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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"
"testing"
"golang.org/x/exp/rand"
"gonum.org/v1/gonum/blas"
"gonum.org/v1/gonum/blas/blas64"
)
type Dorgqler interface {
Dorgql(m, n, k int, a []float64, lda int, tau, work []float64, lwork int)
Dlarfger
}
func DorgqlTest(t *testing.T, impl Dorgqler) {
const tol = 1e-14
type Dorg2ler interface {
Dorg2l(m, n, k int, a []float64, lda int, tau, work []float64)
}
dorg2ler, hasDorg2l := impl.(Dorg2ler)
rnd := rand.New(rand.NewSource(1))
for _, m := range []int{0, 1, 2, 3, 4, 5, 7, 10, 15, 30, 50, 150} {
for _, extra := range []int{0, 11} {
for _, wl := range []worklen{minimumWork, mediumWork, optimumWork} {
var k int
if m >= 129 {
// For large matrices make sure that k
// is large enough to trigger blocked
// path.
k = 129 + rnd.Intn(m-129+1)
} else {
k = rnd.Intn(m + 1)
}
n := k + rnd.Intn(m-k+1)
if m == 0 || n == 0 {
m = 0
n = 0
k = 0
}
// Generate k elementary reflectors in the last
// k columns of A.
a := nanGeneral(m, n, n+extra)
tau := make([]float64, k)
for l := 0; l < k; l++ {
jj := m - k + l
v := randomSlice(jj, rnd)
_, tau[l] = impl.Dlarfg(len(v)+1, rnd.NormFloat64(), v, 1)
j := n - k + l
for i := 0; i < jj; i++ {
a.Data[i*a.Stride+j] = v[i]
}
}
aCopy := cloneGeneral(a)
// Compute the full matrix Q by forming the
// Householder reflectors explicitly.
q := eye(m, m)
qCopy := eye(m, m)
for l := 0; l < k; l++ {
h := eye(m, m)
jj := m - k + l
j := n - k + l
v := blas64.Vector{Data: make([]float64, m), Inc: 1}
for i := 0; i < jj; i++ {
v.Data[i] = a.Data[i*a.Stride+j]
}
v.Data[jj] = 1
blas64.Ger(-tau[l], v, v, h)
copy(qCopy.Data, q.Data)
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, h, qCopy, 0, q)
}
// View the last n columns of Q as 'want'.
want := blas64.General{
Rows: m,
Cols: n,
Stride: q.Stride,
Data: q.Data[m-n:],
}
var lwork int
switch wl {
case minimumWork:
lwork = max(1, n)
case mediumWork:
work := make([]float64, 1)
impl.Dorgql(m, n, k, a.Data, a.Stride, tau, work, -1)
lwork = (int(work[0]) + n) / 2
lwork = max(1, lwork)
case optimumWork:
work := make([]float64, 1)
impl.Dorgql(m, n, k, a.Data, a.Stride, tau, work, -1)
lwork = int(work[0])
}
work := make([]float64, lwork)
// Compute the last n columns of Q by a call to
// Dorgql.
impl.Dorgql(m, n, k, a.Data, a.Stride, tau, work, len(work))
prefix := fmt.Sprintf("Case m=%v,n=%v,k=%v,wl=%v", m, n, k, wl)
if !generalOutsideAllNaN(a) {
t.Errorf("%v: out-of-range write to A", prefix)
}
if !equalApproxGeneral(want, a, tol) {
t.Errorf("%v: unexpected Q", prefix)
}
// Compute the last n columns of Q by a call to
// Dorg2l and check that we get the same result.
if !hasDorg2l {
continue
}
dorg2ler.Dorg2l(m, n, k, aCopy.Data, aCopy.Stride, tau, work)
if !equalApproxGeneral(aCopy, a, tol) {
t.Errorf("%v: mismatch between Dorgql and Dorg2l", prefix)
}
}
}
}
}
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