+++ /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"
- "gonum.org/v1/gonum/blas/blas64"
-)
-
-type Dlahqrer interface {
- Dlahqr(wantt, wantz bool, n, ilo, ihi int, h []float64, ldh int, wr, wi []float64, iloz, ihiz int, z []float64, ldz int) int
-}
-
-type dlahqrTest struct {
- h blas64.General
- ilo, ihi int
- iloz, ihiz int
- wantt, wantz bool
-
- evWant []complex128 // Optional slice holding known eigenvalues.
-}
-
-func DlahqrTest(t *testing.T, impl Dlahqrer) {
- rnd := rand.New(rand.NewSource(1))
-
- // Tests that choose the [ilo:ihi+1,ilo:ihi+1] and
- // [iloz:ihiz+1,ilo:ihi+1] blocks randomly.
- for _, wantt := range []bool{true, false} {
- for _, wantz := range []bool{true, false} {
- for _, n := range []int{1, 2, 3, 4, 5, 6, 10, 18, 31, 53} {
- for _, extra := range []int{0, 1, 11} {
- for cas := 0; cas < 100; cas++ {
- ilo := rnd.Intn(n)
- ihi := rnd.Intn(n)
- if ilo > ihi {
- ilo, ihi = ihi, ilo
- }
- iloz := rnd.Intn(ilo + 1)
- ihiz := ihi + rnd.Intn(n-ihi)
- h := randomHessenberg(n, n+extra, rnd)
- if ilo-1 >= 0 {
- h.Data[ilo*h.Stride+ilo-1] = 0
- }
- if ihi+1 < n {
- h.Data[(ihi+1)*h.Stride+ihi] = 0
- }
- test := dlahqrTest{
- h: h,
- ilo: ilo,
- ihi: ihi,
- iloz: iloz,
- ihiz: ihiz,
- wantt: wantt,
- wantz: wantz,
- }
- testDlahqr(t, impl, test)
- }
- }
- }
- }
- }
- // Tests that make sure that some potentially problematic corner cases,
- // like zero-sized matrix, are covered.
- for _, wantt := range []bool{true, false} {
- for _, wantz := range []bool{true, false} {
- for _, extra := range []int{0, 1, 11} {
- for _, test := range []dlahqrTest{
- {
- h: randomHessenberg(0, extra, rnd),
- ilo: 0,
- ihi: -1,
- iloz: 0,
- ihiz: -1,
- },
- {
- h: randomHessenberg(1, 1+extra, rnd),
- ilo: 0,
- ihi: 0,
- iloz: 0,
- ihiz: 0,
- },
- {
- h: randomHessenberg(2, 2+extra, rnd),
- ilo: 1,
- ihi: 1,
- iloz: 1,
- ihiz: 1,
- },
- {
- h: randomHessenberg(2, 2+extra, rnd),
- ilo: 0,
- ihi: 1,
- iloz: 0,
- ihiz: 1,
- },
- {
- h: randomHessenberg(10, 10+extra, rnd),
- ilo: 0,
- ihi: 0,
- iloz: 0,
- ihiz: 0,
- },
- {
- h: randomHessenberg(10, 10+extra, rnd),
- ilo: 0,
- ihi: 9,
- iloz: 0,
- ihiz: 9,
- },
- {
- h: randomHessenberg(10, 10+extra, rnd),
- ilo: 0,
- ihi: 1,
- iloz: 0,
- ihiz: 1,
- },
- {
- h: randomHessenberg(10, 10+extra, rnd),
- ilo: 0,
- ihi: 1,
- iloz: 0,
- ihiz: 9,
- },
- {
- h: randomHessenberg(10, 10+extra, rnd),
- ilo: 9,
- ihi: 9,
- iloz: 0,
- ihiz: 9,
- },
- } {
- if test.ilo-1 >= 0 {
- test.h.Data[test.ilo*test.h.Stride+test.ilo-1] = 0
- }
- if test.ihi+1 < test.h.Rows {
- test.h.Data[(test.ihi+1)*test.h.Stride+test.ihi] = 0
- }
- test.wantt = wantt
- test.wantz = wantz
- testDlahqr(t, impl, test)
- }
- }
- }
- }
-
- // Tests with explicit eigenvalues computed by Octave.
