+++ /dev/null
-// Copyright ©2016 The Gonum Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package testlapack
-
-import (
- "fmt"
- "math"
- "math/cmplx"
- "strconv"
- "testing"
-
- "golang.org/x/exp/rand"
-
- "gonum.org/v1/gonum/blas"
- "gonum.org/v1/gonum/blas/blas64"
- "gonum.org/v1/gonum/floats"
- "gonum.org/v1/gonum/lapack"
-)
-
-type Dgeever interface {
- Dgeev(jobvl lapack.LeftEVJob, jobvr lapack.RightEVJob, n int, a []float64, lda int,
- wr, wi []float64, vl []float64, ldvl int, vr []float64, ldvr int, work []float64, lwork int) int
-}
-
-type dgeevTest struct {
- a blas64.General
- evWant []complex128 // If nil, the eigenvalues are not known.
- valTol float64 // Tolerance for eigenvalue checks.
- vecTol float64 // Tolerance for eigenvector checks.
-}
-
-func DgeevTest(t *testing.T, impl Dgeever) {
- rnd := rand.New(rand.NewSource(1))
-
- for i, test := range []dgeevTest{
- {
- a: A123{}.Matrix(),
- evWant: A123{}.Eigenvalues(),
- },
-
- dgeevTestForAntisymRandom(10, rnd),
- dgeevTestForAntisymRandom(11, rnd),
- dgeevTestForAntisymRandom(50, rnd),
- dgeevTestForAntisymRandom(51, rnd),
- dgeevTestForAntisymRandom(100, rnd),
- dgeevTestForAntisymRandom(101, rnd),
-
- {
- a: Circulant(2).Matrix(),
- evWant: Circulant(2).Eigenvalues(),
- },
- {
- a: Circulant(3).Matrix(),
- evWant: Circulant(3).Eigenvalues(),
- },
- {
- a: Circulant(4).Matrix(),
- evWant: Circulant(4).Eigenvalues(),
- },
- {
- a: Circulant(5).Matrix(),
- evWant: Circulant(5).Eigenvalues(),
- },
- {
- a: Circulant(10).Matrix(),
- evWant: Circulant(10).Eigenvalues(),
- },
- {
- a: Circulant(15).Matrix(),
- evWant: Circulant(15).Eigenvalues(),
- valTol: 1e-12,
- },
- {
- a: Circulant(30).Matrix(),
- evWant: Circulant(30).Eigenvalues(),
- valTol: 1e-11,
- vecTol: 1e-12,
- },
- {
- a: Circulant(50).Matrix(),
- evWant: Circulant(50).Eigenvalues(),
- valTol: 1e-11,
- vecTol: 1e-12,
- },
- {
- a: Circulant(101).Matrix(),
- evWant: Circulant(101).Eigenvalues(),
- valTol: 1e-10,
- vecTol: 1e-11,
- },
- {
- a: Circulant(150).Matrix(),
- evWant: Circulant(150).Eigenvalues(),
- valTol: 1e-9,
- vecTol: 1e-10,
- },
-
- {
- a: Clement(2).Matrix(),
- evWant: Clement(2).Eigenvalues(),
- },
- {
- a: Clement(3).Matrix(),
- evWant: Clement(3).Eigenvalues(),
- },
- {
- a: Clement(4).Matrix(),
- evWant: Clement(4).Eigenvalues(),
- },
- {
- a: Clement(5).Matrix(),
- evWant: Clement(5).Eigenvalues(),
- },
- {
- a: Clement(10).Matrix(),
- evWant: Clement(10).Eigenvalues(),
- },
- {
- a: Clement(15).Matrix(),
- evWant: Clement(15).Eigenvalues(),
- },
- {
- a: Clement(30).Matrix(),
