(|e| Complex::from_real(e)));
s.iter().all(|e| *e >= 0.0) &&
relative_eq!(m, &u * ds * &v_t, epsilon = 1.0e-5) &&
u.is_orthogonal(1.0e-5) &&
v_t.is_orthogonal(1.0e-5)
}
fn svd_static_5_2(m: Matrix5x2<$scalar>) -> bool {
let m = m.map(|e| e.0);
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.map(|e| Complex::from_real(e)));
s.iter().all(|e| *e >= 0.0) &&
relative_eq!(m, &u * ds * &v_t, epsilon = 1.0e-5) &&
u.is_orthogonal(1.0e-5) &&
v_t.is_orthogonal(1.0e-5)
}
fn svd_static_3_5(m: Matrix3x5<$scalar>) -> bool {
let m = m.map(|e| e.0);
let svd = m.svd(true, true);
let (u, s, v_t) = (svd.u.unwrap(), svd.singular_values, svd.v_t.unwrap());
let ds = Matrix3::from_diagonal(&s.map(|e| Complex::from_real(e)));
s.iter().all(|e| *e >= 0.0) &&
relative_eq!(m, u * ds * v_t, epsilon = 1.0e-5)
}
fn svd_static_2_5(m: Matrix2x5<$scalar>) -> bool {
let m = m.map(|e| e.0);
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.map(|e| Complex::from_real(e)));
s.iter().all(|e| *e >= 0.0) &&
relative_eq!(m, u * ds * v_t, epsilon = 1.0e-5)
}
fn svd_static_square(m: Matrix4<$scalar>) -> bool {
let m = m.map(|e| e.0);
let svd = m.svd(true, true);
let (u, s, v_t) = (svd.u.unwrap(), svd.singular_values, svd.v_t.unwrap());
let ds = Matrix4::from_diagonal(&s.map(|e| Complex::from_real(e)));
s.iter().all(|e| *e >= 0.0) &&
relative_eq!(m, u * ds * v_t, epsilon = 1.0e-5) &&
u.is_orthogonal(1.0e-5) &&
v_t.is_orthogonal(1.0e-5)
}
fn svd_static_square_2x2(m: Matrix2<$scalar>) -> bool {
let m = m.map(|e| e.0);
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.map(|e| Complex::from_real(e)));
s.iter().all(|e| *e >= 0.0) &&
relative_eq!(m, u * ds * v_t, epsilon = 1.0e-5) &&
u.is_orthogonal(1.0e-5) &&
v_t.is_orthogonal(1.0e-5)
}
fn svd_pseudo_inverse(m: DMatrix<$scalar>) -> bool {
let m = m.map(|e| e.0);
if m.len() > 0 {
let svd = m.clone().svd(true, true);
let pinv = svd.pseudo_inverse(1.0e-10).unwrap();
if m.nrows() > m.ncols() {
(pinv * m).is_identity(1.0e-5)
}
else {
(m * pinv).is_identity(1.0e-5)
}
}
else {
true
}
}
fn svd_solve(n: usize, nb: usize) -> bool {
let n = cmp::max(1, cmp::min(n, 10));
let nb = cmp::min(nb, 10);
let m = DMatrix::<$scalar>::new_random(n, n).map(|e| e.0);
let svd = m.clone().svd(true, true);
if svd.rank(1.0e-7) == n {
let b1 = DVector::<$scalar>::new_random(n).map(|e| e.0);
let b2 = DMatrix::<$scalar>::new_random(n, nb).map(|e| e.0);
let sol1 = svd.solve(&b1, 1.0e-7).unwrap();
let sol2 = svd.solve(&b2, 1.0e-7).unwrap();
let recomp = svd.recompose().unwrap();
if !relative_eq!(m, recomp, epsilon = 1.0e-6) {
println!("{}{}", m, recomp);
}
if !relative_eq!(&m * &sol1, b1, epsilon = 1.0e-6) {
println!("Problem 1: {:.6}{:.6}", b1, &m * sol1);
return false;
}
if !relative_eq!(&m * &sol2, b2, epsilon = 1.0e-6) {
println!("Problem 2: {:.6}{:.6}", b2, &m * sol2);
return false;
}
}
true
}
Restructure test modules to avoid warnings These warnings occurred only when running the test suite with no features. Lots of uses had to be rescoped into newly created modules to make it easier to separate these issues.
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}
Add the most common matrix decompositions.
