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82 lines
2.0 KiB
Go
82 lines
2.0 KiB
Go
// Copyright ©2023 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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"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 Dptconer interface {
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Dptcon(n int, d, e []float64, anorm float64, work []float64) (rcond float64)
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Dpttrf(n int, d, e []float64) (ok bool)
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Dpttrs(n, nrhs int, d, e []float64, b []float64, ldb int)
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}
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func DptconTest(t *testing.T, impl Dptconer) {
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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, 20, 50, 51, 52, 53, 54, 100} {
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dptconTest(t, impl, rnd, n)
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}
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}
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func dptconTest(t *testing.T, impl Dptconer, rnd *rand.Rand, n int) {
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const tol = 1e-15
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name := fmt.Sprintf("n=%v", n)
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// Generate a random diagonally dominant symmetric tridiagonal matrix A.
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d, e := newRandomSymTridiag(n, rnd)
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aNorm := dlanst(lapack.MaxColumnSum, n, d, e)
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// Compute the Cholesky factorization of A.
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ok := impl.Dpttrf(n, d, e)
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if !ok {
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t.Errorf("%v: bad test matrix, Dpttrf failed", name)
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return
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}
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// Compute the reciprocal of the condition number of A.
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dCopy := make([]float64, len(d))
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copy(dCopy, d)
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eCopy := make([]float64, len(e))
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copy(eCopy, e)
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work := make([]float64, 3*n)
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rcondGot := impl.Dptcon(n, d, e, aNorm, work)
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// Check that Dptcon didn't modify d and e.
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if !floats.Equal(d, dCopy) {
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t.Errorf("%v: unexpected modification of d", name)
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}
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if !floats.Equal(e, eCopy) {
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t.Errorf("%v: unexpected modification of e", name)
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}
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// Compute the norm of A⁻¹.
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aInv, lda := make([]float64, n*n), max(1, n)
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for i := 0; i < n; i++ {
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aInv[i*lda+i] = 1
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}
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impl.Dpttrs(n, n, d, e, aInv, lda)
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aInvNorm := dlange(lapack.MaxColumnSum, n, n, aInv, lda)
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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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diff := math.Abs(rcondGot - rcondWant)
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if diff > tol {
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t.Errorf("%v: unexpected value of rcond. got=%v, want=%v (diff=%v)", name, rcondGot, rcondWant, diff)
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}
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}
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