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/*
-- MAGMA (version 2.5.4) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
@date October 2020
@generated from testing/testing_zgeqrf_gpu.cpp, normal z -> c, Thu Oct 8 23:05:42 2020
*/
// includes, system
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <math.h>
// includes, project
#include "flops.h"
#include "magma_v2.h"
#include "magma_lapack.h"
#include "testings.h"
/* ////////////////////////////////////////////////////////////////////////////
-- Testing cgeqrf
*/
int main( int argc, char** argv)
{
TESTING_CHECK( magma_init() );
magma_print_environment();
const float d_neg_one = MAGMA_D_NEG_ONE;
const float d_one = MAGMA_D_ONE;
const magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
const magmaFloatComplex c_one = MAGMA_C_ONE;
const magmaFloatComplex c_zero = MAGMA_C_ZERO;
const magma_int_t ione = 1;
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf=0, cpu_time=0;
float Anorm, error=0, error2=0;
magmaFloatComplex *h_A, *h_R, *tau, *h_work, tmp[1], unused[1];
magmaFloatComplex_ptr d_A, dT;
magma_int_t M, N, n2, lda, ldda, lwork, info, min_mn, nb, size;
magma_int_t ISEED[4] = {0,0,0,1};
magma_opts opts;
opts.parse_opts( argc, argv );
int status = 0;
float tol = opts.tolerance * lapackf77_slamch("E");
// version 3 can do either check
if (opts.check == 1 && opts.version == 1) {
opts.check = 2;
printf( "%% version 1 requires check 2 (solve A*x=b)\n" );
}
if (opts.check == 2 && opts.version == 2) {
opts.check = 1;
printf( "%% version 2 requires check 1 (R - Q^H*A)\n" );
}
printf( "%% version %lld\n", (long long) opts.version );
if ( opts.check == 1 ) {
printf("%% M N CPU Gflop/s (sec) GPU Gflop/s (sec) |R - Q^H*A| |I - Q^H*Q|\n");
printf("%%==============================================================================\n");
}
else {
printf("%% M N CPU Gflop/s (sec) GPU Gflop/s (sec) |b - A*x|\n");
printf("%%===============================================================\n");
}
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[itest];
N = opts.nsize[itest];
min_mn = min( M, N );
lda = M;
n2 = lda*N;
ldda = magma_roundup( M, opts.align ); // multiple of 32 by default
nb = magma_get_cgeqrf_nb( M, N );
gflops = FLOPS_CGEQRF( M, N ) / 1e9;
// query for workspace size
lwork = -1;
lapackf77_cgeqrf( &M, &N, unused, &M, unused, tmp, &lwork, &info );
lwork = (magma_int_t)MAGMA_C_REAL( tmp[0] );
TESTING_CHECK( magma_cmalloc_cpu( &tau, min_mn ));
TESTING_CHECK( magma_cmalloc_cpu( &h_A, n2 ));
TESTING_CHECK( magma_cmalloc_cpu( &h_work, lwork ));
TESTING_CHECK( magma_cmalloc_pinned( &h_R, n2 ));
TESTING_CHECK( magma_cmalloc( &d_A, ldda*N ));
if ( opts.version == 1 || opts.version == 3 ) {
size = (2*min(M, N) + magma_roundup( N, 32 ) )*nb;
TESTING_CHECK( magma_cmalloc( &dT, size ));
magmablas_claset( MagmaFull, size, 1, c_zero, c_zero, dT, size, opts.queue );
}
/* Initialize the matrix */
magma_generate_matrix( opts, M, N, h_A, lda );
lapackf77_clacpy( MagmaFullStr, &M, &N, h_A, &lda, h_R, &lda );
magma_csetmatrix( M, N, h_R, lda, d_A, ldda, opts.queue );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
nb = magma_get_cgeqrf_nb( M, N );
gpu_time = magma_wtime();
if ( opts.version == 1 ) {
// stores dT, V blocks have zeros, R blocks inverted & stored in dT
magma_cgeqrf_gpu( M, N, d_A, ldda, tau, dT, &info );
}
else if ( opts.version == 2 ) {
// LAPACK complaint arguments
magma_cgeqrf2_gpu( M, N, d_A, ldda, tau, &info );
}
#ifdef HAVE_CUBLAS
else if ( opts.version == 3 ) {
// stores dT, V blocks have zeros, R blocks stored in dT
magma_cgeqrf3_gpu( M, N, d_A, ldda, tau, dT, &info );
}
#endif
else {
printf( "Unknown version %lld\n", (long long) opts.version );
return -1;
}
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0) {
printf("magma_cgeqrf returned error %lld: %s.\n",
(long long) info, magma_strerror( info ));
}
if ( opts.check == 1 && (opts.version == 2 || opts.version == 3) ) {
if ( opts.version == 3 ) {
// copy diagonal blocks of R back to A
for( int i=0; i < min_mn-nb; i += nb ) {
magma_int_t ib = min( min_mn-i, nb );
magmablas_clacpy( MagmaUpper, ib, ib, &dT[min_mn*nb + i*nb], nb, &d_A[ i + i*ldda ], ldda, opts.queue );
}
}
/* =====================================================================
Check the result, following zqrt01 except using the reduced Q.
