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|
/*
-- MAGMA (version 2.9.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
@date January 2025
@author Mark Gates
@generated from testing/testing_dgeev.cpp, normal d -> s, Wed Jan 22 14:40:39 2025
*/
// includes, system
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <math.h>
#include <algorithm> // for sorting
// includes, project
#include "magma_v2.h"
#include "magma_lapack.h"
#include "testings.h"
#define REAL
// comparison operator for sorting
bool lessthan( magmaFloatComplex a, magmaFloatComplex b )
{
return (MAGMA_C_REAL(a) < MAGMA_C_REAL(b)) ||
(MAGMA_C_REAL(a) == MAGMA_C_REAL(b) && MAGMA_C_IMAG(a) < MAGMA_C_IMAG(b));
}
// DLAPY2 returns sqrt(x**2+y**2), taking care not to cause unnecessary overflow.
// TODO: put into auxiliary file. It's useful elsewhere.
extern "C"
float magma_slapy2(float x, float y)
{
float ret_val, d;
float w, z, xabs, yabs;
xabs = MAGMA_S_ABS(x);
yabs = MAGMA_S_ABS(y);
w = max(xabs, yabs);
z = min(xabs, yabs);
if (z == 0.) {
ret_val = w;
} else {
d = z / w;
ret_val = w * sqrt(d * d + 1.);
}
return ret_val;
}
extern "C"
float magma_szlapy2(magmaFloatComplex x)
{
return magma_slapy2( MAGMA_C_REAL(x), MAGMA_C_IMAG(x) );
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing sgeev
*/
int main( int argc, char** argv)
{
TESTING_CHECK( magma_init() );
magma_print_environment();
real_Double_t gpu_time, cpu_time;
float *h_A, *h_R, *VL, *VR, *h_work, *w1, *w2;
float *w1i, *w2i;
magmaFloatComplex *w1copy, *w2copy;
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
float tnrm, result[9];
magma_int_t N, n2, lda, nb, lwork, lwork2, info;
magma_int_t ione = 1;
float ulp, ulpinv, error;
int status = 0;
ulp = lapackf77_slamch( "P" );
ulpinv = 1./ulp;
magma_opts opts;
opts.parse_opts( argc, argv );
// need slightly looser bound (60*eps instead of 30*eps) for some tests
opts.tolerance = max( 60., opts.tolerance );
float tol = opts.tolerance * lapackf77_slamch("E");
float tolulp = opts.tolerance * lapackf77_slamch("P");
// enable at least some minimal checks, if requested
if ( opts.check && !opts.lapack && opts.jobvl == MagmaNoVec && opts.jobvr == MagmaNoVec ) {
fprintf( stderr, "NOTE: Some checks require vectors to be computed;\n"
" set jobvl=V (option -LV), or jobvr=V (option -RV), or both.\n"
" Some checks require running lapack (-l); setting lapack.\n\n");
opts.lapack = true;
}
// pass ngpu = -1 to test multi-GPU code using 1 gpu
magma_int_t abs_ngpu = abs( opts.ngpu );
printf("%% jobvl = %s, jobvr = %s, ngpu = %lld\n",
lapack_vec_const(opts.jobvl), lapack_vec_const(opts.jobvr),
(long long) abs_ngpu );
printf("%% N CPU Time (sec) GPU Time (sec) |W_magma - W_lapack| / |W_lapack|\n");
printf("%%==========================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[itest];
lda = N;
n2 = lda*N;
nb = magma_get_sgehrd_nb(N);
lwork = N*(2 + 2*nb);
if (opts.ngpu != 1) {
lwork += N*nb*abs_ngpu;
}
// generous workspace - required by sget22
lwork2 = max( lwork, N*(5 + 2*N) );
TESTING_CHECK( magma_cmalloc_cpu( &w1copy, N ));
TESTING_CHECK( magma_cmalloc_cpu( &w2copy, N ));
TESTING_CHECK( magma_smalloc_cpu( &w1, N ));
TESTING_CHECK( magma_smalloc_cpu( &w2, N ));
