gonum.org/v1/gonum@v0.14.0/blas/testblas/zhbmv.go (about)

     1  // Copyright ©2018 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 testblas
     6  
     7  import (
     8  	"fmt"
     9  	"math"
    10  	"testing"
    11  
    12  	"golang.org/x/exp/rand"
    13  	"gonum.org/v1/gonum/blas"
    14  )
    15  
    16  type Zhbmver interface {
    17  	Zhbmv(uplo blas.Uplo, n, k int, alpha complex128, ab []complex128, ldab int, x []complex128, incX int, beta complex128, y []complex128, incY int)
    18  
    19  	Zhemver
    20  }
    21  
    22  func ZhbmvTest(t *testing.T, impl Zhbmver) {
    23  	rnd := rand.New(rand.NewSource(1))
    24  	for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
    25  		for _, n := range []int{0, 1, 2, 3, 5} {
    26  			for k := 0; k < n; k++ {
    27  				for _, ldab := range []int{k + 1, k + 1 + 10} {
    28  					// Generate all possible combinations of given increments.
    29  					// Use slices to reduce indentation.
    30  					for _, inc := range allPairs([]int{-11, 1, 7}, []int{-3, 1, 5}) {
    31  						incX := inc[0]
    32  						incY := inc[1]
    33  						for _, ab := range []struct {
    34  							alpha complex128
    35  							beta  complex128
    36  						}{
    37  							// All potentially relevant values of
    38  							// alpha and beta.
    39  							{0, 0},
    40  							{0, 1},
    41  							{0, complex(rnd.NormFloat64(), rnd.NormFloat64())},
    42  							{complex(rnd.NormFloat64(), rnd.NormFloat64()), 0},
    43  							{complex(rnd.NormFloat64(), rnd.NormFloat64()), 1},
    44  							{complex(rnd.NormFloat64(), rnd.NormFloat64()), complex(rnd.NormFloat64(), rnd.NormFloat64())},
    45  						} {
    46  							testZhbmv(t, impl, rnd, uplo, n, k, ab.alpha, ab.beta, ldab, incX, incY)
    47  						}
    48  					}
    49  				}
    50  			}
    51  		}
    52  	}
    53  }
    54  
    55  // testZhbmv tests Zhbmv by comparing its output to that of Zhemv.
    56  func testZhbmv(t *testing.T, impl Zhbmver, rnd *rand.Rand, uplo blas.Uplo, n, k int, alpha, beta complex128, ldab, incX, incY int) {
    57  	const tol = 1e-13
    58  
    59  	// Allocate a dense-storage Hermitian band matrix filled with NaNs that will be
    60  	// used as the reference matrix for Zhemv.
    61  	lda := max(1, n)
    62  	a := makeZGeneral(nil, n, n, lda)
    63  	// Fill the matrix with zeros.
    64  	for i := 0; i < n; i++ {
    65  		for j := 0; j < n; j++ {
    66  			a[i*lda+j] = 0
    67  		}
    68  	}
    69  	// Fill the triangle band with random data, invalidating the imaginary
    70  	// part of diagonal elements because it should not be referenced by
    71  	// Zhbmv and Zhemv.
    72  	if uplo == blas.Upper {
    73  		for i := 0; i < n; i++ {
    74  			a[i*lda+i] = complex(rnd.NormFloat64(), math.NaN())
    75  			for j := i + 1; j < min(n, i+k+1); j++ {
    76  				re := rnd.NormFloat64()
    77  				im := rnd.NormFloat64()
    78  				a[i*lda+j] = complex(re, im)
    79  			}
    80  		}
    81  	} else {
    82  		for i := 0; i < n; i++ {
    83  			for j := max(0, i-k); j < i; j++ {
    84  				re := rnd.NormFloat64()
    85  				im := rnd.NormFloat64()
    86  				a[i*lda+j] = complex(re, im)
    87  			}
    88  			a[i*lda+i] = complex(rnd.NormFloat64(), math.NaN())
    89  		}
    90  	}
    91  	// Create the actual Hermitian band matrix.
    92  	ab := zPackTriBand(k, ldab, uplo, n, a, lda)
    93  	abCopy := make([]complex128, len(ab))
    94  	copy(abCopy, ab)
    95  
    96  	// Generate a random complex vector x.
    97  	xtest := make([]complex128, n)
    98  	for i := range xtest {
    99  		re := rnd.NormFloat64()
   100  		im := rnd.NormFloat64()
   101  		xtest[i] = complex(re, im)
   102  	}
   103  	x := makeZVector(xtest, incX)
   104  	xCopy := make([]complex128, len(x))
   105  	copy(xCopy, x)
   106  
   107  	// Generate a random complex vector y.
   108  	ytest := make([]complex128, n)
   109  	for i := range ytest {
   110  		re := rnd.NormFloat64()
   111  		im := rnd.NormFloat64()
   112  		ytest[i] = complex(re, im)
   113  	}
   114  	y := makeZVector(ytest, incY)
   115  
   116  	want := make([]complex128, len(y))
   117  	copy(want, y)
   118  
   119  	// Compute the reference result of alpha*op(A)*x + beta*y, storing it
   120  	// into want.
   121  	impl.Zhemv(uplo, n, alpha, a, lda, x, incX, beta, want, incY)
   122  	// Compute alpha*op(A)*x + beta*y, storing the result in-place into y.
   123  	impl.Zhbmv(uplo, n, k, alpha, ab, ldab, x, incX, beta, y, incY)
   124  
   125  	prefix := fmt.Sprintf("uplo=%v,n=%v,k=%v,incX=%v,incY=%v,ldab=%v", uplo, n, k, incX, incY, ldab)
   126  	if !zsame(x, xCopy) {
   127  		t.Errorf("%v: unexpected modification of x", prefix)
   128  	}
   129  	if !zsame(ab, abCopy) {
   130  		t.Errorf("%v: unexpected modification of ab", prefix)
   131  	}
   132  	if !zSameAtNonstrided(y, want, incY) {
   133  		t.Errorf("%v: unexpected modification of y", prefix)
   134  	}
   135  	if !zEqualApproxAtStrided(y, want, incY, tol) {
   136  		t.Errorf("%v: unexpected result\nwant %v\ngot  %v", prefix, want, y)
   137  	}
   138  }