// On input, A and ipiv is LU factorization of A. On output, A is overwritten.
// Requires m == n.
// Uses init_matrix() to re-generate original A as needed.
// Generates random RHS b and solves Ax=b.
// Returns residual, |Ax - b| / (n |A| |x|).
double get_residual(
magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs,
magmaDoubleComplex *A, magma_int_t lda, magma_int_t *ipiv,
magmaDoubleComplex *x, magma_int_t ldx,
magmaDoubleComplex *b, magma_int_t ldb)
{
const magmaDoubleComplex c_one = MAGMA_Z_ONE;
const magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
const magma_int_t ione = 1;
// reset to original A
init_matrix( n, n, A, lda );
// compute r = Ax - b, saved in b
blasf77_zgemv( "Notrans", &n, &n, &c_one, A, &lda, x, &ione, &c_neg_one, b, &ione );
// compute residual |Ax - b| / (n*|A|*|x|)
double norm_x, norm_A, norm_r, work[1];
norm_A = lapackf77_zlange( MagmaFullStr, &n, &n, A, &lda, work );
norm_r = lapackf77_zlange( MagmaFullStr, &n, &ione, b, &n, work );
norm_x = lapackf77_zlange( MagmaFullStr, &n, &ione, x, &n, work );
//printf( "r=\n" ); magma_zprint( 1, n, b, 1 );
//printf( "r=%.2e, A=%.2e, x=%.2e, n=%d\n", norm_r, norm_A, norm_x, n );
return norm_r / (n * norm_A * norm_x);
}
// On input, A and ipiv is LU factorization of A. On output, A is overwritten.
// Requires m == n.
// Uses init_matrix() to re-generate original A as needed.
// Generates random RHS b and solves Ax=b.
// Returns residual, |Ax - b| / (n |A| |x|).
double get_residual(
magma_int_t m, magma_int_t n,
magmaDoubleComplex *A, magma_int_t lda,
magma_int_t *ipiv )
{
if ( m != n ) {
printf( "\nERROR: residual check defined only for square matrices\n" );
return -1;
}
const magmaDoubleComplex c_one = MAGMA_Z_ONE;
const magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
const magma_int_t ione = 1;
// this seed should be DIFFERENT than used in init_matrix
// (else x is column of A, so residual can be exactly zero)
magma_int_t ISEED[4] = {0,0,0,2};
magma_int_t info = 0;
magmaDoubleComplex *x, *b;
// initialize RHS
TESTING_MALLOC_CPU( x, magmaDoubleComplex, n );
TESTING_MALLOC_CPU( b, magmaDoubleComplex, n );
lapackf77_zlarnv( &ione, ISEED, &n, b );
blasf77_zcopy( &n, b, &ione, x, &ione );
// solve Ax = b
lapackf77_zgetrs( "Notrans", &n, &ione, A, &lda, ipiv, x, &n, &info );
if (info != 0) {
printf("lapackf77_zgetrs returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
// reset to original A
init_matrix( m, n, A, lda );
// compute r = Ax - b, saved in b
blasf77_zgemv( "Notrans", &m, &n, &c_one, A, &lda, x, &ione, &c_neg_one, b, &ione );
// compute residual |Ax - b| / (n*|A|*|x|)
double norm_x, norm_A, norm_r, work[1];
norm_A = lapackf77_zlange( "F", &m, &n, A, &lda, work );
norm_r = lapackf77_zlange( "F", &n, &ione, b, &n, work );
norm_x = lapackf77_zlange( "F", &n, &ione, x, &n, work );
//printf( "r=\n" ); magma_zprint( 1, n, b, 1 );
TESTING_FREE_CPU( x );
TESTING_FREE_CPU( b );
//printf( "r=%.2e, A=%.2e, x=%.2e, n=%d\n", norm_r, norm_A, norm_x, n );
return norm_r / (n * norm_A * norm_x);
}
void get_QR_error(magma_int_t M, magma_int_t N, magma_int_t min_mn,
magmaDoubleComplex *h_R, magmaDoubleComplex *h_A, magma_int_t lda,
magmaDoubleComplex *tau,
magmaDoubleComplex *Q, magma_int_t ldq,
magmaDoubleComplex *R, magma_int_t ldr,
magmaDoubleComplex *h_work, magma_int_t lwork,
double *work, double *error, double *error2)
{
/* h_R:input the factorized matrix by lapack QR,
h_A:input the original matrix copy
tau: input
*/
const double d_neg_one = MAGMA_D_NEG_ONE;
const double d_one = MAGMA_D_ONE;
const magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
const magmaDoubleComplex c_one = MAGMA_Z_ONE;
const magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
double Anorm;
magma_int_t info;
// generate M by K matrix Q, where K = min(M,N)
lapackf77_zlacpy( "Lower", &M, &min_mn, h_R, &lda, Q, &ldq );
lapackf77_zungqr( &M, &min_mn, &min_mn, Q, &ldq, tau, h_work, &lwork, &info );
assert( info == 0 );
// copy K by N matrix R
lapackf77_zlaset( "Lower", &min_mn, &N, &c_zero, &c_zero, R, &ldr );
lapackf77_zlacpy( "Upper", &min_mn, &N, h_R, &lda, R, &ldr );
// error = || R - Q^H*A || / (N * ||A||)
blasf77_zgemm( "Conj", "NoTrans", &min_mn, &N, &M,
&c_neg_one, Q, &ldq, h_A, &lda, &c_one, R, &ldr );
Anorm = lapackf77_zlange( "1", &M, &N, h_A, &lda, work );
*error = lapackf77_zlange( "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_zlaset( "Upper", &min_mn, &min_mn, &c_zero, &c_one, R, &ldr );
blasf77_zherk( "Upper", "Conj", &min_mn, &M, &d_neg_one, Q, &ldq, &d_one, R, &ldr );
*error2 = safe_lapackf77_zlanhe( "1", "Upper", &min_mn, R, &ldr, work );
if ( N > 0 )
*error2 /= N;
}
// On input, LU and ipiv is LU factorization of A. On output, LU is overwritten.
// Works for any m, n.
// Uses init_matrix() to re-generate original A as needed.
// Returns error in factorization, |PA - LU| / (n |A|)
// This allocates 3 more matrices to store A, L, and U.
double get_LU_error(magma_int_t M, magma_int_t N,
magmaDoubleComplex *LU, magma_int_t lda,
magma_int_t *ipiv)
{
magma_int_t min_mn = min(M,N);
magma_int_t ione = 1;
magma_int_t i, j;
magmaDoubleComplex alpha = MAGMA_Z_ONE;
magmaDoubleComplex beta = MAGMA_Z_ZERO;
magmaDoubleComplex *A, *L, *U;
double work[1], matnorm, residual;
TESTING_MALLOC_CPU( A, magmaDoubleComplex, lda*N );
TESTING_MALLOC_CPU( L, magmaDoubleComplex, M*min_mn );
TESTING_MALLOC_CPU( U, magmaDoubleComplex, min_mn*N );
memset( L, 0, M*min_mn*sizeof(magmaDoubleComplex) );
memset( U, 0, min_mn*N*sizeof(magmaDoubleComplex) );
// set to original A
init_matrix( M, N, A, lda );
lapackf77_zlaswp( &N, A, &lda, &ione, &min_mn, ipiv, &ione);
// copy LU to L and U, and set diagonal to 1
lapackf77_zlacpy( MagmaLowerStr, &M, &min_mn, LU, &lda, L, &M );
lapackf77_zlacpy( MagmaUpperStr, &min_mn, &N, LU, &lda, U, &min_mn );
for(j=0; j<min_mn; j++)
L[j+j*M] = MAGMA_Z_MAKE( 1., 0. );
matnorm = lapackf77_zlange("f", &M, &N, A, &lda, work);
blasf77_zgemm("N", "N", &M, &N, &min_mn,
&alpha, L, &M, U, &min_mn, &beta, LU, &lda);
for( j = 0; j < N; j++ ) {
for( i = 0; i < M; i++ ) {
LU[i+j*lda] = MAGMA_Z_SUB( LU[i+j*lda], A[i+j*lda] );
}
}
residual = lapackf77_zlange("f", &M, &N, LU, &lda, work);
TESTING_FREE_CPU( A );
TESTING_FREE_CPU( L );
TESTING_FREE_CPU( U );
return residual / (matnorm * N);
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zgeqrf
*/
int main( magma_int_t argc, char** argv)
{
magma_int_t nquarkthreads=2;
magma_int_t nthreads=2;
magma_int_t num_gpus = 1;
TRACE = 0;
//magma_qr_params mp;
cuDoubleComplex *h_A, *h_R, *h_work, *tau;
double gpu_perf, cpu_perf, flops;
magma_timestr_t start, end;
magma_qr_params *mp = (magma_qr_params*)malloc(sizeof(magma_qr_params));
/* Matrix size */
magma_int_t M=0, N=0, n2;
magma_int_t size[10] = {1024,2048,3072,4032,5184,6016,7040,8064,9088,10112};
cublasStatus status;
magma_int_t i, j, info;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
mp->nb=-1;
mp->ob=-1;
mp->fb=-1;
mp->ib=32;
magma_int_t loop = argc;
magma_int_t accuracyflag = 1;
char precision;
magma_int_t nc = -1;
magma_int_t ncps = -1;
if (argc != 1)
{
for(i = 1; i<argc; i++){
if (strcmp("-N", argv[i])==0)
N = atoi(argv[++i]);
else if (strcmp("-M", argv[i])==0)
M = atoi(argv[++i]);
else if (strcmp("-F", argv[i])==0)
mp->fb = atoi(argv[++i]);
else if (strcmp("-O", argv[i])==0)
mp->ob = atoi(argv[++i]);
else if (strcmp("-B", argv[i])==0)
mp->nb = atoi(argv[++i]);
else if (strcmp("-b", argv[i])==0)
mp->ib = atoi(argv[++i]);
else if (strcmp("-A", argv[i])==0)
accuracyflag = atoi(argv[++i]);
else if (strcmp("-P", argv[i])==0)
nthreads = atoi(argv[++i]);
else if (strcmp("-Q", argv[i])==0)
nquarkthreads = atoi(argv[++i]);
else if (strcmp("-nc", argv[i])==0)
nc = atoi(argv[++i]);
else if (strcmp("-ncps", argv[i])==0)
ncps = atoi(argv[++i]);
}
if ((M>0 && N>0) || (M==0 && N==0))
{
printf(" testing_zgeqrf-v2 -M %d -N %d\n\n", M, N);
if (M==0 && N==0) {
M = N = size[9];
loop = 1;
}
}
else
{
printf("\nUsage: \n");
printf(" Make sure you set the number of BLAS threads to 1, e.g.,\n");
printf(" > setenv MKL_NUM_THREADS 1\n");
printf(" > testing_zgeqrf-v2 -M %d -N %d -B 128 -T 1\n\n", 1024, 1024);
exit(1);
}
}
else
{
printf("\nUsage: \n");
printf(" Make sure you set the number of BLAS threads to 1, e.g.,\n");
printf(" > setenv MKL_NUM_THREADS 1\n");
printf(" Set number of cores per socket and number of cores.\n");
printf(" > testing_zgeqrf-v2 -M %d -N %d -ncps 6 -nc 12\n\n", 1024, 1024);
printf(" Alternatively, set:\n");
printf(" Q: Number of threads for panel factorization.\n");
printf(" P: Number of threads for trailing matrix update (CPU).\n");
printf(" B: Block size.\n");
printf(" b: Inner block size.\n");
printf(" O: Block size for trailing matrix update (CPU).\n");
printf(" > testing_zgeqrf-v2 -M %d -N %d -Q 4 -P 4 -B 128 -b 32 -O 200\n\n", 10112, 10112);
M = N = size[9];
}
/* Auto tune based on number of cores and number of cores per socket if provided */
if ((nc > 0) && (ncps > 0)) {
precision = 's';
#if (defined(PRECISION_d))
precision = 'd';
#endif
#if (defined(PRECISION_c))
precision = 'c';
#endif
#if (defined(PRECISION_z))
precision = 'z';
#endif
auto_tune('q', precision, nc, ncps, M, N,
&(mp->nb), &(mp->ob), &(mp->ib), &nthreads, &nquarkthreads);
fprintf(stderr,"%d %d %d %d %d\n",mp->nb,mp->ob,mp->ib,nquarkthreads,nthreads);
}
/* Initialize MAGMA hardware context, seeting how many CPU cores
and how many GPUs to be used in the consequent computations */
mp->sync0 = 0;
magma_context *context;
context = magma_init((void*)(mp),cpu_thread, nthreads, nquarkthreads, num_gpus, argc, argv);
context->params = (void *)(mp);
mp->sync1 = (volatile magma_int_t *) malloc (sizeof(int)*nthreads);
for (i = 0; i < nthreads; i++)
mp->sync1[i] = 0;
n2 = M * N;
magma_int_t min_mn = min(M, N);
magma_int_t nb = magma_get_zgeqrf_nb(min_mn);
magma_int_t lwork = N*nb;
/* Allocate host memory for the matrix */
TESTING_MALLOC ( h_A , cuDoubleComplex, n2 );
TESTING_MALLOC ( tau , cuDoubleComplex, min_mn);
TESTING_HOSTALLOC( h_R , cuDoubleComplex, n2 );
TESTING_HOSTALLOC(h_work, cuDoubleComplex, lwork );
printf("\n\n");
printf(" M N CPU GFlop/s GPU GFlop/s ||R||_F / ||A||_F\n");
printf("==========================================================\n");
for(i=0; i<10; i++){
if (loop==1){
M = N = min_mn = size[i];
n2 = M*N;
}
flops = FLOPS( (double)M, (double)N ) / 1000000;
/* Initialize the matrix */
lapackf77_zlarnv( &ione, ISEED, &n2, h_A );
lapackf77_zlacpy( MagmaUpperLowerStr, &M, &N, h_A, &M, h_R, &M );
//magma_zgeqrf(M, N, h_R, M, tau, h_work, lwork, &info);
for(j=0; j<n2; j++)
h_R[j] = h_A[j];
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
magma_qr_init(mp, M, N, h_R, nthreads);
start = get_current_time();
magma_zgeqrf3(context, M, N, h_R, M, tau, h_work, lwork, &info);
end = get_current_time();
gpu_perf = flops / GetTimerValue(start, end);
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
start = get_current_time();
if (accuracyflag == 1)
lapackf77_zgeqrf(&M, &N, h_A, &M, tau, h_work, &lwork, &info);
end = get_current_time();
if (info < 0)
printf("Argument %d of zgeqrf had an illegal value.\n", -info);
cpu_perf = 4.*M*N*min_mn/(3.*1000000*GetTimerValue(start,end));
/* =====================================================================
Check the result compared to LAPACK
=================================================================== */
double work[1], matnorm = 1.;
cuDoubleComplex mone = MAGMA_Z_NEG_ONE;
magma_int_t one = 1;
if (accuracyflag == 1){
matnorm = lapackf77_zlange("f", &M, &N, h_A, &M, work);
blasf77_zaxpy(&n2, &mone, h_A, &one, h_R, &one);
}
if (accuracyflag == 1){
printf("%5d %5d %6.2f %6.2f %e\n",
M, N, cpu_perf, gpu_perf,
lapackf77_zlange("f", &M, &N, h_R, &M, work) / matnorm);
} else {
printf("%5d %5d %6.2f \n",
M, N, gpu_perf);
}
if (loop != 1)
break;
}
/* Memory clean up */
TESTING_FREE ( h_A );
TESTING_FREE ( tau );
TESTING_HOSTFREE(h_work);
TESTING_HOSTFREE( h_R );
/* Shut down the MAGMA context */
magma_finalize(context);
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zgeqlf
*/
int main( int argc, char** argv)
{
TESTING_INIT();
const double d_neg_one = MAGMA_D_NEG_ONE;
const double d_one = MAGMA_D_ONE;
const magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
const magmaDoubleComplex c_one = MAGMA_Z_ONE;
const magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
const magma_int_t ione = 1;
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf=0, cpu_time=0;
double Anorm, error=0, error2=0;
magmaDoubleComplex *h_A, *h_R, *tau, *h_work, tmp[1];
magma_int_t M, N, n2, lda, lwork, info, min_mn, nb;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
double tol = opts.tolerance * lapackf77_dlamch("E");
printf(" M N CPU GFlop/s (sec) GPU GFlop/s (sec) |L - Q^H*A| |I - Q^H*Q|\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;
nb = magma_get_zgeqlf_nb(M);
gflops = FLOPS_ZGEQLF( M, N ) / 1e9;
// query for workspace size
lwork = -1;
lapackf77_zgeqlf(&M, &N, NULL, &M, NULL, tmp, &lwork, &info);
lwork = (magma_int_t)MAGMA_Z_REAL( tmp[0] );
lwork = max( lwork, N*nb );
lwork = max( lwork, 2*nb*nb);
TESTING_MALLOC_CPU( tau, magmaDoubleComplex, min_mn );
TESTING_MALLOC_CPU( h_A, magmaDoubleComplex, n2 );
TESTING_MALLOC_CPU( h_work, magmaDoubleComplex, lwork );
TESTING_MALLOC_PIN( h_R, magmaDoubleComplex, n2 );
/* Initialize the matrix */
lapackf77_zlarnv( &ione, ISEED, &n2, h_A );
lapackf77_zlacpy( MagmaUpperLowerStr, &M, &N, h_A, &lda, h_R, &lda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
magma_zgeqlf( M, N, h_R, lda, tau, h_work, lwork, &info);
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_zgeqlf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Check the result, following zqlt01 except using the reduced Q.
This works for any M,N (square, tall, wide).
=================================================================== */
if ( opts.check ) {
magma_int_t ldq = M;
magma_int_t ldl = min_mn;
magmaDoubleComplex *Q, *L;
double *work;
TESTING_MALLOC_CPU( Q, magmaDoubleComplex, ldq*min_mn ); // M by K
TESTING_MALLOC_CPU( L, magmaDoubleComplex, ldl*N ); // K by N
TESTING_MALLOC_CPU( work, double, min_mn );
// copy M by K matrix V to Q (copying diagonal, which isn't needed) and
// copy K by N matrix L
lapackf77_zlaset( "Full", &min_mn, &N, &c_zero, &c_zero, L, &ldl );
if ( M >= N ) {
// for M=5, N=3: A = [ V V V ] <= V full block (M-N by K)
// K=N [ V V V ]
// [ ----- ]
// [ L V V ] <= V triangle (N by K, copying diagonal too)
// [ L L V ] <= L triangle (K by N)
// [ L L L ]
magma_int_t M_N = M - N;
lapackf77_zlacpy( "Full", &M_N, &min_mn, h_R, &lda, Q, &ldq );
lapackf77_zlacpy( "Upper", &N, &min_mn, &h_R[M_N], &lda, &Q[M_N], &ldq );
lapackf77_zlacpy( "Lower", &min_mn, &N, &h_R[M_N], &lda, L, &ldl );
}
else {
// for M=3, N=5: A = [ L L | L V V ] <= V triangle (K by K)
// K=M [ L L | L L V ] <= L triangle (K by M)
// [ L L | L L L ]
// ^^^============= L full block (K by N-M)
magma_int_t N_M = N - M;
lapackf77_zlacpy( "Upper", &M, &min_mn, &h_R[N_M*lda], &lda, Q, &ldq );
lapackf77_zlacpy( "Full", &min_mn, &N_M, h_R, &lda, L, &ldl );
lapackf77_zlacpy( "Lower", &min_mn, &M, &h_R[N_M*lda], &lda, &L[N_M*ldl], &ldl );
}
// generate M by K matrix Q, where K = min(M,N)
lapackf77_zungql( &M, &min_mn, &min_mn, Q, &ldq, tau, h_work, &lwork, &info );
assert( info == 0 );
// error = || L - Q^H*A || / (N * ||A||)
blasf77_zgemm( "Conj", "NoTrans", &min_mn, &N, &M,
&c_neg_one, Q, &ldq, h_A, &lda, &c_one, L, &ldl );
Anorm = lapackf77_zlange( "1", &M, &N, h_A, &lda, work );
error = lapackf77_zlange( "1", &min_mn, &N, L, &ldl, work );
if ( N > 0 && Anorm > 0 )
error /= (N*Anorm);
// set L = I (K by K identity), then L = I - Q^H*Q
// error = || I - Q^H*Q || / N
lapackf77_zlaset( "Upper", &min_mn, &min_mn, &c_zero, &c_one, L, &ldl );
blasf77_zherk( "Upper", "Conj", &min_mn, &M, &d_neg_one, Q, &ldq, &d_one, L, &ldl );
error2 = lapackf77_zlanhe( "1", "Upper", &min_mn, L, &ldl, work );
if ( N > 0 )
error2 /= N;
TESTING_FREE_CPU( Q ); Q = NULL;
TESTING_FREE_CPU( L ); L = NULL;
TESTING_FREE_CPU( work ); work = NULL;
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
lapackf77_zgeqlf( &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("lapack_zgeqlf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* =====================================================================
Print performance and error.