TESTING_CHECK( magma_smalloc_cpu( &w1i, N ));
TESTING_CHECK( magma_smalloc_cpu( &w2i, N ));
TESTING_CHECK( magma_smalloc_cpu( &h_A, n2 ));
TESTING_CHECK( magma_smalloc_pinned( &h_R, n2 ));
TESTING_CHECK( magma_smalloc_pinned( &VL, n2 ));
TESTING_CHECK( magma_smalloc_pinned( &VR, n2 ));
TESTING_CHECK( magma_smalloc_pinned( &h_work, lwork2 ));
/* Initialize the matrix */
magma_generate_matrix( opts, N, N, h_A, lda );
lapackf77_slacpy( MagmaFullStr, &N, &N, h_A, &lda, h_R, &lda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
if (opts.ngpu == 1) {
magma_sgeev( opts.jobvl, opts.jobvr,
N, h_R, lda, w1, w1i,
VL, lda, VR, lda,
h_work, lwork, &info );
}
else {
magma_sgeev_m( opts.jobvl, opts.jobvr,
N, h_R, lda, w1, w1i,
VL, lda, VR, lda,
h_work, lwork, &info );
}
gpu_time = magma_wtime() - gpu_time;
if (info != 0) {
printf("magma_sgeev returned error %lld: %s.\n",
(long long) info, magma_strerror( info ));
}
/* =====================================================================
Check the result
=================================================================== */
if ( opts.check ) {
/* ===================================================================
* Check the result following LAPACK's [zcds]drvev routine.
* The following tests are performed:
* (1) | A * VR - VR * W | / ( n |A| )
*
* Here VR is the matrix of unit right eigenvectors.
* W is a diagonal matrix with diagonal entries W(j).
*
* (2) | |VR(i)| - 1 | and whether largest component real
*
* VR(i) denotes the i-th column of VR.
*
* (3) | A**T * VL - VL * W**T | / ( n |A| )
*
* Here VL is the matrix of unit left eigenvectors, A**T is the
* transpose of A, and W is as above.
*
* (4) | |VL(i)| - 1 | and whether largest component real
*
* VL(i) denotes the i-th column of VL.
*
* (5) W(full) = W(partial, W only) -- currently skipped
* (6) W(full) = W(partial, W and VR)
* (7) W(full) = W(partial, W and VL)
*
* W(full) denotes the eigenvalues computed when both VR and VL
* are also computed, and W(partial) denotes the eigenvalues
* computed when only W, only W and VR, or only W and VL are
* computed.
*
* (8) VR(full) = VR(partial, W and VR)
*
* VR(full) denotes the right eigenvectors computed when both VR
* and VL are computed, and VR(partial) denotes the result
* when only VR is computed.
*
* (9) VL(full) = VL(partial, W and VL)
*
* VL(full) denotes the left eigenvectors computed when both VR
* and VL are also computed, and VL(partial) denotes the result
* when only VL is computed.
*
* (1, 2) only if jobvr = V
* (3, 4) only if jobvl = V
* (5-9) only if check = 2 (option -c2)
================================================================= */
float vmx, vrmx, vtst;
// Initialize result. -1 indicates test was not run.
for( int j = 0; j < 9; ++j )
result[j] = -1.;
if ( opts.jobvr == MagmaVec ) {
// Do test 1: | A * VR - VR * W | / ( n |A| )
// Note this writes result[1] also
lapackf77_sget22( MagmaNoTransStr, MagmaNoTransStr, MagmaNoTransStr,
&N, h_A, &lda, VR, &lda, w1, w1i,
h_work, &result[0] );
result[0] *= ulp;
// Do test 2: | |VR(i)| - 1 | and whether largest component real
result[1] = -1.;
for( int j = 0; j < N; ++j ) {
tnrm = 1.;
if (w1i[j] == 0.)
tnrm = magma_cblas_snrm2( N, &VR[j*lda], ione );
else if (w1i[j] > 0.)
