/
dsytrd.go
161 lines (144 loc) · 3.79 KB
/
dsytrd.go
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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 Dsytrder interface {
Dsytrd(uplo blas.Uplo, n int, a []float64, lda int, d, e, tau, work []float64, lwork int)
Dorgqr(m, n, k int, a []float64, lda int, tau, work []float64, lwork int)
Dorgql(m, n, k int, a []float64, lda int, tau, work []float64, lwork int)
}
func DsytrdTest(t *testing.T, impl Dsytrder) {
const tol = 1e-13
rnd := rand.New(rand.NewSource(1))
for tc, test := range []struct {
n, lda int
}{
{1, 0},
{2, 0},
{3, 0},
{4, 0},
{10, 0},
{50, 0},
{100, 0},
{150, 0},
{300, 0},
{1, 3},
{2, 3},
{3, 7},
{4, 9},
{10, 20},
{50, 70},
{100, 120},
{150, 170},
{300, 320},
} {
for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
for _, wl := range []worklen{minimumWork, mediumWork, optimumWork} {
n := test.n
lda := test.lda
if lda == 0 {
lda = n
}
a := randomGeneral(n, n, lda, rnd)
for i := 1; i < n; i++ {
for j := 0; j < i; j++ {
a.Data[i*a.Stride+j] = a.Data[j*a.Stride+i]
}
}
aCopy := cloneGeneral(a)
d := nanSlice(n)
e := nanSlice(n - 1)
tau := nanSlice(n - 1)
var lwork int
switch wl {
case minimumWork:
lwork = 1
case mediumWork:
work := make([]float64, 1)
impl.Dsytrd(uplo, n, a.Data, a.Stride, d, e, tau, work, -1)
lwork = (int(work[0]) + 1) / 2
lwork = max(1, lwork)
case optimumWork:
work := make([]float64, 1)
impl.Dsytrd(uplo, n, a.Data, a.Stride, d, e, tau, work, -1)
lwork = int(work[0])
}
work := make([]float64, lwork)
impl.Dsytrd(uplo, n, a.Data, a.Stride, d, e, tau, work, lwork)
prefix := fmt.Sprintf("Case #%v: uplo=%v,n=%v,lda=%v,work=%v",
tc, uplo, n, lda, wl)
if !generalOutsideAllNaN(a) {
t.Errorf("%v: out-of-range write to A", prefix)
}
// Extract Q by doing what Dorgtr does.
q := cloneGeneral(a)
if uplo == blas.Upper {
for j := 0; j < n-1; j++ {
for i := 0; i < j; i++ {
q.Data[i*q.Stride+j] = q.Data[i*q.Stride+j+1]
}
q.Data[(n-1)*q.Stride+j] = 0
}
for i := 0; i < n-1; i++ {
q.Data[i*q.Stride+n-1] = 0
}
q.Data[(n-1)*q.Stride+n-1] = 1
if n > 1 {
work = make([]float64, n-1)
impl.Dorgql(n-1, n-1, n-1, q.Data, q.Stride, tau, work, len(work))
}
} else {
for j := n - 1; j > 0; j-- {
q.Data[j] = 0
for i := j + 1; i < n; i++ {
q.Data[i*q.Stride+j] = q.Data[i*q.Stride+j-1]
}
}
q.Data[0] = 1
for i := 1; i < n; i++ {
q.Data[i*q.Stride] = 0
}
if n > 1 {
work = make([]float64, n-1)
impl.Dorgqr(n-1, n-1, n-1, q.Data[q.Stride+1:], q.Stride, tau, work, len(work))
}
}
if !isOrthogonal(q) {
t.Errorf("%v: Q not orthogonal", prefix)
}
// Contruct symmetric tridiagonal T from d and e.
tMat := zeros(n, n, n)
for i := 0; i < n; i++ {
tMat.Data[i*tMat.Stride+i] = d[i]
}
if uplo == blas.Upper {
for j := 1; j < n; j++ {
tMat.Data[(j-1)*tMat.Stride+j] = e[j-1]
tMat.Data[j*tMat.Stride+j-1] = e[j-1]
}
} else {
for j := 0; j < n-1; j++ {
tMat.Data[(j+1)*tMat.Stride+j] = e[j]
tMat.Data[j*tMat.Stride+j+1] = e[j]
}
}
// Compute Qᵀ * A * Q.
tmp := zeros(n, n, n)
blas64.Gemm(blas.Trans, blas.NoTrans, 1, q, aCopy, 0, tmp)
got := zeros(n, n, n)
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, tmp, q, 0, got)
// Compare with T.
if !equalApproxGeneral(got, tMat, tol) {
t.Errorf("%v: Qᵀ*A*Q != T", prefix)
}
}
}
}
}