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7f0eabc5a2
Dlahqr must not (and does not) write into wr and wi beyond ihi, so it only makes sense to make the slices shorter. Dlaqr4 (the caller) will have the same restriction.
442 lines
10 KiB
Go
442 lines
10 KiB
Go
// Copyright ©2016 The gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package testlapack
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import (
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"fmt"
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"math"
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"math/rand"
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"testing"
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"github.com/gonum/blas"
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"github.com/gonum/blas/blas64"
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)
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type Dlahqrer interface {
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Dlahqr(wantt, wantz bool, n, ilo, ihi int, h []float64, ldh int, wr, wi []float64, iloz, ihiz int, z []float64, ldz int) int
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}
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type dlahqrTest struct {
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h blas64.General
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ilo, ihi int
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iloz, ihiz int
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wantt, wantz bool
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evWant []complex128 // Optional slice holding known eigenvalues.
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}
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func DlahqrTest(t *testing.T, impl Dlahqrer) {
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rnd := rand.New(rand.NewSource(1))
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// Tests that choose the [ilo:ihi+1,ilo:ihi+1] and
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// [iloz:ihiz+1,ilo:ihi+1] blocks randomly.
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for _, wantt := range []bool{true, false} {
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for _, wantz := range []bool{true, false} {
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for _, n := range []int{1, 2, 3, 4, 5, 6, 10, 18, 31, 53} {
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for _, extra := range []int{0, 1, 11} {
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for cas := 0; cas < 100; cas++ {
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ilo := rnd.Intn(n)
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ihi := rnd.Intn(n)
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if ilo > ihi {
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ilo, ihi = ihi, ilo
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}
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iloz := rnd.Intn(ilo + 1)
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ihiz := ihi + rnd.Intn(n-ihi)
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h := randomHessenberg(n, n+extra, rnd)
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if ilo-1 >= 0 {
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h.Data[ilo*h.Stride+ilo-1] = 0
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}
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if ihi+1 < n {
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h.Data[(ihi+1)*h.Stride+ihi] = 0
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}
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test := dlahqrTest{
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h: h,
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ilo: ilo,
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ihi: ihi,
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iloz: iloz,
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ihiz: ihiz,
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wantt: wantt,
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wantz: wantz,
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}
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testDlahqr(t, impl, test)
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}
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}
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}
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}
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}
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// Tests that make sure that some potentially problematic corner cases,
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// like zero-sized matrix, are covered.
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for _, wantt := range []bool{true, false} {
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for _, wantz := range []bool{true, false} {
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for _, extra := range []int{0, 1, 11} {
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for _, test := range []dlahqrTest{
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{
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h: randomHessenberg(0, extra, rnd),
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ilo: 0,
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ihi: -1,
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iloz: 0,
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ihiz: -1,
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},
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{
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h: randomHessenberg(1, 1+extra, rnd),
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ilo: 0,
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ihi: 0,
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iloz: 0,
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ihiz: 0,
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},
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{
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h: randomHessenberg(2, 2+extra, rnd),
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ilo: 1,
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ihi: 1,
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iloz: 1,
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ihiz: 1,
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},
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{
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h: randomHessenberg(2, 2+extra, rnd),
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ilo: 0,
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ihi: 1,
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iloz: 0,
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ihiz: 1,
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},
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{
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h: randomHessenberg(10, 10+extra, rnd),
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ilo: 0,
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ihi: 0,
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iloz: 0,
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ihiz: 0,
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},
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{
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h: randomHessenberg(10, 10+extra, rnd),
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ilo: 0,
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ihi: 9,
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iloz: 0,
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ihiz: 9,
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},
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{
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h: randomHessenberg(10, 10+extra, rnd),
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ilo: 0,
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ihi: 1,
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iloz: 0,
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ihiz: 1,
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},
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{
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h: randomHessenberg(10, 10+extra, rnd),
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ilo: 0,
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ihi: 1,
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iloz: 0,
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ihiz: 9,
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},
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{
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h: randomHessenberg(10, 10+extra, rnd),
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ilo: 9,
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ihi: 9,
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iloz: 0,
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ihiz: 9,
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},
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} {
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if test.ilo-1 >= 0 {
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test.h.Data[test.ilo*test.h.Stride+test.ilo-1] = 0
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}
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if test.ihi+1 < test.h.Rows {
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test.h.Data[(test.ihi+1)*test.h.Stride+test.ihi] = 0
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}
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test.wantt = wantt
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test.wantz = wantz
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testDlahqr(t, impl, test)
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}
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}
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}
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}
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// Tests with explicit eigenvalues computed by Octave.
