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Jul 10, 2020
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Split eigenvalue and eigenvector tests #217

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429 changes: 264 additions & 165 deletions ndarray-linalg/tests/eig.rs
View file
Original file line number Diff line number Diff line change
@@ -1,190 +1,289 @@
use ndarray::*;
use ndarray_linalg::*;

#[test]
fn dgeev() {
// https://software.intel.com/sites/products/documentation/doclib/mkl_sa/11/mkl_lapack_examples/dgeev_ex.f.htm
let a: Array2<f64> = arr2(&[
[-1.01, 0.86, -4.60, 3.31, -4.81],
[3.98, 0.53, -7.04, 5.29, 3.55],
[3.30, 8.26, -3.89, 8.20, -1.51],
[4.43, 4.96, -7.66, -7.33, 6.18],
[7.31, -6.43, -6.16, 2.47, 5.58],
]);
let (e, vecs): (Array1<_>, Array2<_>) = (&a).eig().unwrap();
assert_close_l2!(
&e,
&arr1(&[
c64::new(2.86, 10.76),
c64::new(2.86, -10.76),
c64::new(-0.69, 4.70),
c64::new(-0.69, -4.70),
c64::new(-10.46, 0.00)
]),
1.0e-3
);

/*
let answer = &arr2(&[[c64::new( 0.11, 0.17), c64::new( 0.11, -0.17), c64::new( 0.73, 0.00), c64::new( 0.73, 0.00), c64::new( 0.46, 0.00)],
[c64::new( 0.41, -0.26), c64::new( 0.41, 0.26), c64::new( -0.03, -0.02), c64::new( -0.03, 0.02), c64::new( 0.34, 0.00)],
[c64::new( 0.10, -0.51), c64::new( 0.10, 0.51), c64::new( 0.19, -0.29), c64::new( 0.19, 0.29), c64::new( 0.31, 0.00)],
[c64::new( 0.40, -0.09), c64::new( 0.40, 0.09), c64::new( -0.08, -0.08), c64::new( -0.08, 0.08), c64::new( -0.74, 0.00)],
[c64::new( 0.54, 0.00), c64::new( 0.54, 0.00), c64::new( -0.29, -0.49), c64::new( -0.29, 0.49), c64::new( 0.16, 0.00)]]);
*/

let a_c: Array2<c64> = a.map(|f| c64::new(*f, 0.0));
for (i, v) in vecs.axis_iter(Axis(1)).enumerate() {
let av = a_c.dot(&v);
let ev = v.mapv(|f| e[i] * f);
assert_close_l2!(&av, &ev, 1.0e-7);
}
}

#[test]
fn fgeev() {
// https://software.intel.com/sites/products/documentation/doclib/mkl_sa/11/mkl_lapack_examples/dgeev_ex.f.htm
let a: Array2<f32> = arr2(&[
[-1.01, 0.86, -4.60, 3.31, -4.81],
[3.98, 0.53, -7.04, 5.29, 3.55],
[3.30, 8.26, -3.89, 8.20, -1.51],
[4.43, 4.96, -7.66, -7.33, 6.18],
[7.31, -6.43, -6.16, 2.47, 5.58],
]);
let (e, vecs): (Array1<_>, Array2<_>) = (&a).eig().unwrap();
assert_close_l2!(
&e,
&arr1(&[
c32::new(2.86, 10.76),
c32::new(2.86, -10.76),
c32::new(-0.69, 4.70),
c32::new(-0.69, -4.70),
c32::new(-10.46, 0.00)
]),
1.0e-3
);