- evWant: Clement(30).Eigenvalues(),
- valTol: 1e-11,
- },
- {
- a: Clement(50).Matrix(),
- evWant: Clement(50).Eigenvalues(),
- valTol: 1e-7,
- vecTol: 1e-11,
- },
-
- {
- a: Creation(2).Matrix(),
- evWant: Creation(2).Eigenvalues(),
- },
- {
- a: Creation(3).Matrix(),
- evWant: Creation(3).Eigenvalues(),
- },
- {
- a: Creation(4).Matrix(),
- evWant: Creation(4).Eigenvalues(),
- },
- {
- a: Creation(5).Matrix(),
- evWant: Creation(5).Eigenvalues(),
- },
- {
- a: Creation(10).Matrix(),
- evWant: Creation(10).Eigenvalues(),
- },
- {
- a: Creation(15).Matrix(),
- evWant: Creation(15).Eigenvalues(),
- },
- {
- a: Creation(30).Matrix(),
- evWant: Creation(30).Eigenvalues(),
- },
- {
- a: Creation(50).Matrix(),
- evWant: Creation(50).Eigenvalues(),
- },
- {
- a: Creation(101).Matrix(),
- evWant: Creation(101).Eigenvalues(),
- },
- {
- a: Creation(150).Matrix(),
- evWant: Creation(150).Eigenvalues(),
- },
-
- {
- a: Diagonal(0).Matrix(),
- evWant: Diagonal(0).Eigenvalues(),
- },
- {
- a: Diagonal(10).Matrix(),
- evWant: Diagonal(10).Eigenvalues(),
- },
- {
- a: Diagonal(50).Matrix(),
- evWant: Diagonal(50).Eigenvalues(),
- },
- {
- a: Diagonal(151).Matrix(),
- evWant: Diagonal(151).Eigenvalues(),
- },
-
- {
- a: Downshift(2).Matrix(),
- evWant: Downshift(2).Eigenvalues(),
- },
- {
- a: Downshift(3).Matrix(),
- evWant: Downshift(3).Eigenvalues(),
- },
- {
- a: Downshift(4).Matrix(),
- evWant: Downshift(4).Eigenvalues(),
- },
- {
- a: Downshift(5).Matrix(),
- evWant: Downshift(5).Eigenvalues(),
- },
- {
- a: Downshift(10).Matrix(),
- evWant: Downshift(10).Eigenvalues(),
- },
- {
- a: Downshift(15).Matrix(),
- evWant: Downshift(15).Eigenvalues(),
- },
- {
- a: Downshift(30).Matrix(),
- evWant: Downshift(30).Eigenvalues(),
- },
- {
- a: Downshift(50).Matrix(),
- evWant: Downshift(50).Eigenvalues(),
- },
- {
- a: Downshift(101).Matrix(),
- evWant: Downshift(101).Eigenvalues(),
- },
- {
- a: Downshift(150).Matrix(),
- evWant: Downshift(150).Eigenvalues(),
- },
-
- {
- a: Fibonacci(2).Matrix(),
- evWant: Fibonacci(2).Eigenvalues(),
- },
- {
- a: Fibonacci(3).Matrix(),
- evWant: Fibonacci(3).Eigenvalues(),
- },
- {
- a: Fibonacci(4).Matrix(),
- evWant: Fibonacci(4).Eigenvalues(),
- },
- {
- a: Fibonacci(5).Matrix(),
- evWant: Fibonacci(5).Eigenvalues(),
- },
- {
- a: Fibonacci(10).Matrix(),
- evWant: Fibonacci(10).Eigenvalues(),
- },
- {
- a: Fibonacci(15).Matrix(),
- evWant: Fibonacci(15).Eigenvalues(),
- },
- {
- a: Fibonacci(30).Matrix(),
- evWant: Fibonacci(30).Eigenvalues(),
- },
- {
- a: Fibonacci(50).Matrix(),