This works for any M,N (square, tall, wide).
Only for version 2, which has LAPACK complaint output.
Or for version 3, after restoring diagonal blocks of A above.
=================================================================== */
magma_cgetmatrix( M, N, d_A, ldda, h_R, lda, opts.queue );
magma_int_t ldq = M;
magma_int_t ldr = min_mn;
magmaFloatComplex *Q, *R;
float *work;
TESTING_CHECK( magma_cmalloc_cpu( &Q, ldq*min_mn )); // M by K
TESTING_CHECK( magma_cmalloc_cpu( &R, ldr*N )); // K by N
TESTING_CHECK( magma_smalloc_cpu( &work, min_mn ));
// generate M by K matrix Q, where K = min(M,N)
lapackf77_clacpy( "Lower", &M, &min_mn, h_R, &lda, Q, &ldq );
lapackf77_cungqr( &M, &min_mn, &min_mn, Q, &ldq, tau, h_work, &lwork, &info );
assert( info == 0 );
// copy K by N matrix R
lapackf77_claset( "Lower", &min_mn, &N, &c_zero, &c_zero, R, &ldr );
lapackf77_clacpy( "Upper", &min_mn, &N, h_R, &lda, R, &ldr );
// error = || R - Q^H*A || / (N * ||A||)
blasf77_cgemm( "Conj", "NoTrans", &min_mn, &N, &M,
&c_neg_one, Q, &ldq, h_A, &lda, &c_one, R, &ldr );
Anorm = lapackf77_clange( "1", &M, &N, h_A, &lda, work );
error = lapackf77_clange( "1", &min_mn, &N, R, &ldr, work );
if ( N > 0 && Anorm > 0 )
error /= (N*Anorm);
// set R = I (K by K identity), then R = I - Q^H*Q
// error = || I - Q^H*Q || / N
lapackf77_claset( "Upper", &min_mn, &min_mn, &c_zero, &c_one, R, &ldr );
blasf77_cherk( "Upper", "Conj", &min_mn, &M, &d_neg_one, Q, &ldq, &d_one, R, &ldr );
error2 = safe_lapackf77_clanhe( "1", "Upper", &min_mn, R, &ldr, work );
if ( N > 0 )
error2 /= N;
magma_free_cpu( Q ); Q = NULL;
magma_free_cpu( R ); R = NULL;
magma_free_cpu( work ); work = NULL;
}
else if ( opts.check == 2 && M >= N && (opts.version == 1 || opts.version == 3) ) {
/* =====================================================================
Check the result by solving consistent linear system, A*x = b.
Only for versions 1 & 3 with M >= N.
