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// Copyright ©2023 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 Dgghrder interface {
Dgghrd(compq, compz lapack.OrthoComp, n, ilo, ihi int, a []float64, lda int, b []float64, ldb int, q []float64, ldq int, z []float64, ldz int)
}
func DgghrdTest(t *testing.T, impl Dgghrder) {
rnd := rand.New(rand.NewSource(1))
comps := []lapack.OrthoComp{lapack.OrthoExplicit, lapack.OrthoNone, lapack.OrthoPostmul}
for _, compq := range comps {
for _, compz := range comps {
for _, n := range []int{0, 1, 2, 3, 4, 15} {
for _, ld := range []int{max(1, n), n + 5} {
testDgghrd(t, impl, rnd, compq, compz, n, 0, n-1, ld, ld, ld, ld)
}
}
}
}
}
func testDgghrd(t *testing.T, impl Dgghrder, rnd *rand.Rand, compq, compz lapack.OrthoComp, n, ilo, ihi, lda, ldb, ldq, ldz int) {
const tol = 1e-13
a := randomGeneral(n, n, lda, rnd)
b := randomGeneral(n, n, ldb, rnd)
var q, q1 blas64.General
switch compq {
case lapack.OrthoExplicit:
// Initialize q to a non-orthogonal matrix, Dgghrd should overwrite it
// with an orthogonal Q.
q = randomGeneral(n, n, ldq, rnd)
case lapack.OrthoPostmul:
// Initialize q to an orthogonal matrix Q1, so that the result Q1*Q is
// again orthogonal.
q = randomOrthogonal(n, rnd)
q1 = cloneGeneral(q)
}
var z, z1 blas64.General
switch compz {
case lapack.OrthoExplicit:
z = randomGeneral(n, n, ldz, rnd)
case lapack.OrthoPostmul:
z = randomOrthogonal(n, rnd)
z1 = cloneGeneral(z)
}
hGot := cloneGeneral(a)
tGot := cloneGeneral(b)
impl.Dgghrd(compq, compz, n, ilo, ihi, hGot.Data, hGot.Stride, tGot.Data, tGot.Stride, q.Data, max(1, q.Stride), z.Data, max(1, z.Stride))
if n == 0 {
return
}
name := fmt.Sprintf("Case compq=%v,compz=%v,n=%v,ilo=%v,ihi=%v", compq, compz, n, ilo, ihi)
if !isUpperHessenberg(hGot) {
t.Errorf("%v: H is not upper Hessenberg", name)
}
if !isUpperTriangular(tGot) {
t.Errorf("%v: T is not upper triangular", name)
}
if compq != lapack.OrthoNone {
if resid := residualOrthogonal(q, true); resid > tol {
t.Errorf("%v: Q is not orthogonal, resid=%v", name, resid)
}
}
if compz != lapack.OrthoNone {
if resid := residualOrthogonal(z, true); resid > tol {
t.Errorf("%v: Z is not orthogonal, resid=%v", name, resid)
}
}
if compq != compz {
// Verify reduction only when both Q and Z are computed.
return
}
// Zero out the lower triangle of B.
for i := 1; i < n; i++ {
for j := 0; j < i; j++ {
b.Data[i*b.Stride+j] = 0
}
}
aux := zeros(n, n, n)
switch compq {
case lapack.OrthoExplicit:
// Qᵀ*A*Z = H
hCalc := zeros(n, n, n)
blas64.Gemm(blas.Trans, blas.NoTrans, 1, q, a, 0, aux)
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, aux, z, 1, hCalc)
if !equalApproxGeneral(hGot, hCalc, tol) {
t.Errorf("%v: Qᵀ*A*Z != H", name)
}
// Qᵀ*B*Z = T
tCalc := zeros(n, n, n)
blas64.Gemm(blas.Trans, blas.NoTrans, 1, q, b, 0, aux)
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, aux, z, 1, tCalc)
if !equalApproxGeneral(tGot, tCalc, tol) {
t.Errorf("%v: Qᵀ*B*Z != T", name)
}
case lapack.OrthoPostmul:
// Q1 * A * Z1ᵀ = (Q1*Q) * H * (Z1*Z)ᵀ
lhs := zeros(n, n, n)
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, q1, a, 0, aux)
blas64.Gemm(blas.NoTrans, blas.Trans, 1, aux, z1, 0, lhs)
rhs := zeros(n, n, n)
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, q, hGot, 0, aux)
blas64.Gemm(blas.NoTrans, blas.Trans, 1, aux, z, 0, rhs)
if !equalApproxGeneral(lhs, rhs, tol) {
t.Errorf("%v: Q1 * A * Z1ᵀ != (Q1*Q) * H * (Z1*Z)ᵀ", name)
}
// Q1 * B * Z1ᵀ = (Q1*Q) * T * (Z1*Z)ᵀ
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, q1, b, 0, aux)
blas64.Gemm(blas.NoTrans, blas.Trans, 1, aux, z1, 0, lhs)
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, q, tGot, 0, aux)
blas64.Gemm(blas.NoTrans, blas.Trans, 1, aux, z, 0, rhs)
if !equalApproxGeneral(lhs, rhs, tol) {
t.Errorf("%v: Q1 * B * Z1ᵀ != (Q1*Q) * T * (Z1*Z)ᵀ", name)
}
}
}
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