FLA_Error FLA_Symm_lu_unb_var10( FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C )
{
FLA_Obj BL, BR, B0, b1t, B2;
FLA_Obj CL, CR, C0, c1t, C2;
FLA_Part_1x2( B, &BL, &BR, 0, FLA_RIGHT );
FLA_Part_1x2( C, &CL, &CR, 0, FLA_RIGHT );
while ( FLA_Obj_width( BR ) < FLA_Obj_width( B ) ){
FLA_Repart_1x2_to_1x3( BL, /**/ BR, &B0, &b1t, /**/ &B2,
1, FLA_LEFT );
FLA_Repart_1x2_to_1x3( CL, /**/ CR, &C0, &c1t, /**/ &C2,
1, FLA_LEFT );
/*------------------------------------------------------------*/
/* c1t = c1t + A * b1t */
FLA_Symv_external( FLA_UPPER_TRIANGULAR, alpha, A, b1t, beta, c1t );
/*------------------------------------------------------------*/
FLA_Cont_with_1x3_to_1x2( &BL, /**/ &BR, B0, /**/ b1t, B2,
FLA_RIGHT );
FLA_Cont_with_1x3_to_1x2( &CL, /**/ &CR, C0, /**/ c1t, C2,
FLA_RIGHT );
}
return FLA_SUCCESS;
}
FLA_Error FLA_Symm_ru_unb_var10( FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C )
{
FLA_Obj BT, B0,
BB, b1t,
B2;
FLA_Obj CT, C0,
CB, c1t,
C2;
FLA_Part_2x1( B, &BT,
&BB, 0, FLA_BOTTOM );
FLA_Part_2x1( C, &CT,
&CB, 0, FLA_BOTTOM );
while ( FLA_Obj_length( BB ) < FLA_Obj_length( B ) ){
FLA_Repart_2x1_to_3x1( BT, &B0,
&b1t,
/* ** */ /* ** */
BB, &B2, 1, FLA_TOP );
FLA_Repart_2x1_to_3x1( CT, &C0,
&c1t,
/* ** */ /* ** */
CB, &C2, 1, FLA_TOP );
/*------------------------------------------------------------*/
/* c1t = c1t + b1t * A */
/* c1t' = c1t' + A' * b1t' */
FLA_Symv_external( FLA_UPPER_TRIANGULAR, alpha, A, b1t, beta, c1t );
/*------------------------------------------------------------*/
FLA_Cont_with_3x1_to_2x1( &BT, B0,
/* ** */ /* ** */
b1t,
&BB, B2, FLA_BOTTOM );
FLA_Cont_with_3x1_to_2x1( &CT, C0,
/* ** */ /* ** */
c1t,
&CB, C2, FLA_BOTTOM );
}
return FLA_SUCCESS;
}
void libfla_test_symm_experiment( test_params_t params,
unsigned int var,
char* sc_str,
FLA_Datatype datatype,
unsigned int p_cur,
unsigned int pci,
unsigned int n_repeats,
signed int impl,
double* perf,
double* residual )
{
dim_t b_flash = params.b_flash;
dim_t b_alg_flat = params.b_alg_flat;
double time_min = 1e9;
double time;
unsigned int i;
unsigned int m;
signed int m_input = -1;
unsigned int n;
signed int n_input = -1;
FLA_Side side;
FLA_Uplo uplo;
FLA_Obj A, B, C, x, y, z, w, norm;
FLA_Obj alpha, beta;
FLA_Obj C_save;
FLA_Obj A_test, B_test, C_test;
// Determine the dimensions.
if ( m_input < 0 ) m = p_cur / abs(m_input);
else m = p_cur;
if ( n_input < 0 ) n = p_cur / abs(n_input);
else n = p_cur;
// Translate parameter characters to libflame constants.
FLA_Param_map_char_to_flame_side( &pc_str[pci][0], &side );
FLA_Param_map_char_to_flame_uplo( &pc_str[pci][1], &uplo );
// Create the matrices for the current operation.
if ( side == FLA_LEFT )
{
libfla_test_obj_create( datatype, FLA_NO_TRANSPOSE, sc_str[0], m, m, &A );
// Create vectors for use in test.
FLA_Obj_create( datatype, n, 1, 0, 0, &x );
FLA_Obj_create( datatype, m, 1, 0, 0, &y );
FLA_Obj_create( datatype, m, 1, 0, 0, &z );
FLA_Obj_create( datatype, m, 1, 0, 0, &w );
}
else
{
libfla_test_obj_create( datatype, FLA_NO_TRANSPOSE, sc_str[0], n, n, &A );
// Create vectors for use in test.