=================================================================== */
printf("%5d %5d ", (int) M, (int) 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 ) {
bool okay = (error < tol && error2 < tol);
status += ! okay;
printf( "%11.2e %11.2e %s\n", error, error2, (okay ? "ok" : "failed") );
}
else {
printf( " ---\n" );
}
TESTING_FREE_CPU( tau );
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_work );
TESTING_FREE_PIN( h_R );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
int main(int argc, char **argv)
{
TESTING_INIT();
real_Double_t gflops, magma_perf, magma_time, dev_perf, dev_time, cpu_perf, cpu_time;
double magma_error, dev_error, work[1];
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t M, N, Xm, Ym, lda, ldda, sizeA, sizeX, sizeY;
magma_int_t incx = 1;
magma_int_t incy = 1;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex alpha = MAGMA_Z_MAKE( 1.5, -2.3 );
magmaDoubleComplex beta = MAGMA_Z_MAKE( -0.6, 0.8 );
magmaDoubleComplex *A, *X, *Y, *Ydev, *Ymagma;
magmaDoubleComplex_ptr dA, dX, dY;
magma_int_t status = 0;
magma_opts opts;
opts.parse_opts( argc, argv );
double tol = opts.tolerance * lapackf77_dlamch("E");
printf("%% trans = %s\n", lapack_trans_const(opts.transA) );
#ifdef HAVE_CUBLAS
printf("%% M N MAGMA Gflop/s (ms) %s Gflop/s (ms) CPU Gflop/s (ms) MAGMA error %s error\n",
g_platform_str, g_platform_str );
#else
printf("%% M N %s Gflop/s (ms) CPU Gflop/s (ms) %s error\n",
g_platform_str, g_platform_str );
#endif
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];
lda = M;
ldda = magma_roundup( M, opts.align ); // multiple of 32 by default
gflops = FLOPS_ZGEMV( M, N ) / 1e9;
if ( opts.transA == MagmaNoTrans ) {
Xm = N;
Ym = M;
} else {
Xm = M;
Ym = N;
}
sizeA = lda*N;
sizeX = incx*Xm;
sizeY = incy*Ym;
TESTING_MALLOC_CPU( A, magmaDoubleComplex, sizeA );
TESTING_MALLOC_CPU( X, magmaDoubleComplex, sizeX );
TESTING_MALLOC_CPU( Y, magmaDoubleComplex, sizeY );
TESTING_MALLOC_CPU( Ydev, magmaDoubleComplex, sizeY );
TESTING_MALLOC_CPU( Ymagma, magmaDoubleComplex, sizeY );
TESTING_MALLOC_DEV( dA, magmaDoubleComplex, ldda*N );
TESTING_MALLOC_DEV( dX, magmaDoubleComplex, sizeX );
TESTING_MALLOC_DEV( dY, magmaDoubleComplex, sizeY );
/* Initialize the matrix */
lapackf77_zlarnv( &ione, ISEED, &sizeA, A );
lapackf77_zlarnv( &ione, ISEED, &sizeX, X );
lapackf77_zlarnv( &ione, ISEED, &sizeY, Y );
/* =====================================================================
Performs operation using CUBLAS
=================================================================== */
magma_zsetmatrix( M, N, A, lda, dA, ldda, opts.queue );
magma_zsetvector( Xm, X, incx, dX, incx, opts.queue );
magma_zsetvector( Ym, Y, incy, dY, incy, opts.queue );
dev_time = magma_sync_wtime( opts.queue );
#ifdef HAVE_CUBLAS
cublasZgemv( opts.handle, cublas_trans_const(opts.transA),
M, N, &alpha, dA, ldda, dX, incx, &beta, dY, incy );
#else
magma_zgemv( opts.transA, M, N,
alpha, dA, ldda,
dX, incx,
beta, dY, incy );
#endif
dev_time = magma_sync_wtime( opts.queue ) - dev_time;
dev_perf = gflops / dev_time;
magma_zgetvector( Ym, dY, incy, Ydev, incy, opts.queue );
/* =====================================================================
Performs operation using MAGMABLAS (currently only with CUDA)
=================================================================== */
#ifdef HAVE_CUBLAS
magma_zsetvector( Ym, Y, incy, dY, incy, opts.queue );
magma_time = magma_sync_wtime( opts.queue );
magmablas_zgemv( opts.transA, M, N, alpha, dA, ldda, dX, incx, beta, dY, incy, opts.queue );
magma_time = magma_sync_wtime( opts.queue ) - magma_time;
magma_perf = gflops / magma_time;
magma_zgetvector( Ym, dY, incy, Ymagma, incy, opts.queue );
#endif
/* =====================================================================
Performs operation using CPU BLAS
=================================================================== */
cpu_time = magma_wtime();
blasf77_zgemv( lapack_trans_const(opts.transA), &M, &N,
&alpha, A, &lda,
X, &incx,
&beta, Y, &incy );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
/* =====================================================================
Check the result
=================================================================== */
double Anorm = lapackf77_zlange( "F", &M, &N, A, &lda, work );
double Xnorm = lapackf77_zlange( "F", &Xm, &ione, X, &Xm, work );
blasf77_zaxpy( &Ym, &c_neg_one, Y, &incy, Ydev, &incy );
dev_error = lapackf77_zlange( "F", &Ym, &ione, Ydev, &Ym, work ) / (Anorm * Xnorm);
#ifdef HAVE_CUBLAS
blasf77_zaxpy( &Ym, &c_neg_one, Y, &incy, Ymagma, &incy );
magma_error = lapackf77_zlange( "F", &Ym, &ione, Ymagma, &Ym, work ) / (Anorm * Xnorm);
bool okay = (magma_error < tol) && (dev_error < tol);
status += ! okay;
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %8.2e %s\n",
(int) M, (int) N,
magma_perf, 1000.*magma_time,
dev_perf, 1000.*dev_time,
cpu_perf, 1000.*cpu_time,
magma_error, dev_error,
(okay ? "ok" : "failed"));
#else
bool okay = (dev_error < tol);
status += ! okay;
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %s\n",
(int) M, (int) N,
dev_perf, 1000.*dev_time,
cpu_perf, 1000.*cpu_time,
dev_error,
(okay ? "ok" : "failed"));
#endif
TESTING_FREE_CPU( A );
TESTING_FREE_CPU( X );
TESTING_FREE_CPU( Y );
TESTING_FREE_CPU( Ydev );
TESTING_FREE_CPU( Ymagma );
TESTING_FREE_DEV( dA );
TESTING_FREE_DEV( dX );
TESTING_FREE_DEV( dY );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zgetrf
*/
int main( int argc, char** argv )
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
magmaDoubleComplex *h_A, *h_R, *work;
magmaDoubleComplex_ptr d_A, dwork;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magma_int_t N, n2, lda, ldda, info, lwork, ldwork;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magmaDoubleComplex tmp;
double error, rwork[1];
magma_int_t *ipiv;
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
opts.lapack |= opts.check; // check (-c) implies lapack (-l)
// need looser bound (3000*eps instead of 30*eps) for tests
// TODO: should compute ||I - A*A^{-1}|| / (n*||A||*||A^{-1}||)
opts.tolerance = max( 3000., opts.tolerance );
double tol = opts.tolerance * lapackf77_dlamch("E");
printf(" N CPU GFlop/s (sec) GPU GFlop/s (sec) ||R||_F / (N*||A||_F)\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;
ldda = ((N+31)/32)*32;
ldwork = N * magma_get_zgetri_nb( N );
gflops = FLOPS_ZGETRI( N ) / 1e9;
// query for workspace size
lwork = -1;
lapackf77_zgetri( &N, NULL, &lda, NULL, &tmp, &lwork, &info );
if (info != 0)
printf("lapackf77_zgetri returned error %d: %s.\n",
(int) info, magma_strerror( info ));
lwork = int( MAGMA_Z_REAL( tmp ));
TESTING_MALLOC_CPU( ipiv, magma_int_t, N );
TESTING_MALLOC_CPU( work, magmaDoubleComplex, lwork );
TESTING_MALLOC_CPU( h_A, magmaDoubleComplex, n2 );
TESTING_MALLOC_PIN( h_R, magmaDoubleComplex, n2 );
TESTING_MALLOC_DEV( d_A, magmaDoubleComplex, ldda*N );
TESTING_MALLOC_DEV( dwork, magmaDoubleComplex, ldwork );
/* Initialize the matrix */
lapackf77_zlarnv( &ione, ISEED, &n2, h_A );
error = lapackf77_zlange( "f", &N, &N, h_A, &lda, rwork ); // norm(A)
/* Factor the matrix. Both MAGMA and LAPACK will use this factor. */
magma_zsetmatrix( N, N, h_A, lda, d_A, 0, ldda, opts.queue );
magma_zgetrf_gpu( N, N, d_A, 0, ldda, ipiv, opts.queue, &info );
magma_zgetmatrix( N, N, d_A, 0, ldda, h_A, lda, opts.queue );
if ( info != 0 )
printf("magma_zgetrf_gpu returned error %d: %s.\n",
(int) info, magma_strerror( info ));
// check for exact singularity
//h_A[ 10 + 10*lda ] = MAGMA_Z_MAKE( 0.0, 0.0 );
//magma_zsetmatrix( N, N, h_A, lda, d_A, 0, ldda, opts.queue );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
magma_zgetri_gpu( N, d_A, 0, ldda, ipiv, dwork, 0, ldwork, opts.queues2, &info );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_zgetri_gpu returned error %d: %s.\n",
(int) info, magma_strerror( info ));
magma_zgetmatrix( N, N, d_A, 0, ldda, h_R, lda, opts.queue );
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
lapackf77_zgetri( &N, h_A, &lda, ipiv, work, &lwork, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_zgetri returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Check the result compared to LAPACK
=================================================================== */
blasf77_zaxpy( &n2, &c_neg_one, h_A, &ione, h_R, &ione );
error = lapackf77_zlange( "f", &N, &N, h_R, &lda, rwork ) / (N*error);
printf( "%5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %s\n",
(int) N, cpu_perf, cpu_time, gpu_perf, gpu_time,
error, (error < tol ? "ok" : "failed"));
status += ! (error < tol);
}
else {
printf( "%5d --- ( --- ) %7.2f (%7.2f) ---\n",
(int) N, gpu_perf, gpu_time );
}
TESTING_FREE_CPU( ipiv );
TESTING_FREE_CPU( work );
TESTING_FREE_CPU( h_A );
TESTING_FREE_PIN( h_R );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( dwork );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zgetrf
*/
int main( int argc, char** argv)
{
real_Double_t gflops, gpu_perf, cpu_perf, gpu_time, cpu_time, error;
magmaDoubleComplex *h_A, *h_R;
magmaDoubleComplex_ptr d_A, dwork;
magma_int_t N = 0, n2, lda, ldda;
magma_int_t size[10] = { 1024, 2048, 3072, 4032, 5184, 5600, 5600, 5600, 5600, 5600 };
magma_int_t ntest = 10;
magma_int_t i, info;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0, 0, 0, 1};
magmaDoubleComplex *work;
magmaDoubleComplex tmp;
double rwork[1];
magma_int_t *ipiv;
magma_int_t lwork, ldwork;
double A_norm, R_norm;
if (argc != 1){
for(i = 1; i<argc; i++){
if (strcmp("-N", argv[i])==0)
N = atoi(argv[++i]);
}
if (N>0) size[0] = size[ntest-1] = N;
else exit(1);
}
else {
printf("\nUsage: \n");
printf(" testing_zgetri_gpu -N %d\n\n", 1024);
}
/* query for Lapack workspace size */
N = size[ntest-1];
lda = N;
work = &tmp;
lwork = -1;
lapackf77_zgetri( &N, h_A, &lda, ipiv, work, &lwork, &info );
if (info != 0)
printf("lapackf77_zgetri returned error %d\n", (int) info);
lwork = int( MAGMA_Z_REAL( *work ));
/* query for Magma workspace size */
ldwork = N * magma_get_zgetri_nb( N );
/* Initialize */
magma_queue_t queue;
magma_device_t device[ MagmaMaxGPUs ];
int num = 0;
magma_err_t err;
magma_init();
err = magma_get_devices( device, MagmaMaxGPUs, &num );
if ( err != 0 || num < 1 ) {
fprintf( stderr, "magma_get_devices failed: %d\n", err );
exit(-1);
}
err = magma_queue_create( device[0], &queue );
if ( err != 0 ) {
fprintf( stderr, "magma_queue_create failed: %d\n", err );
exit(-1);
}
/* Allocate memory */
n2 = N * N;
ldda = ((N+31)/32) * 32;
TESTING_MALLOC_CPU( ipiv, magma_int_t, N );
TESTING_MALLOC_CPU( work, magmaDoubleComplex, lwork );
TESTING_MALLOC_CPU( h_A, magmaDoubleComplex, n2 );
TESTING_MALLOC_PIN( h_R, magmaDoubleComplex, n2 );
TESTING_MALLOC_DEV( d_A, magmaDoubleComplex, ldda*N );
TESTING_MALLOC_DEV( dwork, magmaDoubleComplex, ldwork );
printf(" N CPU GFlop/s GPU GFlop/s ||R||_F / ||A||_F\n");
printf("========================================================\n");
for( i=0; i < ntest; i++ ){
N = size[i];
lda = N;
n2 = lda*N;
gflops = FLOPS_ZGETRI( (double)N ) / 1e9;
ldda = ((N+31)/32)*32;
/* Initialize the matrix */
lapackf77_zlarnv( &ione, ISEED, &n2, h_A );
A_norm = lapackf77_zlange( "f", &N, &N, h_A, &lda, rwork );
/* Factor the matrix. Both MAGMA and LAPACK will use this factor. */
magma_zsetmatrix( N, N, h_A, 0, lda, d_A, 0, ldda, queue );
magma_zgetrf_gpu( N, N, d_A, 0, ldda, ipiv, &info, queue );
magma_zgetmatrix( N, N, d_A, 0, ldda, h_A, 0, lda, queue );
// check for exact singularity
//h_A[ 10 + 10*lda ] = MAGMA_Z_MAKE( 0.0, 0.0 );
//magma_zsetmatrix( N, N, h_A, lda, d_A, ldda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
//warm-up
magma_zgetri_gpu( N, d_A, 0, ldda, ipiv, dwork, 0, ldwork, &info, queue );
magma_zsetmatrix( N, N, h_A, 0, lda, d_A, 0, ldda, queue );
gpu_time = magma_wtime();
magma_zgetri_gpu( N, d_A, 0, ldda, ipiv, dwork, 0, ldwork, &info, queue );
gpu_time = magma_wtime()-gpu_time;
if (info != 0)
printf("magma_zgetri_gpu returned error %d\n", (int) info);
gpu_perf = gflops / gpu_time;
magma_zgetmatrix( N, N, d_A, 0, ldda, h_R, 0, lda, queue );
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
lapackf77_zgetri( &N, h_A, &lda, ipiv, work, &lwork, &info );
cpu_time = magma_wtime() - cpu_time;
if (info != 0)
printf("lapackf77_zgetri returned error %d\n", (int) info);
cpu_perf = gflops / cpu_time;
/* =====================================================================
Check the result compared to LAPACK
=================================================================== */
blasf77_zaxpy( &n2, &c_neg_one, h_A, &ione, h_R, &ione );
R_norm = lapackf77_zlange( "f", &N, &N, h_R, &lda, rwork );
printf( "%5d %6.2f %6.2f %e\n",
(int) N, cpu_perf, gpu_perf, R_norm / A_norm );
if (argc != 1)
break;
}
/* Memory clean up */
TESTING_FREE_CPU( ipiv );
TESTING_FREE_CPU( work );
TESTING_FREE_CPU( h_A );
TESTING_FREE_PIN( h_R );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( dwork );
/* Shutdown */
magma_queue_destroy( queue );
magma_finalize();
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zlarfb_gpu
*/
int main( int argc, char** argv )
{
TESTING_INIT();
magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magma_int_t M, N, K, size, ldc, ldv, ldt, ldw, nv;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
double error, work[1];
// test all combinations of input parameters
const char side[] = { MagmaLeft, MagmaRight };
const char trans[] = { MagmaConjTrans, MagmaNoTrans };
const char direct[] = { MagmaForward, MagmaBackward };
const char storev[] = { MagmaColumnwise, MagmaRowwise };
magma_opts opts;
parse_opts( argc, argv, &opts );
printf(" M N K storev side direct trans ||R||_F / ||HC||_F\n");
printf("========================================================================\n");
for( int i = 0; i < opts.ntest; ++i ) {
M = opts.msize[i];
N = opts.nsize[i];
K = opts.ksize[i];
if ( M < K || N < K || K <= 0 ) {
printf( "skipping M %d, N %d, K %d; requires M >= K, N >= K, K >= 0.\n", (int) M, (int) N, (int) K );
continue;
}
for( int istor = 0; istor < 2; ++istor ) {
for( int iside = 0; iside < 2; ++iside ) {
for( int idir = 0; idir < 2; ++idir ) {
for( int itran = 0; itran < 2; ++itran ) {
ldc = ((M+31)/32)*32;
ldt = ((K+31)/32)*32;
ldw = (side[iside] == MagmaLeft ? N : M);
// (ldv, nv) get swapped later if rowwise
ldv = (side[iside] == MagmaLeft ? M : N);
nv = K;
// Allocate memory for matrices
magmaDoubleComplex *C, *R, *V, *T, *W;
TESTING_MALLOC( C, magmaDoubleComplex, ldc*N );
TESTING_MALLOC( R, magmaDoubleComplex, ldc*N );
TESTING_MALLOC( V, magmaDoubleComplex, ldv*K );
TESTING_MALLOC( T, magmaDoubleComplex, ldt*K );
TESTING_MALLOC( W, magmaDoubleComplex, ldw*K );
magmaDoubleComplex *dC, *dV, *dT, *dW;
TESTING_DEVALLOC( dC, magmaDoubleComplex, ldc*N );
TESTING_DEVALLOC( dV, magmaDoubleComplex, ldv*K );
TESTING_DEVALLOC( dT, magmaDoubleComplex, ldt*K );
TESTING_DEVALLOC( dW, magmaDoubleComplex, ldw*K );
// C is M x N.
size = ldc*N;
lapackf77_zlarnv( &ione, ISEED, &size, C );
//printf( "C=" ); magma_zprint( M, N, C, ldc );
// V is ldv x nv. See larfb docs for description.
// if column-wise and left, M x K
// if column-wise and right, N x K
// if row-wise and left, K x M
// if row-wise and right, K x N
size = ldv*nv;
lapackf77_zlarnv( &ione, ISEED, &size, V );
if ( storev[istor] == MagmaColumnwise ) {
if ( direct[idir] == MagmaForward ) {
lapackf77_zlaset( MagmaUpperStr, &K, &K, &c_zero, &c_one, V, &ldv );
}
else {
lapackf77_zlaset( MagmaLowerStr, &K, &K, &c_zero, &c_one, &V[(ldv-K)], &ldv );
}
}
else {
// rowwise, swap V's dimensions
std::swap( ldv, nv );
if ( direct[idir] == MagmaForward ) {
lapackf77_zlaset( MagmaLowerStr, &K, &K, &c_zero, &c_one, V, &ldv );
}
else {
lapackf77_zlaset( MagmaUpperStr, &K, &K, &c_zero, &c_one, &V[(nv-K)*ldv], &ldv );
}
}
//printf( "# ldv %d, nv %d\n", ldv, nv );
//printf( "V=" ); magma_zprint( ldv, nv, V, ldv );
// T is K x K, upper triangular for forward, and lower triangular for backward
magma_int_t k1 = K-1;
size = ldt*K;
lapackf77_zlarnv( &ione, ISEED, &size, T );
if ( direct[idir] == MagmaForward ) {
lapackf77_zlaset( MagmaLowerStr, &k1, &k1, &c_zero, &c_zero, &T[1], &ldt );
}
else {
lapackf77_zlaset( MagmaUpperStr, &k1, &k1, &c_zero, &c_zero, &T[1*ldt], &ldt );
}
//printf( "T=" ); magma_zprint( K, K, T, ldt );
magma_zsetmatrix( M, N, C, ldc, dC, ldc );
magma_zsetmatrix( ldv, nv, V, ldv, dV, ldv );
magma_zsetmatrix( K, K, T, ldt, dT, ldt );
lapackf77_zlarfb( &side[iside], &trans[itran], &direct[idir], &storev[istor],
&M, &N, &K,
V, &ldv, T, &ldt, C, &ldc, W, &ldw );
//printf( "HC=" ); magma_zprint( M, N, C, ldc );
magma_zlarfb_gpu( side[iside], trans[itran], direct[idir], storev[istor],
M, N, K,
dV, ldv, dT, ldt, dC, ldc, dW, ldw );
magma_zgetmatrix( M, N, dC, ldc, R, ldc );
//printf( "dHC=" ); magma_zprint( M, N, R, ldc );
// compute relative error |HC_magma - HC_lapack| / |HC_lapack|
error = lapackf77_zlange( "Fro", &M, &N, C, &ldc, work );
size = ldc*N;
blasf77_zaxpy( &size, &c_neg_one, C, &ione, R, &ione );
error = lapackf77_zlange( "Fro", &M, &N, R, &ldc, work ) / error;
printf( "%5d %5d %5d %c %c %c %c %8.2e\n",
(int) M, (int) N, (int) K,
storev[istor], side[iside], direct[idir], trans[itran], error );
TESTING_FREE( C );
TESTING_FREE( R );
TESTING_FREE( V );
TESTING_FREE( T );
TESTING_FREE( W );
TESTING_DEVFREE( dC );
TESTING_DEVFREE( dV );
TESTING_DEVFREE( dT );
TESTING_DEVFREE( dW );
}}}}
printf( "\n" );
}
TESTING_FINALIZE();
return 0;
}
extern "C" magma_int_t
magma_zgeev(magma_vec_t jobvl, magma_vec_t jobvr, magma_int_t n,
magmaDoubleComplex *a, magma_int_t lda,
magmaDoubleComplex *geev_w_array,
magmaDoubleComplex *vl, magma_int_t ldvl,
magmaDoubleComplex *vr, magma_int_t ldvr,
magmaDoubleComplex *work, magma_int_t lwork,
double *rwork, magma_int_t *info, magma_queue_t queue)
{
/* -- clMAGMA (version 1.0.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
September 2012
Purpose
=======
ZGEEV computes for an N-by-N complex nonsymmetric matrix A, the
eigenvalues and, optionally, the left and/or right eigenvectors.
The right eigenvector v(j) of A satisfies
A * v(j) = lambda(j) * v(j)
where lambda(j) is its eigenvalue.
The left eigenvector u(j) of A satisfies
u(j)**H * A = lambda(j) * u(j)**H
where u(j)**H denotes the conjugate transpose of u(j).
The computed eigenvectors are normalized to have Euclidean norm
equal to 1 and largest component real.
Arguments
=========
JOBVL (input) CHARACTER*1
= 'N': left eigenvectors of A are not computed;
= 'V': left eigenvectors of are computed.
JOBVR (input) CHARACTER*1
= 'N': right eigenvectors of A are not computed;
= 'V': right eigenvectors of A are computed.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the N-by-N matrix A.
On exit, A has been overwritten.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
W (output) COMPLEX*16 array, dimension (N)
W contains the computed eigenvalues.
VL (output) COMPLEX*16 array, dimension (LDVL,N)
If JOBVL = 'V', the left eigenvectors u(j) are stored one
after another in the columns of VL, in the same order
as their eigenvalues.
If JOBVL = 'N', VL is not referenced.
u(j) = VL(:,j), the j-th column of VL.
LDVL (input) INTEGER
The leading dimension of the array VL. LDVL >= 1; if
JOBVL = 'V', LDVL >= N.
VR (output) COMPLEX*16 array, dimension (LDVR,N)
If JOBVR = 'V', the right eigenvectors v(j) are stored one
after another in the columns of VR, in the same order
as their eigenvalues.
If JOBVR = 'N', VR is not referenced.
v(j) = VR(:,j), the j-th column of VR.
LDVR (input) INTEGER
The leading dimension of the array VR. LDVR >= 1; if
JOBVR = 'V', LDVR >= N.
WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= (1+nb)*N.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
RWORK (workspace) DOUBLE PRECISION array, dimension (2*N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, the QR algorithm failed to compute all the
eigenvalues, and no eigenvectors have been computed;
elements and i+1:N of W contain eigenvalues which have
converged.
