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// 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"
"testing"
"golang.org/x/exp/rand"
"gonum.org/v1/gonum/blas"
"gonum.org/v1/gonum/blas/blas64"
"gonum.org/v1/gonum/lapack"
)
type Dlaqr5er interface {
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)
}
func Dlaqr5Test(t *testing.T, impl Dlaqr5er) {
rnd := rand.New(rand.NewSource(1))
for _, n := range []int{1, 2, 3, 4, 5, 6, 10, 30} {
for _, extra := range []int{0, 1, 20} {
for _, kacc22 := range []int{0, 1, 2} {
for cas := 0; cas < 100; cas++ {
testDlaqr5(t, impl, n, extra, kacc22, rnd)
}
}
}
}
}
func testDlaqr5(t *testing.T, impl Dlaqr5er, n, extra, kacc22 int, rnd *rand.Rand) {
const tol = 1e-14
wantt := true
wantz := true
nshfts := 2 * n
sr := make([]float64, nshfts)
si := make([]float64, nshfts)
for i := 0; i < nshfts; {
if i == nshfts-1 || rnd.Float64() < 0.5 {
re := rnd.NormFloat64()
sr[i], si[i] = re, 0
i++
continue
}
re := rnd.NormFloat64()
im := rnd.NormFloat64()
sr[i], sr[i+1] = re, re
si[i], si[i+1] = im, -im
i += 2
}
ktop := rnd.Intn(n)
kbot := rnd.Intn(n)
if kbot < ktop {
ktop, kbot = kbot, ktop
}
v := randomGeneral(nshfts/2, 3, 3+extra, rnd)
u := randomGeneral(2*nshfts, 2*nshfts, 2*nshfts+extra, rnd)
nh := n
wh := randomGeneral(2*nshfts, n, n+extra, rnd)
nv := n
wv := randomGeneral(n, 2*nshfts, 2*nshfts+extra, rnd)
h := randomHessenberg(n, n+extra, rnd)
if ktop > 0 {
h.Data[ktop*h.Stride+ktop-1] = 0
}
if kbot < n-1 {
h.Data[(kbot+1)*h.Stride+kbot] = 0
}
hCopy := h
hCopy.Data = make([]float64, len(h.Data))
copy(hCopy.Data, h.Data)
z := eye(n, n+extra)
impl.Dlaqr5(wantt, wantz, kacc22,
n, ktop, kbot,
nshfts, sr, si,
h.Data, h.Stride,
0, n-1, z.Data, z.Stride,
v.Data, v.Stride,
u.Data, u.Stride,
nv, wv.Data, wv.Stride,
nh, wh.Data, wh.Stride)
prefix := fmt.Sprintf("Case n=%v, extra=%v, kacc22=%v", n, extra, kacc22)
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 !generalOutsideAllNaN(u) {
t.Errorf("%v: out-of-range write to U\n%v", prefix, u.Data)
}
if !generalOutsideAllNaN(v) {
t.Errorf("%v: out-of-range write to V\n%v", prefix, v.Data)
}
if !generalOutsideAllNaN(wh) {
t.Errorf("%v: out-of-range write to WH\n%v", prefix, wh.Data)
}
if !generalOutsideAllNaN(wv) {
t.Errorf("%v: out-of-range write to WV\n%v", prefix, wv.Data)
}
for i := 0; i < n; i++ {
for j := 0; j < i-1; j++ {
if h.Data[i*h.Stride+j] != 0 {
t.Errorf("%v: H is not Hessenberg, H[%v,%v]!=0", prefix, i, j)
}
}
}
// Check that Z is orthogonal.
if resid := residualOrthogonal(z, false); resid > tol*float64(n) {
t.Errorf("Case %v: Z is not orthogonal; resid=%v, want<=%v", prefix, resid, tol*float64(n))
}
// Check that |Zᵀ*HOrig*Z - H| is small where H is the result from Dlaqr5.
hz := zeros(n, n, n)
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, hCopy, z, 0, hz)
zhz := cloneGeneral(h)
blas64.Gemm(blas.Trans, blas.NoTrans, 1, z, hz, -1, zhz)
resid := dlange(lapack.MaxColumnSum, n, n, zhz.Data, zhz.Stride)
if resid > tol*float64(n) {
t.Errorf("%v: |Zᵀ*HOrig*Z - H|=%v, want<=%v", prefix, resid, tol*float64(n))
}
}
|
