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// Copyright ©2019 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 Dpotrier interface {
Dpotri(uplo blas.Uplo, n int, a []float64, lda int) bool
Dpotrf(uplo blas.Uplo, n int, a []float64, lda int) bool
}
func DpotriTest(t *testing.T, impl Dpotrier) {
for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
name := uploToString(uplo)
t.Run(name, func(t *testing.T) {
// Include small and large sizes to make sure that both
// unblocked and blocked paths are taken.
ns := []int{0, 1, 2, 3, 4, 5, 10, 25, 31, 32, 33, 63, 64, 65, 127, 128, 129}
const tol = 1e-12
bi := blas64.Implementation()
rnd := rand.New(rand.NewSource(1))
for _, n := range ns {
for _, lda := range []int{max(1, n), n + 11} {
prefix := fmt.Sprintf("n=%v,lda=%v", n, lda)
// Generate a random diagonal matrix D with positive entries.
d := make([]float64, n)
Dlatm1(d, 3, 10000, false, 2, rnd)
// Construct a positive definite matrix A as
// A = U * D * Uᵀ
// where U is a random orthogonal matrix.
a := make([]float64, n*lda)
Dlagsy(n, 0, d, a, lda, rnd, make([]float64, 2*n))
// Create a copy of A.
aCopy := make([]float64, len(a))
copy(aCopy, a)
// Compute the Cholesky factorization of A.
ok := impl.Dpotrf(uplo, n, a, lda)
if !ok {
t.Fatalf("%v: unexpected Cholesky failure", prefix)
}
// Compute the inverse inv(A).
ok = impl.Dpotri(uplo, n, a, lda)
if !ok {
t.Errorf("%v: unexpected failure", prefix)
continue
}
// Check that the triangle of A opposite to uplo has not been modified.
if uplo == blas.Upper && !sameLowerTri(n, aCopy, lda, a, lda) {
t.Errorf("%v: unexpected modification in lower triangle", prefix)
continue
}
if uplo == blas.Lower && !sameUpperTri(n, aCopy, lda, a, lda) {
t.Errorf("%v: unexpected modification in upper triangle", prefix)
continue
}
// Change notation for the sake of clarity.
ainv := a
ldainv := lda
// Expand ainv into a full dense matrix so that we can call Dsymm below.
if uplo == blas.Upper {
for i := 1; i < n; i++ {
for j := 0; j < i; j++ {
ainv[i*ldainv+j] = ainv[j*ldainv+i]
}
}
} else {
for i := 0; i < n-1; i++ {
for j := i + 1; j < n; j++ {
ainv[i*ldainv+j] = ainv[j*ldainv+i]
}
}
}
// Compute A*inv(A) and store the result into want.
ldwant := max(1, n)
want := make([]float64, n*ldwant)
bi.Dsymm(blas.Left, uplo, n, n, 1, aCopy, lda, ainv, ldainv, 0, want, ldwant)
// Check that want is close to the identity matrix.
dist := distFromIdentity(n, want, ldwant)
if dist > tol {
t.Errorf("%v: |A * inv(A) - I| = %v is too large", prefix, dist)
}
}
}
})
}
}
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