===================================================================== */
magma_int_t c__1 = 1;
magma_int_t c__0 = 0;
magma_int_t a_dim1, a_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1,
i__2, i__3;
double d__1, d__2;
magmaDoubleComplex z__1, z__2;
magma_int_t i__, k, ihi;
double scl;
magma_int_t ilo;
double dum[1], eps;
magmaDoubleComplex tmp;
magma_int_t ibal;
double anrm;
magma_int_t ierr, itau, iwrk, nout;
magma_int_t scalea;
double cscale;
magma_int_t select[1];
double bignum;
magma_int_t minwrk;
magma_int_t wantvl;
double smlnum;
magma_int_t irwork;
magma_int_t lquery, wantvr;
magma_int_t nb = 0;
magmaDoubleComplex_ptr dT;
//magma_timestr_t start, end;
char side[2] = {0, 0};
magma_vec_t jobvl_ = jobvl;
magma_vec_t jobvr_ = jobvr;
*info = 0;
lquery = lwork == -1;
wantvl = lapackf77_lsame(lapack_const(jobvl_), "V");
wantvr = lapackf77_lsame(lapack_const(jobvr_), "V");
if (! wantvl && ! lapackf77_lsame(lapack_const(jobvl_), "N")) {
*info = -1;
} else if (! wantvr && ! lapackf77_lsame(lapack_const(jobvr_), "N")) {
*info = -2;
} else if (n < 0) {
*info = -3;
} else if (lda < max(1,n)) {
*info = -5;
} else if ( (ldvl < 1) || (wantvl && (ldvl < n))) {
*info = -8;
} else if ( (ldvr < 1) || (wantvr && (ldvr < n))) {
*info = -10;
}
/* Compute workspace */
if (*info == 0) {
nb = magma_get_zgehrd_nb(n);
minwrk = (1+nb)*n;
work[0] = MAGMA_Z_MAKE((double) minwrk, 0.);
if (lwork < minwrk && ! lquery) {
*info = -12;
}
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
/* Quick return if possible */
if (n == 0) {
return *info;
}
// if eigenvectors are needed
#if defined(VERSION3)
if (MAGMA_SUCCESS != magma_malloc(&dT, nb*n*sizeof(magmaDoubleComplex) )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
#endif
a_dim1 = lda;
a_offset = 1 + a_dim1;
a -= a_offset;
vl_dim1 = ldvl;
vl_offset = 1 + vl_dim1;
vl -= vl_offset;
vr_dim1 = ldvr;
vr_offset = 1 + vr_dim1;
vr -= vr_offset;
--work;
--rwork;
/* Get machine constants */
eps = lapackf77_dlamch("P");
smlnum = lapackf77_dlamch("S");
bignum = 1. / smlnum;
lapackf77_dlabad(&smlnum, &bignum);
smlnum = magma_dsqrt(smlnum) / eps;
bignum = 1. / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = lapackf77_zlange("M", &n, &n, &a[a_offset], &lda, dum);
scalea = 0;
if (anrm > 0. && anrm < smlnum) {
scalea = 1;
cscale = smlnum;
} else if (anrm > bignum) {
scalea = 1;
cscale = bignum;
}
if (scalea) {
lapackf77_zlascl("G", &c__0, &c__0, &anrm, &cscale, &n, &n, &a[a_offset], &lda, &
ierr);
}
/* Balance the matrix
(CWorkspace: none)
(RWorkspace: need N) */
ibal = 1;
lapackf77_zgebal("B", &n, &a[a_offset], &lda, &ilo, &ihi, &rwork[ibal], &ierr);
/* Reduce to upper Hessenberg form
(CWorkspace: need 2*N, prefer N+N*NB)
(RWorkspace: none) */
itau = 1;
iwrk = itau + n;
i__1 = lwork - iwrk + 1;
//start = get_current_time();
#if defined(VERSION1)
/*
* Version 1 - LAPACK
*/
lapackf77_zgehrd(&n, &ilo, &ihi, &a[a_offset], &lda,
&work[itau], &work[iwrk], &i__1, &ierr);
#elif defined(VERSION2)
/*
* Version 2 - LAPACK consistent HRD
*/
magma_zgehrd2(n, ilo, ihi, &a[a_offset], lda,
&work[itau], &work[iwrk], &i__1, &ierr);
#elif defined(VERSION3)
/*
* Version 3 - LAPACK consistent MAGMA HRD + matrices T stored,
*/
magma_zgehrd(n, ilo, ihi, &a[a_offset], lda,
&work[itau], &work[iwrk], i__1, dT, 0, &ierr, queue);
#endif
//end = get_current_time();
//printf(" Time for zgehrd = %5.2f sec\n", GetTimerValue(start,end)/1000.);
if (wantvl) {
/* Want left eigenvectors
Copy Householder vectors to VL */
side[0] = 'L';
lapackf77_zlacpy(MagmaLowerStr, &n, &n,
&a[a_offset], &lda, &vl[vl_offset], &ldvl);
/* Generate unitary matrix in VL
(CWorkspace: need 2*N-1, prefer N+(N-1)*NB)
(RWorkspace: none) */
i__1 = lwork - iwrk + 1;
//start = get_current_time();
#if defined(VERSION1) || defined(VERSION2)
/*
* Version 1 & 2 - LAPACK
*/
lapackf77_zunghr(&n, &ilo, &ihi, &vl[vl_offset], &ldvl,
&work[itau], &work[iwrk], &i__1, &ierr);
#elif defined(VERSION3)
/*
* Version 3 - LAPACK consistent MAGMA HRD + matrices T stored
*/
magma_zunghr(n, ilo, ihi, &vl[vl_offset], ldvl, &work[itau],
dT, 0, nb, &ierr, queue);
#endif
//end = get_current_time();
//printf(" Time for zunghr = %5.2f sec\n", GetTimerValue(start,end)/1000.);
/* Perform QR iteration, accumulating Schur vectors in VL
(CWorkspace: need 1, prefer HSWORK (see comments) )
(RWorkspace: none) */
iwrk = itau;
i__1 = lwork - iwrk + 1;
lapackf77_zhseqr("S", "V", &n, &ilo, &ihi, &a[a_offset], &lda, geev_w_array,
&vl[vl_offset], &ldvl, &work[iwrk], &i__1, info);
if (wantvr)
{
/* Want left and right eigenvectors
Copy Schur vectors to VR */
side[0] = 'B';
lapackf77_zlacpy("F", &n, &n, &vl[vl_offset], &ldvl, &vr[vr_offset], &ldvr);
}
} else if (wantvr) {
/* Want right eigenvectors
Copy Householder vectors to VR */
side[0] = 'R';
lapackf77_zlacpy("L", &n, &n, &a[a_offset], &lda, &vr[vr_offset], &ldvr);
/* Generate unitary matrix in VR
(CWorkspace: need 2*N-1, prefer N+(N-1)*NB)
(RWorkspace: none) */
i__1 = lwork - iwrk + 1;
//start = get_current_time();
#if defined(VERSION1) || defined(VERSION2)
/*
* Version 1 & 2 - LAPACK
*/
lapackf77_zunghr(&n, &ilo, &ihi, &vr[vr_offset], &ldvr,
&work[itau], &work[iwrk], &i__1, &ierr);
#elif defined(VERSION3)
/*
* Version 3 - LAPACK consistent MAGMA HRD + matrices T stored
*/
magma_zunghr(n, ilo, ihi, &vr[vr_offset], ldvr,
&work[itau], dT, 0, nb, &ierr, queue);
#endif
//end = get_current_time();
//printf(" Time for zunghr = %5.2f sec\n", GetTimerValue(start,end)/1000.);
/* Perform QR iteration, accumulating Schur vectors in VR
(CWorkspace: need 1, prefer HSWORK (see comments) )
(RWorkspace: none) */
iwrk = itau;
i__1 = lwork - iwrk + 1;
lapackf77_zhseqr("S", "V", &n, &ilo, &ihi, &a[a_offset], &lda, geev_w_array,
&vr[vr_offset], &ldvr, &work[iwrk], &i__1, info);
} else {
/* Compute eigenvalues only
(CWorkspace: need 1, prefer HSWORK (see comments) )
(RWorkspace: none) */
iwrk = itau;
i__1 = lwork - iwrk + 1;
lapackf77_zhseqr("E", "N", &n, &ilo, &ihi, &a[a_offset], &lda, geev_w_array,
&vr[vr_offset], &ldvr, &work[iwrk], &i__1, info);
}
/* If INFO > 0 from ZHSEQR, then quit */
if (*info > 0) {
goto L50;
}
if (wantvl || wantvr) {
/* Compute left and/or right eigenvectors
(CWorkspace: need 2*N)
(RWorkspace: need 2*N) */
irwork = ibal + n;
lapackf77_ztrevc(side, "B", select, &n, &a[a_offset], &lda, &vl[vl_offset], &ldvl,
&vr[vr_offset], &ldvr, &n, &nout, &work[iwrk], &rwork[irwork],
&ierr);
}
if (wantvl) {
/* Undo balancing of left eigenvectors
(CWorkspace: none)
(RWorkspace: need N) */
lapackf77_zgebak("B", "L", &n, &ilo, &ihi, &rwork[ibal], &n,
&vl[vl_offset], &ldvl, &ierr);
/* Normalize left eigenvectors and make largest component real */
for (i__ = 1; i__ <= n; ++i__) {
scl = 1. / cblas_dznrm2(n, &vl[i__ * vl_dim1 + 1], 1);
cblas_zdscal(n, scl, &vl[i__ * vl_dim1 + 1], 1);
i__2 = n;
for (k = 1; k <= i__2; ++k)
{
i__3 = k + i__ * vl_dim1;
/* Computing 2nd power */
d__1 = MAGMA_Z_REAL(vl[i__3]);
/* Computing 2nd power */
d__2 = MAGMA_Z_IMAG(vl[k + i__ * vl_dim1]);
rwork[irwork + k - 1] = d__1 * d__1 + d__2 * d__2;
}
/* Comment:
Fortran BLAS does not have to add 1
C BLAS must add one to cblas_idamax */
k = cblas_idamax(n, &rwork[irwork], 1)+1;
z__2 = MAGMA_Z_CNJG(vl[k + i__ * vl_dim1]);
d__1 = magma_dsqrt(rwork[irwork + k - 1]);
MAGMA_Z_DSCALE(z__1, z__2, d__1);
tmp = z__1;
cblas_zscal(n, CBLAS_SADDR(tmp), &vl[i__ * vl_dim1 + 1], 1);
i__2 = k + i__ * vl_dim1;
i__3 = k + i__ * vl_dim1;
d__1 = MAGMA_Z_REAL(vl[i__3]);
MAGMA_Z_SET2REAL(z__1, d__1);
vl[i__2] = z__1;
}
}
if (wantvr) {
/* Undo balancing of right eigenvectors
(CWorkspace: none)
(RWorkspace: need N) */
lapackf77_zgebak("B", "R", &n, &ilo, &ihi, &rwork[ibal], &n,
&vr[vr_offset], &ldvr, &ierr);
/* Normalize right eigenvectors and make largest component real */
for (i__ = 1; i__ <= n; ++i__) {
scl = 1. / cblas_dznrm2(n, &vr[i__ * vr_dim1 + 1], 1);
cblas_zdscal(n, scl, &vr[i__ * vr_dim1 + 1], 1);
i__2 = n;
for (k = 1; k <= i__2; ++k) {
i__3 = k + i__ * vr_dim1;
/* Computing 2nd power */
d__1 = MAGMA_Z_REAL(vr[i__3]);
/* Computing 2nd power */
d__2 = MAGMA_Z_IMAG(vr[k + i__ * vr_dim1]);
rwork[irwork + k - 1] = d__1 * d__1 + d__2 * d__2;
}
/* Comment:
Fortran BLAS does not have to add 1
C BLAS must add one to cblas_idamax */
k = cblas_idamax(n, &rwork[irwork], 1)+1;
z__2 = MAGMA_Z_CNJG(vr[k + i__ * vr_dim1]);
d__1 = magma_dsqrt(rwork[irwork + k - 1]);
MAGMA_Z_DSCALE(z__1, z__2, d__1);
tmp = z__1;
cblas_zscal(n, CBLAS_SADDR(tmp), &vr[i__ * vr_dim1 + 1], 1);
i__2 = k + i__ * vr_dim1;
i__3 = k + i__ * vr_dim1;
d__1 = MAGMA_Z_REAL(vr[i__3]);
MAGMA_Z_SET2REAL(z__1, d__1);
vr[i__2] = z__1;
}
}
/* Undo scaling if necessary */
L50:
if (scalea) {
i__1 = n - *info;
/* Computing MAX */
i__3 = n - *info;
i__2 = max(i__3,1);
lapackf77_zlascl("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1,
geev_w_array + *info, &i__2, &ierr);
if (*info > 0) {
i__1 = ilo - 1;
lapackf77_zlascl("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1,
geev_w_array, &n, &ierr);
}
}
#if defined(VERSION3)
magma_free( dT );
#endif
return *info;
} /* magma_zgeev */
// --------------------
int main(int argc, char **argv)
{
TESTING_INIT();
real_Double_t gflops, cpu_time=0, cpu_perf=0, gpu_time, gpu_perf, mgpu_time, mgpu_perf, cuda_time, cuda_perf;
double Ynorm, error=0, error2=0, work[1];
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magma_int_t n_local[MagmaMaxGPUs];
magma_int_t N, Noffset, lda, ldda, blocks, lhwork, ldwork, matsize, vecsize;
magma_int_t incx = 1;
magmaDoubleComplex alpha = MAGMA_Z_MAKE( 1.5, -2.3 );
magmaDoubleComplex beta = MAGMA_Z_MAKE( -0.6, 0.8 );
magmaDoubleComplex *A, *X, *Y, *Ylapack, *Ycublas, *Ymagma, *Ymagma1, *hwork;
magmaDoubleComplex_ptr dA, dX, dY;
magmaDoubleComplex_ptr d_lA[MagmaMaxGPUs], dwork[MagmaMaxGPUs];
magma_device_t dev;
magma_queue_t queues[MagmaMaxGPUs];
magma_int_t status = 0;
magma_opts opts;
opts.parse_opts( argc, argv );
opts.ngpu = abs( opts.ngpu ); // always uses multi-GPU code
double tol = opts.tolerance * lapackf77_dlamch("E");
magma_int_t nb = 64; // required by magmablas_zhemv_mgpu implementation
for( dev=0; dev < opts.ngpu; ++dev ) {
magma_queue_create( dev, &queues[dev] );
}
// currently, tests all offsets in the offsets array;
// comment out loop below to test a specific offset.
magma_int_t offset = opts.offset;
magma_int_t offsets[] = { 0, 1, 31, 32, 33, 63, 64, 65, 100, 200 };
magma_int_t noffsets = sizeof(offsets) / sizeof(*offsets);
printf("%% uplo = %s, ngpu %d, block size = %d, offset %d\n",
lapack_uplo_const(opts.uplo), (int) opts.ngpu, (int) nb, (int) offset );
printf( "%% BLAS CUBLAS MAGMA 1 GPU MAGMA MGPU Error rel Error rel\n"
"%% N offset Gflop/s (msec) Gflop/s (msec) Gflop/s (msec) Gflop/s (msec) to CUBLAS to LAPACK\n"
"%%==================================================================================================================\n" );
for( int itest = 0; itest < opts.ntest; ++itest ) {
// comment out these two lines & end of loop to test a specific offset
for( int ioffset=0; ioffset < noffsets; ioffset += 1 ) {
offset = offsets[ioffset];
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[itest];
Noffset = N + offset;
lda = Noffset;
ldda = magma_roundup( Noffset, opts.align ); // multiple of 32 by default
matsize = Noffset*ldda;
vecsize = (Noffset-1)*incx + 1;
gflops = FLOPS_ZHEMV( N ) / 1e9;
blocks = magma_ceildiv( N + (offset % nb), nb );
lhwork = N*opts.ngpu;
ldwork = ldda*(blocks + 1);
TESTING_MALLOC_CPU( A, magmaDoubleComplex, matsize );
TESTING_MALLOC_CPU( Y, magmaDoubleComplex, vecsize );
TESTING_MALLOC_CPU( Ycublas, magmaDoubleComplex, vecsize );
TESTING_MALLOC_CPU( Ymagma, magmaDoubleComplex, vecsize );
TESTING_MALLOC_CPU( Ymagma1, magmaDoubleComplex, vecsize );
TESTING_MALLOC_CPU( Ylapack, magmaDoubleComplex, vecsize );
TESTING_MALLOC_PIN( X, magmaDoubleComplex, vecsize );
TESTING_MALLOC_PIN( hwork, magmaDoubleComplex, lhwork );
magma_setdevice( opts.device );
TESTING_MALLOC_DEV( dA, magmaDoubleComplex, matsize );
TESTING_MALLOC_DEV( dX, magmaDoubleComplex, vecsize );
TESTING_MALLOC_DEV( dY, magmaDoubleComplex, vecsize );
// TODO make magma_zmalloc_bcyclic helper function?
for( dev=0; dev < opts.ngpu; dev++ ) {
n_local[dev] = ((Noffset/nb)/opts.ngpu)*nb;
if (dev < (Noffset/nb) % opts.ngpu)
n_local[dev] += nb;
else if (dev == (Noffset/nb) % opts.ngpu)
n_local[dev] += Noffset % nb;
magma_setdevice( dev );
TESTING_MALLOC_DEV( d_lA[dev], magmaDoubleComplex, ldda*n_local[dev] );
TESTING_MALLOC_DEV( dwork[dev], magmaDoubleComplex, ldwork );
}
//////////////////////////////////////////////////////////////////////////
/* Initialize the matrix */
lapackf77_zlarnv( &ione, ISEED, &matsize, A );
magma_zmake_hermitian( Noffset, A, lda );
lapackf77_zlarnv( &ione, ISEED, &vecsize, X );
lapackf77_zlarnv( &ione, ISEED, &vecsize, Y );
/* =====================================================================
Performs operation using CUBLAS
=================================================================== */
magma_setdevice( opts.device );
magma_zsetmatrix( Noffset, Noffset, A, lda, dA, ldda, opts.queue );
magma_zsetvector( Noffset, X, incx, dX, incx, opts.queue );
magma_zsetvector( Noffset, Y, incx, dY, incx, opts.queue );
cuda_time = magma_sync_wtime(0);
cublasZhemv( opts.handle, cublas_uplo_const(opts.uplo), N,
&alpha, dA + offset + offset*ldda, ldda,
dX + offset, incx,
&beta, dY + offset, incx );
cuda_time = magma_sync_wtime(0) - cuda_time;
cuda_perf = gflops / cuda_time;
magma_zgetvector( Noffset, dY, incx, Ycublas, incx, opts.queue );
/* =====================================================================
Performs operation using MAGMABLAS (1 GPU)
=================================================================== */
magma_setdevice( opts.device );
magma_zsetvector( Noffset, Y, incx, dY, incx, opts.queue );
gpu_time = magma_sync_wtime( opts.queue );
magmablas_zhemv_work( opts.uplo, N,
alpha, dA + offset + offset*ldda, ldda,
dX + offset, incx,
beta, dY + offset, incx, dwork[ opts.device ], ldwork,
opts.queue );
gpu_time = magma_sync_wtime( opts.queue ) - gpu_time;
gpu_perf = gflops / gpu_time;
magma_zgetvector( Noffset, dY, incx, Ymagma1, incx, opts.queue );
/* =====================================================================
Performs operation using MAGMABLAS (multi-GPU)
=================================================================== */
magma_zsetmatrix_1D_col_bcyclic( Noffset, Noffset, A, lda, d_lA, ldda, opts.ngpu, nb, queues );
blasf77_zcopy( &Noffset, Y, &incx, Ymagma, &incx );
// workspaces do NOT need to be zero -- set to NAN to prove
for( dev=0; dev < opts.ngpu; ++dev ) {
magma_setdevice( dev );
magmablas_zlaset( MagmaFull, ldwork, 1, MAGMA_Z_NAN, MAGMA_Z_NAN, dwork[dev], ldwork, opts.queue );
}
lapackf77_zlaset( "Full", &lhwork, &ione, &MAGMA_Z_NAN, &MAGMA_Z_NAN, hwork, &lhwork );
mgpu_time = magma_sync_wtime(0);
magma_int_t info;
info = magmablas_zhemv_mgpu(
opts.uplo, N,
alpha,
d_lA, ldda, offset,
X + offset, incx,
beta,
Ymagma + offset, incx,
hwork, lhwork,
dwork, ldwork,
opts.ngpu, nb, queues );
if (info != 0) {
printf("magmablas_zhemv_mgpu returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
info = magmablas_zhemv_mgpu_sync(
opts.uplo, N,
alpha,
d_lA, ldda, offset,
X + offset, incx,
beta,
Ymagma + offset, incx,
hwork, lhwork,
dwork, ldwork,
opts.ngpu, nb, queues );
if (info != 0) {
printf("magmablas_zhemv_sync returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
mgpu_time = magma_sync_wtime(0) - mgpu_time;
mgpu_perf = gflops / mgpu_time;
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
blasf77_zcopy( &Noffset, Y, &incx, Ylapack, &incx );
cpu_time = magma_wtime();
blasf77_zhemv( lapack_uplo_const(opts.uplo), &N,
&alpha, A + offset + offset*lda, &lda,
X + offset, &incx,
&beta, Ylapack + offset, &incx );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
/* =====================================================================
Compute the Difference LAPACK vs. Magma
=================================================================== */
Ynorm = lapackf77_zlange( "F", &Noffset, &ione, Ylapack, &Noffset, work );
blasf77_zaxpy( &Noffset, &c_neg_one, Ymagma, &incx, Ylapack, &incx );
error2 = lapackf77_zlange( "F", &Noffset, &ione, Ylapack, &Noffset, work ) / Ynorm;
}
/* =====================================================================
Compute the Difference Cublas vs. Magma
=================================================================== */
Ynorm = lapackf77_zlange( "F", &Noffset, &ione, Ycublas, &Noffset, work );
blasf77_zaxpy( &Noffset, &c_neg_one, Ymagma, &incx, Ycublas, &incx );
error = lapackf77_zlange( "F", &Noffset, &ione, Ycublas, &Noffset, work ) / Ynorm;
bool okay = (error < tol && error2 < tol);
status += ! okay;
if ( opts.lapack ) {
printf( "%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %8.2e %s\n",
(int) N, (int) offset,
cpu_perf, cpu_time*1000.,
cuda_perf, cuda_time*1000.,
gpu_perf, gpu_time*1000.,
mgpu_perf, mgpu_time*1000.,
error, error2, (okay ? "ok" : "failed") );
}
else {
printf( "%5d %5d --- ( --- ) %7.2f (%7.2f) %7.2f (%7.2f) %7.2f (%7.2f) %8.2e --- %s\n",
(int) N, (int) offset,
cuda_perf, cuda_time*1000.,
gpu_perf, gpu_time*1000.,
mgpu_perf, mgpu_time*1000.,
error, (okay ? "ok" : "failed") );
}
/* Free Memory */
TESTING_FREE_CPU( A );
TESTING_FREE_CPU( Y );
TESTING_FREE_CPU( Ycublas );
TESTING_FREE_CPU( Ymagma );
TESTING_FREE_CPU( Ymagma1 );
TESTING_FREE_CPU( Ylapack );
TESTING_FREE_PIN( X );
TESTING_FREE_PIN( hwork );
magma_setdevice( opts.device );
TESTING_FREE_DEV( dA );
TESTING_FREE_DEV( dX );
TESTING_FREE_DEV( dY );
for( dev=0; dev < opts.ngpu; dev++ ) {
magma_setdevice( dev );
TESTING_FREE_DEV( d_lA[dev] );
TESTING_FREE_DEV( dwork[dev] );
}
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
// comment out these two lines line & top of loop test a specific offset
} // end for ioffset
printf( "\n" );
}
for( dev=0; dev < opts.ngpu; ++dev ) {
magma_queue_destroy( queues[dev] );
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zunmqr
*/
int main( int argc, char** argv )
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
double error, work[1];
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magma_int_t ione = 1;
magma_int_t mm, m, n, k, size, info;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t nb, ldc, lda, lwork, lwork_max;
magmaDoubleComplex *C, *R, *A, *W, *tau;
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
// need slightly looser bound (60*eps instead of 30*eps) for some tests
opts.tolerance = max( 60., opts.tolerance );
double tol = opts.tolerance * lapackf77_dlamch("E");
// test all combinations of input parameters
magma_side_t side [] = { MagmaLeft, MagmaRight };
magma_trans_t trans[] = { MagmaConjTrans, MagmaNoTrans };
printf(" M N K side trans CPU GFlop/s (sec) GPU GFlop/s (sec) ||R||_F / ||QC||_F\n");
printf("===============================================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iside = 0; iside < 2; ++iside ) {
for( int itran = 0; itran < 2; ++itran ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
m = opts.msize[itest];
n = opts.nsize[itest];
k = opts.ksize[itest];
nb = magma_get_zgeqrf_nb( m );
ldc = m;
// A is m x k (left) or n x k (right)
mm = (side[iside] == MagmaLeft ? m : n);
lda = mm;
gflops = FLOPS_ZUNMQR( m, n, k, side[iside] ) / 1e9;
if ( side[iside] == MagmaLeft && m < k ) {
printf( "%5d %5d %5d %4c %5c skipping because side=left and m < k\n",
(int) m, (int) n, (int) k,
lapacke_side_const( side[iside] ),
lapacke_trans_const( trans[itran] ) );
continue;
}
if ( side[iside] == MagmaRight && n < k ) {
printf( "%5d %5d %5d %4c %5c skipping because side=right and n < k\n",
(int) m, (int) n, (int) k,
lapacke_side_const( side[iside] ),
lapacke_trans_const( trans[itran] ) );
continue;
}
// need at least 2*nb*nb for geqrf
lwork_max = max( max( m*nb, n*nb ), 2*nb*nb );
TESTING_MALLOC_CPU( C, magmaDoubleComplex, ldc*n );
TESTING_MALLOC_CPU( R, magmaDoubleComplex, ldc*n );
TESTING_MALLOC_CPU( A, magmaDoubleComplex, lda*k );
TESTING_MALLOC_CPU( W, magmaDoubleComplex, lwork_max );
TESTING_MALLOC_CPU( tau, magmaDoubleComplex, k );
// C is full, m x n
size = ldc*n;
lapackf77_zlarnv( &ione, ISEED, &size, C );
lapackf77_zlacpy( "Full", &m, &n, C, &ldc, R, &ldc );
size = lda*k;
lapackf77_zlarnv( &ione, ISEED, &size, A );
// compute QR factorization to get Householder vectors in A, tau
magma_zgeqrf( mm, k, A, lda, tau, W, lwork_max, &info );
if (info != 0)
printf("magma_zgeqrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
lapackf77_zunmqr( lapack_side_const( side[iside] ), lapack_trans_const( trans[itran] ),
&m, &n, &k,
A, &lda, tau, C, &ldc, W, &lwork_max, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_zunmqr returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
// query for workspace size
lwork = -1;
magma_zunmqr( side[iside], trans[itran],
m, n, k,
A, lda, tau, R, ldc, W, lwork, &info );
if (info != 0)
printf("magma_zunmqr (lwork query) returned error %d: %s.\n",
(int) info, magma_strerror( info ));
lwork = (magma_int_t) MAGMA_Z_REAL( W[0] );
if ( lwork < 0 || lwork > lwork_max ) {
printf("optimal lwork %d > lwork_max %d\n", (int) lwork, (int) lwork_max );
lwork = lwork_max;
}
gpu_time = magma_wtime();
magma_zunmqr( side[iside], trans[itran],
m, n, k,
A, lda, tau, R, ldc, W, lwork, &info );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_zunmqr returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
compute relative error |QC_magma - QC_lapack| / |QC_lapack|
=================================================================== */
error = lapackf77_zlange( "Fro", &m, &n, C, &ldc, work );
size = ldc*n;
blasf77_zaxpy( &size, &c_neg_one, C, &ione, R, &ione );
error = lapackf77_zlange( "Fro", &m, &n, R, &ldc, work ) / error;
printf( "%5d %5d %5d %4c %5c %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %s\n",
(int) m, (int) n, (int) k,
lapacke_side_const( side[iside] ),
lapacke_trans_const( trans[itran] ),
cpu_perf, cpu_time, gpu_perf, gpu_time,
error, (error < tol ? "ok" : "failed") );
status += ! (error < tol);
TESTING_FREE_CPU( C );
TESTING_FREE_CPU( R );
TESTING_FREE_CPU( A );
TESTING_FREE_CPU( W );
TESTING_FREE_CPU( tau );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}} // end iside, itran
printf( "\n" );
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zgeadd
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
double error, work[1];
magmaDoubleComplex *h_A, *h_B, *d_A, *d_B;
magmaDoubleComplex alpha = MAGMA_Z_MAKE( 3.1415, 2.718 );
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magma_int_t M, N, size, lda, ldda;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_opts opts;
parse_opts( argc, argv, &opts );
/* Uncomment these lines to check parameters.