- evWant: Fibonacci(50).Eigenvalues(),
- },
- {
- a: Fibonacci(101).Matrix(),
- evWant: Fibonacci(101).Eigenvalues(),
- },
- {
- a: Fibonacci(150).Matrix(),
- evWant: Fibonacci(150).Eigenvalues(),
- },
-
- {
- a: Gear(2).Matrix(),
- evWant: Gear(2).Eigenvalues(),
- },
- {
- a: Gear(3).Matrix(),
- evWant: Gear(3).Eigenvalues(),
- },
- {
- a: Gear(4).Matrix(),
- evWant: Gear(4).Eigenvalues(),
- valTol: 1e-7,
- },
- {
- a: Gear(5).Matrix(),
- evWant: Gear(5).Eigenvalues(),
- },
- {
- a: Gear(10).Matrix(),
- evWant: Gear(10).Eigenvalues(),
- valTol: 1e-8,
- },
- {
- a: Gear(15).Matrix(),
- evWant: Gear(15).Eigenvalues(),
- },
- {
- a: Gear(30).Matrix(),
- evWant: Gear(30).Eigenvalues(),
- valTol: 1e-8,
- },
- {
- a: Gear(50).Matrix(),
- evWant: Gear(50).Eigenvalues(),
- valTol: 1e-8,
- },
- {
- a: Gear(101).Matrix(),
- evWant: Gear(101).Eigenvalues(),
- },
- {
- a: Gear(150).Matrix(),
- evWant: Gear(150).Eigenvalues(),
- valTol: 1e-8,
- },
-
- {
- a: Grcar{N: 10, K: 3}.Matrix(),
- evWant: Grcar{N: 10, K: 3}.Eigenvalues(),
- },
- {
- a: Grcar{N: 10, K: 7}.Matrix(),
- evWant: Grcar{N: 10, K: 7}.Eigenvalues(),
- },
- {
- a: Grcar{N: 11, K: 7}.Matrix(),
- evWant: Grcar{N: 11, K: 7}.Eigenvalues(),
- },
- {
- a: Grcar{N: 50, K: 3}.Matrix(),
- evWant: Grcar{N: 50, K: 3}.Eigenvalues(),
- },
- {
- a: Grcar{N: 51, K: 3}.Matrix(),
- evWant: Grcar{N: 51, K: 3}.Eigenvalues(),
- },
- {
- a: Grcar{N: 50, K: 10}.Matrix(),
- evWant: Grcar{N: 50, K: 10}.Eigenvalues(),
- },
- {
- a: Grcar{N: 51, K: 10}.Matrix(),
- evWant: Grcar{N: 51, K: 10}.Eigenvalues(),
- },
- {
- a: Grcar{N: 50, K: 30}.Matrix(),
- evWant: Grcar{N: 50, K: 30}.Eigenvalues(),
- },
- {
- a: Grcar{N: 150, K: 2}.Matrix(),
- evWant: Grcar{N: 150, K: 2}.Eigenvalues(),
- },
- {
- a: Grcar{N: 150, K: 148}.Matrix(),
- evWant: Grcar{N: 150, K: 148}.Eigenvalues(),
- },
-
- {
- a: Hanowa{N: 6, Alpha: 17}.Matrix(),
- evWant: Hanowa{N: 6, Alpha: 17}.Eigenvalues(),
- },
- {
- a: Hanowa{N: 50, Alpha: -1}.Matrix(),
- evWant: Hanowa{N: 50, Alpha: -1}.Eigenvalues(),
- },
- {
- a: Hanowa{N: 100, Alpha: -1}.Matrix(),
- evWant: Hanowa{N: 100, Alpha: -1}.Eigenvalues(),
- },
-
- {
- a: Lesp(2).Matrix(),
- evWant: Lesp(2).Eigenvalues(),
- },
- {
- a: Lesp(3).Matrix(),
- evWant: Lesp(3).Eigenvalues(),
- },
- {
- a: Lesp(4).Matrix(),
- evWant: Lesp(4).Eigenvalues(),
- },
- {
- a: Lesp(5).Matrix(),
- evWant: Lesp(5).Eigenvalues(),
- },
- {
- a: Lesp(10).Matrix(),
- evWant: Lesp(10).Eigenvalues(),
- },
- {
- a: Lesp(15).Matrix(),
- evWant: Lesp(15).Eigenvalues(),
- },
- {
- a: Lesp(30).Matrix(),
