mirror of
https://github.com/gonum/gonum.git
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17ea55aedb
Apply (with manual curation after the fact):
* s/^T/U+1d40/g
* s/^H/U+1d34/g
* s/, {2,3}if / $1/g
Some additional manual editing of odd formatting.
97 lines
2.7 KiB
Go
97 lines
2.7 KiB
Go
// Copyright ©2019 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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"gonum.org/v1/gonum/blas/blas64"
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"gonum.org/v1/gonum/floats"
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)
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type Dpbtrser interface {
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Dpbtrs(uplo blas.Uplo, n, kd, nrhs int, ab []float64, ldab int, b []float64, ldb int)
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Dpbtrfer
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}
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// DpbtrsTest tests Dpbtrs by comparing the computed and known, generated solutions of
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// a linear system with a random symmetric positive definite band matrix.
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func DpbtrsTest(t *testing.T, impl Dpbtrser) {
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rnd := rand.New(rand.NewSource(1))
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for _, n := range []int{0, 1, 2, 3, 4, 5, 65, 100, 129} {
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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 _, nrhs := range []int{0, 1, 2, 5} {
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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 + 3} {
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for _, ldb := range []int{max(1, nrhs), nrhs + 4} {
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dpbtrsTest(t, impl, rnd, uplo, n, kd, nrhs, ldab, ldb)
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}
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}
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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 dpbtrsTest(t *testing.T, impl Dpbtrser, rnd *rand.Rand, uplo blas.Uplo, n, kd, nrhs int, ldab, ldb int) {
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const tol = 1e-12
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name := fmt.Sprintf("uplo=%v,n=%v,kd=%v,nrhs=%v,ldab=%v,ldb=%v", string(uplo), n, kd, nrhs, ldab, ldb)
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// Generate a random symmetric positive definite band matrix.
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ab := randSymBand(uplo, n, kd, ldab, rnd)
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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.Dpbtrf(uplo, n, kd, abFac, ldab)
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if !ok {
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t.Fatalf("%v: bad test matrix, Dpbtrs failed", name)
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}
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abFacCopy := make([]float64, len(abFac))
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copy(abFacCopy, abFac)
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// Generate a random solution.
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xWant := make([]float64, n*ldb)
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for i := range xWant {
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xWant[i] = rnd.NormFloat64()
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}
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// Compute the corresponding right-hand side.
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bi := blas64.Implementation()
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b := make([]float64, len(xWant))
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if n > 0 {
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for j := 0; j < nrhs; j++ {
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bi.Dsbmv(uplo, n, kd, 1, ab, ldab, xWant[j:], ldb, 0, b[j:], ldb)
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}
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}
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// Solve Uᵀ * U * X = B or L * Lᵀ * X = B.
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impl.Dpbtrs(uplo, n, kd, nrhs, abFac, ldab, b, ldb)
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xGot := b
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// Check that the Cholesky factorization matrix has not been modified.
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if !floats.Equal(abFac, abFacCopy) {
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t.Errorf("%v: unexpected modification of ab", name)
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}
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// Compute and check the max-norm difference between the computed and generated solutions.
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var diff float64
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for i := 0; i < n; i++ {
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for j := 0; j < nrhs; j++ {
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diff = math.Max(diff, math.Abs(xWant[i*ldb+j]-xGot[i*ldb+j]))
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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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