- for _, test := range []dlahqrTest{
- {
- h: blas64.General{
- Rows: 1,
- Cols: 1,
- Stride: 1,
- Data: []float64{7.09965484086874e-1},
- },
- ilo: 0,
- ihi: 0,
- iloz: 0,
- ihiz: 0,
- evWant: []complex128{7.09965484086874e-1},
- },
- {
- h: blas64.General{
- Rows: 2,
- Cols: 2,
- Stride: 2,
- Data: []float64{
- 0, -1,
- 1, 0,
- },
- },
- ilo: 0,
- ihi: 1,
- iloz: 0,
- ihiz: 1,
- evWant: []complex128{1i, -1i},
- },
- {
- h: blas64.General{
- Rows: 2,
- Cols: 2,
- Stride: 2,
- Data: []float64{
- 6.25219991450918e-1, 8.17510791994361e-1,
- 3.31218891622294e-1, 1.24103744878131e-1,
- },
- },
- ilo: 0,
- ihi: 1,
- iloz: 0,
- ihiz: 1,
- evWant: []complex128{9.52203547663447e-1, -2.02879811334398e-1},
- },
- {
- h: blas64.General{
- Rows: 4,
- Cols: 4,
- Stride: 4,
- Data: []float64{
- 1, 0, 0, 0,
- 0, 6.25219991450918e-1, 8.17510791994361e-1, 0,
- 0, 3.31218891622294e-1, 1.24103744878131e-1, 0,
- 0, 0, 0, 1,
- },
- },
- ilo: 1,
- ihi: 2,
- iloz: 0,
- ihiz: 3,
- evWant: []complex128{9.52203547663447e-1, -2.02879811334398e-1},
- },
- {
- h: blas64.General{
- Rows: 2,
- Cols: 2,
- Stride: 2,
- Data: []float64{
- -1.1219562276608, 6.85473513349362e-1,
- -8.19951061145131e-1, 1.93728523178888e-1,
- },
- },
- ilo: 0,
- ihi: 1,
- iloz: 0,
- ihiz: 1,
- evWant: []complex128{
- -4.64113852240958e-1 + 3.59580510817350e-1i,
- -4.64113852240958e-1 - 3.59580510817350e-1i,
- },
- },
- {
- h: blas64.General{
- Rows: 5,
- Cols: 5,
- Stride: 5,
- Data: []float64{
- 9.57590178533658e-1, -5.10651295522708e-1, 9.24974510015869e-1, -1.30016306879522e-1, 2.92601986926954e-2,
- -1.08084756637964, 1.77529701001213, -1.36480197632509, 2.23196371219601e-1, 1.12912853063308e-1,
- 0, -8.44075612174676e-1, 1.067867614486, -2.55782915176399e-1, -2.00598563137468e-1,
- 0, 0, -5.67097237165410e-1, 2.07205057427341e-1, 6.54998340743380e-1,
- 0, 0, 0, -1.89441413886041e-1, -4.18125416021786e-1,
- },
- },
- ilo: 0,
- ihi: 4,
- iloz: 0,
- ihiz: 4,
- evWant: []complex128{
- 2.94393309555622,
- 4.97029793606701e-1 + 3.63041654992384e-1i,
- 4.97029793606701e-1 - 3.63041654992384e-1i,
- -1.74079119166145e-1 + 2.01570009462092e-1i,
- -1.74079119166145e-1 - 2.01570009462092e-1i,
- },
- },
- } {
- test.wantt = true
- test.wantz = true
- testDlahqr(t, impl, test)
- }
-}
-
-func testDlahqr(t *testing.T, impl Dlahqrer, test dlahqrTest) {
- const tol = 1e-14
-
- h := cloneGeneral(test.h)
- n := h.Cols
- extra := h.Stride - h.Cols
- wantt := test.wantt
- wantz := test.wantz
- ilo := test.ilo
- ihi := test.ihi
- iloz := test.iloz
- ihiz := test.ihiz
-
- var z, zCopy blas64.General
- if wantz {
- z = eye(n, n+extra)
- zCopy = cloneGeneral(z)
- }
-
- wr := nanSlice(ihi + 1)
- wi := nanSlice(ihi + 1)
-
- unconverged := impl.Dlahqr(wantt, wantz, n, ilo, ihi, h.Data, h.Stride, wr, wi, iloz, ihiz, z.Data, z.Stride)
-
- prefix := fmt.Sprintf("Case wantt=%v, wantz=%v, n=%v, ilo=%v, ihi=%v, iloz=%v, ihiz=%v, extra=%v",
- wantt, wantz, n, ilo, ihi, iloz, ihiz, extra)
-
- if !generalOutsideAllNaN(h) {
- t.Errorf("%v: out-of-range write to H\n%v", prefix, h.Data)
- }
- if !generalOutsideAllNaN(z) {
- t.Errorf("%v: out-of-range write to Z\n%v", prefix, z.Data)
- }
-
- if !isUpperHessenberg(h) {
- t.Logf("%v: H is not Hessenberg", prefix)
- }
-
- start := ilo // Index of the first computed eigenvalue.
- if unconverged != 0 {
- start = unconverged
- if start == ihi+1 {
- t.Logf("%v: no eigenvalue has converged", prefix)
- }
- }
-
- // Check that wr and wi have not been modified in [:start].
