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127 lines
3.5 KiB
Go
127 lines
3.5 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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"testing"
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"golang.org/x/exp/rand"
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"gonum.org/v1/gonum/blas"
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"gonum.org/v1/gonum/blas/blas64"
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"gonum.org/v1/gonum/lapack"
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)
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type Dlaqr5er interface {
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Dlaqr5(wantt, wantz bool, kacc22 int, n, ktop, kbot, nshfts int, sr, si []float64, h []float64, ldh int, iloz, ihiz int, z []float64, ldz int, v []float64, ldv int, u []float64, ldu int, nh int, wh []float64, ldwh int, nv int, wv []float64, ldwv int)
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}
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func Dlaqr5Test(t *testing.T, impl Dlaqr5er) {
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rnd := rand.New(rand.NewSource(1))
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for _, n := range []int{1, 2, 3, 4, 5, 6, 10, 30} {
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for _, extra := range []int{0, 1, 20} {
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for _, kacc22 := range []int{0, 1, 2} {
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for cas := 0; cas < 100; cas++ {
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testDlaqr5(t, impl, n, extra, kacc22, rnd)
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}
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}
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}
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}
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}
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func testDlaqr5(t *testing.T, impl Dlaqr5er, n, extra, kacc22 int, rnd *rand.Rand) {
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const tol = 1e-14
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wantt := true
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wantz := true
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nshfts := 2 * n
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sr := make([]float64, nshfts)
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si := make([]float64, nshfts)
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for i := 0; i < n; i++ {
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re := rnd.NormFloat64()
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im := rnd.NormFloat64()
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sr[2*i], sr[2*i+1] = re, re
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si[2*i], si[2*i+1] = im, -im
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}
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ktop := rnd.Intn(n)
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kbot := rnd.Intn(n)
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if kbot < ktop {
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ktop, kbot = kbot, ktop
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}
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v := randomGeneral(nshfts/2, 3, 3+extra, rnd)
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u := randomGeneral(3*nshfts-3, 3*nshfts-3, 3*nshfts-3+extra, rnd)
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nh := n
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wh := randomGeneral(3*nshfts-3, n, n+extra, rnd)
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nv := n
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wv := randomGeneral(n, 3*nshfts-3, 3*nshfts-3+extra, rnd)
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h := randomHessenberg(n, n+extra, rnd)
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if ktop > 0 {
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h.Data[ktop*h.Stride+ktop-1] = 0
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}
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if kbot < n-1 {
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h.Data[(kbot+1)*h.Stride+kbot] = 0
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}
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hCopy := h
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hCopy.Data = make([]float64, len(h.Data))
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copy(hCopy.Data, h.Data)
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z := eye(n, n+extra)
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impl.Dlaqr5(wantt, wantz, kacc22,
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n, ktop, kbot,
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nshfts, sr, si,
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h.Data, h.Stride,
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0, n-1, z.Data, z.Stride,
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v.Data, v.Stride,
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u.Data, u.Stride,
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nv, wv.Data, wv.Stride,
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nh, wh.Data, wh.Stride)
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prefix := fmt.Sprintf("Case n=%v, extra=%v, kacc22=%v", n, extra, kacc22)
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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 !generalOutsideAllNaN(u) {
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t.Errorf("%v: out-of-range write to U\n%v", prefix, u.Data)
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}
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if !generalOutsideAllNaN(v) {
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t.Errorf("%v: out-of-range write to V\n%v", prefix, v.Data)
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}
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if !generalOutsideAllNaN(wh) {
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t.Errorf("%v: out-of-range write to WH\n%v", prefix, wh.Data)
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}
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if !generalOutsideAllNaN(wv) {
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t.Errorf("%v: out-of-range write to WV\n%v", prefix, wv.Data)
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}
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for i := 0; i < n; i++ {
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for j := 0; j < i-1; j++ {
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if h.Data[i*h.Stride+j] != 0 {
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t.Errorf("%v: H is not Hessenberg, H[%v,%v]!=0", prefix, i, j)
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}
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}
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}
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// Check that Z is orthogonal.
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if resid := residualOrthogonal(z, false); resid > tol*float64(n) {
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t.Errorf("Case %v: Z is not orthogonal; resid=%v, want<=%v", prefix, resid, tol*float64(n))
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}
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// Check that |Zᵀ*HOrig*Z - H| is small where H is the result from Dlaqr5.
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hz := zeros(n, n, n)
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blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, hCopy, z, 0, hz)
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zhz := cloneGeneral(h)
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blas64.Gemm(blas.Trans, blas.NoTrans, 1, z, hz, -1, zhz)
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resid := dlange(lapack.MaxColumnSum, n, n, zhz.Data, zhz.Stride)
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if resid > tol*float64(n) {
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t.Errorf("%v: |Zᵀ*HOrig*Z - H|=%v, want<=%v", prefix, resid, tol*float64(n))
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}
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}
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