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// 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_pbrfs_work( Params& params, bool run )
{
using real_t = blas::real_type< scalar_t >;
// get & mark input values
lapack::Uplo uplo = params.uplo();
int64_t n = params.dim.n();
int64_t kd = params.kd();
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
int64_t ldab = roundup( kd+1, 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_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< 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] );
X_tst = B;
// diagonally dominant -> positive definite
if (uplo == lapack::Uplo::Upper) {
for (int64_t j = 0; j < n; ++j) {
AB[ kd + j*ldab ] += n;
}
}
else { // lower
for (int64_t j = 0; j < n; ++j) {
AB[ j*ldab ] += n;
}
}
AFB = AB;
// Factor
int64_t info = lapack::pbtrf( uplo, n, kd, &AFB[0], ldafb );
if (info != 0) {
fprintf( stderr, "lapack::pbtrf returned error %lld\n", llong( info ) );
}
// Solve in X_tst
info = lapack::pbtrs ( uplo, n, kd, nrhs, &AFB[0], ldab, &X_tst[0], ldx );
if (info != 0) {
fprintf( stderr, "lapack::pbtrs returned error %lld\n", llong( info ) );
}
X_ref = X_tst;
if (verbose >= 2) {
printf( "A_factor = " ); print_matrix( kd+1, n, &AFB[0], ldafb );
printf( "X = " ); print_matrix( n, nrhs, &X_tst[0], ldx );
}
// ---------- run test
testsweeper::flush_cache( params.cache() );
double time = testsweeper::get_wtime();
// Refine solution in X_tst, using original AB and B, factored AFB.
int64_t info_tst = lapack::pbrfs(
uplo, n, kd, nrhs, &AB[0], ldab, &AFB[0], ldafb,
&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::pbrfs returned error %lld\n", llong( info_tst ) );
}
params.time() = time;
//double gflop = lapack::Gflop< scalar_t >::pbrfs( n, kd, 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 hbmm, so loop over RHS.
for (int64_t j = 0; j < nrhs; ++j) {
// B_ref -= A * B_tst
cblas_hbmv( CblasColMajor, cblas_uplo_const(uplo), n, kd,
-1.0, &AB[0], 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::lanhb( lapack::Norm::One, uplo, n, kd, &AB[0], 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_pbrfs(
to_char( uplo ), n, kd, nrhs, &AB[0], ldab, &AFB[0], ldafb,
&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_pbrfs returned error %lld\n", llong( info_ref ) );
}
params.ref_time() = time;
//params.ref_gflops() = gflop / time;
}
}
// -----------------------------------------------------------------------------
void test_pbrfs( Params& params, bool run )
{
switch (params.datatype()) {
case testsweeper::DataType::Single:
test_pbrfs_work< float >( params, run );
break;
case testsweeper::DataType::Double:
test_pbrfs_work< double >( params, run );
break;
case testsweeper::DataType::SingleComplex:
test_pbrfs_work< std::complex<float> >( params, run );
break;
case testsweeper::DataType::DoubleComplex:
test_pbrfs_work< std::complex<double> >( params, run );
break;
default:
throw std::runtime_error( "unknown datatype" );
break;
}
}
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