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96 lines
2.6 KiB
Go
96 lines
2.6 KiB
Go
// Copyright ©2017 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/blas"
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)
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type Dpbtf2er interface {
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Dpbtf2(uplo blas.Uplo, n, kd int, ab []float64, ldab int) (ok bool)
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}
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// Dpbtf2Test tests Dpbtf2 on random symmetric positive definite band matrices
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// by checking that the Cholesky factors multiply back to the original matrix.
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func Dpbtf2Test(t *testing.T, impl Dpbtf2er) {
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// TODO(vladimir-ch): include expected-failure test case.
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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} {
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for _, kd := range []int{0, (n + 1) / 4, (3*n - 1) / 4, (5*n + 1) / 4} {
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for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
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for _, ldab := range []int{kd + 1, kd + 1 + 7} {
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dpbtf2Test(t, impl, rnd, uplo, n, kd, ldab)
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}
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}
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}
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}
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}
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func dpbtf2Test(t *testing.T, impl Dpbtf2er, rnd *rand.Rand, uplo blas.Uplo, n, kd int, ldab int) {
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const tol = 1e-12
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name := fmt.Sprintf("uplo=%v,n=%v,kd=%v,ldab=%v", string(uplo), n, kd, ldab)
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// Allocate a band matrix and fill it with random numbers.
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ab := make([]float64, n*ldab)
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for i := range ab {
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ab[i] = rnd.NormFloat64()
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}
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// Make sure that the matrix U or L has a sufficiently positive diagonal.
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switch uplo {
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case blas.Upper:
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for i := 0; i < n; i++ {
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ab[i*ldab] = 2 + rnd.Float64()
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}
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case blas.Lower:
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for i := 0; i < n; i++ {
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ab[i*ldab+kd] = 2 + rnd.Float64()
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}
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}
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// Compute U^T*U or L*L^T. The resulting (symmetric) matrix A will be positive definite.
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dsbmm(uplo, n, kd, ab, ldab)
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// Compute the Cholesky decomposition of A.
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abFac := make([]float64, len(ab))
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copy(abFac, ab)
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ok := impl.Dpbtf2(uplo, n, kd, abFac, ldab)
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if !ok {
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t.Fatalf("%v: bad test matrix, Dpbtf2 failed", name)
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}
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if n == 0 {
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return
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}
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// Reconstruct an symmetric band matrix from the U^T*U or L*L^T factorization, overwriting abFac.
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dsbmm(uplo, n, kd, abFac, ldab)
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// Compute and check the max-norm distance between the reconstructed and original matrix A.
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var diff float64
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switch uplo {
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case blas.Upper:
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for i := 0; i < n; i++ {
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for j := 0; j < min(kd+1, n-i); j++ {
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diff = math.Max(diff, math.Abs(abFac[i*ldab+j]-ab[i*ldab+j]))
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}
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}
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case blas.Lower:
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for i := 0; i < n; i++ {
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for j := max(0, kd-i); j < kd+1; j++ {
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diff = math.Max(diff, math.Abs(abFac[i*ldab+j]-ab[i*ldab+j]))
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}
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}
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}
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if diff > tol {
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t.Errorf("%v: unexpected result, diff=%v", name, diff)
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}
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}
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