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88 lines
2.0 KiB
Go
88 lines
2.0 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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"math"
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"math/rand"
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"testing"
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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 Dlasq1er interface {
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Dlasq1(n int, d, e, work []float64) int
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Dgetrfer
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}
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func Dlasq1Test(t *testing.T, impl Dlasq1er) {
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rnd := rand.New(rand.NewSource(1))
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bi := blas64.Implementation()
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// TODO(btracey): Increase the size of this test when we have a more numerically
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// stable way to test the singular values.
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for _, n := range []int{1, 2, 5, 8} {
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work := make([]float64, 4*n)
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d := make([]float64, n)
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e := make([]float64, n-1)
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for cas := 0; cas < 1; cas++ {
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for i := range work {
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work[i] = rnd.Float64()
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}
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for i := range d {
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d[i] = rnd.NormFloat64() + 10
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}
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for i := range e {
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e[i] = rnd.NormFloat64()
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}
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ldm := n
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m := make([]float64, n*ldm)
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// Set up the matrix
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for i := 0; i < n; i++ {
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m[i*ldm+i] = d[i]
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if i != n-1 {
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m[(i+1)*ldm+i] = e[i]
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}
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}
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ldmm := n
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mm := make([]float64, n*ldmm)
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bi.Dgemm(blas.Trans, blas.NoTrans, n, n, n, 1, m, ldm, m, ldm, 0, mm, ldmm)
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impl.Dlasq1(n, d, e, work)
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// Check that they are singular values. The
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// singular values are the square roots of the
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// eigenvalues of X^T * X
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mmCopy := make([]float64, len(mm))
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copy(mmCopy, mm)
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ipiv := make([]int, n)
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for elem, sv := range d[0:n] {
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copy(mm, mmCopy)
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lambda := sv * sv
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for i := 0; i < n; i++ {
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mm[i*ldm+i] -= lambda
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}
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// Compute LU.
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ok := impl.Dgetrf(n, n, mm, ldmm, ipiv)
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if !ok {
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// Definitely singular.
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continue
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}
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// Compute determinant
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var logdet float64
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for i := 0; i < n; i++ {
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v := mm[i*ldm+i]
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logdet += math.Log(math.Abs(v))
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}
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if math.Exp(logdet) > 2 {
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t.Errorf("Incorrect singular value. n = %d, cas = %d, elem = %d, det = %v", n, cas, elem, math.Exp(logdet))
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}
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}
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}
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}
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}
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