tnrm = magma_slapy2( magma_cblas_snrm2( N, &VR[j*lda], ione ),
magma_cblas_snrm2( N, &VR[(j+1)*lda], ione ));
result[1] = max( result[1], min( ulpinv, MAGMA_S_ABS(tnrm-1.)/ulp ));
if (w1i[j] > 0.) {
vmx = vrmx = 0.;
for( int jj = 0; jj < N; ++jj ) {
vtst = magma_slapy2( VR[jj+j*lda], VR[jj+(j+1)*lda]);
if (vtst > vmx)
vmx = vtst;
if ( (VR[jj + (j+1)*lda]) == 0. &&
MAGMA_S_ABS( VR[jj+j*lda] ) > vrmx)
{
vrmx = MAGMA_S_ABS( VR[jj+j*lda] );
}
}
if (vrmx / vmx < 1. - ulp*2.)
result[1] = ulpinv;
}
}
result[1] *= ulp;
}
if ( opts.jobvl == MagmaVec ) {
// Do test 3: | A**T * VL - VL * W**T | / ( n |A| )
// Note this writes result[3] also
lapackf77_sget22( MagmaTransStr, MagmaNoTransStr, MagmaTransStr,
&N, h_A, &lda, VL, &lda, w1, w1i,
h_work, &result[2] );
result[2] *= ulp;
// Do test 4: | |VL(i)| - 1 | and whether largest component real
result[3] = -1.;
for( int j = 0; j < N; ++j ) {
tnrm = 1.;
if (w1i[j] == 0.)
tnrm = magma_cblas_snrm2( N, &VL[j*lda], ione );
else if (w1i[j] > 0.)
tnrm = magma_slapy2( magma_cblas_snrm2( N, &VL[j*lda], ione ),
magma_cblas_snrm2( N, &VL[(j+1)*lda], ione ));
result[3] = max( result[3], min( ulpinv, MAGMA_S_ABS(tnrm-1.)/ulp ));
if (w1i[j] > 0.) {
vmx = vrmx = 0.;
for( int jj = 0; jj < N; ++jj ) {
vtst = magma_slapy2( VL[jj+j*lda], VL[jj+(j+1)*lda]);
if (vtst > vmx)
vmx = vtst;
if ( (VL[jj + (j+1)*lda]) == 0. &&
MAGMA_S_ABS( VL[jj+j*lda]) > vrmx)
{
vrmx = MAGMA_S_ABS( VL[jj+j*lda] );
}
}
if (vrmx / vmx < 1. - ulp*2.)
result[3] = ulpinv;
}
}
result[3] *= ulp;
}
}
if ( opts.check == 2 ) {
// more extensive tests
// this is really slow because it calls magma_sgeev multiple times
float *LRE, DUM;
TESTING_CHECK( magma_smalloc_pinned( &LRE, n2 ));
magma_generate_matrix( opts, N, N, h_A, lda );
lapackf77_slacpy( MagmaFullStr, &N, &N, h_A, &lda, h_R, &lda );
// ----------
// Compute eigenvalues, left and right eigenvectors
if (opts.ngpu == 1) {
magma_sgeev( MagmaVec, MagmaVec,
N, h_R, lda, w1, w1i,
VL, lda, VR, lda,
h_work, lwork, &info );
}
else {
magma_sgeev_m( MagmaVec, MagmaVec,
N, h_R, lda, w1, w1i,
VL, lda, VR, lda,
h_work, lwork, &info );
}
if (info != 0) {
printf("magma_sgeev (case V, V) returned error %lld: %s.\n",
(long long) info, magma_strerror( info ));
}
// ----------
// Compute eigenvalues only
// These are not exactly equal, and not in the same order, so skip for now.