FLA_Obj_create( datatype, n, 1, 0, 0, &x );
FLA_Obj_create( datatype, m, 1, 0, 0, &y );
FLA_Obj_create( datatype, m, 1, 0, 0, &z );
FLA_Obj_create( datatype, n, 1, 0, 0, &w );
}
libfla_test_obj_create( datatype, FLA_NO_TRANSPOSE, sc_str[1], m, n, &B );
libfla_test_obj_create( datatype, FLA_NO_TRANSPOSE, sc_str[2], m, n, &C );
// Create a norm scalar.
FLA_Obj_create( FLA_Obj_datatype_proj_to_real( A ), 1, 1, 0, 0, &norm );
// Initialize the test matrices.
FLA_Random_symm_matrix( uplo, A );
FLA_Random_matrix( B );
FLA_Random_matrix( C );
// Initialize the test vectors.
FLA_Random_matrix( x );
FLA_Set( FLA_ZERO, y );
FLA_Set( FLA_ZERO, z );
FLA_Set( FLA_ZERO, w );
// Set constants.
alpha = FLA_TWO;
beta = FLA_MINUS_ONE;
// Save the original object contents in a temporary object.
FLA_Obj_create_copy_of( FLA_NO_TRANSPOSE, C, &C_save );
// Use hierarchical matrices if we're testing the FLASH front-end.
if ( impl == FLA_TEST_HIER_FRONT_END )
{
FLASH_Obj_create_hier_copy_of_flat( A, 1, &b_flash, &A_test );
FLASH_Obj_create_hier_copy_of_flat( B, 1, &b_flash, &B_test );
FLASH_Obj_create_hier_copy_of_flat( C, 1, &b_flash, &C_test );
}
else
{
A_test = A;
B_test = B;
C_test = C;
}
// Create a control tree for the individual variants.
if ( impl == FLA_TEST_FLAT_UNB_VAR ||
impl == FLA_TEST_FLAT_OPT_VAR ||
impl == FLA_TEST_FLAT_BLK_VAR ||
impl == FLA_TEST_FLAT_UNB_EXT ||
impl == FLA_TEST_FLAT_BLK_EXT )
libfla_test_symm_cntl_create( var, b_alg_flat );
// Repeat the experiment n_repeats times and record results.
for ( i = 0; i < n_repeats; ++i )
{
if ( impl == FLA_TEST_HIER_FRONT_END )
FLASH_Obj_hierarchify( C_save, C_test );
else
FLA_Copy_external( C_save, C_test );
time = FLA_Clock();
libfla_test_symm_impl( impl, side, uplo, alpha, A_test, B_test, beta, C_test );
time = FLA_Clock() - time;
time_min = min( time_min, time );
}
// Copy the solution to flat matrix X.
if ( impl == FLA_TEST_HIER_FRONT_END )
{
FLASH_Obj_flatten( C_test, C );
}
else
{
// No action needed since C_test and C refer to the same object.
}
// Free the hierarchical matrices if we're testing the FLASH front-end.
if ( impl == FLA_TEST_HIER_FRONT_END )
{
FLASH_Obj_free( &A_test );
FLASH_Obj_free( &B_test );
FLASH_Obj_free( &C_test );
}
// Free the control trees if we're testing the variants.
if ( impl == FLA_TEST_FLAT_UNB_VAR ||
impl == FLA_TEST_FLAT_OPT_VAR ||
impl == FLA_TEST_FLAT_BLK_VAR ||
impl == FLA_TEST_FLAT_UNB_EXT ||
impl == FLA_TEST_FLAT_BLK_EXT )
libfla_test_symm_cntl_free();
// Compute the performance of the best experiment repeat.
