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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"
"math"
"testing"
"golang.org/x/exp/rand"
"gonum.org/v1/gonum/blas"
"gonum.org/v1/gonum/blas/blas64"
)
type Dorghrer interface {
Dorghr(n, ilo, ihi int, a []float64, lda int, tau, work []float64, lwork int)
Dgehrder
}
func DorghrTest(t *testing.T, impl Dorghrer) {
rnd := rand.New(rand.NewSource(1))
for _, n := range []int{1, 2, 3, 4, 5, 6, 7, 8, 23, 34} {
for _, extra := range []int{0, 1, 13} {
for _, optwork := range []bool{true, false} {
for cas := 0; cas < 100; cas++ {
ilo := rnd.Intn(n)
ihi := rnd.Intn(n)
if ilo > ihi {
ilo, ihi = ihi, ilo
}
testDorghr(t, impl, n, ilo, ihi, extra, optwork, rnd)
}
}
}
}
testDorghr(t, impl, 0, 0, -1, 0, false, rnd)
testDorghr(t, impl, 0, 0, -1, 0, true, rnd)
}
func testDorghr(t *testing.T, impl Dorghrer, n, ilo, ihi, extra int, optwork bool, rnd *rand.Rand) {
const tol = 1e-14
// Construct the matrix A with elementary reflectors and scalar factors tau.
a := randomGeneral(n, n, n+extra, rnd)
var tau []float64
if n > 1 {
tau = nanSlice(n - 1)
}
work := nanSlice(max(1, n)) // Minimum work for Dgehrd.
impl.Dgehrd(n, ilo, ihi, a.Data, a.Stride, tau, work, len(work))
// Extract Q for later comparison.
q := eye(n, n)
qCopy := cloneGeneral(q)
for j := ilo; j < ihi; j++ {
h := eye(n, n)
v := blas64.Vector{
Inc: 1,
Data: make([]float64, n),
}
v.Data[j+1] = 1
for i := j + 2; i < ihi+1; i++ {
v.Data[i] = a.Data[i*a.Stride+j]
}
blas64.Ger(-tau[j], v, v, h)
copy(qCopy.Data, q.Data)
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, qCopy, h, 0, q)
}
if optwork {
work = nanSlice(1)
impl.Dorghr(n, ilo, ihi, a.Data, a.Stride, tau, work, -1)
work = nanSlice(int(work[0]))
} else {
work = nanSlice(max(1, ihi-ilo))
}
impl.Dorghr(n, ilo, ihi, a.Data, a.Stride, tau, work, len(work))
prefix := fmt.Sprintf("Case n=%v, ilo=%v, ihi=%v, extra=%v, optwork=%v", n, ilo, ihi, extra, optwork)
if !generalOutsideAllNaN(a) {
t.Errorf("%v: out-of-range write to A\n%v", prefix, a.Data)
}
if resid := residualOrthogonal(a, false); resid > tol {
t.Errorf("%v: A is not orthogonal; resid=%v, want<=%v", prefix, resid, tol)
}
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
aij := a.Data[i*a.Stride+j]
qij := q.Data[i*q.Stride+j]
if math.Abs(aij-qij) > tol {
t.Errorf("%v: unexpected value of A[%v,%v]. want %v, got %v", prefix, i, j, qij, aij)
}
}
}
}