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}
}
Cleanup warnings and rename Schur -> RealSchur
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);
Add the most common matrix decompositions.
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Cleanup warnings and rename Schur -> RealSchur
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gen_tests!(complex, RandComplex<f64>);
gen_tests!(f64, RandScalar<f64>);
Add the most common matrix decompositions.
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}
Fix most tests.
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Add the most common matrix decompositions.
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// Test proposed on the issue #176 of rulinalg.
#[test]
fn svd_singular() {
let m = DMatrix::from_row_slice(24, 24, &[
1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 1.0, 1.0, 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,
-1.0, -1.0, -1.0, -1.0, -1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 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, 0.0, -1.0, -1.0, -1.0, -1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 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, 0.0, 0.0, -1.0, -1.0, -1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 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, 0.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, 0.0, 1.0, 1.0, 1.0,
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, 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, 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, 0.0, 0.0, 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, 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, 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, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, -4.0, 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, 0.0, 0.0,
0.0, 0.0, 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, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 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,
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, 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, 0.0, 4.0, 0.0, 0.0, 0.0, -4.0, 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, 4.0, 0.0, 0.0, 0.0, -4.0, 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, -4.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, -4.0, 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, -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, 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, 0.0, 0.0, -4.0, 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, 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, 0.0, 0.0, 4.0, 0.0, 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, 0.0, -4.0, 4.0, 0.0, 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, -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]);
Add methods for computing decompositions.
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let svd = m.clone().svd(true, true);
Add the most common matrix decompositions.
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let (u, s, v_t) = (svd.u.unwrap(), svd.singular_values, svd.v_t.unwrap());
let ds = DMatrix::from_diagonal(&s);
assert!(s.iter().all(|e| *e >= 0.0));
assert!(u.is_orthogonal(1.0e-5));
assert!(v_t.is_orthogonal(1.0e-5));
Fix mint tests.
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assert_relative_eq!(m, &u * ds * &v_t, epsilon = 1.0e-5);
Add the most common matrix decompositions.
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}
// Same as the previous test but with one additional row.
#[test]
fn svd_singular_vertical() {
let m = DMatrix::from_row_slice(25, 24, &[
1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 1.0, 1.0, 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,
-1.0, -1.0, -1.0, -1.0, -1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 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, 0.0, -1.0, -1.0, -1.0, -1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 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, 0.0, 0.0, -1.0, -1.0, -1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 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, 0.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, 0.0, 1.0, 1.0, 1.0,
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, 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, 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, 0.0, 0.0, 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, 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, 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, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, -4.0, 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, 0.0, 0.0,
0.0, 0.0, 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, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 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,
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, 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, 0.0, 4.0, 0.0, 0.0, 0.0, -4.0, 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, 4.0, 0.0, 0.0, 0.0, -4.0, 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, -4.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, -4.0, 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, -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, 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, 0.0, 0.0, -4.0, 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, 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, 0.0, 0.0, 4.0, 0.0, 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, 0.0, -4.0, 4.0, 0.0, 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, -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,
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]);
Add methods for computing decompositions.
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let svd = m.clone().svd(true, true);
Add the most common matrix decompositions.
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let (u, s, v_t) = (svd.u.unwrap(), svd.singular_values, svd.v_t.unwrap());
let ds = DMatrix::from_diagonal(&s);
assert!(s.iter().all(|e| *e >= 0.0));
Fix mint tests.
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assert_relative_eq!(m, &u * ds * &v_t, epsilon = 1.0e-5);
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}
// Same as the previous test but with one additional column.
