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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 Dtrexcer interface {
Dtrexc(compq lapack.UpdateSchurComp, n int, t []float64, ldt int, q []float64, ldq int, ifst, ilst int, work []float64) (ifstOut, ilstOut int, ok bool)
}
func DtrexcTest(t *testing.T, impl Dtrexcer) {
rnd := rand.New(rand.NewSource(1))
for _, n := range []int{0, 1, 2, 3, 4, 5, 6, 10, 18, 31, 53} {
for _, extra := range []int{0, 3} {
for cas := 0; cas < 100; cas++ {
var ifst, ilst int
if n > 0 {
ifst = rnd.Intn(n)
ilst = rnd.Intn(n)
}
dtrexcTest(t, impl, rnd, n, ifst, ilst, extra)
}
}
}
}
func dtrexcTest(t *testing.T, impl Dtrexcer, rnd *rand.Rand, n, ifst, ilst, extra int) {
const tol = 1e-13
tmat, _, _ := randomSchurCanonical(n, n+extra, true, rnd)
tmatCopy := cloneGeneral(tmat)
fstSize, fstFirst := schurBlockSize(tmat, ifst)
lstSize, lstFirst := schurBlockSize(tmat, ilst)
name := fmt.Sprintf("Case n=%v,ifst=%v,nbfst=%v,ilst=%v,nblst=%v,extra=%v",
n, ifst, fstSize, ilst, lstSize, extra)
// 1. Test without accumulating Q.
compq := lapack.UpdateSchurNone
work := nanSlice(n)
ifstGot, ilstGot, ok := impl.Dtrexc(compq, n, tmat.Data, tmat.Stride, nil, 1, ifst, ilst, work)
if !generalOutsideAllNaN(tmat) {
t.Errorf("%v: out-of-range write to T", name)
}
// 2. Test with accumulating Q.
compq = lapack.UpdateSchur
tmat2 := cloneGeneral(tmatCopy)
q := eye(n, n+extra)
qCopy := cloneGeneral(q)
work = nanSlice(n)
ifstGot2, ilstGot2, ok2 := impl.Dtrexc(compq, n, tmat2.Data, tmat2.Stride, q.Data, q.Stride, ifst, ilst, work)
if !generalOutsideAllNaN(tmat2) {
t.Errorf("%v: out-of-range write to T2", name)
}
if !generalOutsideAllNaN(q) {
t.Errorf("%v: out-of-range write to Q", name)
}
// Check that outputs from cases 1. and 2. are exactly equal, then check one of them.
if ifstGot != ifstGot2 {
t.Errorf("%v: ifstGot != ifstGot2", name)
}
if ilstGot != ilstGot2 {
t.Errorf("%v: ilstGot != ilstGot2", name)
}
if ok != ok2 {
t.Errorf("%v: ok != ok2", name)
}
if !equalGeneral(tmat, tmat2) {
t.Errorf("%v: T != T2", name)
}
// Check that the index of the first block was correctly updated (if
// necessary).
ifstWant := ifst
if !fstFirst {
ifstWant = ifst - 1
}
if ifstWant != ifstGot {
t.Errorf("%v: unexpected ifst=%v, want %v", name, ifstGot, ifstWant)
}
// Check that the index of the last block is as expected when ok=true.
// When ok=false, we don't know at which block the algorithm failed, so
// we don't check.
ilstWant := ilst
if !lstFirst {
ilstWant--
}
if ok {
if ifstWant < ilstWant {
// If the blocks are swapped backwards, these
// adjustments are not necessary, the first row of the
// last block will end up at ifst.
switch {
case fstSize == 2 && lstSize == 1:
ilstWant--
case fstSize == 1 && lstSize == 2:
ilstWant++
}
}
if ilstWant != ilstGot {
t.Errorf("%v: unexpected ilst=%v, want %v", name, ilstGot, ilstWant)
}
}
if n <= 1 || ifstGot == ilstGot {
// Too small matrix or no swapping.
// Check that T was not modified.
if !equalGeneral(tmat, tmatCopy) {
t.Errorf("%v: unexpected modification of T when no swapping", name)
}
// Check that Q was not modified.
if !equalGeneral(q, qCopy) {
t.Errorf("%v: unexpected modification of Q when no swapping", name)
}
// Nothing more to check
return
}
if !isSchurCanonicalGeneral(tmat) {
t.Errorf("%v: T is not in Schur canonical form", name)
}
// Check that T was not modified except above the second subdiagonal in
// rows and columns [modMin,modMax].
modMin := min(ifstGot, ilstGot)
modMax := max(ifstGot, ilstGot) + fstSize
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
if modMin <= i && i < modMax && j+1 >= i {
continue
}
if modMin <= j && j < modMax && j+1 >= i {
continue
}
diff := tmat.Data[i*tmat.Stride+j] - tmatCopy.Data[i*tmatCopy.Stride+j]
if diff != 0 {
t.Errorf("%v: unexpected modification at T[%v,%v]", name, i, j)
}
}
}
// Check that Q is orthogonal.
resid := residualOrthogonal(q, false)
if resid > tol {
t.Errorf("%v: Q is not orthogonal; resid=%v, want<=%v", name, resid, tol)
}
// Check that Q is unchanged outside of columns [modMin,modMax].
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
if modMin <= j && j < modMax {
continue
}
if q.Data[i*q.Stride+j] != qCopy.Data[i*qCopy.Stride+j] {
t.Errorf("%v: unexpected modification of Q[%v,%v]", name, i, j)
}
}
}
// Check that Qᵀ * TOrig * Q == T
qt := zeros(n, n, n)
blas64.Gemm(blas.Trans, blas.NoTrans, 1, q, tmatCopy, 0, qt)
qtq := cloneGeneral(tmat)
blas64.Gemm(blas.NoTrans, blas.NoTrans, -1, qt, q, 1, qtq)
resid = dlange(lapack.MaxColumnSum, n, n, qtq.Data, qtq.Stride)
if resid > tol {
t.Errorf("%v: mismatch between Qᵀ*(initial T)*Q and (final T); resid=%v, want<=%v",
name, resid, tol)
}
}
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