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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 Dgehd2er interface {
Dgehd2(n, ilo, ihi int, a []float64, lda int, tau, work []float64)
}
func Dgehd2Test(t *testing.T, impl Dgehd2er) {
rnd := rand.New(rand.NewSource(1))
for _, n := range []int{1, 2, 3, 4, 5, 7, 10, 30} {
for _, extra := range []int{0, 1, 13} {
for cas := 0; cas < 100; cas++ {
testDgehd2(t, impl, n, extra, rnd)
}
}
}
}
func testDgehd2(t *testing.T, impl Dgehd2er, n, extra int, rnd *rand.Rand) {
const tol = 1e-14
ilo := rnd.Intn(n)
ihi := rnd.Intn(n)
if ilo > ihi {
ilo, ihi = ihi, ilo
}
tau := nanSlice(n - 1)
work := nanSlice(n)
a := randomGeneral(n, n, n+extra, rnd)
// NaN out elements under the diagonal except
// for the [ilo:ihi,ilo:ihi] block.
for i := 1; i <= ihi; i++ {
for j := 0; j < min(ilo, i); j++ {
a.Data[i*a.Stride+j] = math.NaN()
}
}
for i := ihi + 1; i < n; i++ {
for j := 0; j < i; j++ {
a.Data[i*a.Stride+j] = math.NaN()
}
}
aCopy := a
aCopy.Data = make([]float64, len(a.Data))
copy(aCopy.Data, a.Data)
impl.Dgehd2(n, ilo, ihi, a.Data, a.Stride, tau, work)
prefix := fmt.Sprintf("Case n=%v, ilo=%v, ihi=%v, extra=%v", n, ilo, ihi, extra)
// Check any invalid modifications of a.
if !generalOutsideAllNaN(a) {
t.Errorf("%v: out-of-range write to A\n%v", prefix, a.Data)
}
for i := ilo; i <= ihi; i++ {
for j := 0; j < min(ilo, i); j++ {
if !math.IsNaN(a.Data[i*a.Stride+j]) {
t.Errorf("%v: expected NaN at A[%v,%v]", prefix, i, j)
}
}
}
for i := ihi + 1; i < n; i++ {
for j := 0; j < i; j++ {
if !math.IsNaN(a.Data[i*a.Stride+j]) {
t.Errorf("%v: expected NaN at A[%v,%v]", prefix, i, j)
}
}
}
for i := 0; i <= ilo; i++ {
for j := i; j < ilo+1; j++ {
if a.Data[i*a.Stride+j] != aCopy.Data[i*aCopy.Stride+j] {
t.Errorf("%v: unexpected modification at A[%v,%v]", prefix, i, j)
}
}
for j := ihi + 1; j < n; j++ {
if a.Data[i*a.Stride+j] != aCopy.Data[i*aCopy.Stride+j] {
t.Errorf("%v: unexpected modification at A[%v,%v]", prefix, i, j)
}
}
}
for i := ihi + 1; i < n; i++ {
for j := i; j < n; j++ {
if a.Data[i*a.Stride+j] != aCopy.Data[i*aCopy.Stride+j] {
t.Errorf("%v: unexpected modification at A[%v,%v]", prefix, i, j)
}
}
}
// Check that tau has been assigned properly.
for i, v := range tau {
if i < ilo || i >= ihi {
if !math.IsNaN(v) {
t.Errorf("%v: expected NaN at tau[%v]", prefix, i)
}
} else {
if math.IsNaN(v) {
t.Errorf("%v: unexpected NaN at tau[%v]", prefix, i)
}
}
}
// Extract Q and check that it is orthogonal.
q := blas64.General{
Rows: n,
Cols: n,
Stride: n,
Data: make([]float64, n*n),
}
for i := 0; i < q.Rows; i++ {
q.Data[i*q.Stride+i] = 1
}
qCopy := q
qCopy.Data = make([]float64, len(q.Data))
for j := ilo; j < ihi; j++ {
h := blas64.General{
Rows: n,
Cols: n,
Stride: n,
Data: make([]float64, n*n),
}
for i := 0; i < h.Rows; i++ {
h.Data[i*h.Stride+i] = 1
}
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 resid := residualOrthogonal(q, false); resid > tol {
t.Errorf("%v: Q is not orthogonal; resid=%v, want<=%v", prefix, resid, tol)
}
// Overwrite NaN elements of aCopy with zeros
// (we will multiply with it below).
for i := 1; i <= ihi; i++ {
for j := 0; j < min(ilo, i); j++ {
aCopy.Data[i*aCopy.Stride+j] = 0
}
}
for i := ihi + 1; i < n; i++ {
for j := 0; j < i; j++ {
aCopy.Data[i*aCopy.Stride+j] = 0
}
}
// Construct Qᵀ * AOrig * Q and check that it is
// equal to A from Dgehd2.
aq := blas64.General{
Rows: n,
Cols: n,
Stride: n,
Data: make([]float64, n*n),
}
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, aCopy, q, 0, aq)
qaq := blas64.General{
Rows: n,
Cols: n,
Stride: n,
Data: make([]float64, n*n),
}
blas64.Gemm(blas.Trans, blas.NoTrans, 1, q, aq, 0, qaq)
for i := ilo; i <= ihi; i++ {
for j := ilo; j <= ihi; j++ {
qaqij := qaq.Data[i*qaq.Stride+j]
if j < i-1 {
if math.Abs(qaqij) > tol {
t.Errorf("%v: Qᵀ*A*Q is not upper Hessenberg, [%v,%v]=%v", prefix, i, j, qaqij)
}
continue
}
diff := qaqij - a.Data[i*a.Stride+j]
if math.Abs(diff) > tol {
t.Errorf("%v: Qᵀ*AOrig*Q and A are not equal, diff at [%v,%v]=%v", prefix, i, j, diff)
}
}
}
}
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