* magma_xerbla calls lapack's xerbla to print out error. */
//magmablas_zgeadd( -1, N, alpha, d_A, ldda, d_B, ldda );
//magmablas_zgeadd( M, -1, alpha, d_A, ldda, d_B, ldda );
//magmablas_zgeadd( M, N, alpha, d_A, M-1, d_B, ldda );
//magmablas_zgeadd( M, N, alpha, d_A, ldda, d_B, N-1 );
printf(" M N CPU GFlop/s (sec) GPU GFlop/s (sec) |Bl-Bm|/|Bl|\n");
printf("=========================================================================\n");
for( int i = 0; i < opts.ntest; ++i ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[i];
N = opts.nsize[i];
lda = M;
ldda = ((M+31)/32)*32;
size = lda*N;
gflops = 2.*M*N / 1e9;
TESTING_MALLOC( h_A, magmaDoubleComplex, lda *N );
TESTING_MALLOC( h_B, magmaDoubleComplex, lda *N );
TESTING_DEVALLOC( d_A, magmaDoubleComplex, ldda*N );
TESTING_DEVALLOC( d_B, magmaDoubleComplex, ldda*N );
lapackf77_zlarnv( &ione, ISEED, &size, h_A );
lapackf77_zlarnv( &ione, ISEED, &size, h_B );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
magma_zsetmatrix( M, N, h_A, lda, d_A, ldda );
magma_zsetmatrix( M, N, h_B, lda, d_B, ldda );
gpu_time = magma_sync_wtime( NULL );
magmablas_zgeadd( M, N, alpha, d_A, ldda, d_B, ldda );
gpu_time = magma_sync_wtime( NULL ) - gpu_time;
gpu_perf = gflops / gpu_time;
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
for( int j = 0; j < N; ++j ) {
blasf77_zaxpy( &M, &alpha, &h_A[j*lda], &ione, &h_B[j*lda], &ione );
}
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
/* =====================================================================
Check result
=================================================================== */
magma_zgetmatrix( M, N, d_B, ldda, h_A, lda );
error = lapackf77_zlange( "F", &M, &N, h_B, &lda, work );
blasf77_zaxpy( &size, &c_neg_one, h_A, &ione, h_B, &ione );
error = lapackf77_zlange( "F", &M, &N, h_B, &lda, work ) / error;
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e\n",
(int) M, (int) N, cpu_perf, cpu_time, gpu_perf, gpu_time, error );
TESTING_FREE( h_A );
TESTING_FREE( h_B );
TESTING_DEVFREE( d_A );
TESTING_DEVFREE( d_B );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return 0;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing ztrmv
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, cublas_perf, cublas_time, cpu_perf, cpu_time;
double cublas_error, Cnorm, work[1];
magma_int_t N;
magma_int_t Ak;
magma_int_t sizeA;
magma_int_t lda, ldda;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magmaDoubleComplex *h_A, *h_x, *h_xcublas;
magmaDoubleComplex *d_A, *d_x;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magma_opts opts;
parse_opts( argc, argv, &opts );
printf("If running lapack (option --lapack), MAGMA and CUBLAS error are both computed\n"
"relative to CPU BLAS result. Else, MAGMA error is computed relative to CUBLAS result.\n\n"
"uplo = %c, transA = %c, diag = %c \n", opts.uplo, opts.transA, opts.diag );
printf(" N CUBLAS Gflop/s (ms) CPU Gflop/s (ms) CUBLAS error\n");
printf("==================================================================\n");
for( int i = 0; i < opts.ntest; ++i ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[i];
gflops = FLOPS_ZTRMM(opts.side, N, 1) / 1e9;
lda = N;
Ak = N;
ldda = ((lda+31)/32)*32;
sizeA = lda*Ak;
TESTING_MALLOC( h_A, magmaDoubleComplex, lda*Ak );
TESTING_MALLOC( h_x, magmaDoubleComplex, N );
TESTING_MALLOC( h_xcublas, magmaDoubleComplex, N );
TESTING_DEVALLOC( d_A, magmaDoubleComplex, ldda*Ak );
TESTING_DEVALLOC( d_x, magmaDoubleComplex, N );
/* Initialize the matrices */
lapackf77_zlarnv( &ione, ISEED, &sizeA, h_A );
lapackf77_zlarnv( &ione, ISEED, &N, h_x );
/* =====================================================================
Performs operation using CUDA-BLAS
=================================================================== */
magma_zsetmatrix( Ak, Ak, h_A, lda, d_A, ldda );
magma_zsetvector( N, h_x, 1, d_x, 1 );
cublas_time = magma_sync_wtime( NULL );
cublasZtrmv( opts.uplo, opts.transA, opts.diag,
N,
d_A, ldda,
d_x, 1 );
cublas_time = magma_sync_wtime( NULL ) - cublas_time;
cublas_perf = gflops / cublas_time;
magma_zgetvector( N, d_x, 1, h_xcublas, 1 );
/* =====================================================================
Performs operation using CPU BLAS
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
blasf77_ztrmv( &opts.uplo, &opts.transA, &opts.diag,
&N,
h_A, &lda,
h_x, &ione );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
}
/* =====================================================================
Check the result
=================================================================== */
if ( opts.lapack ) {
// compute relative error for both magma & cublas, relative to lapack,
// |C_magma - C_lapack| / |C_lapack|
Cnorm = lapackf77_zlange( "M", &N, &ione, h_x, &N, work );
blasf77_zaxpy( &N, &c_neg_one, h_x, &ione, h_xcublas, &ione );
cublas_error = lapackf77_zlange( "M", &N, &ione, h_xcublas, &N, work ) / Cnorm;
printf("%5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e\n",
(int) N,
cublas_perf, 1000.*cublas_time,
cpu_perf, 1000.*cpu_time,
cublas_error );
}
else {
printf("%5d %7.2f (%7.2f) --- ( --- ) --- ---\n",
(int) N,
cublas_perf, 1000.*cublas_time);
}
TESTING_FREE( h_A );
TESTING_FREE( h_x );
TESTING_FREE( h_xcublas );
TESTING_DEVFREE( d_A );
TESTING_DEVFREE( d_x );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return 0;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zlaset
Code is very similar to testing_zlacpy.cpp
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gbytes, gpu_perf, gpu_time, cpu_perf, cpu_time;
double error, work[1];
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex *h_A, *h_R;
magmaDoubleComplex_ptr d_A;
magmaDoubleComplex offdiag, diag;
magma_int_t M, N, size, lda, ldda;
magma_int_t ione = 1;
magma_int_t status = 0;
magma_opts opts;
opts.parse_opts( argc, argv );
magma_uplo_t uplo[] = { MagmaLower, MagmaUpper, MagmaFull };
printf("%% uplo M N offdiag diag CPU GByte/s (ms) GPU GByte/s (ms) check\n");
printf("%%===================================================================================\n");
for( int iuplo = 0; iuplo < 3; ++iuplo ) {
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
for( int ival = 0; ival < 4; ++ival ) {
// test combinations of zero & non-zero:
// ival offdiag diag
// 0 0 0
// 1 0 3.14
// 2 1.23 0
// 3 1.23 3.14
offdiag = MAGMA_Z_MAKE( 1.2345, 6.7890 ) * (ival / 2);
diag = MAGMA_Z_MAKE( 3.1415, 2.7183 ) * (ival % 2);
M = opts.msize[itest];
N = opts.nsize[itest];
//M += 2; // space for insets
//N += 2;
lda = M;
ldda = magma_roundup( M, opts.align );
size = lda*N;
if ( uplo[iuplo] == MagmaLower ) {
// save lower trapezoid (with diagonal)
if ( M > N ) {
gbytes = sizeof(magmaDoubleComplex) * (1.*M*N - 0.5*N*(N-1)) / 1e9;
} else {
gbytes = sizeof(magmaDoubleComplex) * 0.5*M*(M+1) / 1e9;
}
}
else if ( uplo[iuplo] == MagmaUpper ) {
// save upper trapezoid (with diagonal)
if ( N > M ) {
gbytes = sizeof(magmaDoubleComplex) * (1.*M*N - 0.5*M*(M-1)) / 1e9;
} else {
gbytes = sizeof(magmaDoubleComplex) * 0.5*N*(N+1) / 1e9;
}
}
else {
// save entire matrix
gbytes = sizeof(magmaDoubleComplex) * 1.*M*N / 1e9;
}
TESTING_MALLOC_CPU( h_A, magmaDoubleComplex, size );
TESTING_MALLOC_CPU( h_R, magmaDoubleComplex, size );
TESTING_MALLOC_DEV( d_A, magmaDoubleComplex, ldda*N );
/* Initialize the matrix */
for( int j = 0; j < N; ++j ) {
for( int i = 0; i < M; ++i ) {
h_A[i + j*lda] = MAGMA_Z_MAKE( i + j/10000., j );
}
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
magma_zsetmatrix( M, N, h_A, lda, d_A, ldda );
magmablasSetKernelStream( opts.queue );
gpu_time = magma_sync_wtime( opts.queue );
//magmablas_zlaset( uplo[iuplo], M-2, N-2, offdiag, diag, d_A+1+ldda, ldda ); // inset by 1 row & col
magmablas_zlaset( uplo[iuplo], M, N, offdiag, diag, d_A, ldda );
gpu_time = magma_sync_wtime( opts.queue ) - gpu_time;
gpu_perf = gbytes / gpu_time;
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
//magma_int_t M2 = M-2; // inset by 1 row & col
//magma_int_t N2 = N-2;
//lapackf77_zlaset( lapack_uplo_const( uplo[iuplo] ), &M2, &N2, &offdiag, &diag, h_A+1+lda, &lda );
lapackf77_zlaset( lapack_uplo_const( uplo[iuplo] ), &M, &N, &offdiag, &diag, h_A, &lda );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gbytes / cpu_time;
if ( opts.verbose ) {
printf( "A= " ); magma_zprint( M, N, h_A, lda );
printf( "dA=" ); magma_zprint_gpu( M, N, d_A, ldda );
}
/* =====================================================================
Check the result
=================================================================== */
magma_zgetmatrix( M, N, d_A, ldda, h_R, lda );
blasf77_zaxpy(&size, &c_neg_one, h_A, &ione, h_R, &ione);
error = lapackf77_zlange("f", &M, &N, h_R, &lda, work);
bool okay = (error == 0);
status += ! okay;
printf("%5s %5d %5d %9.4f %6.4f %7.2f (%7.2f) %7.2f (%7.2f) %s\n",
lapack_uplo_const( uplo[iuplo] ), (int) M, (int) N,
real(offdiag), real(diag),
cpu_perf, cpu_time*1000., gpu_perf, gpu_time*1000.,
(okay ? "ok" : "failed") );
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_R );
TESTING_FREE_DEV( d_A );
fflush( stdout );
}
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
printf( "\n" );
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
int main(int argc, char **argv)
{
TESTING_INIT();
real_Double_t gflops, magma_perf, magma_time, cublas_perf, cublas_time, cpu_perf, cpu_time;
double magma_error, cublas_error, work[1];
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t N, lda, sizeA, sizeX, sizeY, blocks, ldwork;
magma_int_t incx = 1;
magma_int_t incy = 1;
magma_int_t nb = 64;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex alpha = MAGMA_Z_MAKE( 1.5, -2.3 );
magmaDoubleComplex beta = MAGMA_Z_MAKE( -0.6, 0.8 );
magmaDoubleComplex *A, *X, *Y, *Ycublas, *Ymagma;
magmaDoubleComplex *dA, *dX, *dY, *dC_work;
magma_opts opts;
parse_opts( argc, argv, &opts );
printf(" N MAGMA Gflop/s (ms) CUBLAS Gflop/s (ms) CPU Gflop/s (ms) MAGMA error CUBLAS error\n");
printf("=============================================================================================\n");
for( int i = 0; i < opts.ntest; ++i ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[i];
lda = ((N + 31)/32)*32;
sizeA = N*lda;
sizeX = N*incx;
sizeY = N*incy;
gflops = FLOPS_ZHEMV( N ) / 1e9;
TESTING_MALLOC( A, magmaDoubleComplex, sizeA );
TESTING_MALLOC( X, magmaDoubleComplex, sizeX );
TESTING_MALLOC( Y, magmaDoubleComplex, sizeY );
TESTING_MALLOC( Ycublas, magmaDoubleComplex, sizeY );
TESTING_MALLOC( Ymagma, magmaDoubleComplex, sizeY );
TESTING_DEVALLOC( dA, magmaDoubleComplex, sizeA );
TESTING_DEVALLOC( dX, magmaDoubleComplex, sizeX );
TESTING_DEVALLOC( dY, magmaDoubleComplex, sizeY );
blocks = (N + nb - 1) / nb;
ldwork = lda * (blocks + 1);
TESTING_DEVALLOC( dC_work, magmaDoubleComplex, ldwork );
/* Initialize the matrix */
lapackf77_zlarnv( &ione, ISEED, &sizeA, A );
magma_zmake_hermitian( N, A, lda );
lapackf77_zlarnv( &ione, ISEED, &sizeX, X );
lapackf77_zlarnv( &ione, ISEED, &sizeY, Y );
/* =====================================================================
Performs operation using CUBLAS
=================================================================== */
magma_zsetmatrix( N, N, A, lda, dA, lda );
magma_zsetvector( N, X, incx, dX, incx );
magma_zsetvector( N, Y, incy, dY, incy );
cublas_time = magma_sync_wtime( 0 );
cublasZhemv( opts.uplo, N, alpha, dA, lda, dX, incx, beta, dY, incy );
cublas_time = magma_sync_wtime( 0 ) - cublas_time;
cublas_perf = gflops / cublas_time;
magma_zgetvector( N, dY, incy, Ycublas, incy );
/* =====================================================================
Performs operation using MAGMA BLAS
=================================================================== */
magma_zsetvector( N, Y, incy, dY, incy );
magma_time = magma_sync_wtime( 0 );
#if (GPUSHMEM >= 200)
magmablas_zhemv2( opts.uplo, N, alpha, dA, lda, dX, incx, beta, dY, incy, dC_work, ldwork );
#else
magmablas_zhemv( opts.uplo, N, alpha, dA, lda, dX, incx, beta, dY, incy );
#endif
magma_time = magma_sync_wtime( 0 ) - magma_time;
magma_perf = gflops / magma_time;
magma_zgetvector( N, dY, incy, Ymagma, incy );
/* =====================================================================
Performs operation using CPU BLAS
=================================================================== */
cpu_time = magma_wtime();
blasf77_zhemv( &opts.uplo, &N, &alpha, A, &lda, X, &incx, &beta, Y, &incy );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
/* =====================================================================
Check the result
=================================================================== */
blasf77_zaxpy( &N, &c_neg_one, Y, &incy, Ymagma, &incy );
magma_error = lapackf77_zlange( "M", &N, &ione, Ymagma, &N, work ) / N;
blasf77_zaxpy( &N, &c_neg_one, Y, &incy, Ycublas, &incy );
cublas_error = lapackf77_zlange( "M", &N, &ione, Ycublas, &N, work ) / N;
printf("%5d %7.2f (%7.2f) %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %8.2e\n",
(int) N,
magma_perf, 1000.*magma_time,
cublas_perf, 1000.*cublas_time,
cpu_perf, 1000.*cpu_time,
magma_error, cublas_error );
TESTING_FREE( A );
TESTING_FREE( X );
TESTING_FREE( Y );
TESTING_FREE( Ycublas );
TESTING_FREE( Ymagma );
TESTING_DEVFREE( dA );
TESTING_DEVFREE( dX );
TESTING_DEVFREE( dY );
TESTING_DEVFREE( dC_work );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return 0;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing magma_zhemm_mgpu
*/
int main( int argc, char** argv)
{
TESTING_INIT();
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex calpha = MAGMA_Z_MAKE( 3.456, 5.678 );
magmaDoubleComplex cbeta = MAGMA_Z_MAKE( 1.234, 2.456 );
real_Double_t gflops, gpu_perf=0., cpu_perf=0., gpu_time=0., cpu_time=0.;
real_Double_t gpu_perf2=0., gpu_time2=0.;
double error=0., errorbis=0., work[1];
magmaDoubleComplex *hA, *hX, *hB, *hR;
magmaDoubleComplex_ptr dA[MagmaMaxGPUs], dX[MagmaMaxGPUs], dB[MagmaMaxGPUs], dwork[MagmaMaxGPUs], hwork[MagmaMaxGPUs+1];
magmaDoubleComplex_ptr dA2;
magma_int_t M, N, size, lda, ldda, msize, nb, nstream;
magma_int_t ione = 1;
magma_int_t iseed[4] = {0,0,0,1};
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
double tol = opts.tolerance * lapackf77_dlamch("E");
// default values
nb = (opts.nb > 0 ? opts.nb : 64);
nstream = (opts.nstream > 0 ? opts.nstream : 2);
magma_int_t gnode[MagmaMaxGPUs][MagmaMaxGPUs+2];
magma_int_t nbcmplx = 0;
magma_buildconnection_mgpu(gnode, &nbcmplx, opts.ngpu);
printf("Initializing communication pattern... GPU-ncmplx %d\n\n", (int) nbcmplx);
for (int i=0; i < nbcmplx; ++i) {
int myngpu = gnode[i][MagmaMaxGPUs];
printf("cmplx %d has %d gpu ", i, myngpu);
for(int j=0; j < myngpu; ++j)
printf(" %d", (int) gnode[i][j]);
printf("\n");
}
magma_int_t nbevents = 2;
magma_queue_t streams[MagmaMaxGPUs][20];
magma_event_t redevents[MagmaMaxGPUs][20];
magma_event_t redevents2[MagmaMaxGPUs][MagmaMaxGPUs*MagmaMaxGPUs+10];
for( int d = 0; d < opts.ngpu; ++d ) {
for( magma_int_t i = 0; i < nstream; ++i ) {
magma_queue_create( &streams[d][i] );
}
for( magma_int_t i = 0; i < nbevents; ++i ) {
cudaEventCreateWithFlags(&redevents[d][i], cudaEventDisableTiming);
cudaEventCreateWithFlags(&redevents2[d][i], cudaEventDisableTiming);
}
}
printf( "nb %d, ngpu %d, nstream %d version %d\n", (int) nb, (int) opts.ngpu, (int) nstream, (int) opts.version );
printf(" M N nb offset CPU GFlop/s (sec) GPU GFlop/s (sec) CUBLAS hemm (sec) ||R|| / ||A||*||X||\n");
printf("=========================================================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
M = opts.msize[itest];
N = opts.nsize[itest];
for( int offset = 0; offset < N; offset += min(N,nb) ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
msize = M - offset;
lda = M;
ldda = ((M + 31)/32)*32;
size = lda*M;
gflops = FLOPS_ZHEMM( MagmaLeft, (double)msize, (double)N ) / 1e9;
magma_int_t dworksiz = ldda*N*3;
magma_int_t hworksiz = lda*N;
