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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"
)
type Dtrtrier interface {
Dtrtri(uplo blas.Uplo, diag blas.Diag, n int, a []float64, lda int) bool
}
func DtrtriTest(t *testing.T, impl Dtrtrier) {
const tol = 1e-10
rnd := rand.New(rand.NewSource(1))
bi := blas64.Implementation()
for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
for _, diag := range []blas.Diag{blas.NonUnit, blas.Unit} {
for _, test := range []struct {
n, lda int
}{
{3, 0},
{70, 0},
{200, 0},
{3, 5},
{70, 92},
{200, 205},
} {
n := test.n
lda := test.lda
if lda == 0 {
lda = n
}
// Allocate n×n matrix A and fill it with random numbers.
a := make([]float64, n*lda)
for i := range a {
a[i] = rnd.Float64()
}
for i := 0; i < n; i++ {
// This keeps the matrices well conditioned.
a[i*lda+i] += float64(n)
}
aCopy := make([]float64, len(a))
copy(aCopy, a)
// Compute the inverse of the uplo triangle.
impl.Dtrtri(uplo, diag, n, a, lda)
// Zero out the opposite triangle.
if uplo == blas.Upper {
for i := 1; i < n; i++ {
for j := 0; j < i; j++ {
aCopy[i*lda+j] = 0
a[i*lda+j] = 0
}
}
} else {
for i := 0; i < n; i++ {
for j := i + 1; j < n; j++ {
aCopy[i*lda+j] = 0
a[i*lda+j] = 0
}
}
}
if diag == blas.Unit {
// Set the diagonal explicitly to 1.
for i := 0; i < n; i++ {
a[i*lda+i] = 1
aCopy[i*lda+i] = 1
}
}
// Compute A^{-1} * A and store the result in ans.
ans := make([]float64, len(a))
bi.Dgemm(blas.NoTrans, blas.NoTrans, n, n, n, 1, a, lda, aCopy, lda, 0, ans, lda)
// Check that ans is the identity matrix.
dist := distFromIdentity(n, ans, lda)
if dist > tol {
t.Errorf("|inv(A) * A - I| = %v is too large. Upper = %v, unit = %v, n = %v, lda = %v",
dist, uplo == blas.Upper, diag == blas.Unit, n, lda)
}
}
}
}
}
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