- evWant: Lesp(30).Eigenvalues(),
- },
- {
- a: Lesp(50).Matrix(),
- evWant: Lesp(50).Eigenvalues(),
- valTol: 1e-12,
- vecTol: 1e-12,
- },
- {
- a: Lesp(101).Matrix(),
- evWant: Lesp(101).Eigenvalues(),
- valTol: 1e-12,
- vecTol: 1e-12,
- },
- {
- a: Lesp(150).Matrix(),
- evWant: Lesp(150).Eigenvalues(),
- valTol: 1e-12,
- vecTol: 1e-12,
- },
-
- {
- a: Rutis{}.Matrix(),
- evWant: Rutis{}.Eigenvalues(),
- },
-
- {
- a: Tris{N: 74, X: 1, Y: -2, Z: 1}.Matrix(),
- evWant: Tris{N: 74, X: 1, Y: -2, Z: 1}.Eigenvalues(),
- },
- {
- a: Tris{N: 74, X: 1, Y: 2, Z: -3}.Matrix(),
- evWant: Tris{N: 74, X: 1, Y: 2, Z: -3}.Eigenvalues(),
- },
- {
- a: Tris{N: 75, X: 1, Y: 2, Z: -3}.Matrix(),
- evWant: Tris{N: 75, X: 1, Y: 2, Z: -3}.Eigenvalues(),
- },
-
- {
- a: Wilk4{}.Matrix(),
- evWant: Wilk4{}.Eigenvalues(),
- },
- {
- a: Wilk12{}.Matrix(),
- evWant: Wilk12{}.Eigenvalues(),
- valTol: 1e-7,
- },
- {
- a: Wilk20(0).Matrix(),
- evWant: Wilk20(0).Eigenvalues(),
- },
- {
- a: Wilk20(1e-10).Matrix(),
- evWant: Wilk20(1e-10).Eigenvalues(),
- valTol: 1e-12,
- vecTol: 1e-12,
- },
-
- {
- a: Zero(1).Matrix(),
- evWant: Zero(1).Eigenvalues(),
- },
- {
- a: Zero(10).Matrix(),
- evWant: Zero(10).Eigenvalues(),
- },
- {
- a: Zero(50).Matrix(),
- evWant: Zero(50).Eigenvalues(),
- },
- {
- a: Zero(100).Matrix(),
- evWant: Zero(100).Eigenvalues(),
- },
- } {
- for _, jobvl := range []lapack.LeftEVJob{lapack.ComputeLeftEV, lapack.None} {
- for _, jobvr := range []lapack.RightEVJob{lapack.ComputeRightEV, lapack.None} {
- for _, extra := range []int{0, 11} {
- for _, wl := range []worklen{minimumWork, mediumWork, optimumWork} {
- testDgeev(t, impl, strconv.Itoa(i), test, jobvl, jobvr, extra, wl)
- }
- }
- }
- }
- }
-
- for _, n := range []int{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 50, 51, 100, 101} {
- for _, jobvl := range []lapack.LeftEVJob{lapack.ComputeLeftEV, lapack.None} {
- for _, jobvr := range []lapack.RightEVJob{lapack.ComputeRightEV, lapack.None} {
- for cas := 0; cas < 10; cas++ {
- // Create a block diagonal matrix with
- // random eigenvalues of random multiplicity.
- ev := make([]complex128, n)
- tmat := zeros(n, n, n)
- for i := 0; i < n; {
- re := rnd.NormFloat64()
- if i == n-1 || rnd.Float64() < 0.5 {
- // Real eigenvalue.
- nb := rnd.Intn(min(4, n-i)) + 1
- for k := 0; k < nb; k++ {
- tmat.Data[i*tmat.Stride+i] = re
- ev[i] = complex(re, 0)
- i++
- }
- continue
- }
- // Complex eigenvalue.
- im := rnd.NormFloat64()
- nb := rnd.Intn(min(4, (n-i)/2)) + 1
- for k := 0; k < nb; k++ {
- // 2×2 block for the complex eigenvalue.