/*
let answer = &arr2(&[[c32::new( 0.11, 0.17), c32::new( 0.11, -0.17), c32::new( 0.73, 0.00), c32::new( 0.73, 0.00), c32::new( 0.46, 0.00)],
[c32::new( 0.41, -0.26), c32::new( 0.41, 0.26), c32::new( -0.03, -0.02), c32::new( -0.03, 0.02), c32::new( 0.34, 0.00)],
[c32::new( 0.10, -0.51), c32::new( 0.10, 0.51), c32::new( 0.19, -0.29), c32::new( 0.19, 0.29), c32::new( 0.31, 0.00)],
[c32::new( 0.40, -0.09), c32::new( 0.40, 0.09), c32::new( -0.08, -0.08), c32::new( -0.08, 0.08), c32::new( -0.74, 0.00)],
[c32::new( 0.54, 0.00), c32::new( 0.54, 0.00), c32::new( -0.29, -0.49), c32::new( -0.29, 0.49), c32::new( 0.16, 0.00)]]);
*/

let a_c: Array2<c32> = a.map(|f| c32::new(*f, 0.0));
for (i, v) in vecs.axis_iter(Axis(1)).enumerate() {
let av = a_c.dot(&v);
let ev = v.mapv(|f| e[i] * f);
assert_close_l2!(&av, &ev, 1.0e-5);
// Test Av_i = e_i v_i for i = 0..n
fn test_eig<T: Scalar>(a: Array2<T>, eigs: Array1<T::Complex>, vecs: Array2<T::Complex>)
where
T::Complex: Lapack,
{
println!("a\n{:+.4}", &a);
println!("eigs\n{:+.4}", &eigs);
println!("vec\n{:+.4}", &vecs);
let a: Array2<T::Complex> = a.map(|v| v.as_c());
for (&e, v) in eigs.iter().zip(vecs.axis_iter(Axis(1))) {
let av = a.dot(&v);
let ev = v.mapv(|val| val * e);
println!("av = {:+.4}", &av);
println!("ev = {:+.4}", &ev);
assert_close_l2!(&av, &ev, T::real(1e-3));
}
}

#[test]
fn zgeev() {
// https://software.intel.com/sites/products/documentation/doclib/mkl_sa/11/mkl_lapack_examples/zgeev_ex.f.htm
let a: Array2<c64> = arr2(&[
// Test case for real Eigenvalue problem
//
// -1.01 0.86 -4.60 3.31 -4.81
// 3.98 0.53 -7.04 5.29 3.55
// 3.30 8.26 -3.89 8.20 -1.51
// 4.43 4.96 -7.66 -7.33 6.18
// 7.31 -6.43 -6.16 2.47 5.58
//
// Eigenvalues
// ( 2.86, 10.76) ( 2.86,-10.76) ( -0.69, 4.70) ( -0.69, -4.70) -10.46
//
// Left eigenvectors
// ( 0.04, 0.29) ( 0.04, -0.29) ( -0.13, -0.33) ( -0.13, 0.33) 0.04
// ( 0.62, 0.00) ( 0.62, 0.00) ( 0.69, 0.00) ( 0.69, 0.00) 0.56
// ( -0.04, -0.58) ( -0.04, 0.58) ( -0.39, -0.07) ( -0.39, 0.07) -0.13
// ( 0.28, 0.01) ( 0.28, -0.01) ( -0.02, -0.19) ( -0.02, 0.19) -0.80
// ( -0.04, 0.34) ( -0.04, -0.34) ( -0.40, 0.22) ( -0.40, -0.22) 0.18
//
// Right eigenvectors
// ( 0.11, 0.17) ( 0.11, -0.17) ( 0.73, 0.00) ( 0.73, 0.00) 0.46
// ( 0.41, -0.26) ( 0.41, 0.26) ( -0.03, -0.02) ( -0.03, 0.02) 0.34
// ( 0.10, -0.51) ( 0.10, 0.51) ( 0.19, -0.29) ( 0.19, 0.29) 0.31
// ( 0.40, -0.09) ( 0.40, 0.09) ( -0.08, -0.08) ( -0.08, 0.08) -0.74
// ( 0.54, 0.00) ( 0.54, 0.00) ( -0.29, -0.49) ( -0.29, 0.49) 0.16
//
// - https://software.intel.com/sites/products/documentation/doclib/mkl_sa/11/mkl_lapack_examples/dgeev_ex.f.htm
//
fn test_matrix_real<T: Scalar>() -> Array2<T::Real> {
array![
[
c64::new(-3.84, 2.25),
c64::new(-8.94, -4.75),
c64::new(8.95, -6.53),
c64::new(-9.87, 4.82),
T::real(-1.01),
T::real(0.86),
T::real(-4.60),
T::real(3.31),
T::real(-4.81)
],
[
c64::new(-0.66, 0.83),
c64::new(-4.40, -3.82),
c64::new(-3.50, -4.26),
c64::new(-3.15, 7.36),
T::real(3.98),
T::real(0.53),
T::real(-7.04),
T::real(5.29),
T::real(3.55)
],
[
c64::new(-3.99, -4.73),
c64::new(-5.88, -6.60),
c64::new(-3.36, -0.40),
c64::new(-0.75, 5.23),
T::real(3.30),
T::real(8.26),
T::real(-3.89),
T::real(8.20),
T::real(-1.51)
],
[
c64::new(7.74, 4.18),
c64::new(3.66, -7.53),
c64::new(2.58, 3.60),
c64::new(4.59, 5.41),
T::real(4.43),
T::real(4.96),
T::real(-7.66),
T::real(-7.33),
T::real(6.18)
],
]);
let (e, vecs): (Array1<_>, Array2<_>) = (&a).eig().unwrap();
assert_close_l2!(
&e,
&arr1(&[
c64::new(-9.43, -12.98),
c64::new(-3.44, 12.69),
c64::new(0.11, -3.40),
c64::new(5.76, 7.13)
]),
1.0e-3
);

