+++ /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"
- "testing"
-
- "golang.org/x/exp/rand"
-
- "gonum.org/v1/gonum/blas/blas64"
- "gonum.org/v1/gonum/floats"
- "gonum.org/v1/gonum/lapack"
-)
-
-type Dtrevc3er interface {
- Dtrevc3(side lapack.EVSide, howmny lapack.HowMany, selected []bool, n int, t []float64, ldt int, vl []float64, ldvl int, vr []float64, ldvr int, mm int, work []float64, lwork int) int
-}
-
-func Dtrevc3Test(t *testing.T, impl Dtrevc3er) {
- rnd := rand.New(rand.NewSource(1))
- for _, side := range []lapack.EVSide{lapack.RightEV, lapack.LeftEV, lapack.RightLeftEV} {
- for _, howmny := range []lapack.HowMany{lapack.AllEV, lapack.AllEVMulQ, lapack.SelectedEV} {
- for _, n := range []int{0, 1, 2, 3, 4, 5, 10, 34, 100} {
- for _, extra := range []int{0, 11} {
- for _, optwork := range []bool{true, false} {
- for cas := 0; cas < 10; cas++ {
- tmat := randomSchurCanonical(n, n+extra, rnd)
- testDtrevc3(t, impl, side, howmny, tmat, optwork, rnd)
- }
- }
- }
- }
- }
- }
-}
-
-func testDtrevc3(t *testing.T, impl Dtrevc3er, side lapack.EVSide, howmny lapack.HowMany, tmat blas64.General, optwork bool, rnd *rand.Rand) {
- const tol = 1e-14
-
- n := tmat.Rows
- extra := tmat.Stride - tmat.Cols
- right := side != lapack.LeftEV
- left := side != lapack.RightEV
-
- var selected, selectedWant []bool
- var mWant int // How many columns will the eigenvectors occupy.
- if howmny == lapack.SelectedEV {
- selected = make([]bool, n)
- selectedWant = make([]bool, n)
- // Dtrevc3 will compute only selected eigenvectors. Pick them
- // randomly disregarding whether they are real or complex.
- for i := range selected {
- if rnd.Float64() < 0.5 {
- selected[i] = true
- }
- }
- // Dtrevc3 will modify (standardize) the slice selected based on
- // whether the corresponding eigenvalues are real or complex. Do
- // the same process here to fill selectedWant.
- for i := 0; i < n; {
- if i == n-1 || tmat.Data[(i+1)*tmat.Stride+i] == 0 {
- // Real eigenvalue.
- if selected[i] {
- selectedWant[i] = true
- mWant++ // Real eigenvectors occupy one column.
- }
- i++
- } else {
- // Complex eigenvalue.
- if selected[i] || selected[i+1] {
- // Dtrevc3 will modify selected so that
- // only the first element of the pair is
- // true.
- selectedWant[i] = true
- mWant += 2 // Complex eigenvectors occupy two columns.
- }
- i += 2
- }
- }
- } else {
- // All eigenvectors occupy n columns.
- mWant = n
- }
-
- var vr blas64.General
- if right {
- if howmny == lapack.AllEVMulQ {
- vr = eye(n, n+extra)
- } else {
- // VR will be overwritten.
- vr = nanGeneral(n, mWant, n+extra)
- }
- }
-
- var vl blas64.General
- if left {
- if howmny == lapack.AllEVMulQ {
- vl = eye(n, n+extra)
- } else {
- // VL will be overwritten.