TESTING_MALLOC_CPU( hA, magmaDoubleComplex, lda*M );
TESTING_MALLOC_CPU( hX, magmaDoubleComplex, lda*N );
TESTING_MALLOC_CPU( hB, magmaDoubleComplex, lda*N );
TESTING_MALLOC_PIN( hR, magmaDoubleComplex, lda*N );
for( int d = 0; d < opts.ngpu; ++d ) {
magma_int_t mlocal = ((M / nb) / opts.ngpu + 1) * nb;
magma_setdevice( d );
TESTING_MALLOC_DEV( dA[d], magmaDoubleComplex, ldda*mlocal );
TESTING_MALLOC_DEV( dX[d], magmaDoubleComplex, ldda*N );
TESTING_MALLOC_DEV( dB[d], magmaDoubleComplex, ldda*N );
TESTING_MALLOC_DEV( dwork[d], magmaDoubleComplex, dworksiz );
TESTING_MALLOC_PIN( hwork[d], magmaDoubleComplex, hworksiz );
}
TESTING_MALLOC_PIN( hwork[opts.ngpu], magmaDoubleComplex, lda*N );
if ( opts.check ) {
magma_setdevice( 0 );
TESTING_MALLOC_DEV( dA2, magmaDoubleComplex, ldda*M );
}
lapackf77_zlarnv( &ione, iseed, &size, hA );
magma_zmake_hermitian( M, hA, lda );
size = lda*N;
lapackf77_zlarnv( &ione, iseed, &size, hX );
lapackf77_zlarnv( &ione, iseed, &size, hB );
lapackf77_zlacpy( "Full", &M, &N, hB, &lda, hR, &lda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
magma_zsetmatrix_1D_col_bcyclic( M, M, hA, lda, dA, ldda, opts.ngpu, nb );
for( int d = 0; d < opts.ngpu; ++d ) {
magma_setdevice( d );
//magmablasSetKernelStream( streams[ d ][ 0 ] );
magma_zsetmatrix( M, N, hX, lda, dX[d], ldda );
//if (d == 0) magma_zsetmatrix( M, N, hB, lda, dB[d], ldda ); // this is wrong coz when offset != 0 the gpu who do the beta*C may be not 0 so this should be related to stdev(starting device who own i=0 first col)
magma_zsetmatrix( M, N, hB, lda, dB[d], ldda );
}
//memset(hR, 0, lda*N*sizeof(magmaDoubleComplex));
trace_init( 1, opts.ngpu, nstream, (magma_queue_t*) streams );
//magma_int_t offset = 0; //nb;
gpu_time = magma_sync_wtime(0);
magmablas_zhemm_mgpu_com(
MagmaLeft, MagmaLower, msize, N,
calpha, dA, ldda, offset,
dX, ldda,
cbeta, dB, ldda, dwork, dworksiz, hR, lda, hwork, hworksiz,
opts.ngpu, nb, streams, nstream, redevents2, nbevents, gnode, nbcmplx);
gpu_time = magma_sync_wtime(0) - gpu_time;
gpu_perf = gflops / gpu_time;
#ifdef TRACING
char buf[80];
snprintf( buf, sizeof(buf), "zhemm-m%d-n%d-nb%d-stream%d-ngpu%d-run%d.svg",
(int) M, (int) N, (int) nb, (int) nstream, (int) opts.ngpu, (int) iter );
trace_finalize( buf, "trace.css" );
#endif
/* ====================================================================
Performs operation using CUBLAS
=================================================================== */
if ( opts.check && iter == 0 ) {
magma_setdevice( 0 );
magmablasSetKernelStream( 0 );
magma_zsetmatrix( M, M, hA, lda, dA2, ldda );
magma_zsetmatrix( M, N, hX, lda, dX[0], ldda );
magma_zsetmatrix( M, N, hB, lda, dwork[0], ldda );
gpu_time2 = magma_sync_wtime(0);
magma_zhemm(
MagmaLeft, MagmaLower, msize, N,
calpha, dA2+offset*ldda+offset, ldda,
dX[0], ldda,
cbeta, dwork[0], ldda );
gpu_time2 = magma_sync_wtime(0) - gpu_time2;
gpu_perf2 = gflops / gpu_time2;
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.check ) {
// store ||A||*||X||
errorbis = lapackf77_zlange("fro", &msize, &msize, hA+offset*lda+offset, &lda, work );
errorbis *= lapackf77_zlange("fro", &msize, &N, hX, &lda, work );
//printf( "A =" ); magma_zprint( M, M, hA, lda );
//printf( "X =" ); magma_zprint( M, N, hX, lda );
//printf( "B =" ); magma_zprint( M, N, hB, lda );
cpu_time = magma_wtime();
blasf77_zhemm( "Left", "Lower", &msize, &N,
&calpha, hA+offset*lda+offset, &lda,
hX, &lda,
&cbeta, hB, &lda );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
/*
trace_file = fopen("AJETE/C", "w");
for (int j = 0; j < N; j++)
for (int i = 0; i < siz; i++)
fprintf(trace_file, "%10d%10d%40.30e\n", i+1, j+1, hB[j*lda+i]);
fclose(trace_file);
*/
magma_int_t firstprint=0;
for(magma_int_t dev=0; dev < opts.ngpu; ++dev) {
magma_setdevice( dev );
magma_zgetmatrix( M, N, dB[dev], ldda, hR, lda );
// compute relative error ||R||/||A||*||X||, where R := B_magma - B_lapack = R - B
size = lda*N;
blasf77_zaxpy( &size, &c_neg_one, hB, &ione, hR, &ione );
error = lapackf77_zlange("fro", &msize, &N, hR, &lda, work) / errorbis;
//printf( "R =" ); magma_zprint( M, N, hR, lda );
if (firstprint == 0) {
printf( "%5d %5d %5d %5d %7.1f (%7.4f) %7.1f (%7.4f) %7.1f (%7.4f) %8.2e %s\n",
(int) M, (int) N, (int) nb, (int) offset,
cpu_perf, cpu_time,
gpu_perf, gpu_time,
gpu_perf2, gpu_time2,
error, (error < tol ? "ok" : "failed") );
}
else {
printf( "%89s %8.2e %s\n", " ",
error, (error < tol ? "ok" : "failed") );
}
status += ! (error < tol);
firstprint =1;
}
} else {
printf( "%5d %5d %5d %5d --- ( --- ) %7.1f (%7.4f) --- ( --- ) ---\n",
(int) M, (int) N, (int) nb, (int) offset,
gpu_perf, gpu_time );
}
TESTING_FREE_CPU( hA );
TESTING_FREE_CPU( hX );
TESTING_FREE_CPU( hB );
TESTING_FREE_PIN( hR );
for( int d = 0; d < opts.ngpu; ++d ) {
magma_setdevice( d );
TESTING_FREE_DEV( dA[d] );
TESTING_FREE_DEV( dX[d] );
TESTING_FREE_DEV( dB[d] );
TESTING_FREE_DEV( dwork[d] );
TESTING_FREE_PIN( hwork[d] );
}
TESTING_FREE_PIN( hwork[opts.ngpu] );
if ( opts.check ) {
magma_setdevice( 0 );
TESTING_FREE_DEV( dA2 );
}
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
} // offset
printf( "\n" );
}
for( int d = 0; d < opts.ngpu; ++d ) {
magma_setdevice( d );
for( magma_int_t i = 0; i < nstream; ++i ) {
magma_queue_destroy( streams[d][i] );
}
for( magma_int_t i = 0; i < nbevents; ++i ) {
magma_event_destroy( redevents[d][i] );
magma_event_destroy( redevents2[d][i] );
}
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zher2k
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, cublas_perf, cublas_time, cpu_perf, cpu_time;
double cublas_error, Cnorm, work[1];
magma_int_t N, K;
magma_int_t Ak, An, Bk, Bn;
magma_int_t sizeA, sizeB, sizeC;
magma_int_t lda, ldb, ldc, ldda, lddb, lddc;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magmaDoubleComplex *h_A, *h_B, *h_C, *h_Ccublas;
magmaDoubleComplex *d_A, *d_B, *d_C;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex alpha = MAGMA_Z_MAKE( 0.29, -0.86 );
double beta = MAGMA_D_MAKE( -0.48, 0.38 );
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
opts.lapack |= opts.check; // check (-c) implies lapack (-l)
double tol = opts.tolerance * lapackf77_dlamch("E");
printf("If running lapack (option --lapack), CUBLAS error is computed\n"
"relative to CPU BLAS result.\n\n");
printf("uplo = %s, transA = %s\n",
lapack_uplo_const(opts.uplo), lapack_trans_const(opts.transA) );
printf(" N K CUBLAS Gflop/s (ms) CPU Gflop/s (ms) CUBLAS error\n");
printf("==================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.msize[itest];
K = opts.ksize[itest];
gflops = FLOPS_ZHER2K(K, N) / 1e9;
if ( opts.transA == MagmaNoTrans ) {
lda = An = N;
Ak = K;
ldb = Bn = N;
Bk = K;
} else {
lda = An = K;
Ak = N;
ldb = Bn = K;
Bk = N;
}
ldc = N;
ldda = ((lda+31)/32)*32;
lddb = ((ldb+31)/32)*32;
lddc = ((ldc+31)/32)*32;
sizeA = lda*Ak;
sizeB = ldb*Ak;
sizeC = ldc*N;
TESTING_MALLOC_CPU( h_A, magmaDoubleComplex, lda*Ak );
TESTING_MALLOC_CPU( h_B, magmaDoubleComplex, ldb*Bk );
TESTING_MALLOC_CPU( h_C, magmaDoubleComplex, ldc*N );
TESTING_MALLOC_CPU( h_Ccublas, magmaDoubleComplex, ldc*N );
TESTING_MALLOC_DEV( d_A, magmaDoubleComplex, ldda*Ak );
TESTING_MALLOC_DEV( d_B, magmaDoubleComplex, lddb*Bk );
TESTING_MALLOC_DEV( d_C, magmaDoubleComplex, lddc*N );
/* Initialize the matrices */
lapackf77_zlarnv( &ione, ISEED, &sizeA, h_A );
lapackf77_zlarnv( &ione, ISEED, &sizeB, h_B );
lapackf77_zlarnv( &ione, ISEED, &sizeC, h_C );
/* =====================================================================
Performs operation using CUBLAS
=================================================================== */
magma_zsetmatrix( An, Ak, h_A, lda, d_A, ldda );
magma_zsetmatrix( Bn, Bk, h_B, ldb, d_B, lddb );
magma_zsetmatrix( N, N, h_C, ldc, d_C, lddc );
cublas_time = magma_sync_wtime( NULL );
cublasZher2k( handle, cublas_uplo_const(opts.uplo), cublas_trans_const(opts.transA), N, K,
&alpha, d_A, ldda,
d_B, lddb,
&beta, d_C, lddc );
cublas_time = magma_sync_wtime( NULL ) - cublas_time;
cublas_perf = gflops / cublas_time;
magma_zgetmatrix( N, N, d_C, lddc, h_Ccublas, ldc );
/* =====================================================================
Performs operation using CPU BLAS
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
blasf77_zher2k( lapack_uplo_const(opts.uplo), lapack_trans_const(opts.transA), &N, &K,
&alpha, h_A, &lda,
h_B, &ldb,
&beta, h_C, &ldc );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
}
/* =====================================================================
Check the result
=================================================================== */
if ( opts.lapack ) {
// compute relative error for both magma & cublas, relative to lapack,
// |C_magma - C_lapack| / |C_lapack|
Cnorm = lapackf77_zlange( "M", &N, &N, h_C, &ldc, work );
blasf77_zaxpy( &sizeC, &c_neg_one, h_C, &ione, h_Ccublas, &ione );
cublas_error = lapackf77_zlange( "M", &N, &N, h_Ccublas, &ldc, work ) / Cnorm;
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %s\n",
(int) N, (int) K,
cublas_perf, 1000.*cublas_time,
cpu_perf, 1000.*cpu_time,
cublas_error, (cublas_error < tol ? "ok" : "failed"));
status += ! (cublas_error < tol);
}
else {
printf("%5d %5d %7.2f (%7.2f) --- ( --- ) --- ---\n",
(int) N, (int) K,
cublas_perf, 1000.*cublas_time);
}
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_B );
TESTING_FREE_CPU( h_C );
TESTING_FREE_CPU( h_Ccublas );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( d_B );
TESTING_FREE_DEV( d_C );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zgeqrf
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
double error, work[1];
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex *h_A, *h_R, *tau, *dtau, *h_work, tmp[1];
magmaDoubleComplex *d_A;
double *dwork;
magma_int_t M, N, n2, lda, ldda, lwork, info, min_mn;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_opts opts;
parse_opts( argc, argv, &opts );
opts.lapack |= opts.check; // check (-c) implies lapack (-l)
printf(" M N CPU GFlop/s (ms) GPU GFlop/s (ms) ||R||_F / ||A||_F\n");
printf("=======================================================================\n");
for( int i = 0; i < opts.ntest; ++i ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[i];
N = opts.nsize[i];
min_mn = min(M, N);
lda = M;
n2 = lda*N;
ldda = ((M+31)/32)*32;
gflops = FLOPS_ZGEQRF( M, N ) / 1e9;
lwork = -1;
lapackf77_zgeqrf(&M, &N, h_A, &M, tau, tmp, &lwork, &info);
lwork = (magma_int_t)MAGMA_Z_REAL( tmp[0] );
TESTING_MALLOC( tau, magmaDoubleComplex, min_mn );
TESTING_MALLOC( h_A, magmaDoubleComplex, n2 );
TESTING_HOSTALLOC( h_R, magmaDoubleComplex, n2 );
TESTING_DEVALLOC( d_A, magmaDoubleComplex, ldda*N );
TESTING_DEVALLOC( dtau, magmaDoubleComplex, min_mn );
TESTING_DEVALLOC(dwork, double, min_mn );
TESTING_MALLOC( h_work, magmaDoubleComplex, lwork );
/* Initialize the matrix */
lapackf77_zlarnv( &ione, ISEED, &n2, h_A );
lapackf77_zlacpy( MagmaUpperLowerStr, &M, &N, h_A, &lda, h_R, &lda );
magma_zsetmatrix( M, N, h_R, lda, d_A, ldda );
// warmup
magma_zgeqr2_gpu( M, N, d_A, ldda, dtau, dwork, &info );
magma_zsetmatrix( M, N, h_R, lda, d_A, ldda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_sync_wtime( 0 );
magma_zgeqr2_gpu( M, N, d_A, ldda, dtau, dwork, &info );
gpu_time = magma_sync_wtime( 0 ) - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_zgeqrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
if ( opts.lapack ) {
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
lapackf77_zgeqrf(&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_zgeqrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Check the result compared to LAPACK
=================================================================== */
magma_zgetmatrix( M, N, d_A, ldda, h_R, M );
error = lapackf77_zlange("f", &M, &N, h_A, &lda, work);
blasf77_zaxpy(&n2, &c_neg_one, h_A, &ione, h_R, &ione);
error = lapackf77_zlange("f", &M, &N, h_R, &lda, work) / error;
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e\n",
(int) M, (int) N, cpu_perf, 1000.*cpu_time, gpu_perf, 1000.*gpu_time, error );
}
else {
printf("%5d %5d --- ( --- ) %7.2f (%7.2f) --- \n",
(int) M, (int) N, gpu_perf, 1000.*gpu_time );
}
TESTING_FREE( tau );
TESTING_FREE( h_A );
TESTING_FREE( h_work );
TESTING_HOSTFREE( h_R );
TESTING_DEVFREE( d_A );
TESTING_DEVFREE( dtau );
TESTING_DEVFREE( dwork );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return 0;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zhegvdx
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gpu_time;
magmaDoubleComplex *h_A, *h_R, *h_B, *h_S, *h_work;
#if defined(PRECISION_z) || defined(PRECISION_c)
double *rwork;
magma_int_t lrwork;
#endif
/* Matrix size */
double *w1, *w2, result[2]={0,0};
magma_int_t *iwork;
magma_int_t N, n2, info, lwork, liwork;
magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
double tol = opts.tolerance * lapackf77_dlamch("E");
double tolulp = opts.tolerance * lapackf77_dlamch("P");
magma_range_t range = MagmaRangeAll;
if (opts.fraction != 1)
range = MagmaRangeI;
if ( opts.check && opts.jobz == MagmaNoVec ) {
fprintf( stderr, "checking results requires vectors; setting jobz=V (option -JV)\n" );
opts.jobz = MagmaVec;
}
printf("using: itype = %d, jobz = %s, range = %s, uplo = %s, opts.check = %d, fraction = %6.4f\n",
(int) opts.itype, lapack_vec_const(opts.jobz), lapack_range_const(range), lapack_uplo_const(opts.uplo),
(int) opts.check, opts.fraction);
printf(" N M GPU Time (sec)\n");
printf("============================\n");
magma_int_t threads = magma_get_parallel_numthreads();
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[itest];
n2 = N*N;
#if defined(PRECISION_z) || defined(PRECISION_c)
lwork = magma_zbulge_get_lq2(N, threads) + 2*N + N*N;
lrwork = 1 + 5*N +2*N*N;
#else
lwork = magma_zbulge_get_lq2(N, threads) + 1 + 6*N + 2*N*N;
#endif
liwork = 3 + 5*N;
/* Allocate host memory for the matrix */
TESTING_MALLOC_CPU( h_A, magmaDoubleComplex, n2 );
TESTING_MALLOC_CPU( h_B, magmaDoubleComplex, n2 );
TESTING_MALLOC_CPU( w1, double, N );
TESTING_MALLOC_CPU( w2, double, N );
TESTING_MALLOC_CPU( iwork, magma_int_t, liwork );
TESTING_MALLOC_PIN( h_R, magmaDoubleComplex, n2 );
TESTING_MALLOC_PIN( h_S, magmaDoubleComplex, n2 );
TESTING_MALLOC_PIN( h_work, magmaDoubleComplex, lwork );
#if defined(PRECISION_z) || defined(PRECISION_c)
TESTING_MALLOC_PIN( rwork, double, lrwork);
#endif
/* Initialize the matrix */
lapackf77_zlarnv( &ione, ISEED, &n2, h_A );
lapackf77_zlarnv( &ione, ISEED, &n2, h_B );
magma_zmake_hpd( N, h_B, N );
magma_zmake_hermitian( N, h_A, N );
magma_int_t m1 = 0;
double vl = 0;
double vu = 0;
magma_int_t il = 0;
magma_int_t iu = 0;
if (range == MagmaRangeI) {
il = 1;
iu = (int) (opts.fraction*N);
}
// ==================================================================
// Warmup using MAGMA
// ==================================================================
if (opts.warmup) {
lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );
magma_zhegvdx_2stage(opts.itype, opts.jobz, range, opts.uplo,
N, h_R, N, h_S, N, vl, vu, il, iu, &m1, w1,
h_work, lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, lrwork,
#endif
iwork, liwork,
&info);
}
// ===================================================================
// Performs operation using MAGMA
// ===================================================================
lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );
gpu_time = magma_wtime();
magma_zhegvdx_2stage(opts.itype, opts.jobz, range, opts.uplo,
N, h_R, N, h_S, N, vl, vu, il, iu, &m1, w1,
h_work, lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, lrwork,
#endif
iwork, liwork,
&info);
gpu_time = magma_wtime() - gpu_time;
if ( opts.check && opts.jobz != MagmaNoVec ) {
/* =====================================================================
Check the results following the LAPACK's [zc]hegvdx routine.
