/*-------------------------------------------------------------------
* Check the orthogonality of Q
*/
static magma_int_t check_orthogonality(magma_int_t M, magma_int_t N, double *Q, magma_int_t LDQ, double eps)
{
double done = 1.0;
double mdone = -1.0;
double c_zero = MAGMA_D_ZERO;
double c_one = MAGMA_D_ONE;
double normQ, result;
magma_int_t info_ortho;
magma_int_t minMN = min(M, N);
double *work;
magma_dmalloc_cpu( &work, minMN );
/* Build the idendity matrix */
double *Id;
magma_dmalloc_cpu( &Id, minMN*minMN );
lapackf77_dlaset("A", &minMN, &minMN, &c_zero, &c_one, Id, &minMN);
/* Perform Id - Q'Q */
if (M >= N)
blasf77_dsyrk("U", "C", &N, &M, &done, Q, &LDQ, &mdone, Id, &N);
else
blasf77_dsyrk("U", "N", &M, &N, &done, Q, &LDQ, &mdone, Id, &M);
normQ = lapackf77_dlansy("I", "U", &minMN, Id, &minMN, work);
result = normQ / (minMN * eps);
printf( " %12.2e", result*eps );
//printf(" ======================================================\n");
//printf(" ||Id-Q'*Q||_oo / (minMN*eps) : %15.3E \n", result );
//printf(" ======================================================\n");
if ( isnan(result) || isinf(result) || (result > 60.0) ) {
//printf("-- Orthogonality is suspicious ! \n");
info_ortho=1;
}
else {
//printf("-- Orthogonality is CORRECT ! \n");
info_ortho=0;
}
magma_free_cpu(work);
magma_free_cpu(Id);
return info_ortho;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing dgeqrf
*/
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 double c_neg_one = MAGMA_D_NEG_ONE;
const double c_one = MAGMA_D_ONE;
const double c_zero = MAGMA_D_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;
double *h_A, *h_R, *tau, *h_work, tmp[1];
magmaDouble_ptr d_A, dT;
magma_int_t M, N, n2, lda, ldda, lwork, info, min_mn, nb, size;
magma_int_t ISEED[4] = {0,0,0,1};
magma_opts opts;
parse_opts( argc, argv, &opts );
magma_int_t status = 0;
double tol = opts.tolerance * lapackf77_dlamch("E");
printf( "version %d\n", (int) opts.version );
if ( opts.version == 2 ) {
printf(" M N CPU GFlop/s (sec) GPU GFlop/s (sec) |R - Q^H*A| |I - Q^H*Q|\n");
printf("===============================================================================\n");
}
else {
printf(" M N CPU GFlop/s (sec) GPU GFlop/s (sec) |b - A*x|\n");
printf("================================================================\n");
}
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[itest];
N = opts.nsize[itest];
min_mn = min(M, N);
lda = M;
n2 = lda*N;
ldda = ((M+31)/32)*32;
gflops = FLOPS_DGEQRF( M, N ) / 1e9;
// query for workspace size
lwork = -1;
lapackf77_dgeqrf(&M, &N, NULL, &M, NULL, tmp, &lwork, &info);
lwork = (magma_int_t)MAGMA_D_REAL( tmp[0] );
TESTING_MALLOC_CPU( tau, double, min_mn );
TESTING_MALLOC_CPU( h_A, double, n2 );
TESTING_MALLOC_CPU( h_work, double, lwork );
TESTING_MALLOC_PIN( h_R, double, n2 );
TESTING_MALLOC_DEV( d_A, double, ldda*N );
/* Initialize the matrix */
lapackf77_dlarnv( &ione, ISEED, &n2, h_A );
lapackf77_dlacpy( MagmaUpperLowerStr, &M, &N, h_A, &lda, h_R, &lda );
magma_dsetmatrix( M, N, h_R, lda, d_A, ldda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
if ( opts.version == 2 ) {
// LAPACK complaint arguments
magma_dgeqrf2_gpu( M, N, d_A, ldda, tau, &info );
}
else {
nb = magma_get_dgeqrf_nb( M );
size = (2*min(M, N) + (N+31)/32*32 )*nb;
TESTING_MALLOC_DEV( dT, double, size );
if ( opts.version == 1 ) {
// stores dT, V blocks have zeros, R blocks inverted & stored in dT
magma_dgeqrf_gpu( M, N, d_A, ldda, tau, dT, &info );
}
#ifdef HAVE_CUBLAS
else if ( opts.version == 3 ) {
// stores dT, V blocks have zeros, R blocks stored in dT
magma_dgeqrf3_gpu( M, N, d_A, ldda, tau, dT, &info );
}
#endif
else {
printf( "Unknown version %d\n", (int) opts.version );
exit(1);
}
}
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_dgeqrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
if ( opts.check && opts.version == 2 ) {
/* =====================================================================
Check the result, following zqrt01 except using the reduced Q.
