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// Copyright ©2015 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 Dgerqfer interface {
Dgerqf(m, n int, a []float64, lda int, tau, work []float64, lwork int)
}
func DgerqfTest(t *testing.T, impl Dgerqfer) {
rnd := rand.New(rand.NewSource(1))
for _, m := range []int{0, 1, 2, 3, 4, 5, 6, 12, 129, 160} {
for _, n := range []int{0, 1, 2, 3, 4, 5, 6, 12, 129, 160} {
for _, lda := range []int{max(1, n), n + 4} {
dgerqfTest(t, impl, rnd, m, n, lda)
}
}
}
}
func dgerqfTest(t *testing.T, impl Dgerqfer, rnd *rand.Rand, m, n, lda int) {
const tol = 1e-14
a := randomGeneral(m, n, lda, rnd)
aCopy := cloneGeneral(a)
k := min(m, n)
tau := make([]float64, k)
for i := range tau {
tau[i] = rnd.Float64()
}
work := []float64{0}
impl.Dgerqf(m, n, a.Data, a.Stride, tau, work, -1)
lwkopt := int(work[0])
for _, wk := range []struct {
name string
length int
}{
{name: "short", length: m},
{name: "medium", length: lwkopt - 1},
{name: "long", length: lwkopt},
} {
name := fmt.Sprintf("m=%d,n=%d,lda=%d,work=%v", m, n, lda, wk.name)
lwork := max(max(1, m), wk.length)
work = make([]float64, lwork)
for i := range work {
work[i] = rnd.Float64()
}
copyGeneral(a, aCopy)
impl.Dgerqf(m, n, a.Data, a.Stride, tau, work, lwork)
// Test that the RQ factorization has completed successfully. Compute
// Q based on the vectors.
q := constructQ("RQ", m, n, a.Data, a.Stride, tau)
// Check that Q is orthogonal.
if resid := residualOrthogonal(q, false); resid > tol*float64(m) {
t.Errorf("Case %v: Q not orthogonal; resid=%v, want<=%v", name, resid, tol*float64(m))
}
// Check that A = R * Q
r := zeros(m, n, n)
for i := 0; i < m; i++ {
off := m - n
for j := max(0, i-off); j < n; j++ {
r.Data[i*r.Stride+j] = a.Data[i*a.Stride+j]
}
}
qra := cloneGeneral(aCopy)
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, r, q, -1, qra)
resid := dlange(lapack.MaxColumnSum, qra.Rows, qra.Cols, qra.Data, qra.Stride)
if resid > tol*float64(m) {
t.Errorf("Case %v: |R*Q - A|=%v, want<=%v", name, resid, tol*float64(m))
}
}
}