A x = lambda B x is solved
and the following 3 tests computed:
(1) | A Z - B Z D | / ( |A||Z| N ) (itype = 1)
| A B Z - Z D | / ( |A||Z| N ) (itype = 2)
| B A Z - Z D | / ( |A||Z| N ) (itype = 3)
(2) | S(with V) - S(w/o V) | / | S |
=================================================================== */
#if defined(PRECISION_d) || defined(PRECISION_s)
double *rwork = h_work + N*N;
#endif
result[0] = 1.;
result[0] /= lapackf77_zlanhe("1", lapack_uplo_const(opts.uplo), &N, h_A, &N, rwork);
result[0] /= lapackf77_zlange("1", &N, &m1, h_R, &N, rwork);
if (opts.itype == 1) {
blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_A, &N, h_R, &N, &c_zero, h_work, &N);
for(int i=0; i<m1; ++i)
blasf77_zdscal(&N, &w1[i], &h_R[i*N], &ione);
blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_neg_one, h_B, &N, h_R, &N, &c_one, h_work, &N);
result[0] *= lapackf77_zlange("1", &N, &m1, h_work, &N, rwork)/N;
}
else if (opts.itype == 2) {
blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_B, &N, h_R, &N, &c_zero, h_work, &N);
for(int i=0; i<m1; ++i)
blasf77_zdscal(&N, &w1[i], &h_R[i*N], &ione);
blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_A, &N, h_work, &N, &c_neg_one, h_R, &N);
result[0] *= lapackf77_zlange("1", &N, &m1, h_R, &N, rwork)/N;
}
else if (opts.itype == 3) {
blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_A, &N, h_R, &N, &c_zero, h_work, &N);
for(int i=0; i<m1; ++i)
blasf77_zdscal(&N, &w1[i], &h_R[i*N], &ione);
blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_B, &N, h_work, &N, &c_neg_one, h_R, &N);
result[0] *= lapackf77_zlange("1", &N, &m1, h_R, &N, rwork)/N;
}
lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );
magma_int_t m2 = m1;
lapackf77_zhegvd(&opts.itype, "N", lapack_uplo_const(opts.uplo), &N,
h_R, &N, h_S, &N, w2,
h_work, &lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, &lrwork,
#endif
iwork, &liwork,
&info);
double maxw=0, diff=0;
for(int j=0; j<m2; j++) {
maxw = max(maxw, fabs(w1[j]));
maxw = max(maxw, fabs(w2[j]));
diff = max(diff, fabs(w1[j] - w2[j]));
}
result[1] = diff / (m2*maxw);
}
/* =====================================================================
Print execution time
=================================================================== */
printf("%5d %5d %7.2f\n",
(int) N, (int) m1, gpu_time);
if ( opts.check && opts.jobz != MagmaNoVec ) {
printf("Testing the eigenvalues and eigenvectors for correctness:\n");
if (opts.itype==1) {
printf(" | A Z - B Z D | / (|A| |Z| N) = %8.2e %s\n", result[0], (result[0] < tol ? "ok" : "failed"));
}
else if (opts.itype==2) {
printf(" | A B Z - Z D | / (|A| |Z| N) = %8.2e %s\n", result[0], (result[0] < tol ? "ok" : "failed"));
}
else if (opts.itype==3) {
printf(" | B A Z - Z D | / (|A| |Z| N) = %8.2e %s\n", result[0], (result[0] < tol ? "ok" : "failed"));
}
printf( " | D(w/ Z) - D(w/o Z) | / |D| = %8.2e %s\n\n", result[1], (result[1] < tolulp ? "ok" : "failed"));
status += ! (result[0] < tol && result[1] < tolulp);
}
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_B );
TESTING_FREE_CPU( w1 );
TESTING_FREE_CPU( w2 );
TESTING_FREE_CPU( iwork );
TESTING_FREE_PIN( h_R );
TESTING_FREE_PIN( h_S );
TESTING_FREE_PIN( h_work );
#if defined(PRECISION_z) || defined(PRECISION_c)
TESTING_FREE_PIN( rwork );
#endif
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
/* Shutdown */
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zposv_batched
*/
int main(int argc, char **argv)
{
TESTING_INIT();
real_Double_t gflops, cpu_perf, cpu_time, gpu_perf, gpu_time;
double err = 0.0, Rnorm, Anorm, Xnorm, *work;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex *h_A, *h_B, *h_X;
magmaDoubleComplex_ptr d_A, d_B;
magma_int_t *dinfo_array;
magma_int_t N, nrhs, lda, ldb, ldda, lddb, info, sizeA, sizeB;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t status = 0;
magma_int_t batchCount = 1;
magmaDoubleComplex **dA_array = NULL;
magmaDoubleComplex **dB_array = NULL;
magma_queue_t queue = magma_stream;
magma_opts opts;
parse_opts( argc, argv, &opts );
double tol = opts.tolerance * lapackf77_dlamch("E");
nrhs = opts.nrhs;
batchCount = opts.batchcount ;
printf("uplo = %s\n", lapack_uplo_const(opts.uplo) );
printf("BatchCount N NRHS CPU GFlop/s (sec) GPU GFlop/s (sec) ||B - AX|| / N*||A||*||X||\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;
ldb = lda;
ldda = ((N+31)/32)*32;
lddb = ldda;
gflops = ( FLOPS_ZPOTRF( N) + FLOPS_ZPOTRS( N, nrhs ) ) / 1e9 * batchCount;
sizeA = lda*N*batchCount;
sizeB = ldb*nrhs*batchCount;
TESTING_MALLOC_CPU( h_A, magmaDoubleComplex, sizeA );
TESTING_MALLOC_CPU( h_B, magmaDoubleComplex, sizeB );
TESTING_MALLOC_CPU( h_X, magmaDoubleComplex, sizeB );
TESTING_MALLOC_CPU( work, double, N);
TESTING_MALLOC_DEV( d_A, magmaDoubleComplex, ldda*N*batchCount );
TESTING_MALLOC_DEV( d_B, magmaDoubleComplex, lddb*nrhs*batchCount );
TESTING_MALLOC_DEV( dinfo_array, magma_int_t, batchCount );
magma_malloc((void**)&dA_array, batchCount * sizeof(*dA_array));
magma_malloc((void**)&dB_array, batchCount * sizeof(*dB_array));
/* Initialize the matrices */
lapackf77_zlarnv( &ione, ISEED, &sizeA, h_A );
lapackf77_zlarnv( &ione, ISEED, &sizeB, h_B );
for(int i=0; i<batchCount; i++)
{
magma_zmake_hpd( N, h_A + i * lda * N, lda );// need modification
}
magma_zsetmatrix( N, N*batchCount, h_A, lda, d_A, ldda );
magma_zsetmatrix( N, nrhs*batchCount, h_B, ldb, d_B, lddb );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
zset_pointer(dA_array, d_A, ldda, 0, 0, ldda*N, batchCount, queue);
zset_pointer(dB_array, d_B, lddb, 0, 0, lddb*nrhs, batchCount, queue);
gpu_time = magma_wtime();
info = magma_zposv_batched(opts.uplo, N, nrhs, dA_array, ldda, dB_array, lddb, dinfo_array, batchCount, queue);
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
// check correctness of results throught "dinfo_magma" and correctness of argument throught "info"
magma_int_t *cpu_info = (magma_int_t*) malloc(batchCount*sizeof(magma_int_t));
magma_getvector( batchCount, sizeof(magma_int_t), dinfo_array, 1, cpu_info, 1);
for(int i=0; i<batchCount; i++)
{
if(cpu_info[i] != 0 ){
printf("magma_zposv_batched matrix %d returned internal error %d\n",i, (int)cpu_info[i] );
}
}
if (info != 0)
printf("magma_zposv_batched returned argument error %d: %s.\n", (int) info, magma_strerror( info ));
//=====================================================================
// Residual
//=====================================================================
magma_zgetmatrix( N, nrhs*batchCount, d_B, lddb, h_X, ldb );
for(magma_int_t s=0; s<batchCount; s++)
{
Anorm = lapackf77_zlange("I", &N, &N, h_A + s * lda * N, &lda, work);
Xnorm = lapackf77_zlange("I", &N, &nrhs, h_X + s * ldb * nrhs, &ldb, work);
blasf77_zgemm( MagmaNoTransStr, MagmaNoTransStr, &N, &nrhs, &N,
&c_one, h_A + s * lda * N, &lda,
h_X + s * ldb * nrhs, &ldb,
&c_neg_one, h_B + s * ldb * nrhs, &ldb);
Rnorm = lapackf77_zlange("I", &N, &nrhs, h_B + s * ldb * nrhs, &ldb, work);
double error = Rnorm/(N*Anorm*Xnorm);
if ( isnan(error) || isinf(error) ) {
err = error;
break;
}
err = max(err, error);
}
status += ! (err < tol);
/* ====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
for(magma_int_t s=0; s<batchCount; s++)
{
lapackf77_zposv( lapack_uplo_const(opts.uplo), &N, &nrhs, h_A + s * lda * N, &lda, h_B + s * ldb * nrhs, &ldb, &info );
}
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_zposv returned err %d: %s.\n",
(int) info, magma_strerror( info ));
printf( "%10d %5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %s\n",
(int)batchCount, (int) N, (int) nrhs, cpu_perf, cpu_time, gpu_perf, gpu_time,
err, (err < tol ? "ok" : "failed"));
}
else {
printf( "%10d %5d %5d --- ( --- ) %7.2f (%7.2f) %8.2e %s\n",
(int)batchCount, (int) N, (int) nrhs, gpu_perf, gpu_time,
err, (err < tol ? "ok" : "failed"));
}
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_B );
TESTING_FREE_CPU( h_X );
TESTING_FREE_CPU( work );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( d_B );
TESTING_FREE_DEV( dinfo_array );
magma_free(dA_array);
magma_free(dB_array);
free(cpu_info);
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zcgeqrsv
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time, gpu_perfd, gpu_perfs;
double error, gpu_error, cpu_error, Anorm, work[1];
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex *h_A, *h_A2, *h_B, *h_X, *h_R;
magmaDoubleComplex_ptr d_A, d_B, d_X, d_T;
magmaFloatComplex *d_SA, *d_SB;
magmaDoubleComplex *h_workd, *tau, tmp[1];
magmaFloatComplex *h_works;
magma_int_t lda, ldb, lhwork, lworkgpu;
magma_int_t ldda, lddb, lddx;
magma_int_t M, N, nrhs, qrsv_iters, info, size, min_mn, max_mn, nb;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
printf("Epsilon(double): %8.6e\n"
"Epsilon(single): %8.6e\n\n",
lapackf77_dlamch("Epsilon"), lapackf77_slamch("Epsilon") );
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
double tol = opts.tolerance * lapackf77_dlamch("E");
nrhs = opts.nrhs;
printf(" CPU Gflop/s GPU Gflop/s |b-Ax|| / (N||A||) ||dx-x||/(N||A||)\n");
printf(" M N NRHS double double single mixed Iter CPU GPU \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];
if ( M < N ) {
printf( "%5d %5d %5d skipping because M < N is not yet supported.\n", (int) M, (int) N, (int) nrhs );
continue;
}
min_mn = min(M, N);
max_mn = max(M, N);
lda = M;
ldb = max_mn;
ldda = ((M+31)/32) * 32;
lddb = ((max_mn+31)/32)*32;
lddx = ((N+31)/32) * 32;
nb = max( magma_get_zgeqrf_nb( M ), magma_get_cgeqrf_nb( M ) );
gflops = (FLOPS_ZGEQRF( M, N ) + FLOPS_ZGEQRS( M, N, nrhs )) / 1e9;
lworkgpu = (M - N + nb)*(nrhs + nb) + nrhs*nb;
// query for workspace size
lhwork = -1;
lapackf77_zgels( MagmaNoTransStr, &M, &N, &nrhs,
NULL, &lda, NULL, &ldb, tmp, &lhwork, &info );
lhwork = (magma_int_t) MAGMA_Z_REAL( tmp[0] );
lhwork = max( lhwork, lworkgpu );
TESTING_MALLOC_CPU( tau, magmaDoubleComplex, min_mn );
TESTING_MALLOC_CPU( h_A, magmaDoubleComplex, lda*N );
TESTING_MALLOC_CPU( h_A2, magmaDoubleComplex, lda*N );
TESTING_MALLOC_CPU( h_B, magmaDoubleComplex, ldb*nrhs );
TESTING_MALLOC_CPU( h_X, magmaDoubleComplex, ldb*nrhs );
TESTING_MALLOC_CPU( h_R, magmaDoubleComplex, ldb*nrhs );
TESTING_MALLOC_CPU( h_workd, magmaDoubleComplex, lhwork );
h_works = (magmaFloatComplex*)h_workd;
TESTING_MALLOC_DEV( d_A, magmaDoubleComplex, ldda*N );
TESTING_MALLOC_DEV( d_B, magmaDoubleComplex, lddb*nrhs );
TESTING_MALLOC_DEV( d_X, magmaDoubleComplex, lddx*nrhs );
TESTING_MALLOC_DEV( d_T, magmaDoubleComplex, ( 2*min_mn + (N+31)/32*32 )*nb );
/* Initialize the matrices */
size = lda*N;
lapackf77_zlarnv( &ione, ISEED, &size, h_A );
lapackf77_zlacpy( MagmaUpperLowerStr, &M, &N, h_A, &lda, h_A2, &lda );
// make random RHS
size = ldb*nrhs;
lapackf77_zlarnv( &ione, ISEED, &size, h_B );
lapackf77_zlacpy( MagmaUpperLowerStr, &M, &nrhs, h_B, &ldb, h_R, &ldb );
magma_zsetmatrix( M, N, h_A, lda, d_A, ldda );
magma_zsetmatrix( M, nrhs, h_B, ldb, d_B, lddb );
//=====================================================================
// Mixed Precision Iterative Refinement - GPU
//=====================================================================
gpu_time = magma_wtime();
magma_zcgeqrsv_gpu( M, N, nrhs,
d_A, ldda, d_B, lddb,
d_X, lddx, &qrsv_iters, &info );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_zcgeqrsv returned error %d: %s.\n",
(int) info, magma_strerror( info ));
// compute the residual
magma_zgetmatrix( N, nrhs, d_X, lddx, h_X, ldb );
blasf77_zgemm( MagmaNoTransStr, MagmaNoTransStr, &M, &nrhs, &N,
&c_neg_one, h_A, &lda,
h_X, &ldb,
&c_one, h_R, &ldb);
Anorm = lapackf77_zlange("f", &M, &N, h_A, &lda, work);
//=====================================================================
// Double Precision Solve
//=====================================================================
magma_zsetmatrix( M, N, h_A, lda, d_A, ldda );
magma_zsetmatrix( M, nrhs, h_B, ldb, d_B, lddb );
gpu_time = magma_wtime();
magma_zgels_gpu( MagmaNoTrans, M, N, nrhs, d_A, ldda,
d_B, lddb, h_workd, lworkgpu, &info);
gpu_time = magma_wtime() - gpu_time;
gpu_perfd = gflops / gpu_time;
//=====================================================================
// Single Precision Solve
//=====================================================================
magma_zsetmatrix( M, N, h_A, lda, d_A, ldda );
magma_zsetmatrix( M, nrhs, h_B, ldb, d_B, lddb );
/* The allocation of d_SA and d_SB is done here to avoid
* to double the memory used on GPU with zcgeqrsv */
TESTING_MALLOC_DEV( d_SA, magmaFloatComplex, ldda*N );
TESTING_MALLOC_DEV( d_SB, magmaFloatComplex, lddb*nrhs );
magmablas_zlag2c( M, N, d_A, ldda, d_SA, ldda, &info );
magmablas_zlag2c( N, nrhs, d_B, lddb, d_SB, lddb, &info );
gpu_time = magma_wtime();
magma_cgels_gpu( MagmaNoTrans, M, N, nrhs, d_SA, ldda,
d_SB, lddb, h_works, lhwork, &info);
gpu_time = magma_wtime() - gpu_time;
gpu_perfs = gflops / gpu_time;
TESTING_FREE_DEV( d_SA );
TESTING_FREE_DEV( d_SB );
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
lapackf77_zlacpy( MagmaUpperLowerStr, &M, &nrhs, h_B, &ldb, h_X, &ldb );
cpu_time = magma_wtime();
lapackf77_zgels( MagmaNoTransStr, &M, &N, &nrhs,
h_A, &lda, h_X, &ldb, h_workd, &lhwork, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_zgels returned error %d: %s.\n",
(int) info, magma_strerror( info ));
blasf77_zgemm( MagmaNoTransStr, MagmaNoTransStr, &M, &nrhs, &N,
&c_neg_one, h_A2, &lda,
h_X, &ldb,
&c_one, h_B, &ldb );
cpu_error = lapackf77_zlange("f", &M, &nrhs, h_B, &ldb, work) / (min_mn*Anorm);
gpu_error = lapackf77_zlange("f", &M, &nrhs, h_R, &ldb, work) / (min_mn*Anorm);
// error relative to LAPACK
size = M*nrhs;
blasf77_zaxpy( &size, &c_neg_one, h_B, &ione, h_R, &ione );
error = lapackf77_zlange("f", &M, &nrhs, h_R, &ldb, work) / (min_mn*Anorm);
printf("%5d %5d %5d %7.2f %7.2f %7.2f %7.2f %4d %8.2e %8.2e %8.2e %s\n",
(int) M, (int) N, (int) nrhs,
cpu_perf, gpu_perfd, gpu_perfs, gpu_perf,
(int) qrsv_iters,
cpu_error, gpu_error, error, (error < tol ? "ok" : "failed"));
status += ! (error < tol);
TESTING_FREE_CPU( tau );
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_A2 );
TESTING_FREE_CPU( h_B );
TESTING_FREE_CPU( h_X );
TESTING_FREE_CPU( h_R );
TESTING_FREE_CPU( h_workd );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( d_B );
TESTING_FREE_DEV( d_X );
TESTING_FREE_DEV( d_T );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
int main( int argc, char** argv )
{
TESTING_INIT();
real_Double_t gflops, t1, t2;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magma_int_t ione = 1;
magma_trans_t trans[] = { MagmaNoTrans, MagmaConjTrans, MagmaTrans };
magma_uplo_t uplo [] = { MagmaLower, MagmaUpper };
magma_diag_t diag [] = { MagmaUnit, MagmaNonUnit };
magma_side_t side [] = { MagmaLeft, MagmaRight };
magmaDoubleComplex *A, *B, *C, *C2, *LU;
magmaDoubleComplex *dA, *dB, *dC1, *dC2;
magmaDoubleComplex alpha = MAGMA_Z_MAKE( 0.5, 0.1 );
magmaDoubleComplex beta = MAGMA_Z_MAKE( 0.7, 0.2 );
double dalpha = 0.6;
double dbeta = 0.8;
double work[1], error, total_error;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t m, n, k, size, maxn, ld, info;
magma_int_t *piv;
magma_int_t err;
magma_opts opts;
parse_opts( argc, argv, &opts );
printf( "Compares magma wrapper function to cublas function; all diffs should be exactly 0.\n\n" );
total_error = 0.;
for( int itest = 0; itest < opts.ntest; ++itest ) {
m = opts.msize[itest];
n = opts.nsize[itest];
k = opts.ksize[itest];
printf("=========================================================================\n");
printf( "m=%d, n=%d, k=%d\n", (int) m, (int) n, (int) k );
// allocate matrices
// over-allocate so they can be any combination of {m,n,k} x {m,n,k}.
maxn = max( max( m, n ), k );
ld = max( 1, maxn );
size = ld*maxn;
err = magma_malloc_cpu( (void**) &piv, maxn*sizeof(magma_int_t) ); assert( err == 0 );
err = magma_zmalloc_pinned( &A, size ); assert( err == 0 );
err = magma_zmalloc_pinned( &B, size ); assert( err == 0 );
err = magma_zmalloc_pinned( &C, size ); assert( err == 0 );
err = magma_zmalloc_pinned( &C2, size ); assert( err == 0 );
err = magma_zmalloc_pinned( &LU, size ); assert( err == 0 );
err = magma_zmalloc( &dA, size ); assert( err == 0 );
err = magma_zmalloc( &dB, size ); assert( err == 0 );
err = magma_zmalloc( &dC1, size ); assert( err == 0 );
err = magma_zmalloc( &dC2, size ); assert( err == 0 );
// initialize matrices
size = maxn*maxn;
lapackf77_zlarnv( &ione, ISEED, &size, A );
lapackf77_zlarnv( &ione, ISEED, &size, B );
lapackf77_zlarnv( &ione, ISEED, &size, C );
printf( "========== Level 1 BLAS ==========\n" );
// ----- test ZSWAP
// swap columns 2 and 3 of dA, then copy to C2 and compare with A
if ( n >= 3 ) {
magma_zsetmatrix( m, n, A, ld, dA, ld );
magma_zsetmatrix( m, n, A, ld, dB, ld );
magma_zswap( m, dA(0,1), 1, dA(0,2), 1 );
magma_zswap( m, dB(0,1), 1, dB(0,2), 1 );
// check results, storing diff between magma and cuda calls in C2
cublasZaxpy( handle, ld*n, &c_neg_one, dA, 1, dB, 1 );
magma_zgetmatrix( m, n, dB, ld, C2, ld );
error = lapackf77_zlange( "F", &m, &k, C2, &ld, work );
total_error += error;
printf( "zswap diff %.2g\n", error );
}
else {
printf( "zswap skipped for n < 3\n" );
}
// ----- test IZAMAX
// get argmax of column of A
magma_zsetmatrix( m, k, A, ld, dA, ld );
error = 0;
for( int j = 0; j < k; ++j ) {
magma_int_t i1 = magma_izamax( m, dA(0,j), 1 );
int i2; // NOT magma_int_t, for cublas
cublasIzamax( handle, m, dA(0,j), 1, &i2 );
// todo need sync here?
assert( i1 == i2 );
error += abs( i1 - i2 );
}
total_error += error;
gflops = (double)m * k / 1e9;
printf( "izamax diff %.2g\n", error );
printf( "\n" );
printf( "========== Level 2 BLAS ==========\n" );
// ----- test ZGEMV
// c = alpha*A*b + beta*c, with A m*n; b,c m or n-vectors
// try no-trans/trans
for( int ia = 0; ia < 3; ++ia ) {
magma_zsetmatrix( m, n, A, ld, dA, ld );
magma_zsetvector( maxn, B, 1, dB, 1 );
magma_zsetvector( maxn, C, 1, dC1, 1 );
magma_zsetvector( maxn, C, 1, dC2, 1 );
t1 = magma_sync_wtime( 0 );
magma_zgemv( trans[ia], m, n, alpha, dA, ld, dB, 1, beta, dC1, 1 );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasZgemv( handle, cublas_trans_const(trans[ia]),
m, n, &alpha, dA, ld, dB, 1, &beta, dC2, 1 );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
size = (trans[ia] == MagmaNoTrans ? m : n);
cublasZaxpy( handle, size, &c_neg_one, dC1, 1, dC2, 1 );
magma_zgetvector( size, dC2, 1, C2, 1 );
error = lapackf77_zlange( "F", &size, &ione, C2, &ld, work );
total_error += error;
gflops = FLOPS_ZGEMV( m, n ) / 1e9;
printf( "zgemv( %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_trans_const(trans[ia]), error, gflops/t1, gflops/t2 );
}
printf( "\n" );
// ----- test ZHEMV
// c = alpha*A*b + beta*c, with A m*m symmetric; b,c m-vectors
// try upper/lower
for( int iu = 0; iu < 2; ++iu ) {
magma_zsetmatrix( m, m, A, ld, dA, ld );
magma_zsetvector( m, B, 1, dB, 1 );
magma_zsetvector( m, C, 1, dC1, 1 );
magma_zsetvector( m, C, 1, dC2, 1 );
t1 = magma_sync_wtime( 0 );
magma_zhemv( uplo[iu], m, alpha, dA, ld, dB, 1, beta, dC1, 1 );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasZhemv( handle, cublas_uplo_const(uplo[iu]),
m, &alpha, dA, ld, dB, 1, &beta, dC2, 1 );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasZaxpy( handle, m, &c_neg_one, dC1, 1, dC2, 1 );
magma_zgetvector( m, dC2, 1, C2, 1 );
error = lapackf77_zlange( "F", &m, &ione, C2, &ld, work );
total_error += error;
gflops = FLOPS_ZHEMV( m ) / 1e9;
printf( "zhemv( %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_uplo_const(uplo[iu]), error, gflops/t1, gflops/t2 );
}
printf( "\n" );
// ----- test ZTRSV
// solve A*c = c, with A m*m triangular; c m-vector
// try upper/lower, no-trans/trans, unit/non-unit diag
// Factor A into LU to get well-conditioned triangles, else solve yields garbage.
// Still can give garbage if solves aren't consistent with LU factors,
// e.g., using unit diag for U, so copy lower triangle to upper triangle.
// Also used for trsm later.
