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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"
)
type Dtrti2er interface {
Dtrti2(uplo blas.Uplo, diag blas.Diag, n int, a []float64, lda int)
}
func Dtrti2Test(t *testing.T, impl Dtrti2er) {
const tol = 1e-14
for _, test := range []struct {
a []float64
n int
uplo blas.Uplo
diag blas.Diag
ans []float64
}{
{
a: []float64{
2, 3, 4,
0, 5, 6,
8, 0, 8},
n: 3,
uplo: blas.Upper,
diag: blas.NonUnit,
ans: []float64{
0.5, -0.3, -0.025,
0, 0.2, -0.15,
8, 0, 0.125,
},
},
{
a: []float64{
5, 3, 4,
0, 7, 6,
10, 0, 8},
n: 3,
uplo: blas.Upper,
diag: blas.Unit,
ans: []float64{
5, -3, 14,
0, 7, -6,
10, 0, 8,
},
},
{
a: []float64{
2, 0, 0,
3, 5, 0,
4, 6, 8},
n: 3,
uplo: blas.Lower,
diag: blas.NonUnit,
ans: []float64{
0.5, 0, 0,
-0.3, 0.2, 0,
-0.025, -0.15, 0.125,
},
},
{
a: []float64{
1, 0, 0,
3, 1, 0,
4, 6, 1},
n: 3,
uplo: blas.Lower,
diag: blas.Unit,
ans: []float64{
1, 0, 0,
-3, 1, 0,
14, -6, 1,
},
},
} {
impl.Dtrti2(test.uplo, test.diag, test.n, test.a, test.n)
if !floats.EqualApprox(test.ans, test.a, tol) {
t.Errorf("Matrix inverse mismatch. Want %v, got %v.", test.ans, test.a)
}
}
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
}{
{1, 0},
{2, 0},
{3, 0},
{1, 5},
{2, 5},
{3, 5},
} {
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.Dtrti2(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 of A^{-1} and A 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 close to the identity matrix.
dist := distFromIdentity(n, ans, lda)
if dist > tol {
t.Errorf("|inv(A) * A - I| = %v. Upper = %v, unit = %v, ans = %v", dist, uplo == blas.Upper, diag == blas.Unit, ans)
}
}
}
}
}
|