#[test]
fn svd_singular_horizontal() {
let m = DMatrix::from_row_slice(24, 25, &[
1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 1.0, 1.0, 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, 0.0,
-1.0, -1.0, -1.0, -1.0, -1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 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, 0.0, 0.0, -1.0, -1.0, -1.0, -1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 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, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 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, 0.0, 0.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, 0.0, 1.0, 1.0, 1.0, 1.0,
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, 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, 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, 0.0, 0.0, 0.0, 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, 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, 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, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, -4.0, 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, 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, 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,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 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, 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, -4.0, 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, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, -4.0, 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, 0.0, -4.0, 4.0, 0.0, 0.0, 0.0, -4.0, 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, -4.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, -4.0, 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, -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, 0.0, 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, 0.0, 0.0, 0.0, -4.0, 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, 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, 0.0, 0.0, 0.0, 4.0, 0.0, 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, 0.0, 0.0, -4.0, 4.0, 0.0, 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, -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]);
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let svd = m.clone().svd(true, true);
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let (u, s, v_t) = (svd.u.unwrap(), svd.singular_values, svd.v_t.unwrap());
let ds = DMatrix::from_diagonal(&s);
assert!(s.iter().all(|e| *e >= 0.0));
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assert_relative_eq!(m, &u * ds * &v_t, epsilon = 1.0e-5);
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}
#[test]
fn svd_zeros() {
let m = DMatrix::from_element(10, 10, 0.0);
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let svd = m.clone().svd(true, true);
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assert_eq!(Ok(m), svd.recompose());
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}
#[test]
fn svd_identity() {
let m = DMatrix::<f64>::identity(10, 10);
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let svd = m.clone().svd(true, true);
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assert_eq!(Ok(m), svd.recompose());
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let m = DMatrix::<f64>::identity(10, 15);
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let svd = m.clone().svd(true, true);
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assert_eq!(Ok(m), svd.recompose());
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let m = DMatrix::<f64>::identity(15, 10);
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let svd = m.clone().svd(true, true);
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assert_eq!(Ok(m), svd.recompose());
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}
#[test]
fn svd_with_delimited_subproblem() {
let mut m = DMatrix::<f64>::from_element(10, 10, 0.0);
m[(0,0)] = 1.0; m[(0,1)] = 2.0;
m[(1,1)] = 0.0; m[(1,2)] = 3.0;
m[(2,2)] = 4.0; m[(2,3)] = 5.0;
m[(3,3)] = 6.0; m[(3,4)] = 0.0;
m[(4,4)] = 8.0; m[(3,5)] = 9.0;
m[(5,5)] = 10.0; m[(3,6)] = 11.0;
m[(6,6)] = 12.0; m[(3,7)] = 12.0;
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;
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let svd = m.clone().svd(true, true);
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assert_relative_eq!(m, svd.recompose().unwrap(), epsilon = 1.0e-7);
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// Rectangular versions.
let mut m = DMatrix::<f64>::from_element(15, 10, 0.0);
m[(0,0)] = 1.0; m[(0,1)] = 2.0;
m[(1,1)] = 0.0; m[(1,2)] = 3.0;
m[(2,2)] = 4.0; m[(2,3)] = 5.0;
m[(3,3)] = 6.0; m[(3,4)] = 0.0;
m[(4,4)] = 8.0; m[(3,5)] = 9.0;
m[(5,5)] = 10.0; m[(3,6)] = 11.0;
m[(6,6)] = 12.0; m[(3,7)] = 12.0;
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;
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let svd = m.clone().svd(true, true);
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assert_relative_eq!(m, svd.recompose().unwrap(), epsilon = 1.0e-7);
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let svd = m.transpose().svd(true, true);
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assert_relative_eq!(m.transpose(), svd.recompose().unwrap(), epsilon = 1.0e-7);
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}
#[test]
fn svd_fail() {
let m = Matrix6::new(
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0.9299319121545955, 0.9955870335651049, 0.8824725266413644, 0.28966880207132295, 0.06102723649846409, 0.9311880746048009,
0.5938395242304351, 0.8398522876024204, 0.06672831951963198, 0.9941213119963099, 0.9431846038057834, 0.8159885168706427,
0.9121962883152357, 0.6471119669367571, 0.4823309702814407, 0.6420516076705516, 0.7731203925207113, 0.7424069470756647,
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0.07311092531259344, 0.5579247949052946, 0.14518764691585773, 0.03502980663114896, 0.7991329455957719, 0.4929930019965745,
0.12293810556077789, 0.6617084679545999, 0.9002240700227326, 0.027153062135304884, 0.3630189466989524, 0.18207502727558866,
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0.843196731466686, 0.08951878746549924, 0.7533450877576973, 0.009558876499740077, 0.9429679490873482, 0.9355764454129878);
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let svd = m.clone().svd(true, true);
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let recomp = svd.recompose().unwrap();
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assert_relative_eq!(m, recomp, epsilon = 1.0e-5);
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}
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#[test]
fn svd_err() {
let m = DMatrix::from_element(10, 10, 0.0);
let svd = m.clone().svd(false, false);
assert_eq!(Err("SVD recomposition: U and V^t have not been computed."), svd.clone().recompose());
assert_eq!(Err("SVD pseudo inverse: the epsilon must be non-negative."), svd.clone().pseudo_inverse(-1.0));
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}