lapackf77_zlacpy( "Full", &maxn, &maxn, A, &ld, LU, &ld );
lapackf77_zgetrf( &maxn, &maxn, LU, &ld, piv, &info );
for( int j = 0; j < maxn; ++j ) {
for( int i = 0; i < j; ++i ) {
*LU(i,j) = *LU(j,i);
}
}
for( int iu = 0; iu < 2; ++iu ) {
for( int it = 0; it < 3; ++it ) {
for( int id = 0; id < 2; ++id ) {
magma_zsetmatrix( m, m, LU, ld, dA, ld );
magma_zsetvector( m, C, 1, dC1, 1 );
magma_zsetvector( m, C, 1, dC2, 1 );
t1 = magma_sync_wtime( 0 );
magma_ztrsv( uplo[iu], trans[it], diag[id], m, dA, ld, dC1, 1 );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasZtrsv( handle, cublas_uplo_const(uplo[iu]), cublas_trans_const(trans[it]),
cublas_diag_const(diag[id]), m, dA, ld, dC2, 1 );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasZaxpy( handle, m, &c_neg_one, dC1, 1, dC2, 1 );
magma_zgetvector( m, dC2, 1, C2, 1 );
error = lapackf77_zlange( "F", &m, &ione, C2, &ld, work );
total_error += error;
gflops = FLOPS_ZTRSM( MagmaLeft, m, 1 ) / 1e9;
printf( "ztrsv( %c, %c, %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_uplo_const(uplo[iu]), lapacke_trans_const(trans[it]), lapacke_diag_const(diag[id]),
error, gflops/t1, gflops/t2 );
}}}
printf( "\n" );
printf( "========== Level 3 BLAS ==========\n" );
// ----- test ZGEMM
// C = alpha*A*B + beta*C, with A m*k or k*m; B k*n or n*k; C m*n
// try combinations of no-trans/trans
for( int ia = 0; ia < 3; ++ia ) {
for( int ib = 0; ib < 3; ++ib ) {
bool nta = (trans[ia] == MagmaNoTrans);
bool ntb = (trans[ib] == MagmaNoTrans);
magma_zsetmatrix( (nta ? m : k), (nta ? m : k), A, ld, dA, ld );
magma_zsetmatrix( (ntb ? k : n), (ntb ? n : k), B, ld, dB, ld );
magma_zsetmatrix( m, n, C, ld, dC1, ld );
magma_zsetmatrix( m, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_zgemm( trans[ia], trans[ib], m, n, k, alpha, dA, ld, dB, ld, beta, dC1, ld );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasZgemm( handle, cublas_trans_const(trans[ia]), cublas_trans_const(trans[ib]),
m, n, k, &alpha, dA, ld, dB, ld, &beta, dC2, ld );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasZaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_zgetmatrix( m, n, dC2, ld, C2, ld );
error = lapackf77_zlange( "F", &m, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_ZGEMM( m, n, k ) / 1e9;
printf( "zgemm( %c, %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_trans_const(trans[ia]), lapacke_trans_const(trans[ib]),
error, gflops/t1, gflops/t2 );
}}
printf( "\n" );
// ----- test ZHEMM
// C = alpha*A*B + beta*C (left) with A m*m symmetric; B,C m*n; or
// C = alpha*B*A + beta*C (right) with A n*n symmetric; B,C m*n
// try left/right, upper/lower
for( int is = 0; is < 2; ++is ) {
for( int iu = 0; iu < 2; ++iu ) {
magma_zsetmatrix( m, m, A, ld, dA, ld );
magma_zsetmatrix( m, n, B, ld, dB, ld );
magma_zsetmatrix( m, n, C, ld, dC1, ld );
magma_zsetmatrix( m, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_zhemm( side[is], uplo[iu], m, n, alpha, dA, ld, dB, ld, beta, dC1, ld );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasZhemm( handle, cublas_side_const(side[is]), cublas_uplo_const(uplo[iu]),
m, n, &alpha, dA, ld, dB, ld, &beta, dC2, ld );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasZaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_zgetmatrix( m, n, dC2, ld, C2, ld );
error = lapackf77_zlange( "F", &m, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_ZHEMM( side[is], m, n ) / 1e9;
printf( "zhemm( %c, %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_side_const(side[is]), lapacke_uplo_const(uplo[iu]),
error, gflops/t1, gflops/t2 );
}}
printf( "\n" );
// ----- test ZHERK
// C = alpha*A*A^H + beta*C (no-trans) with A m*k and C m*m symmetric; or
// C = alpha*A^H*A + beta*C (trans) with A k*m and C m*m symmetric
// try upper/lower, no-trans/trans
for( int iu = 0; iu < 2; ++iu ) {
for( int it = 0; it < 3; ++it ) {
magma_zsetmatrix( n, k, A, ld, dA, ld );
magma_zsetmatrix( n, n, C, ld, dC1, ld );
magma_zsetmatrix( n, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_zherk( uplo[iu], trans[it], n, k, dalpha, dA, ld, dbeta, dC1, ld );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasZherk( handle, cublas_uplo_const(uplo[iu]), cublas_trans_const(trans[it]),
n, k, &dalpha, dA, ld, &dbeta, dC2, ld );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasZaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_zgetmatrix( n, n, dC2, ld, C2, ld );
error = lapackf77_zlange( "F", &n, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_ZHERK( k, n ) / 1e9;
printf( "zherk( %c, %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_uplo_const(uplo[iu]), lapacke_trans_const(trans[it]),
error, gflops/t1, gflops/t2 );
}}
printf( "\n" );
// ----- test ZHER2K
// C = alpha*A*B^H + ^alpha*B*A^H + beta*C (no-trans) with A,B n*k; C n*n symmetric; or
// C = alpha*A^H*B + ^alpha*B^H*A + beta*C (trans) with A,B k*n; C n*n symmetric
// try upper/lower, no-trans/trans
for( int iu = 0; iu < 2; ++iu ) {
for( int it = 0; it < 3; ++it ) {
bool nt = (trans[it] == MagmaNoTrans);
magma_zsetmatrix( (nt ? n : k), (nt ? n : k), A, ld, dA, ld );
magma_zsetmatrix( n, n, C, ld, dC1, ld );
magma_zsetmatrix( n, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_zher2k( uplo[iu], trans[it], n, k, alpha, dA, ld, dB, ld, dbeta, dC1, ld );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasZher2k( handle, cublas_uplo_const(uplo[iu]), cublas_trans_const(trans[it]),
n, k, &alpha, dA, ld, dB, ld, &dbeta, dC2, ld );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasZaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_zgetmatrix( n, n, dC2, ld, C2, ld );
error = lapackf77_zlange( "F", &n, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_ZHER2K( k, n ) / 1e9;
printf( "zher2k( %c, %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_uplo_const(uplo[iu]), lapacke_trans_const(trans[it]),
error, gflops/t1, gflops/t2 );
}}
printf( "\n" );
// ----- test ZTRMM
// C = alpha*A*C (left) with A m*m triangular; C m*n; or
// C = alpha*C*A (right) with A n*n triangular; C m*n
// try left/right, upper/lower, no-trans/trans, unit/non-unit
for( int is = 0; is < 2; ++is ) {
for( int iu = 0; iu < 2; ++iu ) {
for( int it = 0; it < 3; ++it ) {
for( int id = 0; id < 2; ++id ) {
bool left = (side[is] == MagmaLeft);
magma_zsetmatrix( (left ? m : n), (left ? m : n), A, ld, dA, ld );
magma_zsetmatrix( m, n, C, ld, dC1, ld );
magma_zsetmatrix( m, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_ztrmm( side[is], uplo[iu], trans[it], diag[id], m, n, alpha, dA, ld, dC1, ld );
t1 = magma_sync_wtime( 0 ) - t1;
// note cublas does trmm out-of-place (i.e., adds output matrix C),
// but allows C=B to do in-place.
t2 = magma_sync_wtime( 0 );
cublasZtrmm( handle, cublas_side_const(side[is]), cublas_uplo_const(uplo[iu]),
cublas_trans_const(trans[it]), cublas_diag_const(diag[id]),
m, n, &alpha, dA, ld, dC2, ld, dC2, ld );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasZaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_zgetmatrix( m, n, dC2, ld, C2, ld );
error = lapackf77_zlange( "F", &n, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_ZTRMM( side[is], m, n ) / 1e9;
printf( "ztrmm( %c, %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_uplo_const(uplo[iu]), lapacke_trans_const(trans[it]),
error, gflops/t1, gflops/t2 );
}}}}
printf( "\n" );
// ----- test ZTRSM
// solve A*X = alpha*B (left) with A m*m triangular; B m*n; or
// solve X*A = alpha*B (right) with A n*n triangular; B m*n
// try left/right, upper/lower, no-trans/trans, unit/non-unit
for( int is = 0; is < 2; ++is ) {
for( int iu = 0; iu < 2; ++iu ) {
for( int it = 0; it < 3; ++it ) {
for( int id = 0; id < 2; ++id ) {
bool left = (side[is] == MagmaLeft);
magma_zsetmatrix( (left ? m : n), (left ? m : n), LU, ld, dA, ld );
magma_zsetmatrix( m, n, C, ld, dC1, ld );
magma_zsetmatrix( m, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_ztrsm( side[is], uplo[iu], trans[it], diag[id], m, n, alpha, dA, ld, dC1, ld );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasZtrsm( handle, cublas_side_const(side[is]), cublas_uplo_const(uplo[iu]),
cublas_trans_const(trans[it]), cublas_diag_const(diag[id]),
m, n, &alpha, dA, ld, dC2, ld );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasZaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_zgetmatrix( m, n, dC2, ld, C2, ld );
error = lapackf77_zlange( "F", &n, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_ZTRSM( side[is], m, n ) / 1e9;
printf( "ztrsm( %c, %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_uplo_const(uplo[iu]), lapacke_trans_const(trans[it]),
error, gflops/t1, gflops/t2 );
}}}}
printf( "\n" );
// cleanup
magma_free_cpu( piv );
magma_free_pinned( A );
magma_free_pinned( B );
magma_free_pinned( C );
magma_free_pinned( C2 );
magma_free_pinned( LU );
magma_free( dA );
magma_free( dB );
magma_free( dC1 );
magma_free( dC2 );
fflush( stdout );
}
if ( total_error != 0. ) {
printf( "total error %.2g -- ought to be 0 -- some test failed (see above).\n",
total_error );
}
else {
printf( "all tests passed\n" );
}
TESTING_FINALIZE();
int status = (total_error != 0.);
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zgetri_batched
*/
int main( int argc, char** argv)
{
TESTING_INIT();
// constants
const magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
const magmaDoubleComplex c_one = MAGMA_Z_ONE;
const magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
magmaDoubleComplex *h_A, *h_Ainv, *h_R, *work;
magmaDoubleComplex_ptr d_A, d_invA;
magmaDoubleComplex_ptr *dA_array;
magmaDoubleComplex_ptr *dinvA_array;
magma_int_t **dipiv_array;
magma_int_t *dinfo_array;
magma_int_t *ipiv, *cpu_info;
magma_int_t *d_ipiv, *d_info;
magma_int_t N, n2, lda, ldda, info, info1, info2, lwork;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magmaDoubleComplex tmp;
double error, rwork[1];
magma_int_t columns;
magma_int_t status = 0;
magma_opts opts( MagmaOptsBatched );
opts.parse_opts( argc, argv );
magma_int_t batchCount = opts.batchcount;
double tol = opts.tolerance * lapackf77_dlamch("E");
printf("%% batchCount N CPU Gflop/s (ms) GPU Gflop/s (ms) ||I - A*A^{-1}||_1 / (N*cond(A))\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 * batchCount;
ldda = magma_roundup( N, opts.align ); // multiple of 32 by default
// This is the correct flops but since this getri_batched is based on
// 2 trsm = getrs and to know the real flops I am using the getrs one
//gflops = (FLOPS_ZGETRF( N, N ) + FLOPS_ZGETRI( N ))/ 1e9 * batchCount;
gflops = (FLOPS_ZGETRF( N, N ) + FLOPS_ZGETRS( N, N ))/ 1e9 * batchCount;
// query for workspace size
lwork = -1;
lapackf77_zgetri( &N, NULL, &lda, NULL, &tmp, &lwork, &info );
if (info != 0) {
printf("lapackf77_zgetri returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
lwork = magma_int_t( MAGMA_Z_REAL( tmp ));
TESTING_MALLOC_CPU( cpu_info, magma_int_t, batchCount );
TESTING_MALLOC_CPU( ipiv, magma_int_t, N * batchCount );
TESTING_MALLOC_CPU( work, magmaDoubleComplex, lwork*batchCount );
TESTING_MALLOC_CPU( h_A, magmaDoubleComplex, n2 );
TESTING_MALLOC_CPU( h_Ainv, magmaDoubleComplex, n2 );
TESTING_MALLOC_CPU( h_R, magmaDoubleComplex, n2 );
TESTING_MALLOC_DEV( d_A, magmaDoubleComplex, ldda*N * batchCount );
TESTING_MALLOC_DEV( d_invA, magmaDoubleComplex, ldda*N * batchCount );
TESTING_MALLOC_DEV( d_ipiv, magma_int_t, N * batchCount );
TESTING_MALLOC_DEV( d_info, magma_int_t, batchCount );
TESTING_MALLOC_DEV( dA_array, magmaDoubleComplex*, batchCount );
TESTING_MALLOC_DEV( dinvA_array, magmaDoubleComplex*, batchCount );
TESTING_MALLOC_DEV( dinfo_array, magma_int_t, batchCount );
TESTING_MALLOC_DEV( dipiv_array, magma_int_t*, batchCount );
/* Initialize the matrix */
lapackf77_zlarnv( &ione, ISEED, &n2, h_A );
columns = N * batchCount;
lapackf77_zlacpy( MagmaFullStr, &N, &columns, h_A, &lda, h_R, &lda );
lapackf77_zlacpy( MagmaFullStr, &N, &columns, h_A, &lda, h_Ainv, &lda );
magma_zsetmatrix( N, columns, h_R, lda, d_A, ldda, opts.queue );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
magma_zset_pointer( dA_array, d_A, ldda, 0, 0, ldda * N, batchCount, opts.queue );
magma_zset_pointer( dinvA_array, d_invA, ldda, 0, 0, ldda * N, batchCount, opts.queue );
magma_iset_pointer( dipiv_array, d_ipiv, 1, 0, 0, N, batchCount, opts.queue );
gpu_time = magma_sync_wtime( opts.queue );
info1 = magma_zgetrf_batched( N, N, dA_array, ldda, dipiv_array, dinfo_array, batchCount, opts.queue);
info2 = magma_zgetri_outofplace_batched( N, dA_array, ldda, dipiv_array, dinvA_array, ldda, dinfo_array, batchCount, opts.queue);
gpu_time = magma_sync_wtime( opts.queue ) - gpu_time;
gpu_perf = gflops / gpu_time;
// check correctness of results throught "dinfo_magma" and correctness of argument throught "info"
magma_getvector( batchCount, sizeof(magma_int_t), dinfo_array, 1, cpu_info, 1, opts.queue );
for (magma_int_t i=0; i < batchCount; i++)
{
if (cpu_info[i] != 0 ) {
printf("magma_zgetrf_batched matrix %d returned error %d\n", (int) i, (int)cpu_info[i] );
}
}
if (info1 != 0) printf("magma_zgetrf_batched returned argument error %d: %s.\n", (int) info1, magma_strerror( info1 ));
if (info2 != 0) printf("magma_zgetri_batched returned argument error %d: %s.\n", (int) info2, magma_strerror( info2 ));
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
#if !defined (BATCHED_DISABLE_PARCPU) && defined(_OPENMP)
magma_int_t nthreads = magma_get_lapack_numthreads();
magma_set_lapack_numthreads(1);
magma_set_omp_numthreads(nthreads);
#pragma omp parallel for schedule(dynamic)
#endif
for (int i=0; i < batchCount; i++)
{
magma_int_t locinfo;
lapackf77_zgetrf(&N, &N, h_Ainv + i*lda*N, &lda, ipiv + i*N, &locinfo);
if (locinfo != 0) {
printf("lapackf77_zgetrf returned error %d: %s.\n",
(int) locinfo, magma_strerror( locinfo ));
}
lapackf77_zgetri(&N, h_Ainv + i*lda*N, &lda, ipiv + i*N, work + i*lwork, &lwork, &locinfo );
if (locinfo != 0) {
printf("lapackf77_zgetri returned error %d: %s.\n",
(int) locinfo, magma_strerror( locinfo ));
}
}
#if !defined (BATCHED_DISABLE_PARCPU) && defined(_OPENMP)
magma_set_lapack_numthreads(nthreads);
#endif
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
printf("%10d %5d %7.2f (%7.2f) %7.2f (%7.2f)",
(int) batchCount, (int) N, cpu_perf, cpu_time*1000., gpu_perf, gpu_time*1000. );
}
else {
printf("%10d %5d --- ( --- ) %7.2f (%7.2f)",
(int) batchCount, (int) N, gpu_perf, gpu_time*1000. );
}
/* =====================================================================
Check the result
=================================================================== */
if ( opts.check ) {
magma_igetvector( N*batchCount, d_ipiv, 1, ipiv, 1, opts.queue );
magma_zgetmatrix( N, N*batchCount, d_invA, ldda, h_Ainv, lda, opts.queue );
error = 0;
for (magma_int_t i=0; i < batchCount; i++)
{
for (magma_int_t k=0; k < N; k++) {
if (ipiv[i*N+k] < 1 || ipiv[i*N+k] > N )
{
printf("error for matrix %d ipiv @ %d = %d\n", (int) i, (int) k, (int) ipiv[i*N+k]);
error = -1;
}
}
if (error == -1) {
break;
}
// compute 1-norm condition number estimate, following LAPACK's zget03
double normA, normAinv, rcond, err;
normA = lapackf77_zlange( "1", &N, &N, h_A + i*lda*N, &lda, rwork );
normAinv = lapackf77_zlange( "1", &N, &N, h_Ainv + i*lda*N, &lda, rwork );
if ( normA <= 0 || normAinv <= 0 ) {
rcond = 0;
err = 1 / (tol/opts.tolerance); // == 1/eps
}
else {
rcond = (1 / normA) / normAinv;
// R = I
// R -= A*A^{-1}
// err = ||I - A*A^{-1}|| / ( N ||A||*||A^{-1}|| ) = ||R|| * rcond / N, using 1-norm
lapackf77_zlaset( "full", &N, &N, &c_zero, &c_one, h_R + i*lda*N, &lda );
blasf77_zgemm( "no", "no", &N, &N, &N, &c_neg_one,
h_A + i*lda*N, &lda,
h_Ainv + i*lda*N, &lda, &c_one,
h_R + i*lda*N, &lda );
err = lapackf77_zlange( "1", &N, &N, h_R + i*lda*N, &lda, rwork );
err = err * rcond / N;
}
if ( isnan(err) || isinf(err) ) {
error = err;
break;
}
error = max( err, error );
}
bool okay = (error < tol);
status += ! okay;
printf(" %8.2e %s\n", error, (okay ? "ok" : "failed") );
}
else {
printf("\n");
}
TESTING_FREE_CPU( cpu_info );
TESTING_FREE_CPU( ipiv );
TESTING_FREE_CPU( work );
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_Ainv );
TESTING_FREE_CPU( h_R );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( d_invA );
TESTING_FREE_DEV( d_ipiv );
TESTING_FREE_DEV( d_info );
TESTING_FREE_DEV( dA_array );
TESTING_FREE_DEV( dinvA_array );
TESTING_FREE_DEV( dinfo_array );
TESTING_FREE_DEV( dipiv_array );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
extern "C" magma_int_t
magma_zcposv_gpu(char uplo, magma_int_t n, magma_int_t nrhs,
magmaDoubleComplex *dA, magma_int_t ldda,
magmaDoubleComplex *dB, magma_int_t lddb,
magmaDoubleComplex *dX, magma_int_t lddx,
magmaDoubleComplex *dworkd, magmaFloatComplex *dworks,
magma_int_t *iter, magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
ZCPOSV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian positive definite matrix and X and B
are N-by-NRHS matrices.
ZCPOSV first attempts to factorize the matrix in complex SINGLE PRECISION
and use this factorization within an iterative refinement procedure
to produce a solution with complex DOUBLE PRECISION norm-wise backward error
quality (see below). If the approach fails the method switches to a
complex DOUBLE PRECISION factorization and solve.
The iterative refinement is not going to be a winning strategy if
the ratio complex SINGLE PRECISION performance over complex DOUBLE PRECISION
performance is too small. A reasonable strategy should take the
number of right-hand sides and the size of the matrix into account.
This might be done with a call to ILAENV in the future. Up to now, we
always try iterative refinement.
The iterative refinement process is stopped if
ITER > ITERMAX
or for all the RHS we have:
RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX
where
o ITER is the number of the current iteration in the iterative
refinement process
o RNRM is the infinity-norm of the residual
o XNRM is the infinity-norm of the solution
o ANRM is the infinity-operator-norm of the matrix A
o EPS is the machine epsilon returned by DLAMCH('Epsilon')
The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00 respectively.
Arguments
=========
UPLO (input) CHARACTER
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
dA (input or input/output) COMPLEX_16 array on the GPU, dimension (LDDA,N)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading
N-by-N upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, if iterative refinement has been successfully used
(INFO.EQ.0 and ITER.GE.0, see description below), then A is
unchanged, if double factorization has been used
(INFO.EQ.0 and ITER.LT.0, see description below), then the
array dA contains the factor U or L from the Cholesky
factorization A = U**T*U or A = L*L**T.
LDDA (input) INTEGER
The leading dimension of the array dA. LDDA >= max(1,N).
dB (input) COMPLEX_16 array on the GPU, dimension (LDDB,NRHS)
The N-by-NRHS right hand side matrix B.
LDDB (input) INTEGER
The leading dimension of the array dB. LDDB >= max(1,N).
dX (output) COMPLEX_16 array on the GPU, dimension (LDDX,NRHS)
If INFO = 0, the N-by-NRHS solution matrix X.
LDDX (input) INTEGER
The leading dimension of the array dX. LDDX >= max(1,N).
dworkd (workspace) COMPLEX_16 array on the GPU, dimension (N*NRHS)
This array is used to hold the residual vectors.
dworks (workspace) COMPLEX array on the GPU, dimension (N*(N+NRHS))
This array is used to store the complex single precision matrix
and the right-hand sides or solutions in single precision.
ITER (output) INTEGER
< 0: iterative refinement has failed, double precision
factorization has been performed
-1 : the routine fell back to full precision for
implementation- or machine-specific reasons
-2 : narrowing the precision induced an overflow,
the routine fell back to full precision
-3 : failure of SPOTRF
-31: stop the iterative refinement after the 30th iteration
> 0: iterative refinement has been successfully used.
Returns the number of iterations
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading minor of order i of (DOUBLE
PRECISION) A is not positive definite, so the
factorization could not be completed, and the solution
has not been computed.
===================================================================== */
#define dB(i,j) (dB + (i) + (j)*lddb)
#define dX(i,j) (dX + (i) + (j)*lddx)
#define dR(i,j) (dR + (i) + (j)*lddr)
#define dSX(i,j) (dSX + (i) + (j)*lddsx)
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magma_int_t ione = 1;
magmaDoubleComplex *dR;
magmaFloatComplex *dSA, *dSX;
magmaDoubleComplex Xnrmv, Rnrmv;
double Anrm, Xnrm, Rnrm, cte, eps;
magma_int_t i, j, iiter, lddsa, lddsx, lddr;
/* Check arguments */
*iter = 0;
*info = 0;
if ( n < 0 )
*info = -1;
else if ( nrhs < 0 )
*info = -2;
else if ( ldda < max(1,n))
*info = -4;
else if ( lddb < max(1,n))
*info = -7;
else if ( lddx < max(1,n))
*info = -9;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
if ( n == 0 || nrhs == 0 )
return *info;
lddsa = n;
lddsx = n;
lddr = n;
dSA = dworks;
dSX = dSA + lddsa*n;
dR = dworkd;
eps = lapackf77_dlamch("Epsilon");
Anrm = magmablas_zlanhe('I', uplo, n, dA, ldda, (double*)dworkd );
cte = Anrm * eps * pow((double)n, 0.5) * BWDMAX;
/*
* Convert to single precision
*/
magmablas_zlag2c( n, nrhs, dB, lddb, dSX, lddsx, info );
if (*info != 0) {
*iter = -2;
goto FALLBACK;
}
magmablas_zlat2c( uplo, n, dA, ldda, dSA, lddsa, info );
if (*info != 0) {
*iter = -2;
goto FALLBACK;
}
// factor dSA in single precision
magma_cpotrf_gpu( uplo, n, dSA, lddsa, info );
if (*info != 0) {
*iter = -3;
goto FALLBACK;
}
// solve dSA*dSX = dB in single precision
magma_cpotrs_gpu( uplo, n, nrhs, dSA, lddsa, dSX, lddsx, info );
// residual dR = dB - dA*dX in double precision
magmablas_clag2z( n, nrhs, dSX, lddsx, dX, lddx, info );
magmablas_zlacpy( MagmaUpperLower, n, nrhs, dB, lddb, dR, lddr );
if ( nrhs == 1 ) {
magma_zhemv( uplo, n,
c_neg_one, dA, ldda,
dX, 1,
c_one, dR, 1 );
}
else {
magma_zhemm( MagmaLeft, uplo, n, nrhs,
c_neg_one, dA, ldda,
dX, lddx,
c_one, dR, lddr );
}
// TODO: use MAGMA_Z_ABS( dX(i,j) ) instead of zlange?