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for _, test := range []dlahqrTest{
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{
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h: blas64.General{
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Rows: 1,
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Cols: 1,
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Stride: 1,
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Data: []float64{7.09965484086874e-1},
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},
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ilo: 0,
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ihi: 0,
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iloz: 0,
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ihiz: 0,
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evWant: []complex128{7.09965484086874e-1},
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},
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{
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h: blas64.General{
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Rows: 2,
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Cols: 2,
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Stride: 2,
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Data: []float64{
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0, -1,
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1, 0,
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},
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},
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ilo: 0,
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ihi: 1,
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iloz: 0,
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ihiz: 1,
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evWant: []complex128{1i, -1i},
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},
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{
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h: blas64.General{
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Rows: 2,
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Cols: 2,
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Stride: 2,
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Data: []float64{
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6.25219991450918e-1, 8.17510791994361e-1,
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3.31218891622294e-1, 1.24103744878131e-1,
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},
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},
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ilo: 0,
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ihi: 1,
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iloz: 0,
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ihiz: 1,
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evWant: []complex128{9.52203547663447e-1, -2.02879811334398e-1},
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},
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{
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h: blas64.General{
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Rows: 4,
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Cols: 4,
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Stride: 4,
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Data: []float64{
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1, 0, 0, 0,
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0, 6.25219991450918e-1, 8.17510791994361e-1, 0,
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0, 3.31218891622294e-1, 1.24103744878131e-1, 0,
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0, 0, 0, 1,
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},
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},
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ilo: 1,
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ihi: 2,
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iloz: 0,
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ihiz: 3,
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evWant: []complex128{9.52203547663447e-1, -2.02879811334398e-1},
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},
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{
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h: blas64.General{
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Rows: 2,
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Cols: 2,
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Stride: 2,
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Data: []float64{
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-1.1219562276608, 6.85473513349362e-1,
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-8.19951061145131e-1, 1.93728523178888e-1,
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},
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},
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ilo: 0,
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ihi: 1,
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iloz: 0,
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ihiz: 1,
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evWant: []complex128{
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-4.64113852240958e-1 + 3.59580510817350e-1i,
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-4.64113852240958e-1 - 3.59580510817350e-1i,
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},
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},
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{
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h: blas64.General{
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Rows: 5,
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Cols: 5,
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Stride: 5,
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Data: []float64{
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9.57590178533658e-1, -5.10651295522708e-1, 9.24974510015869e-1, -1.30016306879522e-1, 2.92601986926954e-2,
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-1.08084756637964, 1.77529701001213, -1.36480197632509, 2.23196371219601e-1, 1.12912853063308e-1,
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0, -8.44075612174676e-1, 1.067867614486, -2.55782915176399e-1, -2.00598563137468e-1,
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0, 0, -5.67097237165410e-1, 2.07205057427341e-1, 6.54998340743380e-1,
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0, 0, 0, -1.89441413886041e-1, -4.18125416021786e-1,
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},
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},
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ilo: 0,
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ihi: 4,
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iloz: 0,
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ihiz: 4,
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evWant: []complex128{
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2.94393309555622,
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4.97029793606701e-1 + 3.63041654992384e-1i,
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4.97029793606701e-1 - 3.63041654992384e-1i,
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-1.74079119166145e-1 + 2.01570009462092e-1i,
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-1.74079119166145e-1 - 2.01570009462092e-1i,
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},
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},
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} {
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test.wantt = true
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test.wantz = true
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testDlahqr(t, impl, test)
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}
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}
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func testDlahqr(t *testing.T, impl Dlahqrer, test dlahqrTest) {
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const tol = 1e-14
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h := cloneGeneral(test.h)
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n := h.Cols
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extra := h.Stride - h.Cols
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wantt := test.wantt
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wantz := test.wantz
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ilo := test.ilo
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ihi := test.ihi
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iloz := test.iloz
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ihiz := test.ihiz
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var z, zCopy blas64.General
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if wantz {
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z = eye(n, n+extra)
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zCopy = cloneGeneral(z)
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}
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wr := nanSlice(ihi + 1)
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wi := nanSlice(ihi + 1)
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unconverged := impl.Dlahqr(wantt, wantz, n, ilo, ihi, h.Data, h.Stride, wr, wi, iloz, ihiz, z.Data, z.Stride)
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prefix := fmt.Sprintf("Case wantt=%v, wantz=%v, n=%v, ilo=%v, ihi=%v, iloz=%v, ihiz=%v, extra=%v",
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wantt, wantz, n, ilo, ihi, iloz, ihiz, extra)
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if !generalOutsideAllNaN(h) {
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t.Errorf("%v: out-of-range write to H\n%v", prefix, h.Data)
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}
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if !generalOutsideAllNaN(z) {
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t.Errorf("%v: out-of-range write to Z\n%v", prefix, z.Data)
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}
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if !isUpperHessenberg(h) {
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t.Logf("%v: H is not Hessenberg", prefix)
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}
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start := ilo // Index of the first computed eigenvalue.
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if unconverged != 0 {
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start = unconverged
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if start == ihi+1 {
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t.Logf("%v: no eigenvalue has converged", prefix)
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}
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}
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// Check that wr and wi have not been modified outside [start:ihi+1].
