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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. | ||
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package testlapack | ||
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import ( | ||
"fmt" | ||
"math" | ||
"math/rand" | ||
"testing" | ||
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"github.com/gonum/blas/blas64" | ||
) | ||
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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 | ||
} | ||
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func DlahqrTest(t *testing.T, impl Dlahqrer) { | ||
rnd := rand.New(rand.NewSource(1)) | ||
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 < 10; 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) | ||
testDlahqr(t, impl, wantt, wantz, n, ilo, ihi, iloz, ihiz, extra, rnd) | ||
} | ||
} | ||
} | ||
} | ||
} | ||
for _, wantt := range []bool{true, false} { | ||
for _, wantz := range []bool{true, false} { | ||
testDlahqr(t, impl, wantt, wantz, 0, 0, -1, 0, -1, 0, rnd) | ||
} | ||
} | ||
} | ||
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func testDlahqr(t *testing.T, impl Dlahqrer, wantt, wantz bool, n, ilo, ihi, iloz, ihiz, extra int, rnd *rand.Rand) { | ||
const tol = 1e-14 | ||
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var z, zCopy blas64.General | ||
if wantz { | ||
z = eye(n, n+extra) | ||
zCopy = cloneGeneral(z) | ||
} | ||
h := randomHessenberg(n, n+extra, rnd) | ||
if ilo > 0 { | ||
h.Data[ilo*h.Stride+ilo-1] = 0 | ||
} | ||
wr := nanSlice(n) | ||
wi := nanSlice(n) | ||
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info := 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 n=%v, ilo=%v, ihi=%v, iloz=%v, ihiz=%v, wantt=%v, wantz=%v, extra=%v", n, ilo, ihi, iloz, ihiz, wantt, wantz, extra) | ||
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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) | ||
} | ||
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if wantz { | ||
// 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) | ||
} | ||
} | ||
} | ||
} | ||
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start := ilo | ||
if info > 0 { | ||
start = info + 1 | ||
} | ||
// Check that wr and wi have not been modified outside [start:ihi+1]. | ||
for _, v := range wr[:start] { | ||
if !math.IsNaN(v) { | ||
t.Errorf("%v: wr modified before [ilo:ihiz+1] block", prefix) | ||
} | ||
} | ||
for _, v := range wr[ihi+1:] { | ||
if !math.IsNaN(v) { | ||
t.Errorf("%v: wr modified after [ilo:ihiz+1] block", prefix) | ||
} | ||
} | ||
for _, v := range wi[:start] { | ||
if !math.IsNaN(v) { | ||
t.Errorf("%v: wi modified before [ilo:ihiz+1] block", prefix) | ||
} | ||
} | ||
for _, v := range wi[ihi+1:] { | ||
if !math.IsNaN(v) { | ||
t.Errorf("%v: wi modified after [ilo:ihiz+1] block", prefix) | ||
} | ||
} | ||
var nReal int | ||
for i := start; i <= ihi; { | ||
if wi[i] == 0 { | ||
// A real eigenvalue. | ||
nReal++ | ||
if wantt && wr[i] != h.Data[i*h.Stride+i] { | ||
t.Errorf("%v: wr[%v] != H[%v,%v]", prefix, i, i, i) | ||
} | ||
if i > 0 && h.Data[i*h.Stride+i-1] != 0 { | ||
t.Errorf("%v: H[%v,%v] != 0", prefix, i, i-1) | ||
} | ||
if i < ihi && h.Data[(i+1)*h.Stride+i] != 0 { | ||
t.Errorf("%v: H[%v,%v] != 0", prefix, i+1, i) | ||
} | ||
i++ | ||
continue | ||
} | ||
// Complex eigenvalue. | ||
if wr[i] != wr[i+1] { | ||
t.Errorf("%v: real part of conjugate pair not equal, i=%v", prefix, i) | ||
} | ||
if wi[i] < 0 { | ||
t.Errorf("%v: wi[%v] not positive", prefix, i) | ||
} | ||
if wi[i] != -wi[i+1] { | ||
t.Errorf("%v: wi[%v] != wi[%v]", prefix, i, i+1) | ||
} | ||
prod := math.Abs(h.Data[(i+1)*h.Stride+i] * h.Data[i*h.Stride+i+1]) | ||
if wantt && math.Abs(math.Sqrt(prod)-wi[0]) > tol { | ||
t.Errorf("%v: unexpected value of wi[%v]: want %v, got %v", prefix, i, math.Sqrt(prod), wi[i]) | ||
} | ||
if i > 0 && h.Data[i*h.Stride+i-1] != 0 { | ||
t.Errorf("%v: H[%v,%v] != 0", prefix, i, i-1) | ||
} | ||
if i < ihi-1 && h.Data[(i+2)*h.Stride+i+1] != 0 { | ||
t.Errorf("%v: H[%v,%v] != 0", prefix, i+2, i+1) | ||
} | ||
i += 2 | ||
} | ||
if (ihi+1-start)%2 != 0 && nReal == 0 { | ||
t.Errorf("%v: expected at least one real eigenvalue", prefix) | ||
} | ||
} |