This works for any M,N (square, tall, wide).
Only for version 2, which has LAPACK complaint output.
=================================================================== */
magma_dgetmatrix( M, N, d_A, ldda, h_R, lda );
magma_int_t ldq = M;
magma_int_t ldr = min_mn;
double *Q, *R;
double *work;
TESTING_MALLOC_CPU( Q, double, ldq*min_mn ); // M by K
TESTING_MALLOC_CPU( R, double, ldr*N ); // K by N
TESTING_MALLOC_CPU( work, double, min_mn );
// generate M by K matrix Q, where K = min(M,N)
lapackf77_dlacpy( "Lower", &M, &min_mn, h_R, &lda, Q, &ldq );
lapackf77_dorgqr( &M, &min_mn, &min_mn, Q, &ldq, tau, h_work, &lwork, &info );
assert( info == 0 );
// copy K by N matrix R
lapackf77_dlaset( "Lower", &min_mn, &N, &c_zero, &c_zero, R, &ldr );
lapackf77_dlacpy( "Upper", &min_mn, &N, h_R, &lda, R, &ldr );
// error = || R - Q^H*A || / (N * ||A||)
blasf77_dgemm( "Conj", "NoTrans", &min_mn, &N, &M,
&c_neg_one, Q, &ldq, h_A, &lda, &c_one, R, &ldr );
Anorm = lapackf77_dlange( "1", &M, &N, h_A, &lda, work );
error = lapackf77_dlange( "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_dlaset( "Upper", &min_mn, &min_mn, &c_zero, &c_one, R, &ldr );
blasf77_dsyrk( "Upper", "Conj", &min_mn, &M, &d_neg_one, Q, &ldq, &d_one, R, &ldr );
error2 = lapackf77_dlansy( "1", "Upper", &min_mn, R, &ldr, work );
if ( N > 0 )
error2 /= N;
TESTING_FREE_CPU( Q ); Q = NULL;
TESTING_FREE_CPU( R ); R = NULL;
TESTING_FREE_CPU( work ); work = NULL;
}
else if ( opts.check && M >= N ) {
/* =====================================================================
Check the result by solving consistent linear system, A*x = b.
Only for versions 1 & 3 with M >= N.
=================================================================== */
magma_int_t lwork;
double *x, *b, *hwork;
magmaDouble_ptr d_B;
const double c_zero = MAGMA_D_ZERO;
const double c_one = MAGMA_D_ONE;
const double c_neg_one = MAGMA_D_NEG_ONE;
const magma_int_t ione = 1;
// initialize RHS, b = A*random
TESTING_MALLOC_CPU( x, double, N );
TESTING_MALLOC_CPU( b, double, M );
lapackf77_dlarnv( &ione, ISEED, &N, x );
blasf77_dgemv( "Notrans", &M, &N, &c_one, h_A, &lda, x, &ione, &c_zero, b, &ione );
// copy to GPU
TESTING_MALLOC_DEV( d_B, double, M );
magma_dsetvector( M, b, 1, d_B, 1 );
if ( opts.version == 1 ) {
// allocate hwork
magma_dgeqrs_gpu( M, N, 1,
d_A, ldda, tau, dT,
d_B, M, tmp, -1, &info );
lwork = (magma_int_t)MAGMA_D_REAL( tmp[0] );
TESTING_MALLOC_CPU( hwork, double, lwork );
// solve linear system
magma_dgeqrs_gpu( M, N, 1,
d_A, ldda, tau, dT,
d_B, M, hwork, lwork, &info );
if (info != 0)
printf("magma_dgeqrs returned error %d: %s.\n",
(int) info, magma_strerror( info ));
TESTING_FREE_CPU( hwork );
}
#ifdef HAVE_CUBLAS
else if ( opts.version == 3 ) {
// allocate hwork
magma_dgeqrs3_gpu( M, N, 1,
d_A, ldda, tau, dT,
d_B, M, tmp, -1, &info );
lwork = (magma_int_t)MAGMA_D_REAL( tmp[0] );
TESTING_MALLOC_CPU( hwork, double, lwork );
// solve linear system
magma_dgeqrs3_gpu( M, N, 1,
d_A, ldda, tau, dT,
d_B, M, hwork, lwork, &info );
if (info != 0)
printf("magma_dgeqrs3 returned error %d: %s.\n",
(int) info, magma_strerror( info ));
TESTING_FREE_CPU( hwork );
}
#endif
else {
printf( "Unknown version %d\n", (int) opts.version );
exit(1);
}
magma_dgetvector( N, d_B, 1, x, 1 );
// compute r = Ax - b, saved in b
blasf77_dgemv( "Notrans", &M, &N, &c_one, h_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_dlange( "F", &M, &N, h_A, &lda, work );
norm_r = lapackf77_dlange( "F", &M, &ione, b, &M, work );
norm_x = lapackf77_dlange( "F", &N, &ione, x, &N, work );
TESTING_FREE_CPU( x );
TESTING_FREE_CPU( b );
TESTING_FREE_DEV( d_B );
