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// Copyright ©2018 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 Dpotrser interface {
Dpotrs(uplo blas.Uplo, n, nrhs int, a []float64, lda int, b []float64, ldb int)
Dpotrf(uplo blas.Uplo, n int, a []float64, lda int) bool
}
func DpotrsTest(t *testing.T, impl Dpotrser) {
const tol = 1e-14
rnd := rand.New(rand.NewSource(1))
bi := blas64.Implementation()
for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
for _, n := range []int{1, 2, 5} {
for _, nrhs := range []int{1, 2, 5, 10} {
for _, ld := range []struct{ a, b int }{
{n, nrhs},
{n + 7, nrhs},
{n, nrhs + 3},
{n + 7, nrhs + 3},
} {
// Construct a random SPD matrix A by first making a symmetric matrix
// and then ensuring that it is diagonally dominant.
a := nanGeneral(n, n, ld.a)
for i := 0; i < n; i++ {
for j := i; j < n; j++ {
v := rnd.Float64()
a.Data[i*a.Stride+j] = v
a.Data[j*a.Stride+i] = v
}
}
for i := 0; i < n; i++ {
a.Data[i*a.Stride+i] += float64(n)
}
// Generate a random solution X.
want := nanGeneral(n, nrhs, ld.b)
for i := 0; i < n; i++ {
for j := 0; j < nrhs; j++ {
want.Data[i*want.Stride+j] = rnd.NormFloat64()
}
}
// Compute the right-hand side matrix as A * X.
b := nanGeneral(n, nrhs, ld.b)
bi.Dgemm(blas.NoTrans, blas.NoTrans, n, nrhs, n, 1, a.Data, a.Stride, want.Data, want.Stride, 0, b.Data, b.Stride)
// Compute the Cholesky decomposition of A.
ok := impl.Dpotrf(uplo, n, a.Data, a.Stride)
if !ok {
panic("bad test")
}
aCopy := cloneGeneral(a)
// Solve A * X = B.
impl.Dpotrs(uplo, n, nrhs, a.Data, a.Stride, b.Data, b.Stride)
name := fmt.Sprintf("uplo=%v,n=%v,nrhs=%v,lda=%v,ldb=%v", uplo, n, nrhs, a.Stride, b.Stride)
if !generalOutsideAllNaN(a) {
t.Errorf("%v: out-of-range modification of A", name)
}
if !equalApproxGeneral(a, aCopy, 0) {
t.Errorf("%v: unexpected modification of A", name)
}
if !generalOutsideAllNaN(b) {
t.Errorf("%v: out-of-range modification of B", name)
}
if !equalApproxGeneral(b, want, tol) {
t.Errorf("%v: unexpected result\ngot %v\nwant %v", name, b, want)
}
}
}
}
}
}
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