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92 lines
2.4 KiB
Go
92 lines
2.4 KiB
Go
// Copyright ©2015 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/floats"
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"gonum.org/v1/gonum/lapack"
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)
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type Dgeconer interface {
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Dgecon(norm lapack.MatrixNorm, n int, a []float64, lda int, anorm float64, work []float64, iwork []int) float64
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Dgetrier
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Dlanger
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}
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func DgeconTest(t *testing.T, impl Dgeconer) {
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rnd := rand.New(rand.NewSource(1))
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for _, n := range []int{0, 1, 2, 3, 4, 5, 10, 50} {
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for _, lda := range []int{max(1, n), n + 3} {
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dgeconTest(t, impl, rnd, n, lda)
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}
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}
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}
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func dgeconTest(t *testing.T, impl Dgeconer, rnd *rand.Rand, n, lda int) {
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const ratioThresh = 10
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// Generate a random square matrix A with elements uniformly in [-1,1).
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a := make([]float64, max(0, (n-1)*lda+n))
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for i := range a {
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a[i] = 2*rnd.Float64() - 1
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}
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// Allocate work slices.
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iwork := make([]int, n)
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work := make([]float64, max(1, 4*n))
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// Compute the LU factorization of A.
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aFac := make([]float64, len(a))
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copy(aFac, a)
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ipiv := make([]int, n)
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ok := impl.Dgetrf(n, n, aFac, lda, ipiv)
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if !ok {
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t.Fatalf("n=%v,lda=%v: bad matrix, Dgetrf failed", n, lda)
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}
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aFacCopy := make([]float64, len(aFac))
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copy(aFacCopy, aFac)
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// Compute the inverse A^{-1} from the LU factorization.
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aInv := make([]float64, len(aFac))
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copy(aInv, aFac)
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ok = impl.Dgetri(n, aInv, lda, ipiv, work, len(work))
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if !ok {
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t.Fatalf("n=%v,lda=%v: bad matrix, Dgetri failed", n, lda)
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}
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for _, norm := range []lapack.MatrixNorm{lapack.MaxColumnSum, lapack.MaxRowSum} {
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name := fmt.Sprintf("norm=%v,n=%v,lda=%v", string(norm), n, lda)
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// Compute the norm of A and A^{-1}.
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aNorm := impl.Dlange(norm, n, n, a, lda, work)
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aInvNorm := impl.Dlange(norm, n, n, aInv, lda, work)
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// Compute a good estimate of the condition number
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// rcondWant := 1/(norm(A) * norm(inv(A)))
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rcondWant := 1.0
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if aNorm > 0 && aInvNorm > 0 {
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rcondWant = 1 / aNorm / aInvNorm
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}
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// Compute an estimate of rcond using the LU factorization and Dgecon.
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rcondGot := impl.Dgecon(norm, n, aFac, lda, aNorm, work, iwork)
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if !floats.Equal(aFac, aFacCopy) {
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t.Errorf("%v: unexpected modification of aFac", name)
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}
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ratio := rCondTestRatio(rcondGot, rcondWant)
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if ratio >= ratioThresh {
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t.Errorf("%v: unexpected value of rcond; got=%v, want=%v (ratio=%v)",
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name, rcondGot, rcondWant, ratio)
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}
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}
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}
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