--- /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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