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123 lines
3.1 KiB
Go
123 lines
3.1 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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"math"
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"sort"
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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/floats"
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"gonum.org/v1/gonum/lapack"
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)
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type Dlasq2er interface {
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Dlasq2(n int, z []float64) (info int)
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Dsyev(jobz lapack.EVJob, uplo blas.Uplo, n int, a []float64, lda int, w, work []float64, lwork int) (ok bool)
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}
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func Dlasq2Test(t *testing.T, impl Dlasq2er) {
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const tol = 1e-14
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rnd := rand.New(rand.NewSource(1))
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for _, n := range []int{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 25, 50} {
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for k := 0; k < 10; k++ {
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for typ := 0; typ <= 2; typ++ {
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name := fmt.Sprintf("n=%v,typ=%v", n, typ)
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want := make([]float64, n)
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z := make([]float64, 4*n)
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switch typ {
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case 0:
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// L is the identity, U has zero diagonal.
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case 1:
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// L is the identity, U has random diagonal, and so T is upper triangular.
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for i := 0; i < n; i++ {
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z[2*i] = rnd.Float64()
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want[i] = z[2*i]
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}
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sort.Float64s(want)
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case 2:
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// Random tridiagonal matrix
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for i := range z {
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z[i] = rnd.Float64()
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}
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// The slice 'want' is computed below.
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}
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zCopy := make([]float64, len(z))
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copy(zCopy, z)
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// Compute the eigenvalues of the symmetric positive definite
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// tridiagonal matrix associated with the slice z.
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info := impl.Dlasq2(n, z)
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if info != 0 {
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t.Fatalf("%v: Dlasq2 failed", name)
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}
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if n == 0 {
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continue
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}
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got := z[:n]
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if typ == 2 {
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// Compute the expected result.
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// Compute the non-symmetric tridiagonal matrix T = L*U where L and
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// U are represented by the slice z.
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ldt := n
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T := make([]float64, n*ldt)
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for i := 0; i < n; i++ {
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if i == 0 {
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T[0] = zCopy[0]
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} else {
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T[i*ldt+i] = zCopy[2*i-1] + zCopy[2*i]
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}
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if i < n-1 {
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T[i*ldt+i+1] = 1
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T[(i+1)*ldt+i] = zCopy[2*i+1] * zCopy[2*i]
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}
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}
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// Compute the symmetric tridiagonal matrix by applying a similarity
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// transformation on T: D^{-1}*T*D. See discussion and references in
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// http://icl.cs.utk.edu/lapack-forum/viewtopic.php?f=5&t=4839
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d := make([]float64, n)
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d[0] = 1
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for i := 1; i < n; i++ {
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d[i] = d[i-1] * T[i*ldt+i-1] / T[(i-1)*ldt+i]
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}
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for i, di := range d {
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d[i] = math.Sqrt(di)
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}
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for i := 0; i < n; i++ {
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// Update only the upper triangle.
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for j := i; j <= min(i+1, n-1); j++ {
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T[i*ldt+j] *= d[j] / d[i]
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}
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}
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// Compute the eigenvalues of D^{-1}*T*D by using Dsyev. It's call
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// tree doesn't include Dlasq2.
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work := make([]float64, 3*n)
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ok := impl.Dsyev(lapack.EVNone, blas.Upper, n, T, ldt, want, work, len(work))
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if !ok {
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t.Fatalf("%v: Dsyev failed", name)
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}
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}
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sort.Float64s(got)
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diff := floats.Distance(got, want, math.Inf(1))
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if diff > tol {
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t.Errorf("%v: unexpected eigenvalues; diff=%v\n%v\n%v\n\n", name, diff, got, want)
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}
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}
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}
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}
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}
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