=================================================================== */
magma_int_t lwork2;
magmaFloatComplex *x, *b, *hwork;
magmaFloatComplex_ptr d_B;
// initialize RHS, b = A*random
TESTING_CHECK( magma_cmalloc_cpu( &x, N ));
TESTING_CHECK( magma_cmalloc_cpu( &b, M ));
lapackf77_clarnv( &ione, ISEED, &N, x );
blasf77_cgemv( "Notrans", &M, &N, &c_one, h_A, &lda, x, &ione, &c_zero, b, &ione );
// copy to GPU
TESTING_CHECK( magma_cmalloc( &d_B, M ));
magma_csetvector( M, b, 1, d_B, 1, opts.queue );
if ( opts.version == 1 ) {
// allocate hwork
magma_cgeqrs_gpu( M, N, 1,
d_A, ldda, tau, dT,
d_B, M, tmp, -1, &info );
lwork2 = (magma_int_t)MAGMA_C_REAL( tmp[0] );
TESTING_CHECK( magma_cmalloc_cpu( &hwork, lwork2 ));
// solve linear system
magma_cgeqrs_gpu( M, N, 1,
d_A, ldda, tau, dT,
d_B, M, hwork, lwork2, &info );
if (info != 0) {
printf("magma_cgeqrs returned error %lld: %s.\n",
(long long) info, magma_strerror( info ));
}
magma_free_cpu( hwork );
}
#ifdef HAVE_CUBLAS
else if ( opts.version == 3 ) {
// allocate hwork
magma_cgeqrs3_gpu( M, N, 1,
d_A, ldda, tau, dT,
d_B, M, tmp, -1, &info );
lwork2 = (magma_int_t)MAGMA_C_REAL( tmp[0] );
TESTING_CHECK( magma_cmalloc_cpu( &hwork, lwork2 ));
// solve linear system
magma_cgeqrs3_gpu( M, N, 1,
d_A, ldda, tau, dT,
d_B, M, hwork, lwork2, &info );
if (info != 0) {
printf("magma_cgeqrs3 returned error %lld: %s.\n",
(long long) info, magma_strerror( info ));
}
magma_free_cpu( hwork );
}
#endif
else {
printf( "Unknown version %lld\n", (long long) opts.version );
return -1;
}
magma_cgetvector( N, d_B, 1, x, 1, opts.queue );
// compute r = Ax - b, saved in b
blasf77_cgemv( "Notrans", &M, &N, &c_one, h_A, &lda, x, &ione, &c_neg_one, b, &ione );
// compute residual |Ax - b| / (max(m,n)*|A|*|x|)
float norm_x, norm_A, norm_r, work[1];
norm_A = lapackf77_clange( "F", &M, &N, h_A, &lda, work );
norm_r = lapackf77_clange( "F", &M, &ione, b, &M, work );
norm_x = lapackf77_clange( "F", &N, &ione, x, &N, work );
magma_free_cpu( x );
magma_free_cpu( b );
magma_free( d_B );
error = norm_r / (max(M,N) * norm_A * norm_x);
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
lapackf77_cgeqrf( &M, &N, h_A, &lda, tau, h_work, &lwork, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0) {
printf("lapackf77_cgeqrf returned error %lld: %s.\n",
(long long) info, magma_strerror( info ));
}
}
/* =====================================================================
Print performance and error.
=================================================================== */
printf("%5lld %5lld ", (long long) M, (long long) N );
if ( opts.lapack ) {
printf( "%7.2f (%7.2f)", cpu_perf, cpu_time );
}
else {
printf(" --- ( --- )" );
}
printf( " %7.2f (%7.2f) ", gpu_perf, gpu_time );
if ( opts.check == 1 ) {
bool okay = (error < tol && error2 < tol);
status += ! okay;
printf( "%11.2e %11.2e %s\n", error, error2, (okay ? "ok" : "failed") );
}
else if ( opts.check == 2 ) {
if ( M >= N ) {
bool okay = (error < tol);
status += ! okay;
printf( "%10.2e %s\n", error, (okay ? "ok" : "failed") );
}
else {
printf( "(error check only for M >= N)\n" );
}
}
else {
printf( " ---\n" );
}
magma_free_cpu( tau );
magma_free_cpu( h_A );
magma_free_cpu( h_work );
magma_free_pinned( h_R );
magma_free( d_A );
if ( opts.version == 1 || opts.version == 3 ) {
magma_free( dT );
}
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
opts.cleanup();
TESTING_CHECK( magma_finalize() );
return status;
}
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