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111 lines
3.0 KiB
Go
111 lines
3.0 KiB
Go
// Copyright ©2018 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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"gonum.org/v1/gonum/lapack"
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)
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type Dlauu2er interface {
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Dlauu2(uplo blas.Uplo, n int, a []float64, lda int)
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}
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func Dlauu2Test(t *testing.T, impl Dlauu2er) {
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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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ns := []int{0, 1, 2, 3, 4, 5, 10, 25}
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dlauuTest(t, impl.Dlauu2, uplo, ns)
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})
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}
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}
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func dlauuTest(t *testing.T, dlauu func(blas.Uplo, int, []float64, int), uplo blas.Uplo, ns []int) {
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const tol = 1e-13
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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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// Allocate n×n matrix A and fill it with random numbers.
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// Only its uplo triangle will be used below.
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a := make([]float64, n*lda)
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for i := range a {
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a[i] = rnd.NormFloat64()
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}
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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 U*Uᵀ or Lᵀ*L using Dlauu?.
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dlauu(uplo, n, a, lda)
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if n == 0 {
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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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// * Convert the result of Dlauu? into a dense symmetric matrix.
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// * Zero out the triangle in aCopy opposite to uplo.
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if uplo == blas.Upper {
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if !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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for i := 1; i < n; i++ {
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for j := 0; j < i; j++ {
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a[i*lda+j] = a[j*lda+i]
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aCopy[i*lda+j] = 0
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}
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}
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} else {
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if !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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for i := 0; i < n-1; i++ {
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for j := i + 1; j < n; j++ {
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a[i*lda+j] = a[j*lda+i]
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aCopy[i*lda+j] = 0
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}
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}
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}
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// Compute U*Uᵀ or Lᵀ*L using Dgemm with U and L
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// represented as dense triangular matrices.
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r := cloneGeneral(blas64.General{Rows: n, Cols: n, Data: a, Stride: lda})
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if uplo == blas.Upper {
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// Use aCopy as a dense representation of the upper triangular U.
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u := aCopy
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ldu := lda
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// Compute U*Uᵀ - A and store the result into R.
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bi.Dgemm(blas.NoTrans, blas.Trans, n, n, n,
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1, u, ldu, u, ldu, -1, r.Data, r.Stride)
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} else {
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// Use aCopy as a dense representation of the lower triangular L.
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l := aCopy
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ldl := lda
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// Compute Lᵀ*L - A and store the result into R.
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bi.Dgemm(blas.Trans, blas.NoTrans, n, n, n,
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1, l, ldl, l, ldl, -1, r.Data, r.Stride)
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}
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resid := dlange(lapack.MaxColumnSum, r.Rows, r.Cols, r.Data, r.Stride)
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if resid > tol*float64(n) {
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t.Errorf("%v: unexpected result", prefix)
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}
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}
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}
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}
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