/*
let answer = &arr2(&[[c64::new( 0.43, 0.33), c64::new( 0.83, 0.00), c64::new( 0.60, 0.00), c64::new( -0.31, 0.03)],
[c64::new( 0.51, -0.03), c64::new( 0.08, -0.25), c64::new( -0.40, -0.20), c64::new( 0.04, 0.34)],
[c64::new( 0.62, 0.00), c64::new( -0.25, 0.28), c64::new( -0.09, -0.48), c64::new( 0.36, 0.06)],
[c64::new( -0.23, 0.11), c64::new( -0.10, -0.32), c64::new( -0.43, 0.13), c64::new( 0.81, 0.00)]]);
*/

for (i, v) in vecs.axis_iter(Axis(1)).enumerate() {
let av = a.dot(&v);
let ev = v.mapv(|f| e[i] * f);
assert_close_l2!(&av, &ev, 1.0e-7);
}
[
T::real(7.31),
T::real(-6.43),
T::real(-6.16),
T::real(2.47),
T::real(5.58)
],
]
}

#[test]
fn cgeev() {
// https://software.intel.com/sites/products/documentation/doclib/mkl_sa/11/mkl_lapack_examples/zgeev_ex.f.htm
let a: Array2<c32> = arr2(&[
fn test_matrix_real_t<T: Scalar>() -> Array2<T::Real> {
test_matrix_real::<T>().t().permuted_axes([1, 0]).to_owned()
}

fn answer_eig_real<T: Scalar>() -> Array1<T::Complex> {
array![
T::complex(2.86, 10.76),
T::complex(2.86, -10.76),
T::complex(-0.69, 4.70),
T::complex(-0.69, -4.70),
T::complex(-10.46, 0.00),
]
}