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if !isAllNaN(wr[:start]) || !isAllNaN(wr[ihi+1:]) {
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t.Errorf("%v: unexpected modification of wr", prefix)
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}
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if !isAllNaN(wi[:start]) || !isAllNaN(wi[ihi+1:]) {
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t.Errorf("%v: unexpected modification of wi", prefix)
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}
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var hasReal bool
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for i := start; i <= ihi; {
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if wi[i] == 0 { // Real eigenvalue.
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hasReal = true
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// Check that the eigenvalue corresponds to a 1×1 block
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// on the diagonal of H.
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if wantt {
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if wr[i] != h.Data[i*h.Stride+i] {
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t.Errorf("%v: wr[%v] != H[%v,%v]", prefix, i, i, i)
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}
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for _, index := range []struct{ r, c int }{
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{i, i - 1}, // h h h
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{i + 1, i - 1}, // 0 wr[i] h
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{i + 1, i}, // 0 0 h
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} {
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if index.r >= n || index.c < 0 {
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continue
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}
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if h.Data[index.r*h.Stride+index.c] != 0 {
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t.Errorf("%v: H[%v,%v] != 0", prefix, index.r, index.c)
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}
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}
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}
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i++
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continue
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}
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// Complex eigenvalue.
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// In the conjugate pair the real parts must be equal.
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if wr[i] != wr[i+1] {
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t.Errorf("%v: real part of conjugate pair not equal, i=%v", prefix, i)
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}
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// The first imaginary part must be positive.
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if wi[i] < 0 {
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t.Errorf("%v: wi[%v] not positive", prefix, i)
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}
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// The second imaginary part must be negative with the same
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// magnitude.
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if wi[i] != -wi[i+1] {
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t.Errorf("%v: wi[%v] != wi[%v]", prefix, i, i+1)
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}
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if wantt {
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// Check that wi[i] has the correct value.
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if wr[i] != h.Data[i*h.Stride+i] {
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t.Errorf("%v: wr[%v] != H[%v,%v]", prefix, i, i, i)
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}
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if wr[i] != h.Data[(i+1)*h.Stride+i+1] {
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t.Errorf("%v: wr[%v] != H[%v,%v]", prefix, i, i+1, i+1)
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}
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prod := math.Abs(h.Data[(i+1)*h.Stride+i] * h.Data[i*h.Stride+i+1])
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if math.Abs(math.Sqrt(prod)-wi[i]) > tol {
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t.Errorf("%v: unexpected value of wi[%v]: want %v, got %v", prefix, i, math.Sqrt(prod), wi[i])
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}
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// Check that the corresponding diagonal block is 2×2.
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for _, index := range []struct{ r, c int }{
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{i, i - 1}, // i
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{i + 1, i - 1}, // h h h h
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{i + 2, i - 1}, // 0 wr[i] b h i
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{i + 2, i}, // 0 c wr[i+1] h
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{i + 2, i + 1}, // 0 0 0 h
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} {
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if index.r >= n || index.c < 0 {
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continue
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}
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if h.Data[index.r*h.Stride+index.c] != 0 {
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t.Errorf("%v: H[%v,%v] != 0", prefix, index.r, index.c)
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}
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}
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}
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i += 2
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}
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// If the number of found eigenvalues is odd, at least one must be real.
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if (ihi+1-start)%2 != 0 && !hasReal {
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t.Errorf("%v: expected at least one real eigenvalue", prefix)
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}
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// Compare found eigenvalues to the reference, if known.
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if test.evWant != nil {
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for i := start; i <= ihi; i++ {
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ev := complex(wr[i], wi[i])
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if !containsComplex(test.evWant, ev, tol) {
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t.Log(test.evWant, ev)
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t.Errorf("%v: unexpected eigenvalue %v", prefix, ev)
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}
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}
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}
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if !wantz {
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return
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}
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// Z should contain the orthogonal matrix U.
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if !isOrthonormal(z) {
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t.Errorf("%v: Z is not orthogonal", prefix)
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}
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// Z should have been modified only in the
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// [iloz:ihiz+1,ilo:ihi+1] block.
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for i := 0; i < n; i++ {
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for j := 0; j < n; j++ {
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if iloz <= i && i <= ihiz && ilo <= j && j <= ihi {
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continue
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}
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if z.Data[i*z.Stride+j] != zCopy.Data[i*zCopy.Stride+j] {
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t.Errorf("%v: Z modified outside of [iloz:ihiz+1,ilo:ihi+1] block", prefix)
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}
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}
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}
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if wantt {
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hu := eye(n, n)
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blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, test.h, z, 0, hu)
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uhu := eye(n, n)
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blas64.Gemm(blas.Trans, blas.NoTrans, 1, z, hu, 0, uhu)
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if !equalApproxGeneral(uhu, h, 10*tol) {
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t.Errorf("%v: Z^T*(initial H)*Z and (final H) are not equal", prefix)
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}
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}
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}
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