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/
dggsvp3.go
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/
dggsvp3.go
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// Copyright ©2017 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 (
"testing"
"golang.org/x/exp/rand"
"gonum.org/v1/gonum/blas"
"gonum.org/v1/gonum/blas/blas64"
"gonum.org/v1/gonum/lapack"
)
type Dggsvp3er interface {
Dlanger
Dggsvp3(jobU, jobV, jobQ lapack.GSVDJob, m, p, n int, a []float64, lda int, b []float64, ldb int, tola, tolb float64, u []float64, ldu int, v []float64, ldv int, q []float64, ldq int, iwork []int, tau, work []float64, lwork int) (k, l int)
}
func Dggsvp3Test(t *testing.T, impl Dggsvp3er) {
const tol = 1e-14
rnd := rand.New(rand.NewSource(1))
for cas, test := range []struct {
m, p, n, lda, ldb, ldu, ldv, ldq int
}{
{m: 3, p: 3, n: 5, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
{m: 5, p: 5, n: 5, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
{m: 5, p: 5, n: 5, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
{m: 5, p: 5, n: 10, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
{m: 5, p: 5, n: 10, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
{m: 5, p: 5, n: 10, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
{m: 10, p: 5, n: 5, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
{m: 10, p: 5, n: 5, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
{m: 10, p: 10, n: 10, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
{m: 10, p: 10, n: 10, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
{m: 5, p: 5, n: 5, lda: 10, ldb: 10, ldu: 10, ldv: 10, ldq: 10},
{m: 5, p: 5, n: 5, lda: 10, ldb: 10, ldu: 10, ldv: 10, ldq: 10},
{m: 5, p: 5, n: 10, lda: 20, ldb: 20, ldu: 10, ldv: 10, ldq: 20},
{m: 5, p: 5, n: 10, lda: 20, ldb: 20, ldu: 10, ldv: 10, ldq: 20},
{m: 5, p: 5, n: 10, lda: 20, ldb: 20, ldu: 10, ldv: 10, ldq: 20},
{m: 10, p: 5, n: 5, lda: 10, ldb: 10, ldu: 20, ldv: 10, ldq: 10},
{m: 10, p: 5, n: 5, lda: 10, ldb: 10, ldu: 20, ldv: 10, ldq: 10},
{m: 10, p: 10, n: 10, lda: 20, ldb: 20, ldu: 20, ldv: 20, ldq: 20},
{m: 10, p: 10, n: 10, lda: 20, ldb: 20, ldu: 20, ldv: 20, ldq: 20},
} {
m := test.m
p := test.p
n := test.n
lda := test.lda
if lda == 0 {
lda = n
}
ldb := test.ldb
if ldb == 0 {
ldb = n
}
ldu := test.ldu
if ldu == 0 {
ldu = m
}
ldv := test.ldv
if ldv == 0 {
ldv = p
}
ldq := test.ldq
if ldq == 0 {
ldq = n
}
a := randomGeneral(m, n, lda, rnd)
aCopy := cloneGeneral(a)
b := randomGeneral(p, n, ldb, rnd)
bCopy := cloneGeneral(b)
tola := float64(max(m, n)) * impl.Dlange(lapack.Frobenius, m, n, a.Data, a.Stride, nil) * dlamchE
tolb := float64(max(p, n)) * impl.Dlange(lapack.Frobenius, p, n, b.Data, b.Stride, nil) * dlamchE
u := nanGeneral(m, m, ldu)
v := nanGeneral(p, p, ldv)
q := nanGeneral(n, n, ldq)
iwork := make([]int, n)
tau := make([]float64, n)
work := []float64{0}
impl.Dggsvp3(lapack.GSVDU, lapack.GSVDV, lapack.GSVDQ,
m, p, n,
a.Data, a.Stride,
b.Data, b.Stride,
tola, tolb,
u.Data, u.Stride,
v.Data, v.Stride,
q.Data, q.Stride,
iwork, tau,
work, -1)
lwork := int(work[0])
work = make([]float64, lwork)
k, l := impl.Dggsvp3(lapack.GSVDU, lapack.GSVDV, lapack.GSVDQ,
m, p, n,
a.Data, a.Stride,
b.Data, b.Stride,
tola, tolb,
u.Data, u.Stride,
v.Data, v.Stride,
q.Data, q.Stride,
iwork, tau,
work, lwork)
// Check orthogonality of U, V and Q.
if resid := residualOrthogonal(u, false); resid > tol {
t.Errorf("Case %v: U is not orthogonal; resid=%v, want<=%v", cas, resid, tol)
}
if resid := residualOrthogonal(v, false); resid > tol {
t.Errorf("Case %v: V is not orthogonal; resid=%v, want<=%v", cas, resid, tol)
}
if resid := residualOrthogonal(q, false); resid > tol {
t.Errorf("Case %v: Q is not orthogonal; resid=%v, want<=%v", cas, resid, tol)
}
zeroA, zeroB := constructGSVPresults(n, p, m, k, l, a, b)
// Check Uᵀ*A*Q = [ 0 RA ].
uTmp := nanGeneral(m, n, n)
blas64.Gemm(blas.Trans, blas.NoTrans, 1, u, aCopy, 0, uTmp)
uAns := nanGeneral(m, n, n)
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, uTmp, q, 0, uAns)
if !equalApproxGeneral(uAns, zeroA, tol) {
t.Errorf("test %d: Uᵀ*A*Q != [ 0 RA ]\nUᵀ*A*Q:\n%+v\n[ 0 RA ]:\n%+v",
cas, uAns, zeroA)
}
// Check Vᵀ*B*Q = [ 0 RB ].
vTmp := nanGeneral(p, n, n)
blas64.Gemm(blas.Trans, blas.NoTrans, 1, v, bCopy, 0, vTmp)
vAns := nanGeneral(p, n, n)
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, vTmp, q, 0, vAns)
if !equalApproxGeneral(vAns, zeroB, tol) {
t.Errorf("test %d: Vᵀ*B*Q != [ 0 RB ]\nVᵀ*B*Q:\n%+v\n[ 0 RB ]:\n%+v",
cas, vAns, zeroB)
}
}
}