// Test case for {c,z}geev
//
// ( -3.84, 2.25) ( -8.94, -4.75) ( 8.95, -6.53) ( -9.87, 4.82)
// ( -0.66, 0.83) ( -4.40, -3.82) ( -3.50, -4.26) ( -3.15, 7.36)
// ( -3.99, -4.73) ( -5.88, -6.60) ( -3.36, -0.40) ( -0.75, 5.23)
// ( 7.74, 4.18) ( 3.66, -7.53) ( 2.58, 3.60) ( 4.59, 5.41)
//
// Eigenvalues
// ( -9.43,-12.98) ( -3.44, 12.69) ( 0.11, -3.40) ( 5.76, 7.13)
//
// Left eigenvectors
// ( 0.24, -0.18) ( 0.61, 0.00) ( -0.18, -0.33) ( 0.28, 0.09)
// ( 0.79, 0.00) ( -0.05, -0.27) ( 0.82, 0.00) ( -0.55, 0.16)
// ( 0.22, -0.27) ( -0.21, 0.53) ( -0.37, 0.15) ( 0.45, 0.09)
// ( -0.02, 0.41) ( 0.40, -0.24) ( 0.06, 0.12) ( 0.62, 0.00)
//
// Right eigenvectors
// ( 0.43, 0.33) ( 0.83, 0.00) ( 0.60, 0.00) ( -0.31, 0.03)
// ( 0.51, -0.03) ( 0.08, -0.25) ( -0.40, -0.20) ( 0.04, 0.34)
// ( 0.62, 0.00) ( -0.25, 0.28) ( -0.09, -0.48) ( 0.36, 0.06)
// ( -0.23, 0.11) ( -0.10, -0.32) ( -0.43, 0.13) ( 0.81, 0.00)
//
// - https://software.intel.com/sites/products/documentation/doclib/mkl_sa/11/mkl_lapack_examples/zgeev_ex.f.htm
//
fn test_matrix_complex<T: Scalar>() -> Array2<T::Complex> {
array![
[
c32::new(-3.84, 2.25),
c32::new(-8.94, -4.75),
c32::new(8.95, -6.53),
c32::new(-9.87, 4.82),
T::complex(-3.84, 2.25),
T::complex(-8.94, -4.75),
T::complex(8.95, -6.53),
T::complex(-9.87, 4.82)
],
[
c32::new(-0.66, 0.83),
c32::new(-4.40, -3.82),
c32::new(-3.50, -4.26),
c32::new(-3.15, 7.36),
T::complex(-0.66, 0.83),
T::complex(-4.40, -3.82),
T::complex(-3.50, -4.26),
T::complex(-3.15, 7.36)
],
[
c32::new(-3.99, -4.73),
c32::new(-5.88, -6.60),
c32::new(-3.36, -0.40),
c32::new(-0.75, 5.23),
T::complex(-3.99, -4.73),
T::complex(-5.88, -6.60),
T::complex(-3.36, -0.40),
T::complex(-0.75, 5.23)
],
[
c32::new(7.74, 4.18),
c32::new(3.66, -7.53),
c32::new(2.58, 3.60),
c32::new(4.59, 5.41),
T::complex(7.74, 4.18),
T::complex(3.66, -7.53),
T::complex(2.58, 3.60),
T::complex(4.59, 5.41)
]
]
}

fn test_matrix_complex_t<T: Scalar>() -> Array2<T::Complex> {
test_matrix_complex::<T>()
.t()
.permuted_axes([1, 0])
.to_owned()
}

fn answer_eig_complex<T: Scalar>() -> Array1<T::Complex> {
array![
T::complex(-9.43, -12.98),
T::complex(-3.44, 12.69),
T::complex(0.11, -3.40),
T::complex(5.76, 7.13)
]
}

// re-evaluated eigenvalues in f64 accuracy
fn answer_eigvectors_complex<T: Scalar>() -> Array2<T::Complex> {
array![
[
T::complex(0.4308565200776108, 0.32681273781262143),
T::complex(0.8256820507672813, 0.),
T::complex(0.5983959785539453, 0.),
T::complex(-0.30543190348437826, 0.03333164861799901)
],
]);
let (e, vecs): (Array1<_>, Array2<_>) = (&a).eig().unwrap();
assert_close_l2!(
&e,
&arr1(&[
c32::new(-9.43, -12.98),
c32::new(-3.44, 12.69),
c32::new(0.11, -3.40),
c32::new(5.76, 7.13)
]),
1.0e-3
);