error = norm_r / (N * norm_A * norm_x);
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
lapackf77_dgeqrf(&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_dgeqrf 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 ) {
if ( opts.version == 2 ) {
bool okay = (error < tol && error2 < tol);
status += ! okay;
printf( "%11.2e %11.2e %s\n", error, error2, (okay ? "ok" : "failed") );
}
else if ( M >= N ) {
bool okay = (error < tol);
status += ! okay;
printf( "%10.2e %s\n", error, (okay ? "ok" : "failed") );
}
else {
printf( "(error check only for M >= N)\n" );
}
}
else {
printf( " ---\n" );
}
TESTING_FREE_CPU( tau );
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_work );
TESTING_FREE_PIN( h_R );
TESTING_FREE_DEV( d_A );
if ( opts.version != 2 )
TESTING_FREE_DEV( dT );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing dsygvd
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gpu_time, cpu_time;
double *h_A, *h_R, *h_B, *h_S, *h_work;
double *w1, *w2;
magma_int_t *iwork;
magma_int_t N, n2, info, nb, lwork, liwork, lda;
double result[4] = {0};
double c_one = MAGMA_D_ONE;
double c_neg_one = MAGMA_D_NEG_ONE;
double d_zero = 0.;
double d_one = 1.;
double d_neg_one = -1.;
//magma_int_t izero = 0;
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");
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, uplo = %s\n",
(int) opts.itype, lapack_vec_const(opts.jobz), lapack_uplo_const(opts.uplo));
printf(" N CPU Time (sec) GPU Time(sec)\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 = N*lda;
nb = magma_get_dsytrd_nb(N);
lwork = 1 + 6*N*nb + 2* N*N;
liwork = 3 + 5*N;
TESTING_MALLOC_CPU( h_A, double, n2 );
TESTING_MALLOC_CPU( h_B, double, 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, double, n2 );
TESTING_MALLOC_PIN( h_S, double, n2 );
TESTING_MALLOC_PIN( h_work, double, lwork );
/* Initialize the matrix */
lapackf77_dlarnv( &ione, ISEED, &n2, h_A );
lapackf77_dlarnv( &ione, ISEED, &n2, h_B );
magma_dmake_hpd( N, h_B, lda );
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_B, &lda, h_S, &lda );
/* warmup */
if ( opts.warmup ) {
magma_dsygvd( opts.itype, opts.jobz, opts.uplo,
N, h_R, lda, h_S, lda, w1,
h_work, lwork,
iwork, liwork,
&info );
if (info != 0)
printf("magma_dsygvd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_B, &lda, h_S, &lda );
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
magma_dsygvd( opts.itype, opts.jobz, opts.uplo,
N, h_R, lda, h_S, lda, w1,
h_work, lwork,
iwork, liwork,
&info );
gpu_time = magma_wtime() - gpu_time;
if (info != 0)
printf("magma_dsygvd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
if ( opts.check ) {
/* =====================================================================
Check the results following the LAPACK's [zc]hegvd 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) | I - V V' B | / ( N ) (itype = 1,2)
| B - V V' | / ( |B| N ) (itype = 3)
(3) | S(with V) - S(w/o V) | / | S |
=================================================================== */
double temp1, temp2;
//double *tau;
if ( opts.itype == 1 || opts.itype == 2 ) {
lapackf77_dlaset( "A", &N, &N, &d_zero, &c_one, h_S, &lda);
blasf77_dgemm("N", "C", &N, &N, &N, &c_one, h_R, &lda, h_R, &lda, &d_zero, h_work, &N);
blasf77_dsymm("R", lapack_uplo_const(opts.uplo), &N, &N, &c_neg_one, h_B, &lda, h_work, &N, &c_one, h_S, &lda);
result[1] = lapackf77_dlange("1", &N, &N, h_S, &lda, h_work) / N;
}
else if ( opts.itype == 3 ) {
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_B, &lda, h_S, &lda);
blasf77_dsyrk(lapack_uplo_const(opts.uplo), "N", &N, &N, &d_neg_one, h_R, &lda, &d_one, h_S, &lda);
