gonum.org/v1/gonum@v0.14.0/lapack/testlapack/dpbtrs.go (about)

     1  // Copyright ©2019 The Gonum Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package testlapack
     6  
     7  import (
     8  	"fmt"
     9  	"math"
    10  	"testing"
    11  
    12  	"golang.org/x/exp/rand"
    13  
    14  	"gonum.org/v1/gonum/blas"
    15  	"gonum.org/v1/gonum/blas/blas64"
    16  	"gonum.org/v1/gonum/floats"
    17  )
    18  
    19  type Dpbtrser interface {
    20  	Dpbtrs(uplo blas.Uplo, n, kd, nrhs int, ab []float64, ldab int, b []float64, ldb int)
    21  
    22  	Dpbtrfer
    23  }
    24  
    25  // DpbtrsTest tests Dpbtrs by comparing the computed and known, generated solutions of
    26  // a linear system with a random symmetric positive definite band matrix.
    27  func DpbtrsTest(t *testing.T, impl Dpbtrser) {
    28  	rnd := rand.New(rand.NewSource(1))
    29  	for _, n := range []int{0, 1, 2, 3, 4, 5, 65, 100, 129} {
    30  		for _, kd := range []int{0, (n + 1) / 4, (3*n - 1) / 4, (5*n + 1) / 4} {
    31  			for _, nrhs := range []int{0, 1, 2, 5} {
    32  				for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
    33  					for _, ldab := range []int{kd + 1, kd + 1 + 3} {
    34  						for _, ldb := range []int{max(1, nrhs), nrhs + 4} {
    35  							dpbtrsTest(t, impl, rnd, uplo, n, kd, nrhs, ldab, ldb)
    36  						}
    37  					}
    38  				}
    39  			}
    40  		}
    41  	}
    42  }
    43  
    44  func dpbtrsTest(t *testing.T, impl Dpbtrser, rnd *rand.Rand, uplo blas.Uplo, n, kd, nrhs int, ldab, ldb int) {
    45  	const tol = 1e-12
    46  
    47  	name := fmt.Sprintf("uplo=%v,n=%v,kd=%v,nrhs=%v,ldab=%v,ldb=%v", string(uplo), n, kd, nrhs, ldab, ldb)
    48  
    49  	// Generate a random symmetric positive definite band matrix.
    50  	ab := randSymBand(uplo, n, kd, ldab, rnd)
    51  
    52  	// Compute the Cholesky decomposition of A.
    53  	abFac := make([]float64, len(ab))
    54  	copy(abFac, ab)
    55  	ok := impl.Dpbtrf(uplo, n, kd, abFac, ldab)
    56  	if !ok {
    57  		t.Fatalf("%v: bad test matrix, Dpbtrs failed", name)
    58  	}
    59  	abFacCopy := make([]float64, len(abFac))
    60  	copy(abFacCopy, abFac)
    61  
    62  	// Generate a random solution.
    63  	xWant := make([]float64, n*ldb)
    64  	for i := range xWant {
    65  		xWant[i] = rnd.NormFloat64()
    66  	}
    67  
    68  	// Compute the corresponding right-hand side.
    69  	bi := blas64.Implementation()
    70  	b := make([]float64, len(xWant))
    71  	if n > 0 {
    72  		for j := 0; j < nrhs; j++ {
    73  			bi.Dsbmv(uplo, n, kd, 1, ab, ldab, xWant[j:], ldb, 0, b[j:], ldb)
    74  		}
    75  	}
    76  
    77  	// Solve  Uᵀ * U * X = B  or  L * Lᵀ * X = B.
    78  	impl.Dpbtrs(uplo, n, kd, nrhs, abFac, ldab, b, ldb)
    79  	xGot := b
    80  
    81  	// Check that the Cholesky factorization matrix has not been modified.
    82  	if !floats.Equal(abFac, abFacCopy) {
    83  		t.Errorf("%v: unexpected modification of ab", name)
    84  	}
    85  
    86  	// Compute and check the max-norm difference between the computed and generated solutions.
    87  	var diff float64
    88  	for i := 0; i < n; i++ {
    89  		for j := 0; j < nrhs; j++ {
    90  			diff = math.Max(diff, math.Abs(xWant[i*ldb+j]-xGot[i*ldb+j]))
    91  		}
    92  	}
    93  	if diff > tol {
    94  		t.Errorf("%v: unexpected result, diff=%v", name, diff)
    95  	}
    96  }