- vl = nanGeneral(n, mWant, n+extra)
- }
- }
-
- work := make([]float64, max(1, 3*n))
- if optwork {
- impl.Dtrevc3(side, howmny, nil, n, nil, 1, nil, 1, nil, 1, mWant, work, -1)
- work = make([]float64, int(work[0]))
- }
-
- m := impl.Dtrevc3(side, howmny, selected, n, tmat.Data, tmat.Stride,
- vl.Data, vl.Stride, vr.Data, vr.Stride, mWant, work, len(work))
-
- prefix := fmt.Sprintf("Case side=%v, howmny=%v, n=%v, extra=%v, optwk=%v",
- side, howmny, n, extra, optwork)
-
- if !generalOutsideAllNaN(tmat) {
- t.Errorf("%v: out-of-range write to T", prefix)
- }
- 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 m != mWant {
- t.Errorf("%v: unexpected value of m. Want %v, got %v", prefix, mWant, m)
- }
-
- if howmny == lapack.SelectedEV {
- for i := range selected {
- if selected[i] != selectedWant[i] {
- t.Errorf("%v: unexpected selected[%v]", prefix, i)
- }
- }
- }
-
- // Check that the columns of VR and VL are actually eigenvectors and
- // that the magnitude of their largest element is 1.
- var k int
- for j := 0; j < n; {
- re := tmat.Data[j*tmat.Stride+j]
- if j == n-1 || tmat.Data[(j+1)*tmat.Stride+j] == 0 {
- if howmny == lapack.SelectedEV && !selected[j] {
- j++
- continue
- }
- if right {
- ev := columnOf(vr, k)
- norm := floats.Norm(ev, math.Inf(1))
- if math.Abs(norm-1) > tol {
- t.Errorf("%v: magnitude of largest element of VR[:,%v] not 1", prefix, k)
- }
- if !isRightEigenvectorOf(tmat, ev, nil, complex(re, 0), tol) {
- t.Errorf("%v: VR[:,%v] is not real right eigenvector", prefix, k)
- }
- }
- if left {
- ev := columnOf(vl, k)
- norm := floats.Norm(ev, math.Inf(1))
- if math.Abs(norm-1) > tol {
- t.Errorf("%v: magnitude of largest element of VL[:,%v] not 1", prefix, k)
- }
- if !isLeftEigenvectorOf(tmat, ev, nil, complex(re, 0), tol) {
- t.Errorf("%v: VL[:,%v] is not real left eigenvector", prefix, k)
- }
- }
- k++
- j++
- continue
- }
- if howmny == lapack.SelectedEV && !selected[j] {
- j += 2
- continue
- }
- im := math.Sqrt(math.Abs(tmat.Data[(j+1)*tmat.Stride+j])) *
- math.Sqrt(math.Abs(tmat.Data[j*tmat.Stride+j+1]))
- if right {
- evre := columnOf(vr, k)
- evim := columnOf(vr, k+1)
- var evmax float64
- for i, v := range evre {
- evmax = math.Max(evmax, math.Abs(v)+math.Abs(evim[i]))
- }
- if math.Abs(evmax-1) > tol {
- t.Errorf("%v: magnitude of largest element of VR[:,%v] not 1", prefix, k)
- }
- if !isRightEigenvectorOf(tmat, evre, evim, complex(re, im), tol) {
- t.Errorf("%v: VR[:,%v:%v] is not complex right eigenvector", prefix, k, k+1)
- }
- floats.Scale(-1, evim)
- if !isRightEigenvectorOf(tmat, evre, evim, complex(re, -im), tol) {
- t.Errorf("%v: VR[:,%v:%v] is not complex right eigenvector", prefix, k, k+1)
- }
- }
- if left {
- evre := columnOf(vl, k)
- evim := columnOf(vl, k+1)
- var evmax float64
- for i, v := range evre {
- evmax = math.Max(evmax, math.Abs(v)+math.Abs(evim[i]))
- }
- if math.Abs(evmax-1) > tol {
- t.Errorf("%v: magnitude of largest element of VL[:,%v] not 1", prefix, k)
- }
- if !isLeftEigenvectorOf(tmat, evre, evim, complex(re, im), tol) {
- t.Errorf("%v: VL[:,%v:%v] is not complex left eigenvector", prefix, k, k+1)
- }
- floats.Scale(-1, evim)
- if !isLeftEigenvectorOf(tmat, evre, evim, complex(re, -im), tol) {
- t.Errorf("%v: VL[:,%v:%v] is not complex left eigenvector", prefix, k, k+1)
- }
- }
- k += 2
- j += 2
- }
-}
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