for( j=0; j < nrhs; j++ ) {
i = magma_izamax( n, dX(0,j), 1) - 1;
magma_zgetmatrix( 1, 1, dX(i,j), 1, &Xnrmv, 1 );
Xnrm = lapackf77_zlange( "F", &ione, &ione, &Xnrmv, &ione, NULL );
i = magma_izamax ( n, dR(0,j), 1 ) - 1;
magma_zgetmatrix( 1, 1, dR(i,j), 1, &Rnrmv, 1 );
Rnrm = lapackf77_zlange( "F", &ione, &ione, &Rnrmv, &ione, NULL );
if ( Rnrm > Xnrm*cte ) {
goto REFINEMENT;
}
}
*iter = 0;
return *info;
REFINEMENT:
for( iiter=1; iiter < ITERMAX; ) {
*info = 0;
// convert residual dR to single precision dSX
magmablas_zlag2c( n, nrhs, dR, lddr, dSX, lddsx, info );
if (*info != 0) {
*iter = -2;
goto FALLBACK;
}
// solve dSA*dSX = R in single precision
magma_cpotrs_gpu( uplo, n, nrhs, dSA, lddsa, dSX, lddsx, info );
// Add correction and setup residual
// dX += dSX [including conversion] --and--
// dR = dB
for( j=0; j < nrhs; j++ ) {
magmablas_zcaxpycp( n, dSX(0,j), dX(0,j), dB(0,j), dR(0,j) );
}
// residual dR = dB - dA*dX in double precision
if ( nrhs == 1 ) {
magma_zhemv( uplo, n,
c_neg_one, dA, ldda,
dX, 1,
c_one, dR, 1 );
}
else {
magma_zhemm( MagmaLeft, uplo, n, nrhs,
c_neg_one, dA, ldda,
dX, lddx,
c_one, dR, lddr );
}
/* Check whether the nrhs normwise backward errors satisfy the
* stopping criterion. If yes, set ITER=IITER>0 and return. */
for( j=0; j < nrhs; j++ ) {
i = magma_izamax( n, dX(0,j), 1) - 1;
magma_zgetmatrix( 1, 1, dX(i,j), 1, &Xnrmv, 1 );
Xnrm = lapackf77_zlange( "F", &ione, &ione, &Xnrmv, &ione, NULL );
i = magma_izamax ( n, dR(0,j), 1 ) - 1;
magma_zgetmatrix( 1, 1, dR(i,j), 1, &Rnrmv, 1 );
Rnrm = lapackf77_zlange( "F", &ione, &ione, &Rnrmv, &ione, NULL );
if ( Rnrm > Xnrm*cte ) {
goto L20;
}
}
/* If we are here, the nrhs normwise backward errors satisfy
* the stopping criterion, we are good to exit. */
*iter = iiter;
return *info;
L20:
iiter++;
}
/* If we are at this place of the code, this is because we have
* performed ITER=ITERMAX iterations and never satisified the
* stopping criterion. Set up the ITER flag accordingly and follow
* up on double precision routine. */
*iter = -ITERMAX - 1;
FALLBACK:
/* Single-precision iterative refinement failed to converge to a
* satisfactory solution, so we resort to double precision. */
magma_zpotrf_gpu( uplo, n, dA, ldda, info );
if (*info == 0) {
magmablas_zlacpy( MagmaUpperLower, n, nrhs, dB, lddb, dX, lddx );
magma_zpotrs_gpu( uplo, n, nrhs, dA, ldda, dX, lddx, info );
}
return *info;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zgeqrs
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
double gpu_error, cpu_error, matnorm, work[1];
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex *h_A, *h_A2, *h_B, *h_X, *h_R, *tau, *h_work, tmp[1];
magmaDoubleComplex *d_A, *d_B;
magma_int_t M, N, n2, nrhs, lda, ldb, ldda, lddb, min_mn, max_mn, nb, info;
magma_int_t lworkgpu, lhwork, lhwork2;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_opts opts;
parse_opts( argc, argv, &opts );
magma_int_t status = 0;
double tol = opts.tolerance * lapackf77_dlamch("E");
nrhs = opts.nrhs;
printf(" ||b-Ax|| / (N||A||)\n");
printf(" M N NRHS CPU GFlop/s (sec) GPU GFlop/s (sec) CPU GPU \n");
printf("===============================================================================\n");
for( int i = 0; i < opts.ntest; ++i ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[i];
N = opts.nsize[i];
if ( M < N ) {
printf( "skipping M=%d, N=%d because M < N is not yet supported.\n", (int) M, (int) N );
continue;
}
min_mn = min(M, N);
max_mn = max(M, N);
lda = M;
ldb = max_mn;
n2 = lda*N;
ldda = ((M+31)/32)*32;
lddb = ((max_mn+31)/32)*32;
nb = magma_get_zgeqrf_nb(M);
gflops = (FLOPS_ZGEQRF( M, N ) + FLOPS_ZGEQRS( M, N, nrhs )) / 1e9;
// query for workspace size
lworkgpu = (M - N + nb)*(nrhs + nb) + nrhs*nb;
lhwork = -1;
lapackf77_zgeqrf(&M, &N, h_A, &M, tau, tmp, &lhwork, &info);
lhwork2 = (magma_int_t) MAGMA_Z_REAL( tmp[0] );
lhwork = -1;
lapackf77_zunmqr( MagmaLeftStr, MagmaConjTransStr,
&M, &nrhs, &min_mn, h_A, &lda, tau,
h_X, &ldb, tmp, &lhwork, &info);
lhwork = (magma_int_t) MAGMA_Z_REAL( tmp[0] );
lhwork = max( max( lhwork, lhwork2 ), lworkgpu );
TESTING_MALLOC( tau, magmaDoubleComplex, min_mn );
TESTING_MALLOC( h_A, magmaDoubleComplex, lda*N );
TESTING_MALLOC( h_A2, magmaDoubleComplex, lda*N );
TESTING_MALLOC( h_B, magmaDoubleComplex, ldb*nrhs );
TESTING_MALLOC( h_X, magmaDoubleComplex, ldb*nrhs );
TESTING_MALLOC( h_R, magmaDoubleComplex, ldb*nrhs );
TESTING_MALLOC( h_work, magmaDoubleComplex, lhwork );
TESTING_DEVALLOC( d_A, magmaDoubleComplex, ldda*N );
TESTING_DEVALLOC( d_B, magmaDoubleComplex, lddb*nrhs );
/* Initialize the matrices */
lapackf77_zlarnv( &ione, ISEED, &n2, h_A );
lapackf77_zlacpy( MagmaUpperLowerStr, &M, &N, h_A, &lda, h_A2, &lda );
// make random RHS
n2 = M*nrhs;
lapackf77_zlarnv( &ione, ISEED, &n2, h_B );
lapackf77_zlacpy( MagmaUpperLowerStr, &M, &nrhs, h_B, &ldb, h_R, &ldb );
// make consistent RHS
//n2 = N*nrhs;
//lapackf77_zlarnv( &ione, ISEED, &n2, h_X );
//blasf77_zgemm( MagmaNoTransStr, MagmaNoTransStr, &M, &nrhs, &N,
// &c_one, h_A, &lda,
// h_X, &ldb,
// &c_zero, h_B, &ldb );
//lapackf77_zlacpy( MagmaUpperLowerStr, &M, &nrhs, h_B, &ldb, h_R, &ldb );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
magma_zsetmatrix( M, N, h_A, lda, d_A, ldda );
magma_zsetmatrix( M, nrhs, h_B, ldb, d_B, lddb );
gpu_time = magma_wtime();
magma_zgels3_gpu( MagmaNoTrans, M, N, nrhs, d_A, ldda,
d_B, lddb, h_work, lworkgpu, &info);
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_zgels returned error %d: %s.\n",
(int) info, magma_strerror( info ));
// Get the solution in h_X
magma_zgetmatrix( N, nrhs, d_B, lddb, h_X, ldb );
// compute the residual
blasf77_zgemm( MagmaNoTransStr, MagmaNoTransStr, &M, &nrhs, &N,
&c_neg_one, h_A, &lda,
h_X, &ldb,
&c_one, h_R, &ldb);
matnorm = lapackf77_zlange("f", &M, &N, h_A, &lda, work);
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
lapackf77_zlacpy( MagmaUpperLowerStr, &M, &nrhs, h_B, &ldb, h_X, &ldb );
cpu_time = magma_wtime();
lapackf77_zgels( MagmaNoTransStr, &M, &N, &nrhs,
h_A, &lda, h_X, &ldb, h_work, &lhwork, &info);
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_zgels returned error %d: %s.\n",
(int) info, magma_strerror( info ));
blasf77_zgemm( MagmaNoTransStr, MagmaNoTransStr, &M, &nrhs, &N,
&c_neg_one, h_A2, &lda,
h_X, &ldb,
&c_one, h_B, &ldb);
cpu_error = lapackf77_zlange("f", &M, &nrhs, h_B, &ldb, work) / (min_mn*matnorm);
gpu_error = lapackf77_zlange("f", &M, &nrhs, h_R, &ldb, work) / (min_mn*matnorm);
printf("%5d %5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %8.2e",
(int) M, (int) N, (int) nrhs,
cpu_perf, cpu_time, gpu_perf, gpu_time, cpu_error, gpu_error );
printf("%s\n", (gpu_error < tol ? "" : " failed"));
status |= ! (gpu_error < tol);
TESTING_FREE( tau );
TESTING_FREE( h_A );
TESTING_FREE( h_A2 );
TESTING_FREE( h_B );
TESTING_FREE( h_X );
TESTING_FREE( h_R );
TESTING_FREE( h_work );
TESTING_DEVFREE( d_A );
TESTING_DEVFREE( d_B );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zgeqlf
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
double error, work[1];
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex *h_A, *h_R, *tau, *h_work, tmp[1];
magma_int_t M, N, n2, lda, ldda, lwork, info, min_mn, nb;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
double tol = 2. * opts.tolerance * lapackf77_dlamch("E");
printf(" M N CPU GFlop/s (sec) GPU GFlop/s (sec) ||R||_F / ||A||_F\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 = ((M+31)/32)*32;
nb = magma_get_zgeqrf_nb(M);
gflops = FLOPS_ZGEQLF( M, N ) / 1e9;
// query for workspace size
lwork = -1;
lapackf77_zgeqlf(&M, &N, NULL, &M, NULL, tmp, &lwork, &info);
lwork = (magma_int_t)MAGMA_Z_REAL( tmp[0] );
lwork = max( lwork, N*nb );
lwork = max( lwork, 2*nb*nb);
TESTING_MALLOC_CPU( tau, magmaDoubleComplex, min_mn );
TESTING_MALLOC_CPU( h_A, magmaDoubleComplex, n2 );
TESTING_MALLOC_CPU( h_work, magmaDoubleComplex, lwork );
TESTING_MALLOC_PIN( h_R, magmaDoubleComplex, n2 );
/* Initialize the matrix */
lapackf77_zlarnv( &ione, ISEED, &n2, h_A );
lapackf77_zlacpy( MagmaUpperLowerStr, &M, &N, h_A, &lda, h_R, &lda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
magma_zgeqlf( M, N, h_R, lda, tau, h_work, lwork, &info);
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_zgeqlf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
lapackf77_zgeqlf(&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("lapack_zgeqlf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Check the result compared to LAPACK
=================================================================== */
error = lapackf77_zlange("f", &M, &N, h_A, &lda, work);
blasf77_zaxpy(&n2, &c_neg_one, h_A, &ione, h_R, &ione);
error = lapackf77_zlange("f", &M, &N, h_R, &lda, work) / error;
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %s\n",
(int) M, (int) N, cpu_perf, cpu_time, gpu_perf, gpu_time,
error, (error < tol ? "ok" : "failed"));
status += ! (error < tol);
TESTING_FREE_CPU( tau );
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_work );
TESTING_FREE_PIN( h_R );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zpotrf
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
magmaDoubleComplex *h_A, *h_R;
magma_int_t N, n2, lda, info;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
double work[1], error;
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
opts.lapack |= opts.check; // check (-c) implies lapack (-l)
double tol = opts.tolerance * lapackf77_dlamch("E");
printf("ngpu %d, uplo %c\n", (int) opts.ngpu, opts.uplo );
printf(" N CPU GFlop/s (sec) GPU GFlop/s (sec) ||R_magma - R_lapack||_F / ||R_lapack||_F\n");
printf("========================================================\n");
for( int i = 0; i < opts.ntest; ++i ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[i];
lda = N;
n2 = lda*N;
gflops = FLOPS_ZPOTRF( N ) / 1e9;
TESTING_MALLOC( h_A, magmaDoubleComplex, n2 );
TESTING_HOSTALLOC( h_R, magmaDoubleComplex, n2 );
/* Initialize the matrix */
lapackf77_zlarnv( &ione, ISEED, &n2, h_A );
magma_zmake_hpd( N, h_A, lda );
lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
magma_zpotrf( opts.uplo, N, h_R, lda, &info );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_zpotrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
if ( opts.lapack ) {
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
lapackf77_zpotrf( &opts.uplo, &N, h_A, &lda, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_zpotrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Check the result compared to LAPACK
=================================================================== */
error = lapackf77_zlange("f", &N, &N, h_A, &lda, work);
blasf77_zaxpy(&n2, &c_neg_one, h_A, &ione, h_R, &ione);
error = lapackf77_zlange("f", &N, &N, h_R, &lda, work) / error;
printf("%5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e%s\n",
(int) N, cpu_perf, cpu_time, gpu_perf, gpu_time,
error, (error < tol ? "" : " failed") );
status |= ! (error < tol);
}
else {
printf("%5d --- ( --- ) %7.2f (%7.2f) --- \n",
(int) N, gpu_perf, gpu_time );
}
TESTING_FREE( h_A );
TESTING_HOSTFREE( h_R );
}
}
TESTING_FINALIZE();
return status;
}
/**
Purpose
-------
ZCGESV computes the solution to a complex system of linear equations
A * X = B, A**T * X = B, or A**H * X = B,
where A is an N-by-N matrix and X and B are N-by-NRHS matrices.
ZCGESV first attempts to factorize the matrix in complex SINGLE PRECISION
and use this factorization within an iterative refinement procedure
to produce a solution with complex DOUBLE PRECISION norm-wise backward error
quality (see below). If the approach fails the method switches to a
complex DOUBLE PRECISION factorization and solve.
The iterative refinement is not going to be a winning strategy if
the ratio complex SINGLE PRECISION performance over complex DOUBLE PRECISION
performance is too small. A reasonable strategy should take the
number of right-hand sides and the size of the matrix into account.
This might be done with a call to ILAENV in the future. Up to now, we
always try iterative refinement.
The iterative refinement process is stopped if
ITER > ITERMAX
or for all the RHS we have:
RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX
where
o ITER is the number of the current iteration in the iterative
refinement process
o RNRM is the infinity-norm of the residual
o XNRM is the infinity-norm of the solution
o ANRM is the infinity-operator-norm of the matrix A
o EPS is the machine epsilon returned by DLAMCH('Epsilon')
The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00 respectively.
Arguments
---------
@param[in]
trans magma_trans_t
Specifies the form of the system of equations:
- = MagmaNoTrans: A * X = B (No transpose)
- = MagmaTrans: A**T * X = B (Transpose)
- = MagmaConjTrans: A**H * X = B (Conjugate transpose)
@param[in]
n INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.
@param[in]
nrhs INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
@param[in,out]
dA COMPLEX_16 array on the GPU, dimension (ldda,N)
On entry, the N-by-N coefficient matrix A.
On exit, if iterative refinement has been successfully used
(info.EQ.0 and ITER.GE.0, see description below), A is
unchanged. If double precision factorization has been used
(info.EQ.0 and ITER.LT.0, see description below), then the
array dA contains the factors L and U from the factorization
A = P*L*U; the unit diagonal elements of L are not stored.
@param[in]
ldda INTEGER
The leading dimension of the array dA. ldda >= max(1,N).
@param[out]
ipiv INTEGER array, dimension (N)
The pivot indices that define the permutation matrix P;
row i of the matrix was interchanged with row IPIV(i).
Corresponds either to the single precision factorization
(if info.EQ.0 and ITER.GE.0) or the double precision
factorization (if info.EQ.0 and ITER.LT.0).
@param[out]
dipiv INTEGER array on the GPU, dimension (N)
The pivot indices; for 1 <= i <= N, after permuting, row i of the
matrix was moved to row dIPIV(i).
Note this is different than IPIV, where interchanges
are applied one-after-another.
@param[in]
dB COMPLEX_16 array on the GPU, dimension (lddb,NRHS)
The N-by-NRHS right hand side matrix B.
@param[in]
lddb INTEGER
The leading dimension of the array dB. lddb >= max(1,N).
@param[out]
dX COMPLEX_16 array on the GPU, dimension (lddx,NRHS)
If info = 0, the N-by-NRHS solution matrix X.
@param[in]
lddx INTEGER
The leading dimension of the array dX. lddx >= max(1,N).
@param
dworkd (workspace) COMPLEX_16 array on the GPU, dimension (N*NRHS)
This array is used to hold the residual vectors.
@param
dworks (workspace) COMPLEX array on the GPU, dimension (N*(N+NRHS))
This array is used to store the complex single precision matrix
and the right-hand sides or solutions in single precision.
@param[out]
iter INTEGER
- < 0: iterative refinement has failed, double precision
factorization has been performed
+ -1 : the routine fell back to full precision for
implementation- or machine-specific reasons
+ -2 : narrowing the precision induced an overflow,
the routine fell back to full precision
+ -3 : failure of SGETRF
+ -31: stop the iterative refinement after the 30th iteration
- > 0: iterative refinement has been successfully used.
Returns the number of iterations
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if info = -i, the i-th argument had an illegal value
- > 0: if info = i, U(i,i) computed in DOUBLE PRECISION is
exactly zero. The factorization has been completed,
but the factor U is exactly singular, so the solution
could not be computed.
@ingroup magma_zgesv_driver
********************************************************************/
extern "C" magma_int_t
magma_zcgesv_gpu(magma_trans_t trans, magma_int_t n, magma_int_t nrhs,
magmaDoubleComplex *dA, magma_int_t ldda,
magma_int_t *ipiv, magma_int_t *dipiv,
magmaDoubleComplex *dB, magma_int_t lddb,
magmaDoubleComplex *dX, magma_int_t lddx,
magmaDoubleComplex *dworkd, magmaFloatComplex *dworks,
magma_int_t *iter, magma_int_t *info)
{
#define dB(i,j) (dB + (i) + (j)*lddb)
#define dX(i,j) (dX + (i) + (j)*lddx)
#define dR(i,j) (dR + (i) + (j)*lddr)
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magma_int_t ione = 1;
magmaDoubleComplex *dR;
magmaFloatComplex *dSA, *dSX;
magmaDoubleComplex Xnrmv, Rnrmv;
double Anrm, Xnrm, Rnrm, cte, eps;
magma_int_t i, j, iiter, lddsa, lddr;
/* Check arguments */
*iter = 0;
*info = 0;
if ( n < 0 )
*info = -1;
else if ( nrhs < 0 )
*info = -2;
else if ( ldda < max(1,n))
*info = -4;
else if ( lddb < max(1,n))
*info = -8;
else if ( lddx < max(1,n))
*info = -10;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
if ( n == 0 || nrhs == 0 )
return *info;
lddsa = n;
lddr = n;
dSA = dworks;
dSX = dSA + lddsa*n;
dR = dworkd;
eps = lapackf77_dlamch("Epsilon");
Anrm = magmablas_zlange(MagmaInfNorm, n, n, dA, ldda, (double*)dworkd );
cte = Anrm * eps * pow((double)n, 0.5) * BWDMAX;
/*
* Convert to single precision
*/
//magmablas_zlag2c( n, nrhs, dB, lddb, dSX, lddsx, info ); // done inside zcgetrs with pivots
if (*info != 0) {
*iter = -2;
goto FALLBACK;
}
magmablas_zlag2c( n, n, dA, ldda, dSA, lddsa, info );
if (*info != 0) {
*iter = -2;
goto FALLBACK;
}
// factor dSA in single precision
magma_cgetrf_gpu( n, n, dSA, lddsa, ipiv, info );
if (*info != 0) {
*iter = -3;
goto FALLBACK;
}
// Generate parallel pivots
{
magma_int_t *newipiv;
magma_imalloc_cpu( &newipiv, n );
if ( newipiv == NULL ) {
*iter = -3;
goto FALLBACK;
}
swp2pswp( trans, n, ipiv, newipiv );
magma_setvector( n, sizeof(magma_int_t), newipiv, 1, dipiv, 1 );
magma_free_cpu( newipiv );
}
// solve dSA*dSX = dB in single precision
// converts dB to dSX and applies pivots, solves, then converts result back to dX
magma_zcgetrs_gpu( trans, n, nrhs, dSA, lddsa, dipiv, dB, lddb, dX, lddx, dSX, info );
// residual dR = dB - dA*dX in double precision
magmablas_zlacpy( MagmaUpperLower, n, nrhs, dB, lddb, dR, lddr );
if ( nrhs == 1 ) {
magma_zgemv( trans, n, n,
c_neg_one, dA, ldda,
dX, 1,
c_one, dR, 1 );
}
else {
magma_zgemm( trans, MagmaNoTrans, n, nrhs, n,
c_neg_one, dA, ldda,
dX, lddx,
c_one, dR, lddr );
}
// TODO: use MAGMA_Z_ABS( dX(i,j) ) instead of zlange?
for( j=0; j < nrhs; j++ ) {
i = magma_izamax( n, dX(0,j), 1) - 1;
magma_zgetmatrix( 1, 1, dX(i,j), 1, &Xnrmv, 1 );
Xnrm = lapackf77_zlange( "F", &ione, &ione, &Xnrmv, &ione, NULL );
i = magma_izamax ( n, dR(0,j), 1 ) - 1;
magma_zgetmatrix( 1, 1, dR(i,j), 1, &Rnrmv, 1 );
Rnrm = lapackf77_zlange( "F", &ione, &ione, &Rnrmv, &ione, NULL );
if ( Rnrm > Xnrm*cte ) {
goto REFINEMENT;
}
}
*iter = 0;
return *info;
REFINEMENT:
for( iiter=1; iiter < ITERMAX; ) {
*info = 0;
// convert residual dR to single precision dSX
// solve dSA*dSX = R in single precision
// convert result back to double precision dR
// it's okay that dR is used for both dB input and dX output.
magma_zcgetrs_gpu( trans, n, nrhs, dSA, lddsa, dipiv, dR, lddr, dR, lddr, dSX, info );
if (*info != 0) {
*iter = -3;
goto FALLBACK;
}
// Add correction and setup residual
// dX += dR --and--
// dR = dB
// This saves going through dR a second time (if done with one more kernel).
// -- not really: first time is read, second time is write.
for( j=0; j < nrhs; j++ ) {
magmablas_zaxpycp( n, dR(0,j), dX(0,j), dB(0,j) );
}
// residual dR = dB - dA*dX in double precision
if ( nrhs == 1 ) {
magma_zgemv( trans, n, n,
c_neg_one, dA, ldda,
dX, 1,
c_one, dR, 1 );
}
else {
magma_zgemm( trans, MagmaNoTrans, n, nrhs, n,
c_neg_one, dA, ldda,
dX, lddx,
c_one, dR, lddr );
}
/* Check whether the nrhs normwise backward errors satisfy the
* stopping criterion. If yes, set ITER=IITER > 0 and return. */
for( j=0; j < nrhs; j++ ) {
i = magma_izamax( n, dX(0,j), 1) - 1;
magma_zgetmatrix( 1, 1, dX(i,j), 1, &Xnrmv, 1 );
Xnrm = lapackf77_zlange( "F", &ione, &ione, &Xnrmv, &ione, NULL );
i = magma_izamax ( n, dR(0,j), 1 ) - 1;
magma_zgetmatrix( 1, 1, dR(i,j), 1, &Rnrmv, 1 );
Rnrm = lapackf77_zlange( "F", &ione, &ione, &Rnrmv, &ione, NULL );
if ( Rnrm > Xnrm*cte ) {
goto L20;
}
}
/* If we are here, the nrhs normwise backward errors satisfy
* the stopping criterion, we are good to exit. */
*iter = iiter;
return *info;
L20:
iiter++;
}
/* If we are at this place of the code, this is because we have
* performed ITER=ITERMAX iterations and never satisified the
* stopping criterion. Set up the ITER flag accordingly and follow
* up on double precision routine. */
*iter = -ITERMAX - 1;
FALLBACK:
/* Single-precision iterative refinement failed to converge to a
* satisfactory solution, so we resort to double precision. */
magma_zgetrf_gpu( n, n, dA, ldda, ipiv, info );
if (*info == 0) {
magmablas_zlacpy( MagmaUpperLower, n, nrhs, dB, lddb, dX, lddx );
magma_zgetrs_gpu( trans, n, nrhs, dA, ldda, ipiv, dX, lddx, info );
}
return *info;
}