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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 (
"testing"
"golang.org/x/exp/rand"
"gonum.org/v1/gonum/blas"
"gonum.org/v1/gonum/blas/blas64"
"gonum.org/v1/gonum/floats/scalar"
)
type Dpotrfer interface {
Dpotrf(ul blas.Uplo, n int, a []float64, lda int) (ok bool)
}
func DpotrfTest(t *testing.T, impl Dpotrfer) {
const tol = 1e-13
rnd := rand.New(rand.NewSource(1))
bi := blas64.Implementation()
for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
for tc, test := range []struct {
n int
lda int
}{
{1, 0},
{2, 0},
{3, 0},
{10, 0},
{30, 0},
{63, 0},
{65, 0},
{127, 0},
{129, 0},
{500, 0},
{1, 10},
{2, 10},
{3, 10},
{10, 20},
{30, 50},
{63, 100},
{65, 100},
{127, 200},
{129, 200},
{500, 600},
} {
n := test.n
// Random diagonal matrix D with positive entries.
d := make([]float64, n)
Dlatm1(d, 4, 10000, false, 1, rnd)
// Construct a positive definite matrix A as
// A = U * D * Uᵀ
// where U is a random orthogonal matrix.
lda := test.lda
if lda == 0 {
lda = n
}
a := make([]float64, n*lda)
Dlagsy(n, 0, d, a, lda, rnd, make([]float64, 2*n))
aCopy := make([]float64, len(a))
copy(aCopy, a)
ok := impl.Dpotrf(uplo, n, a, lda)
if !ok {
t.Errorf("Case %v: unexpected failure for positive definite matrix", tc)
continue
}
switch uplo {
case blas.Upper:
for i := 0; i < n; i++ {
for j := 0; j < i; j++ {
a[i*lda+j] = 0
}
}
case blas.Lower:
for i := 0; i < n; i++ {
for j := i + 1; j < n; j++ {
a[i*lda+j] = 0
}
}
default:
panic("bad uplo")
}
ans := make([]float64, len(a))
switch uplo {
case blas.Upper:
// Multiply Uᵀ * U.
bi.Dsyrk(uplo, blas.Trans, n, n, 1, a, lda, 0, ans, lda)
case blas.Lower:
// Multiply L * Lᵀ.
bi.Dsyrk(uplo, blas.NoTrans, n, n, 1, a, lda, 0, ans, lda)
}
match := true
switch uplo {
case blas.Upper:
for i := 0; i < n; i++ {
for j := i; j < n; j++ {
if !scalar.EqualWithinAbsOrRel(ans[i*lda+j], aCopy[i*lda+j], tol, tol) {
match = false
}
}
}
case blas.Lower:
for i := 0; i < n; i++ {
for j := 0; j <= i; j++ {
if !scalar.EqualWithinAbsOrRel(ans[i*lda+j], aCopy[i*lda+j], tol, tol) {
match = false
}
}
}
}
if !match {
t.Errorf("Case %v (uplo=%v,n=%v,lda=%v): unexpected result", tc, uplo, n, lda)
}
// Make one element of D negative so that A is not
// positive definite, and check that Dpotrf fails.
d[0] *= -1
Dlagsy(n, 0, d, a, lda, rnd, make([]float64, 2*n))
ok = impl.Dpotrf(uplo, n, a, lda)
if ok {
t.Errorf("Case %v: unexpected success for not positive definite matrix", tc)
}
}
}
}
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