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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 <vector>
// -----------------------------------------------------------------------------
template< typename scalar_t >
void test_potri_work( Params& params, bool run )
{
using blas::conj;
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 align = params.align();
int64_t verbose = params.verbose();
params.matrix.mark();
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) {
params.matrix.kind.set_default( "rand_dominant" );
return;
}
// ---------- setup
int64_t lda = roundup( blas::max( 1, n ), align );
size_t size_A = (size_t) lda * n;
std::vector< scalar_t > A_tst( size_A );
std::vector< scalar_t > A_ref( size_A );
lapack::generate_matrix( params.matrix, n, n, &A_tst[0], lda );
A_ref = A_tst;
if (verbose >= 1) {
printf( "\n"
"A n=%5lld, lda=%5lld\n",
llong( n ), llong( lda ) );
}
if (verbose >= 2) {
printf( "A = " ); print_matrix( n, n, &A_tst[0], lda );
}
// factor A into LL^T
int64_t info = lapack::potrf( uplo, n, &A_tst[0], lda );
if (info != 0) {
fprintf( stderr, "lapack::potrf returned error %lld\n", llong( info ) );
}
// test error exits
if (params.error_exit() == 'y') {
using lapack::Uplo;
assert_throw( lapack::potri( Uplo(0), n, &A_tst[0], lda ), lapack::Error );
assert_throw( lapack::potri( uplo, -1, &A_tst[0], lda ), lapack::Error );
assert_throw( lapack::potri( uplo, n, &A_tst[0], n-1 ), lapack::Error );
}
// ---------- run test
testsweeper::flush_cache( params.cache() );
double time = testsweeper::get_wtime();
int64_t info_tst = lapack::potri( uplo, n, &A_tst[0], lda );
time = testsweeper::get_wtime() - time;
if (info_tst != 0) {
fprintf( stderr, "lapack::potri returned error %lld\n", llong( info_tst ) );
}
params.time() = time;
double gflop = lapack::Gflop< scalar_t >::potri( n );
params.gflops() = gflop / time;
if (verbose >= 2) {
printf( "A2 = " ); print_matrix( n, n, &A_tst[0], lda );
}
if (params.check() == 'y') {
// ---------- check error
// comparing to ref. solution doesn't work due to roundoff errors
// symmetrize A^{-1}, in order to use hemm
if (uplo == blas::Uplo::Lower) {
for (int64_t j = 0; j < n; ++j)
for (int64_t i = 0; i < j; ++i)
A_tst[ i + j*lda ] = conj( A_tst[ j + i*lda ] );
}
else {
for (int64_t j = 0; j < n; ++j)
for (int64_t i = 0; i < j; ++i)
A_tst[ j + i*lda ] = conj( A_tst[ i + j*lda ] );
}
if (verbose >= 2) {
printf( "A2b = " ); print_matrix( n, n, &A_tst[0], lda );
}
// R = I
std::vector< scalar_t > R( size_A );
// todo: laset; needs uplo=general
for (int64_t j = 0; j < n; ++j) {
for (int64_t i = 0; i < n; ++i) {
R[ i + j*lda ] = 0;
}
R[ j + j*lda ] = 1;
}
// R = I - A A^{-1}, A is Hermitian, A^{-1} is treated as general
blas::hemm( blas::Layout::ColMajor, blas::Side::Left, uplo, n, n,
-1.0, &A_ref[0], lda,
&A_tst[0], lda,
1.0, &R[0], lda );
if (verbose >= 2) {
printf( "R = " ); print_matrix( n, n, &R[0], lda );
}
// error = ||I - A A^{-1}|| / (n ||A|| ||A^{-1}||)
real_t Rnorm = lapack::lange( lapack::Norm::Fro, n, n, &R[0], lda );
real_t Anorm = lapack::lanhe( lapack::Norm::Fro, uplo, n, &A_ref[0], lda );
real_t Ainv_norm = lapack::lanhe( lapack::Norm::Fro, uplo, n, &A_tst[0], lda );
real_t error = Rnorm / (n * Anorm * Ainv_norm);
params.error() = error;
params.okay() = (error < tol);
}
if (params.ref() == 'y') {
// factor A into LL^T
info = LAPACKE_potrf( to_char( uplo ), n, &A_ref[0], lda );
if (info != 0) {
fprintf( stderr, "LAPACKE_potrf returned error %lld\n", llong( info ) );
}
// ---------- run reference
testsweeper::flush_cache( params.cache() );
time = testsweeper::get_wtime();
int64_t info_ref = LAPACKE_potri( to_char( uplo ), n, &A_ref[0], lda );
time = testsweeper::get_wtime() - time;
if (info_ref != 0) {
fprintf( stderr, "LAPACKE_potri returned error %lld\n", llong( info_ref ) );
}
params.ref_time() = time;
params.ref_gflops() = gflop / time;
if (verbose >= 2) {
printf( "A2ref = " ); print_matrix( n, n, &A_ref[0], lda );
}
}
}
// -----------------------------------------------------------------------------
void test_potri( Params& params, bool run )
{
switch (params.datatype()) {
case testsweeper::DataType::Single:
test_potri_work< float >( params, run );
break;
case testsweeper::DataType::Double:
test_potri_work< double >( params, run );
break;
case testsweeper::DataType::SingleComplex:
test_potri_work< std::complex<float> >( params, run );
break;
case testsweeper::DataType::DoubleComplex:
test_potri_work< std::complex<double> >( params, run );
break;
default:
throw std::runtime_error( "unknown datatype" );
break;
}
}
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