//lapackf77_slacpy( MagmaFullStr, &N, &N, h_A, &lda, h_R, &lda );
//if (opts.ngpu == 1) {
// magma_sgeev( MagmaNoVec, MagmaNoVec,
// N, h_R, lda, w2, w2i,
// &DUM, 1, &DUM, 1,
// h_work, lwork, &info );
//}
//else {
// magma_sgeev_m( MagmaNoVec, MagmaNoVec,
// N, h_R, lda, w2, w2i,
// &DUM, 1, &DUM, 1,
// h_work, lwork, &info );
//}
//if (info != 0) {
// printf("magma_sgeev (case N, N) returned error %lld: %s.\n",
// (long long) info, magma_strerror( info ));
//}
//
//// Do test 5: W(full) = W(partial, W only)
//result[4] = 1;
//for( int j = 0; j < N; ++j )
// if ( w1[j] != w2[j] || w1i[j] != w2i[j] )
// result[4] = 0;
// ----------
// Compute eigenvalues and right eigenvectors
lapackf77_slacpy( MagmaFullStr, &N, &N, h_A, &lda, h_R, &lda );
if (opts.ngpu == 1) {
magma_sgeev( MagmaNoVec, MagmaVec,
N, h_R, lda, w2, w2i,
&DUM, 1, LRE, lda,
h_work, lwork, &info );
}
else {
magma_sgeev_m( MagmaNoVec, MagmaVec,
N, h_R, lda, w2, w2i,
&DUM, 1, LRE, lda,
h_work, lwork, &info );
}
if (info != 0) {
printf("magma_sgeev (case N, V) returned error %lld: %s.\n",
(long long) info, magma_strerror( info ));
}
// Do test 6: W(full) = W(partial, W and VR)
result[5] = 1;
for( int j = 0; j < N; ++j )
if ( w1[j] != w2[j] || w1i[j] != w2i[j] )
result[5] = 0;
// Do test 8: VR(full) = VR(partial, W and VR)
result[7] = 1;
for( int j = 0; j < N; ++j )
for( int jj = 0; jj < N; ++jj )
if ( ! MAGMA_S_EQUAL( VR[j+jj*lda], LRE[j+jj*lda] ))
result[7] = 0;
// ----------
// Compute eigenvalues and left eigenvectors
lapackf77_slacpy( MagmaFullStr, &N, &N, h_A, &lda, h_R, &lda );
if (opts.ngpu == 1) {
magma_sgeev( MagmaVec, MagmaNoVec,
N, h_R, lda, w2, w2i,
LRE, lda, &DUM, 1,
h_work, lwork, &info );
}
else {
magma_sgeev_m( MagmaVec, MagmaNoVec,
N, h_R, lda, w2, w2i,
LRE, lda, &DUM, 1,
h_work, lwork, &info );
}
if (info != 0) {
printf("magma_sgeev (case V, N) returned error %lld: %s.\n",
(long long) info, magma_strerror( info ));
}
// Do test 7: W(full) = W(partial, W and VL)
result[6] = 1;
for( int j = 0; j < N; ++j )
if ( w1[j] != w2[j] || w1i[j] != w2i[j] )
result[6] = 0;
// Do test 9: VL(full) = VL(partial, W and VL)
result[8] = 1;
for( int j = 0; j < N; ++j )
for( int jj = 0; jj < N; ++jj )
if ( ! MAGMA_S_EQUAL( VL[j+jj*lda], LRE[j+jj*lda] ))
result[8] = 0;
magma_free_pinned( LRE );
}
/* =====================================================================
Performs operation using LAPACK
Do this after checks, because it overwrites VL and VR.