- tmat.Data[i*tmat.Stride+i] = re
- tmat.Data[(i+1)*tmat.Stride+i+1] = re
- tmat.Data[(i+1)*tmat.Stride+i] = -im
- tmat.Data[i*tmat.Stride+i+1] = im
- ev[i] = complex(re, im)
- ev[i+1] = complex(re, -im)
- i += 2
- }
- }
-
- // Compute A = Q T Q^T where Q is an
- // orthogonal matrix.
- q := randomOrthogonal(n, rnd)
- tq := zeros(n, n, n)
- blas64.Gemm(blas.NoTrans, blas.Trans, 1, tmat, q, 0, tq)
- a := zeros(n, n, n)
- blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, q, tq, 0, a)
-
- test := dgeevTest{
- a: a,
- evWant: ev,
- valTol: 1e-12,
- vecTol: 1e-7,
- }
- testDgeev(t, impl, "random", test, jobvl, jobvr, 0, optimumWork)
- }
- }
- }
- }
-}
-
-func testDgeev(t *testing.T, impl Dgeever, tc string, test dgeevTest, jobvl lapack.LeftEVJob, jobvr lapack.RightEVJob, extra int, wl worklen) {
- const defaultTol = 1e-12
- valTol := test.valTol
- if valTol == 0 {
- valTol = defaultTol
- }
- vecTol := test.vecTol
- if vecTol == 0 {
- vecTol = defaultTol
- }
-
- a := cloneGeneral(test.a)
- n := a.Rows
-
- var vl blas64.General
- if jobvl == lapack.ComputeLeftEV {
- vl = nanGeneral(n, n, n)
- }
-
- var vr blas64.General
- if jobvr == lapack.ComputeRightEV {
- vr = nanGeneral(n, n, n)
- }
-
- wr := make([]float64, n)
- wi := make([]float64, n)
-
- var lwork int
- switch wl {
- case minimumWork:
- if jobvl == lapack.ComputeLeftEV || jobvr == lapack.ComputeRightEV {
- lwork = max(1, 4*n)
- } else {
- lwork = max(1, 3*n)
- }
- case mediumWork:
- work := make([]float64, 1)
- impl.Dgeev(jobvl, jobvr, n, nil, 1, nil, nil, nil, 1, nil, 1, work, -1)
- if jobvl == lapack.ComputeLeftEV || jobvr == lapack.ComputeRightEV {
- lwork = (int(work[0]) + 4*n) / 2
- } else {
- lwork = (int(work[0]) + 3*n) / 2
- }
- lwork = max(1, lwork)
- case optimumWork:
- work := make([]float64, 1)
- impl.Dgeev(jobvl, jobvr, n, nil, 1, nil, nil, nil, 1, nil, 1, work, -1)
- lwork = int(work[0])
- }
- work := make([]float64, lwork)
-
- first := impl.Dgeev(jobvl, jobvr, n, a.Data, a.Stride, wr, wi,
- vl.Data, vl.Stride, vr.Data, vr.Stride, work, len(work))
-
- prefix := fmt.Sprintf("Case #%v: n=%v, jobvl=%v, jobvr=%v, extra=%v, work=%v",
- tc, n, jobvl, jobvr, extra, wl)
-
- if !generalOutsideAllNaN(vl) {
- t.Errorf("%v: out-of-range write to VL", prefix)
- }
- if !generalOutsideAllNaN(vr) {
- t.Errorf("%v: out-of-range write to VR", prefix)
- }
-
- if first > 0 {
- t.Logf("%v: all eigenvalues haven't been computed, first=%v", prefix, first)
- }
-
- // Check that conjugate pair eigevalues are ordered correctly.
- for i := first; i < n; {
- if wi[i] == 0 {
- i++
- continue
- }
- if wr[i] != wr[i+1] {
- t.Errorf("%v: real parts of %vth conjugate pair not equal", prefix, i)
- }
- if wi[i] < 0 || wi[i+1] > 0 {
- t.Errorf("%v: unexpected ordering of %vth conjugate pair", prefix, i)
- }
- i += 2
- }
-
- // Check the computed eigenvalues against provided known eigenvalues.
