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dlaqr23.go
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/
dlaqr23.go
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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 Dlaqr23er interface {
Dlaqr23(wantt, wantz bool, n, ktop, kbot, nw int, h []float64, ldh int, iloz, ihiz int, z []float64, ldz int, sr, si []float64, v []float64, ldv int, nh int, t []float64, ldt int, nv int, wv []float64, ldwv int, work []float64, lwork int, recur int) (ns, nd int)
}
type dlaqr23Test struct {
wantt, wantz bool
ktop, kbot int
nw int
h blas64.General
iloz, ihiz int
evWant []complex128 // Optional slice with known eigenvalues.
}
func newDlaqr23TestCase(wantt, wantz bool, n, ldh int, rnd *rand.Rand) dlaqr23Test {
// Generate the deflation window size.
var nw int
if n <= 75 {
// For small matrices any window size works because they will
// always use Dlahrq inside Dlaqr23.
nw = rnd.Intn(n) + 1
} else {
// For sufficiently large matrices generate a large enough
// window to assure that the Dlaqr4 path is taken.
nw = 76 + rnd.Intn(n-75)
}
// Generate a random Hessenberg matrix.
h := randomHessenberg(n, ldh, rnd)
// Generate the block limits of H on which Dlaqr23 will operate so that
// the restriction
// 0 <= nw <= kbot-ktop+1
// is satisfied.
ktop := rnd.Intn(n - nw + 1)
kbot := ktop + nw - 1
kbot += rnd.Intn(n - kbot)
// Make the block isolated by zeroing out the sub-diagonal elements.
if ktop-1 >= 0 {
h.Data[ktop*h.Stride+ktop-1] = 0
}
if kbot+1 < n {
h.Data[(kbot+1)*h.Stride+kbot] = 0
}
// Generate the rows of Z to which transformations will be applied if
// wantz is true.
iloz := rnd.Intn(ktop + 1)
ihiz := kbot + rnd.Intn(n-kbot)
return dlaqr23Test{
wantt: wantt,
wantz: wantz,
ktop: ktop,
kbot: kbot,
nw: nw,
h: h,
iloz: iloz,
ihiz: ihiz,
}
}
func Dlaqr23Test(t *testing.T, impl Dlaqr23er) {
rnd := rand.New(rand.NewSource(1))
// Randomized tests.
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, 100} {
for _, extra := range []int{0, 11} {
for cas := 0; cas < 10; cas++ {
test := newDlaqr23TestCase(wantt, wantz, n, n+extra, rnd)
testDlaqr23(t, impl, test, false, 1, rnd)
testDlaqr23(t, impl, test, true, 1, rnd)
testDlaqr23(t, impl, test, false, 0, rnd)
testDlaqr23(t, impl, test, true, 0, rnd)
}
}
}
}
}
// Tests with n=0.
for _, wantt := range []bool{true, false} {
for _, wantz := range []bool{true, false} {
for _, extra := range []int{0, 1, 11} {
test := dlaqr23Test{
wantt: wantt,
wantz: wantz,
h: randomHessenberg(0, extra, rnd),
ktop: 0,
kbot: -1,
iloz: 0,
ihiz: -1,
nw: 0,
}
testDlaqr23(t, impl, test, true, 1, rnd)
testDlaqr23(t, impl, test, false, 1, rnd)
testDlaqr23(t, impl, test, true, 0, rnd)
testDlaqr23(t, impl, test, false, 0, rnd)
}
}
}
// Tests with explicit eigenvalues computed by Octave.
for _, test := range []dlaqr23Test{
{
h: blas64.General{
Rows: 1,
Cols: 1,
Stride: 1,
Data: []float64{7.09965484086874e-1},
},
ktop: 0,
kbot: 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,
},
},
ktop: 0,
kbot: 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,
},
},
ktop: 0,
kbot: 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,
},
},
ktop: 1,
kbot: 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,
},
},
ktop: 0,
kbot: 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,
},
},
ktop: 0,
kbot: 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
test.nw = test.kbot - test.ktop + 1
testDlaqr23(t, impl, test, true, 1, rnd)
testDlaqr23(t, impl, test, false, 1, rnd)
testDlaqr23(t, impl, test, true, 0, rnd)
testDlaqr23(t, impl, test, false, 0, rnd)
}
}
func testDlaqr23(t *testing.T, impl Dlaqr23er, test dlaqr23Test, opt bool, recur int, rnd *rand.Rand) {
const tol = 1e-14
// Clone the test matrix to avoid modifying test data.
h := cloneGeneral(test.h)
// Extract test values to simplify notation.
