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107 lines
3.0 KiB
Go
107 lines
3.0 KiB
Go
// Copyright ©2019 The Gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package testlapack
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import (
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"fmt"
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"testing"
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"golang.org/x/exp/rand"
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"gonum.org/v1/gonum/blas"
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"gonum.org/v1/gonum/blas/blas64"
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)
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type Dpotrier interface {
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Dpotri(uplo blas.Uplo, n int, a []float64, lda int) bool
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Dpotrf(uplo blas.Uplo, n int, a []float64, lda int) bool
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}
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func DpotriTest(t *testing.T, impl Dpotrier) {
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for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
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name := uploToString(uplo)
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t.Run(name, func(t *testing.T) {
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// Include small and large sizes to make sure that both
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// unblocked and blocked paths are taken.
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ns := []int{0, 1, 2, 3, 4, 5, 10, 25, 31, 32, 33, 63, 64, 65, 127, 128, 129}
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const tol = 1e-12
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bi := blas64.Implementation()
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rnd := rand.New(rand.NewSource(1))
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for _, n := range ns {
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for _, lda := range []int{max(1, n), n + 11} {
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prefix := fmt.Sprintf("n=%v,lda=%v", n, lda)
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// Generate a random diagonal matrix D with positive entries.
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d := make([]float64, n)
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Dlatm1(d, 3, 10000, false, 2, rnd)
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// Construct a positive definite matrix A as
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// A = U * D * Uᵀ
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// where U is a random orthogonal matrix.
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a := make([]float64, n*lda)
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Dlagsy(n, 0, d, a, lda, rnd, make([]float64, 2*n))
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// Create a copy of A.
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aCopy := make([]float64, len(a))
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copy(aCopy, a)
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// Compute the Cholesky factorization of A.
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ok := impl.Dpotrf(uplo, n, a, lda)
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if !ok {
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t.Fatalf("%v: unexpected Cholesky failure", prefix)
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}
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// Compute the inverse inv(A).
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ok = impl.Dpotri(uplo, n, a, lda)
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if !ok {
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t.Errorf("%v: unexpected failure", prefix)
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continue
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}
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// Check that the triangle of A opposite to uplo has not been modified.
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if uplo == blas.Upper && !sameLowerTri(n, aCopy, lda, a, lda) {
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t.Errorf("%v: unexpected modification in lower triangle", prefix)
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continue
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}
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if uplo == blas.Lower && !sameUpperTri(n, aCopy, lda, a, lda) {
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t.Errorf("%v: unexpected modification in upper triangle", prefix)
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continue
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}
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// Change notation for the sake of clarity.
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ainv := a
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ldainv := lda
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// Expand ainv into a full dense matrix so that we can call Dsymm below.
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if uplo == blas.Upper {
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for i := 1; i < n; i++ {
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for j := 0; j < i; j++ {
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ainv[i*ldainv+j] = ainv[j*ldainv+i]
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}
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}
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} else {
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for i := 0; i < n-1; i++ {
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for j := i + 1; j < n; j++ {
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ainv[i*ldainv+j] = ainv[j*ldainv+i]
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}
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}
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}
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// Compute A*inv(A) and store the result into want.
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ldwant := max(1, n)
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want := make([]float64, n*ldwant)
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bi.Dsymm(blas.Left, uplo, n, n, 1, aCopy, lda, ainv, ldainv, 0, want, ldwant)
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// Check that want is close to the identity matrix.
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dist := distFromIdentity(n, want, ldwant)
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if dist > tol {
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t.Errorf("%v: |A * inv(A) - I| = %v is too large", prefix, dist)
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}
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}
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}
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})
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}
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}
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