- if test.evWant != nil {
- used := make([]bool, n)
- for i := first; i < n; i++ {
- evGot := complex(wr[i], wi[i])
- idx := -1
- for k, evWant := range test.evWant {
- if !used[k] && cmplx.Abs(evWant-evGot) < valTol {
- idx = k
- used[k] = true
- break
- }
- }
- if idx == -1 {
- t.Errorf("%v: unexpected eigenvalue %v", prefix, evGot)
- }
- }
- }
-
- if first > 0 || (jobvl == lapack.None && jobvr == lapack.None) {
- // No eigenvectors have been computed.
- return
- }
-
- // Check that the columns of VL and VR are eigenvectors that correspond
- // to the computed eigenvalues.
- for k := 0; k < n; {
- if wi[k] == 0 {
- if jobvl == lapack.ComputeLeftEV {
- ev := columnOf(vl, k)
- if !isLeftEigenvectorOf(test.a, ev, nil, complex(wr[k], 0), vecTol) {
- t.Errorf("%v: VL[:,%v] is not left real eigenvector",
- prefix, k)
- }
-
- norm := floats.Norm(ev, 2)
- if math.Abs(norm-1) >= defaultTol {
- t.Errorf("%v: norm of left real eigenvector %v not equal to 1: got %v",
- prefix, k, norm)
- }
- }
- if jobvr == lapack.ComputeRightEV {
- ev := columnOf(vr, k)
- if !isRightEigenvectorOf(test.a, ev, nil, complex(wr[k], 0), vecTol) {
- t.Errorf("%v: VR[:,%v] is not right real eigenvector",
- prefix, k)
- }
-
- norm := floats.Norm(ev, 2)
- if math.Abs(norm-1) >= defaultTol {
- t.Errorf("%v: norm of right real eigenvector %v not equal to 1: got %v",
- prefix, k, norm)
- }
- }
- k++
- } else {
- if jobvl == lapack.ComputeLeftEV {
- evre := columnOf(vl, k)
- evim := columnOf(vl, k+1)
- if !isLeftEigenvectorOf(test.a, evre, evim, complex(wr[k], wi[k]), vecTol) {
- t.Errorf("%v: VL[:,%v:%v] is not left complex eigenvector",
- prefix, k, k+1)
- }
- floats.Scale(-1, evim)
- if !isLeftEigenvectorOf(test.a, evre, evim, complex(wr[k+1], wi[k+1]), vecTol) {
- t.Errorf("%v: VL[:,%v:%v] is not left complex eigenvector",
- prefix, k, k+1)
- }
-
- norm := math.Hypot(floats.Norm(evre, 2), floats.Norm(evim, 2))
- if math.Abs(norm-1) > defaultTol {
- t.Errorf("%v: norm of left complex eigenvector %v not equal to 1: got %v",
- prefix, k, norm)
- }
- }
- if jobvr == lapack.ComputeRightEV {
- evre := columnOf(vr, k)
- evim := columnOf(vr, k+1)
- if !isRightEigenvectorOf(test.a, evre, evim, complex(wr[k], wi[k]), vecTol) {
- t.Errorf("%v: VR[:,%v:%v] is not right complex eigenvector",
- prefix, k, k+1)
- }
- floats.Scale(-1, evim)
- if !isRightEigenvectorOf(test.a, evre, evim, complex(wr[k+1], wi[k+1]), vecTol) {
- t.Errorf("%v: VR[:,%v:%v] is not right complex eigenvector",
- prefix, k, k+1)
- }
-
- norm := math.Hypot(floats.Norm(evre, 2), floats.Norm(evim, 2))
- if math.Abs(norm-1) > defaultTol {
- t.Errorf("%v: norm of right complex eigenvector %v not equal to 1: got %v",
- prefix, k, norm)
- }
- }
- // We don't test whether the largest component is real
- // because checking it is flaky due to rounding errors.
-
- k += 2
- }
- }
-}
-
-func dgeevTestForAntisymRandom(n int, rnd *rand.Rand) dgeevTest {
- a := NewAntisymRandom(n, rnd)
- return dgeevTest{
- a: a.Matrix(),
- evWant: a.Eigenvalues(),
- }
-}
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