1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
|
// Copyright (c) 2017-2023, University of Tennessee. All rights reserved.
// SPDX-License-Identifier: BSD-3-Clause
// This program is free software: you can redistribute it and/or modify it under
// the terms of the BSD 3-Clause license. See the accompanying LICENSE file.
#include "test.hh"
#include "lapack.hh"
#include "lapack/flops.hh"
#include "print_matrix.hh"
#include "error.hh"
#include "lapacke_wrappers.hh"
#include "cblas_wrappers.hh"
#include <vector>
// -----------------------------------------------------------------------------
template< typename scalar_t >
void test_gbrfs_work( Params& params, bool run )
{
using real_t = blas::real_type< scalar_t >;
// get & mark input values
lapack::Op trans = params.trans();
int64_t n = params.dim.n();
int64_t kl = params.kl();
int64_t ku = params.ku();
int64_t nrhs = params.nrhs();
int64_t align = params.align();
int64_t verbose = params.verbose();
real_t eps = std::numeric_limits< real_t >::epsilon();
real_t tol = params.tol() * eps;
// mark non-standard output values
params.ref_time();
//params.ref_gflops();
//params.gflops();
if (! run)
return;
// ---------- setup
// AB could use kd = kl + ku + 1, but for simplicity make AB = AFB.
int64_t kd = 2*kl + ku + 1; // number of diagonals in factor
int64_t ldab = roundup( kd, align );
int64_t ldafb = ldab;
int64_t ldb = roundup( blas::max( 1, n ), align );
int64_t ldx = ldb;
size_t size_AB = (size_t) ldab * n;
size_t size_AFB = size_AB;
size_t size_ipiv = (size_t) (n);
size_t size_B = (size_t) ldb * nrhs;
size_t size_X = size_B;
size_t size_ferr = (size_t) (nrhs);
size_t size_berr = (size_t) (nrhs);
std::vector< scalar_t > AB( size_AB );
std::vector< scalar_t > AFB( size_AFB );
std::vector< int64_t > ipiv_tst( size_ipiv );
std::vector< lapack_int > ipiv_ref( size_ipiv );
std::vector< scalar_t > B( size_B );
std::vector< scalar_t > X_tst( size_X );
std::vector< scalar_t > X_ref( size_X );
std::vector< real_t > ferr_tst( size_ferr );
std::vector< real_t > ferr_ref( size_ferr );
std::vector< real_t > berr_tst( size_berr );
std::vector< real_t > berr_ref( size_berr );
int64_t idist = 1;
int64_t iseed[4] = { 0, 1, 2, 3 };
lapack::larnv( idist, iseed, AB.size(), &AB[0] );
int64_t iseed_B[4];
std::copy( iseed, iseed+4, iseed_B );
lapack::larnv( idist, iseed, B.size(), &B[0] );
AFB = AB;
X_tst = B;
if (verbose >= 1) {
printf( "\n"
"AB n=%5lld, kl=%5lld, ku=%5lld, kd=%5lld, ldab=%5lld\n"
"B n=%5lld, nrhs=%5lld, ldb=%5lld\n",
llong( n ), llong( kl ), llong( ku ), llong( kd ), llong( ldab ),
llong( n ), llong( nrhs ), llong( ldb ) );
}
if (verbose >= 2) {
printf( "Input data in rows 0 to kl-1 are ignored.\n" );
printf( "AB = " ); print_matrix( kd, n, &AB[0], ldab );
printf( "B = " ); print_matrix( n, nrhs, &B[0], ldb );
}
// Factor
int64_t info = lapack::gbtrf( n, n, kl, ku, &AFB[0], ldafb, &ipiv_tst[0] );
if (info != 0) {
fprintf( stderr, "lapack::gbtrf returned error %lld\n", llong( info ) );
}
// Solve in X_tst
info = lapack::gbtrs( trans, n, kl, ku, nrhs, &AFB[0], ldafb, &ipiv_tst[0], &X_tst[0], ldx );
if (info != 0) {
fprintf( stderr, "lapack::gbtrs returned error %lld\n", llong( info ) );
}
X_ref = X_tst;
if (verbose >= 2) {
printf( "A_factor = " ); print_matrix( kd, n, &AFB[0], ldafb );
printf( "X = " ); print_matrix( n, nrhs, &X_tst[0], ldx );
}
std::copy (ipiv_tst.begin(), ipiv_tst.end(), ipiv_ref.begin() );
// ---------- run test
testsweeper::flush_cache( params.cache() );
double time = testsweeper::get_wtime();
// Refine solution in X_tst, using original AB and B, factored AFB.