/*
let answer = &arr2(&[[c32::new( 0.43, 0.33), c32::new( 0.83, 0.00), c32::new( 0.60, 0.00), c32::new( -0.31, 0.03)],
[c32::new( 0.51, -0.03), c32::new( 0.08, -0.25), c32::new( -0.40, -0.20), c32::new( 0.04, 0.34)],
[c32::new( 0.62, 0.00), c32::new( -0.25, 0.28), c32::new( -0.09, -0.48), c32::new( 0.36, 0.06)],
[c32::new( -0.23, 0.11), c32::new( -0.10, -0.32), c32::new( -0.43, 0.13), c32::new( 0.81, 0.00)]]);
*/

for (i, v) in vecs.axis_iter(Axis(1)).enumerate() {
let av = a.dot(&v);
let ev = v.mapv(|f| e[i] * f);
assert_close_l2!(&av, &ev, 1.0e-5);
}
[
T::complex(0.5087414602970965, -0.02883342170692809),
T::complex(0.07502916788141115, -0.2487285045091665),
T::complex(-0.40047616275207687, -0.2014492227625603),
T::complex(0.03978282815783273, 0.34450765221546126)
],
[
T::complex(0.6198496527657755, 0.),
T::complex(-0.24575578997801528, 0.27887240221169646),
T::complex(-0.09008001907594984, -0.4752646215391732),
T::complex(0.3583254365159844, 0.06064506988524665)
],
[
T::complex(-0.22692824331926856, 0.11043927846403584),
T::complex(-0.10343406372814358, -0.3192014653632327),
T::complex(-0.43484029549540404, 0.13372491785816037),
T::complex(0.8082432893178352, 0.)
]
]
}

macro_rules! impl_test_real {
($real:ty) => {
paste::item! {
#[test]
fn [<$real _eigvals >]() {
let a = test_matrix_real::<$real>();
let (e, _vecs) = a.eig().unwrap();
assert_close_l2!(&e, &answer_eig_real::<$real>(), 1.0e-3);
}

#[test]
fn [<$real _eigvals_t>]() {
let a = test_matrix_real_t::<$real>();
let (e, _vecs) = a.eig().unwrap();
assert_close_l2!(&e, &answer_eig_real::<$real>(), 1.0e-3);
}

#[test]
fn [<$real _eig>]() {
let a = test_matrix_real::<$real>();
let (e, vecs) = a.eig().unwrap();
test_eig(a, e, vecs);
}

#[test]
fn [<$real _eig_t>]() {
let a = test_matrix_real_t::<$real>();
let (e, vecs) = a.eig().unwrap();
test_eig(a, e, vecs);
}

} // paste::item!
};
}

impl_test_real!(f32);
impl_test_real!(f64);

macro_rules! impl_test_complex {
($complex:ty) => {
paste::item! {
#[test]
fn [<$complex _eigvals >]() {
let a = test_matrix_complex::<$complex>();
let (e, _vecs) = a.eig().unwrap();
assert_close_l2!(&e, &answer_eig_complex::<$complex>(), 1.0e-3);
}

#[test]
fn [<$complex _eigvals_t>]() {
let a = test_matrix_complex_t::<$complex>();
let (e, _vecs) = a.eig().unwrap();
assert_close_l2!(&e, &answer_eig_complex::<$complex>(), 1.0e-3);
}

#[test]
fn [<$complex _eigvector>]() {
let a = test_matrix_complex::<$complex>();
let (_e, vecs) = a.eig().unwrap();
assert_close_l2!(&vecs, &answer_eigvectors_complex::<$complex>(), 1.0e-3);
}

#[test]
fn [<$complex _eigvector_t>]() {
let a = test_matrix_complex_t::<$complex>();
let (_e, vecs) = a.eig().unwrap();
assert_close_l2!(&vecs, &answer_eigvectors_complex::<$complex>(), 1.0e-3);
}

#[test]
fn [<$complex _eig>]() {
let a = test_matrix_complex::<$complex>();
let (e, vecs) = a.eig().unwrap();
test_eig(a, e, vecs);
}

#[test]
fn [<$complex _eig_t>]() {
let a = test_matrix_complex_t::<$complex>();
let (e, vecs) = a.eig().unwrap();
test_eig(a, e, vecs);
}
} // paste::item!
};
}

impl_test_complex!(c32);
impl_test_complex!(c64);