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
lapackf77_sgeev( lapack_vec_const(opts.jobvl), lapack_vec_const(opts.jobvr),
&N, h_A, &lda, w2, w2i,
VL, &lda, VR, &lda,
h_work, &lwork, &info );
cpu_time = magma_wtime() - cpu_time;
if (info != 0) {
printf("lapackf77_sgeev returned error %lld: %s.\n",
(long long) info, magma_strerror( info ));
}
// check | W_magma - W_lapack | / | W |
// need to sort eigenvalues first
// copy them into complex vectors for ease
for( int j=0; j < N; ++j ) {
w1copy[j] = MAGMA_C_MAKE( w1[j], w1i[j] );
w2copy[j] = MAGMA_C_MAKE( w2[j], w2i[j] );
}
std::sort( w1copy, &w1copy[N], lessthan );
std::sort( w2copy, &w2copy[N], lessthan );
// adjust sorting to deal with numerical inaccuracy
// search down w2 for eigenvalue that matches w1's eigenvalue
for( int j=0; j < N; ++j ) {
for( int j2=j; j2 < N; ++j2 ) {
magmaFloatComplex diff = MAGMA_C_SUB( w1copy[j], w2copy[j2] );
float diff2 = magma_szlapy2( diff ) / max( magma_szlapy2( w1copy[j] ), tol );
if ( diff2 < 100*tol ) {
if ( j != j2 ) {
std::swap( w2copy[j], w2copy[j2] );
}
break;
}
}
}
blasf77_caxpy( &N, &c_neg_one, w2copy, &ione, w1copy, &ione );
error = magma_cblas_scnrm2( N, w1copy, 1 );
error /= magma_cblas_scnrm2( N, w2copy, 1 );
printf("%5lld %7.2f %7.2f %8.2e %s\n",
(long long) N, cpu_time, gpu_time,
error, (error < tolulp ? "ok" : "failed"));
status += ! (error < tolulp);
}
else {
printf("%5lld --- %7.2f\n",
(long long) N, gpu_time);
}
if ( opts.check ) {
// -1 indicates test was not run
if ( result[0] != -1 ) { printf(" | A * VR - VR * W | / (n |A|) = %8.2e %s\n", result[0], (result[0] < tol ? "ok" : "failed")); }
if ( result[1] != -1 ) { printf(" | |VR(i)| - 1 | = %8.2e %s\n", result[1], (result[1] < tol ? "ok" : "failed")); }
if ( result[2] != -1 ) { printf(" |A^H * VL - VL * W^H| / (n |A|) = %8.2e %s\n", result[2], (result[2] < tol ? "ok" : "failed")); }
if ( result[3] != -1 ) { printf(" | |VL(i)| - 1 | = %8.2e %s\n", result[3], (result[3] < tol ? "ok" : "failed")); }
if ( result[4] != -1 ) { printf(" W (full) == W (partial, W only) %s\n", (result[4] == 1. ? "ok" : "failed")); }
if ( result[5] != -1 ) { printf(" W (full) == W (partial, W and VR) %s\n", (result[5] == 1. ? "ok" : "failed")); }
if ( result[6] != -1 ) { printf(" W (full) == W (partial, W and VL) %s\n", (result[6] == 1. ? "ok" : "failed")); }
if ( result[7] != -1 ) { printf(" VR (full) == VR (partial, W and VR) %s\n", (result[7] == 1. ? "ok" : "failed")); }
if ( result[8] != -1 ) { printf(" VL (full) == VL (partial, W and VL) %s\n", (result[8] == 1. ? "ok" : "failed")); }
bool newline = false;
if ( result[0] != -1 ) { status += ! (result[0] < tol); newline = true; }
if ( result[1] != -1 ) { status += ! (result[1] < tol); newline = true; }
if ( result[2] != -1 ) { status += ! (result[2] < tol); newline = true; }
if ( result[3] != -1 ) { status += ! (result[3] < tol); newline = true; }
if ( result[4] != -1 ) { status += ! (result[4] == 1.); newline = true; }
if ( result[5] != -1 ) { status += ! (result[5] == 1.); newline = true; }
if ( result[6] != -1 ) { status += ! (result[6] == 1.); newline = true; }
if ( result[7] != -1 ) { status += ! (result[7] == 1.); newline = true; }
if ( result[8] != -1 ) { status += ! (result[8] == 1.); newline = true; }
if ( newline ) {
printf( "\n" );
}
}
magma_free_cpu( w1copy );
magma_free_cpu( w2copy );
magma_free_cpu( w1 );
magma_free_cpu( w2 );
magma_free_cpu( w1i );
magma_free_cpu( w2i );
magma_free_cpu( h_A );
magma_free_pinned( h_R );
magma_free_pinned( VL );
magma_free_pinned( VR );
magma_free_pinned( h_work );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
opts.cleanup();
TESTING_CHECK( magma_finalize() );
return status;
}
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