// AB rows 0:kl-1 are ignored; start in row kl.
int64_t info_tst = lapack::gbrfs(
trans, n, kl, ku, nrhs,
&AB[ kl ], ldab, &AFB[0], ldafb, &ipiv_tst[0],
&B[0], ldb, &X_tst[0], ldx, &ferr_tst[0], &berr_tst[0] );
time = testsweeper::get_wtime() - time;
if (info_tst != 0) {
fprintf( stderr, "lapack::gbrfs returned error %lld\n", llong( info_tst ) );
}
params.time() = time;
//double gflop = lapack::Gflop< scalar_t >::gbrfs( trans, n, kl, ku, nrhs );
//params.gflops() = gflop / time;
if (verbose >= 2) {
printf( "Xrfs = " ); print_matrix( n, nrhs, &X_tst[0], ldx );
printf( "ferr = " ); print_vector( n, &ferr_tst[0], 1 );
printf( "berr = " ); print_vector( n, &berr_tst[0], 1 );
}
if (params.check() == 'y') {
// ---------- check error
// Relative backwards error = ||b - Ax|| / (n * ||A|| * ||x||).
// No gbmm, so loop over RHS.
// AB rows 0:kl-1 are ignored; start in row kl.
for (int64_t j = 0; j < nrhs; ++j) {
// B_ref -= A * B_tst
cblas_gbmv( CblasColMajor, cblas_trans_const(trans), n, n, kl, ku,
-1.0, &AB[ kl ], ldab,
&X_tst[ j*ldx ], 1,
1.0, &B[ j*ldb ], 1 );
}
if (verbose >= 2) {
printf( "R = " ); print_matrix( n, nrhs, &B[0], ldb );
}
real_t error = lapack::lange( lapack::Norm::One, n, nrhs, &B[0], ldb );
real_t Xnorm = lapack::lange( lapack::Norm::One, n, nrhs, &X_tst[0], ldx );
real_t Anorm = lapack::langb( lapack::Norm::One, n, kl, ku, &AB[ kl ], ldab );
error /= (n * Anorm * Xnorm);
params.error() = error;
params.okay() = (error < tol);
// Reset B for ref using saved seed.
lapack::larnv( idist, iseed_B, B.size(), &B[0] );
}
if (params.ref() == 'y') {
// ---------- run reference
testsweeper::flush_cache( params.cache() );
time = testsweeper::get_wtime();
int64_t info_ref = LAPACKE_gbrfs(
to_char( trans ), n, kl, ku, nrhs,
&AB[ kl ], ldab, &AFB[0], ldafb, &ipiv_ref[0],
&B[0], ldb, &X_ref[0], ldx, &ferr_ref[0], &berr_ref[0] );
time = testsweeper::get_wtime() - time;
if (info_ref != 0) {
fprintf( stderr, "LAPACKE_gbrfs returned error %lld\n", llong( info_ref ) );
}
params.ref_time() = time;
//params.ref_gflops() = gflop / time;
}
}
// -----------------------------------------------------------------------------
void test_gbrfs( Params& params, bool run )
{
switch (params.datatype()) {
case testsweeper::DataType::Single:
test_gbrfs_work< float >( params, run );
break;
case testsweeper::DataType::Double:
test_gbrfs_work< double >( params, run );
break;
case testsweeper::DataType::SingleComplex:
test_gbrfs_work< std::complex<float> >( params, run );
break;
case testsweeper::DataType::DoubleComplex:
test_gbrfs_work< std::complex<double> >( params, run );
break;
default:
throw std::runtime_error( "unknown datatype" );
break;
}
}
|