result[1] = lapackf77_dlansy("1", lapack_uplo_const(opts.uplo), &N, h_S, &lda, h_work) / N
/ lapackf77_dlansy("1", lapack_uplo_const(opts.uplo), &N, h_B, &lda, h_work);
}
result[0] = 1.;
result[0] /= lapackf77_dlansy("1", lapack_uplo_const(opts.uplo), &N, h_A, &lda, h_work);
result[0] /= lapackf77_dlange("1", &N, &N, h_R, &lda, h_work);
if ( opts.itype == 1 ) {
blasf77_dsymm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_one, h_A, &lda, h_R, &lda, &d_zero, h_work, &N);
for(int i=0; i<N; ++i)
blasf77_dscal(&N, &w1[i], &h_R[i*N], &ione);
blasf77_dsymm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_neg_one, h_B, &lda, h_R, &lda, &c_one, h_work, &N);
result[0] *= lapackf77_dlange("1", &N, &N, h_work, &N, &temp1)/N;
}
else if ( opts.itype == 2 ) {
blasf77_dsymm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_one, h_B, &lda, h_R, &lda, &d_zero, h_work, &N);
for(int i=0; i<N; ++i)
blasf77_dscal(&N, &w1[i], &h_R[i*N], &ione);
blasf77_dsymm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_one, h_A, &lda, h_work, &N, &c_neg_one, h_R, &lda);
result[0] *= lapackf77_dlange("1", &N, &N, h_R, &lda, &temp1)/N;
}
else if ( opts.itype == 3 ) {
blasf77_dsymm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_one, h_A, &lda, h_R, &lda, &d_zero, h_work, &N);
for(int i=0; i<N; ++i)
blasf77_dscal(&N, &w1[i], &h_R[i*N], &ione);
blasf77_dsymm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_one, h_B, &lda, h_work, &N, &c_neg_one, h_R, &lda);
result[0] *= lapackf77_dlange("1", &N, &N, h_R, &lda, &temp1)/N;
}
/*
lapackf77_dsyt21(&ione, lapack_uplo_const(opts.uplo), &N, &izero,
h_A, &lda,
w1, w1,
h_R, &lda,
h_R, &lda,
tau, h_work, rwork, &result[0]);
*/
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_B, &lda, h_S, &lda );
magma_dsygvd( opts.itype, MagmaNoVec, opts.uplo,
N, h_R, lda, h_S, lda, w2,
h_work, lwork,
iwork, liwork,
&info );
if (info != 0)
printf("magma_dsygvd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
temp1 = temp2 = 0;
for(int j=0; j<N; j++) {
temp1 = max(temp1, absv(w1[j]));
temp1 = max(temp1, absv(w2[j]));
temp2 = max(temp2, absv(w1[j]-w2[j]));
}
result[2] = temp2 / temp1;
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
lapackf77_dsygvd( &opts.itype, lapack_vec_const(opts.jobz), lapack_uplo_const(opts.uplo),
&N, h_A, &lda, h_B, &lda, w2,
h_work, &lwork,
iwork, &liwork,
&info );
cpu_time = magma_wtime() - cpu_time;
if (info != 0)
printf("lapackf77_dsygvd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
printf("%5d %7.2f %7.2f\n",
(int) N, cpu_time, gpu_time);
}
else {
printf("%5d --- %7.2f\n",
(int) N, gpu_time);
}
/* =====================================================================
Print execution time
=================================================================== */
if ( opts.check ) {
printf("Testing the eigenvalues and eigenvectors for correctness:\n");
if ( opts.itype==1 ) {
printf("(1) | 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("(1) | 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("(1) | B A Z - Z D | / (|A| |Z| N) = %8.2e %s\n", result[0], (result[0] < tol ? "ok" : "failed") );
}
if ( opts.itype==1 || opts.itype==2 ) {
printf("(2) | I - Z Z' B | / N = %8.2e %s\n", result[1], (result[1] < tol ? "ok" : "failed") );
}
else {
printf("(2) | B - Z Z' | / (|B| N) = %8.2e %s\n", result[1], (result[1] < tol ? "ok" : "failed") );
}
printf( "(3) | D(w/ Z) - D(w/o Z) | / |D| = %8.2e %s\n\n", result[2], (result[2] < tolulp ? "ok" : "failed") );
status += ! (result[0] < tol && result[1] < tol && result[2] < 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 );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}