- if !isAllNaN(wr[:start]) {
- t.Errorf("%v: unexpected modification of wr", prefix)
- }
- if !isAllNaN(wi[:start]) {
- t.Errorf("%v: unexpected modification of wi", prefix)
- }
-
- var hasReal bool
- for i := start; i <= ihi; {
- if wi[i] == 0 { // Real eigenvalue.
- hasReal = true
- // Check that the eigenvalue corresponds to a 1×1 block
- // on the diagonal of H.
- if wantt {
- if wr[i] != h.Data[i*h.Stride+i] {
- t.Errorf("%v: wr[%v] != H[%v,%v]", prefix, i, i, i)
- }
- for _, index := range []struct{ r, c int }{
- {i, i - 1}, // h h h
- {i + 1, i - 1}, // 0 wr[i] h
- {i + 1, i}, // 0 0 h
- } {
- if index.r >= n || index.c < 0 {
- continue
- }
- if h.Data[index.r*h.Stride+index.c] != 0 {
- t.Errorf("%v: H[%v,%v] != 0", prefix, index.r, index.c)
- }
- }
- }
- i++
- continue
- }
-
- // Complex eigenvalue.
-
- // In the conjugate pair the real parts must be equal.
- if wr[i] != wr[i+1] {
- t.Errorf("%v: real part of conjugate pair not equal, i=%v", prefix, i)
- }
- // The first imaginary part must be positive.
- if wi[i] < 0 {
- t.Errorf("%v: wi[%v] not positive", prefix, i)
- }
- // The second imaginary part must be negative with the same
- // magnitude.
- if wi[i] != -wi[i+1] {
- t.Errorf("%v: wi[%v] != -wi[%v]", prefix, i, i+1)
- }
- if wantt {
- // Check that wi[i] has the correct value.
- if wr[i] != h.Data[i*h.Stride+i] {
- t.Errorf("%v: wr[%v] != H[%v,%v]", prefix, i, i, i)
- }
- if wr[i] != h.Data[(i+1)*h.Stride+i+1] {
- t.Errorf("%v: wr[%v] != H[%v,%v]", prefix, i, i+1, i+1)
- }
- prod := math.Abs(h.Data[(i+1)*h.Stride+i] * h.Data[i*h.Stride+i+1])
- if math.Abs(math.Sqrt(prod)-wi[i]) > tol {
- t.Errorf("%v: unexpected value of wi[%v]: want %v, got %v", prefix, i, math.Sqrt(prod), wi[i])
- }
-
- // Check that the corresponding diagonal block is 2×2.
- for _, index := range []struct{ r, c int }{
- {i, i - 1}, // i
- {i + 1, i - 1}, // h h h h
- {i + 2, i - 1}, // 0 wr[i] b h i
- {i + 2, i}, // 0 c wr[i+1] h
- {i + 2, i + 1}, // 0 0 0 h
- } {
- if index.r >= n || index.c < 0 {
- continue
- }
- if h.Data[index.r*h.Stride+index.c] != 0 {
- t.Errorf("%v: H[%v,%v] != 0", prefix, index.r, index.c)
- }
- }
- }
- i += 2
- }
- // If the number of found eigenvalues is odd, at least one must be real.
- if (ihi+1-start)%2 != 0 && !hasReal {
- t.Errorf("%v: expected at least one real eigenvalue", prefix)
- }
-
- // Compare found eigenvalues to the reference, if known.
- if test.evWant != nil {
- for i := start; i <= ihi; i++ {
- ev := complex(wr[i], wi[i])
- found, _ := containsComplex(test.evWant, ev, tol)
- if !found {
- t.Errorf("%v: unexpected eigenvalue %v", prefix, ev)
- }
- }
- }
-
- if !wantz {
- return
- }
-
- // Z should contain the orthogonal matrix U.
- if !isOrthonormal(z) {
- t.Errorf("%v: Z is not orthogonal", prefix)
- }
- // Z should have been modified only in the
- // [iloz:ihiz+1,ilo:ihi+1] block.
- for i := 0; i < n; i++ {
- for j := 0; j < n; j++ {
- if iloz <= i && i <= ihiz && ilo <= j && j <= ihi {
- continue
- }
- if z.Data[i*z.Stride+j] != zCopy.Data[i*zCopy.Stride+j] {
- t.Errorf("%v: Z modified outside of [iloz:ihiz+1,ilo:ihi+1] block", prefix)
- }
- }
- }
- if wantt {
- hu := eye(n, n)
- blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, test.h, z, 0, hu)
- uhu := eye(n, n)
- blas64.Gemm(blas.Trans, blas.NoTrans, 1, z, hu, 0, uhu)
- if !equalApproxGeneral(uhu, h, 10*tol) {
- t.Errorf("%v: Z^T*(initial H)*Z and (final H) are not equal", prefix)
- }
- }
-}
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