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// Copyright ©2020 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"
"math"
"testing"
"golang.org/x/exp/rand"
"gonum.org/v1/gonum/blas"
"gonum.org/v1/gonum/blas/blas64"
"gonum.org/v1/gonum/floats"
"gonum.org/v1/gonum/lapack"
)
type Dtrtrser interface {
Dtrtrs(uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, n, nrhs int, a []float64, lda int, b []float64, ldb int) bool
}
func DtrtrsTest(t *testing.T, impl Dtrtrser) {
rnd := rand.New(rand.NewSource(1))
for _, trans := range []blas.Transpose{blas.NoTrans, blas.Trans, blas.ConjTrans} {
name := transToString(trans)
t.Run(name, func(t *testing.T) {
for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
for _, diag := range []blas.Diag{blas.Unit, blas.NonUnit} {
for _, n := range []int{0, 1, 2, 3, 4, 5, 10} {
for _, nrhs := range []int{0, 1, 2, 3, 4, 5, 10, 15} {
for _, lda := range []int{max(1, n), n + 3} {
for _, ldb := range []int{max(1, nrhs), nrhs + 3} {
if diag == blas.Unit {
dtrtrsTest(t, impl, rnd, uplo, trans, diag, n, nrhs, lda, ldb, false)
} else {
dtrtrsTest(t, impl, rnd, uplo, trans, diag, n, nrhs, lda, ldb, true)
dtrtrsTest(t, impl, rnd, uplo, trans, diag, n, nrhs, lda, ldb, false)
}
}
}
}
}
}
}
})
}
}
func dtrtrsTest(t *testing.T, impl Dtrtrser, rnd *rand.Rand, uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, n, nrhs int, lda, ldb int, singular bool) {
if singular && diag == blas.Unit {
panic("blas.Unit triangular matrix cannot be singular")
}
const tol = 1e-14
if n == 0 {
singular = false
}
name := fmt.Sprintf("uplo=%v,diag=%v,n=%v,nrhs=%v,lda=%v,ldb=%v,sing=%v", string(uplo), string(diag), n, nrhs, lda, ldb, singular)
// Generate a random triangular matrix A. One of its triangles won't be
// referenced.
a := make([]float64, n*lda)
for i := range a {
a[i] = rnd.NormFloat64()
}
if singular {
i := rnd.Intn(n)
a[i*lda+i] = 0
}
aCopy := make([]float64, len(a))
copy(aCopy, a)
// Generate a random solution matrix X.
x := make([]float64, n*ldb)
for i := range x {
x[i] = rnd.NormFloat64()
}
// Generate the right-hand side as A * X or Aᵀ * X.
b := make([]float64, len(x))
copy(b, x)
bi := blas64.Implementation()
bi.Dtrmm(blas.Left, uplo, trans, diag, n, nrhs, 1, a, lda, b, ldb)
got := make([]float64, len(b))
copy(got, b)
ok := impl.Dtrtrs(uplo, trans, diag, n, nrhs, a, lda, got, ldb)
if !floats.Equal(a, aCopy) {
t.Errorf("%v: unexpected modification of A", name)
}
if ok == singular {
t.Errorf("%v: misdetected singular matrix, ok=%v", name, ok)
}
if !ok {
if !floats.Equal(got, b) {
t.Errorf("%v: unexpected modification of B when singular", name)
}
return
}
if n == 0 || nrhs == 0 {
return
}
work := make([]float64, n)
// Compute the 1-norm of A or Aᵀ.
var aNorm float64
if trans == blas.NoTrans {
aNorm = dlantr(lapack.MaxColumnSum, uplo, diag, n, n, a, lda, work)
} else {
aNorm = dlantr(lapack.MaxRowSum, uplo, diag, n, n, a, lda, work)
}
// Compute the maximum over the number of right-hand sides of
// |op(A)*x-b| / (|op(A)| * |x|)
var resid float64
for j := 0; j < nrhs; j++ {
bi.Dcopy(n, got[j:], ldb, work, 1)
bi.Dtrmv(uplo, trans, diag, n, a, lda, work, 1)
bi.Daxpy(n, -1, b[j:], ldb, work, 1)
rjNorm := bi.Dasum(n, work, 1)
xNorm := bi.Dasum(n, got[j:], ldb)
resid = math.Max(resid, rjNorm/aNorm/xNorm)
}
if resid > tol {
t.Errorf("%v: unexpected result; resid=%v,want<=%v", name, resid, tol)
}
}
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