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// Copyright ©2021 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/lapack"
)
type Dpstrfer interface {
Dpstrf(uplo blas.Uplo, n int, a []float64, lda int, piv []int, tol float64, work []float64) (rank int, ok bool)
}
func DpstrfTest(t *testing.T, impl Dpstrfer) {
rnd := rand.New(rand.NewSource(1))
for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
t.Run(uploToString(uplo), func(t *testing.T) {
for _, n := range []int{0, 1, 2, 3, 4, 5, 31, 32, 33, 63, 64, 65, 127, 128, 129} {
for _, lda := range []int{max(1, n), n + 5} {
for _, rank := range []int{int(0.7 * float64(n)), n} {
dpstrfTest(t, impl, rnd, uplo, n, lda, rank)
}
}
}
})
}
}
func dpstrfTest(t *testing.T, impl Dpstrfer, rnd *rand.Rand, uplo blas.Uplo, n, lda, rankWant int) {
const tol = 1e-13
name := fmt.Sprintf("n=%v,lda=%v", n, lda)
bi := blas64.Implementation()
// Generate a random, symmetric A with the given rank by applying rankWant
// rank-1 updates to the zero matrix.
a := make([]float64, n*lda)
for i := 0; i < rankWant; i++ {
x := randomSlice(n, rnd)
bi.Dsyr(uplo, n, 1, x, 1, a, lda)
}
// Make a copy of A for storing the factorization.
aFac := make([]float64, len(a))
copy(aFac, a)
// Allocate a slice for pivots and fill it with invalid index values.
piv := make([]int, n)
for i := range piv {
piv[i] = -1
}
// Allocate the work slice.
work := make([]float64, 2*n)
// Call Dpstrf to Compute the Cholesky factorization with complete pivoting.
rank, ok := impl.Dpstrf(uplo, n, aFac, lda, piv, -1, work)
if ok != (rank == n) {
t.Errorf("%v: unexpected ok; got %v, want %v", name, ok, rank == n)
}
if rank != rankWant {
t.Errorf("%v: unexpected rank; got %v, want %v", name, rank, rankWant)
}
if n == 0 {
return
}
// Check that the residual |P*Uᵀ*U*Pᵀ - A| / n or |P*L*Lᵀ*Pᵀ - A| / n is
// sufficiently small.
resid := residualDpstrf(uplo, n, a, aFac, lda, rank, piv)
if resid > tol || math.IsNaN(resid) {
t.Errorf("%v: residual too large; got %v, want<=%v", name, resid, tol)
}
}
func residualDpstrf(uplo blas.Uplo, n int, a, aFac []float64, lda int, rank int, piv []int) float64 {
bi := blas64.Implementation()
// Reconstruct the symmetric positive semi-definite matrix A from its L or U
// factors and the permutation matrix P.
perm := zeros(n, n, n)
if uplo == blas.Upper {
// Change notation.
u, ldu := aFac, lda
// Zero out last n-rank rows of the factor U.
for i := rank; i < n; i++ {
for j := i; j < n; j++ {
u[i*ldu+j] = 0
}
}
// Extract U to aRec.
aRec := zeros(n, n, n)
for i := 0; i < n; i++ {
for j := i; j < n; j++ {
aRec.Data[i*aRec.Stride+j] = u[i*ldu+j]
}
}
// Multiply U by Uᵀ from the left.
bi.Dtrmm(blas.Left, blas.Upper, blas.Trans, blas.NonUnit, n, n,
1, u, ldu, aRec.Data, aRec.Stride)
// Form P * Uᵀ * U * Pᵀ.
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
if piv[i] > piv[j] {
// Don't set the lower triangle.
continue
}
if i <= j {
perm.Data[piv[i]*perm.Stride+piv[j]] = aRec.Data[i*aRec.Stride+j]
} else {
perm.Data[piv[i]*perm.Stride+piv[j]] = aRec.Data[j*aRec.Stride+i]
}
}
}
// Compute the difference P*Uᵀ*U*Pᵀ - A.
for i := 0; i < n; i++ {
for j := i; j < n; j++ {
perm.Data[i*perm.Stride+j] -= a[i*lda+j]
}
}
} else {
// Change notation.
l, ldl := aFac, lda
// Zero out last n-rank columns of the factor L.
for i := rank; i < n; i++ {
for j := rank; j <= i; j++ {
l[i*ldl+j] = 0
}
}
// Extract L to aRec.
aRec := zeros(n, n, n)
for i := 0; i < n; i++ {
for j := 0; j <= i; j++ {
aRec.Data[i*aRec.Stride+j] = l[i*ldl+j]
}
}
// Multiply L by Lᵀ from the right.
bi.Dtrmm(blas.Right, blas.Lower, blas.Trans, blas.NonUnit, n, n,
1, l, ldl, aRec.Data, aRec.Stride)
// Form P * L * Lᵀ * Pᵀ.
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
if piv[i] < piv[j] {
// Don't set the upper triangle.
continue
}
if i >= j {
perm.Data[piv[i]*perm.Stride+piv[j]] = aRec.Data[i*aRec.Stride+j]
} else {
perm.Data[piv[i]*perm.Stride+piv[j]] = aRec.Data[j*aRec.Stride+i]
}
}
}
// Compute the difference P*L*Lᵀ*Pᵀ - A.
for i := 0; i < n; i++ {
for j := 0; j <= i; j++ {
perm.Data[i*perm.Stride+j] -= a[i*lda+j]
}
}
}
// Compute |P*Uᵀ*U*Pᵀ - A| / n or |P*L*Lᵀ*Pᵀ - A| / n.
return dlansy(lapack.MaxColumnSum, uplo, n, perm.Data, perm.Stride) / float64(n)
}
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