n := h.Cols
extra := h.Stride - h.Cols
wantt := test.wantt
wantz := test.wantz
ktop := test.ktop
kbot := test.kbot
nw := test.nw
iloz := test.iloz
ihiz := test.ihiz
var z, zCopy blas64.General
if wantz {
// Using the identity matrix for Z is the easiest way to check
// that the transformation accumulated into it by Dlaqr23 is orthogonal.
z = eye(n, n+extra)
zCopy = cloneGeneral(z)
}
// Allocate slices for storing the converged eigenvalues, initially
// filled with NaN.
sr := nanSlice(kbot + 1)
si := nanSlice(kbot + 1)
// Allocate work matrices.
v := randomGeneral(nw, nw, nw+extra, rnd)
var nh int
if nw > 0 {
nh = nw + rnd.Intn(nw) // nh must be at least nw.
}
tmat := randomGeneral(nw, nh, nh+extra, rnd)
var nv int
if nw > 0 {
nv = rnd.Intn(nw) + 1
}
wv := randomGeneral(nv, nw, nw+extra, rnd)
var work []float64
if opt {
// Allocate work slice with optimal length.
work = nanSlice(1)
impl.Dlaqr23(wantt, wantz, n, ktop, kbot, nw, h.Data, h.Stride, iloz, ihiz, z.Data, max(1, z.Stride),
sr, si, v.Data, v.Stride, tmat.Cols, tmat.Data, tmat.Stride, wv.Rows, wv.Data, wv.Stride, work, -1, recur)
work = nanSlice(int(work[0]))
} else {
// Allocate work slice with minimum length.
work = nanSlice(max(1, 2*nw))
}
ns, nd := impl.Dlaqr23(wantt, wantz, n, ktop, kbot, nw, h.Data, h.Stride, iloz, ihiz, z.Data, max(1, z.Stride),
sr, si, v.Data, v.Stride, tmat.Cols, tmat.Data, tmat.Stride, wv.Rows, wv.Data, wv.Stride, work, len(work), recur)
prefix := fmt.Sprintf("Case wantt=%v, wantz=%v, n=%v, ktop=%v, kbot=%v, nw=%v, iloz=%v, ihiz=%v, extra=%v",
wantt, wantz, n, ktop, kbot, nw, 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 !generalOutsideAllNaN(v) {
t.Errorf("%v: out-of-range write to V\n%v", prefix, v.Data)
}
if !generalOutsideAllNaN(tmat) {
t.Errorf("%v: out-of-range write to T\n%v", prefix, tmat.Data)
}
if !generalOutsideAllNaN(wv) {
t.Errorf("%v: out-of-range write to WV\n%v", prefix, wv.Data)
}
if !isAllNaN(sr[:kbot-nd-ns+1]) || !isAllNaN(sr[kbot+1:]) {
t.Errorf("%v: out-of-range write to sr", prefix)
}
if !isAllNaN(si[:kbot-nd-ns+1]) || !isAllNaN(si[kbot+1:]) {
t.Errorf("%v: out-of-range write to si", prefix)
}
if !isUpperHessenberg(h) {
t.Errorf("%v: H is not upper Hessenberg", prefix)
}
if test.evWant != nil {
// Check all converged eigenvalues against known eigenvalues.
for i := kbot - nd + 1; i <= kbot; i++ {
ev := complex(sr[i], si[i])
found, _ := containsComplex(test.evWant, ev, tol)
if !found {
t.Errorf("%v: unexpected eigenvalue %v", prefix, ev)
}
}
}
// Checks below need the matrix Z.
if !wantz {
return
}
// Test whether the matrix Z was modified outside the given block.
var zmod bool
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
if z.Data[i*z.Stride+j] == zCopy.Data[i*zCopy.Stride+j] {
continue
}
if i < iloz || ihiz < i || j < kbot-nw+1 || kbot < j {
zmod = true
}
}
}
if zmod {
t.Errorf("%v: unexpected modification of Z", prefix)
}
// 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))
}
if wantt {
// Check that |Zᵀ*HOrig*Z - H| is small where H is the result from Dlaqr23.
hz := zeros(n, n, n)
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, test.h, z, 0, hz)
r := cloneGeneral(h)
blas64.Gemm(blas.Trans, blas.NoTrans, 1, z, hz, -1, r)
resid := dlange(lapack.MaxColumnSum, r.Rows, r.Cols, r.Data, r.Stride)
if resid > tol*float64(n) {
t.Errorf("%v: |Zᵀ*(initial H)*Z - (final H)|=%v, want<=%v", prefix, resid, tol*float64(n))
}
}
}