if ( side == FLA_LEFT )
*perf = ( 1 * m * m * n ) / time_min / FLOPS_PER_UNIT_PERF;
else
*perf = ( 1 * m * n * n ) / time_min / FLOPS_PER_UNIT_PERF;
if ( FLA_Obj_is_complex( A ) ) *perf *= 4.0;
// Compute:
// y = C * x
// and compare to
// z = ( beta * C_orig + alpha * A * B ) x (side = left)
// z = ( beta * C_orig + alpha * B * A ) x (side = right)
FLA_Gemv_external( FLA_NO_TRANSPOSE, FLA_ONE, C, x, FLA_ZERO, y );
if ( side == FLA_LEFT )
{
FLA_Gemv_external( FLA_NO_TRANSPOSE, FLA_ONE, B, x, FLA_ZERO, w );
FLA_Symv_external( uplo, alpha, A, w, FLA_ZERO, z );
}
else
{
FLA_Symv_external( uplo, FLA_ONE, A, x, FLA_ZERO, w );
FLA_Gemv_external( FLA_NO_TRANSPOSE, alpha, B, w, FLA_ZERO, z );
}
FLA_Gemv_external( FLA_NO_TRANSPOSE, beta, C_save, x, FLA_ONE, z );
// Compute || y - z ||.
//FLA_Axpy_external( FLA_MINUS_ONE, y, z );
//FLA_Nrm2_external( z, norm );
//FLA_Obj_extract_real_scalar( norm, residual );
*residual = FLA_Max_elemwise_diff( y, z );
// Free the supporting flat objects.
FLA_Obj_free( &C_save );
// Free the flat test matrices.
FLA_Obj_free( &A );
FLA_Obj_free( &B );
FLA_Obj_free( &C );
FLA_Obj_free( &x );
FLA_Obj_free( &y );
FLA_Obj_free( &z );
FLA_Obj_free( &w );
FLA_Obj_free( &norm );
}
int main( int argc, char *argv[] )
{
int
i, j,
n_threads,
n_repeats,
n_trials,
increment,
begin,
sorting,
caching,
work_stealing,
data_affinity;
dim_t
size,
nb_alg;
FLA_Datatype
datatype = FLA_DOUBLE;
FLA_Inv
inv = FLA_NO_INVERSE;
FLA_Uplo
uplo = FLA_LOWER_TRIANGULAR;
FLA_Obj
A, B, x, b, b_norm,
AH, BH;
double
length,
b_norm_value = 0.0,
dtime,
*dtimes,
*flops;
#ifndef FLA_ENABLE_WINDOWS_BUILD
char
output_file_m[100];
FILE
*fpp;
#endif
fprintf( stdout, "%c Enter number of repeats: ", '%' );
scanf( "%d", &n_repeats );
fprintf( stdout, "%c %d\n", '%', n_repeats );
fprintf( stdout, "%c Enter blocksize: ", '%' );
scanf( "%u", &nb_alg );
fprintf( stdout, "%c %u\n", '%', nb_alg );
fprintf( stdout, "%c Enter problem size parameters: first, inc, num: ", '%' );
scanf( "%d%d%d", &begin, &increment, &n_trials );
fprintf( stdout, "%c %d %d %d\n", '%', begin, increment, n_trials );
fprintf( stdout, "%c Enter number of threads: ", '%' );
scanf( "%d", &n_threads );
fprintf( stdout, "%c %d\n", '%', n_threads );
fprintf( stdout, "%c Enter SuperMatrix parameters: sorting, caching, work stealing, data affinity: ", '%' );
scanf( "%d%d%d%d", &sorting, &caching, &work_stealing, &data_affinity );
fprintf( stdout, "%c %s %s %s %s\n\n", '%', ( sorting ? "TRUE" : "FALSE" ), ( caching ? "TRUE" : "FALSE" ), ( work_stealing ? "TRUE" : "FALSE" ), ( data_affinity ? ( data_affinity == 1 ? "FLASH_QUEUE_AFFINITY_2D_BLOCK_CYCLIC" : "FLASH_QUEUE_AFFINITY_OTHER" ) : "FLASH_QUEUE_AFFINITY_NONE" ) );
#ifdef FLA_ENABLE_WINDOWS_BUILD
fprintf( stdout, "%s_%u = [\n", OUTPUT_FILE, nb_alg );
#else
sprintf( output_file_m, "%s/%s_output.m", OUTPUT_PATH, OUTPUT_FILE );
fpp = fopen( output_file_m, "a" );
fprintf( fpp, "%%\n" );
fprintf( fpp, "%% | Matrix Size | FLASH |\n" );
fprintf( fpp, "%% | n x n | GFlops |\n" );
fprintf( fpp, "%% -----------------------------\n" );
fprintf( fpp, "%s_%u = [\n", OUTPUT_FILE, nb_alg );
#endif
FLA_Init();
dtimes = ( double * ) FLA_malloc( n_repeats * sizeof( double ) );
flops = ( double * ) FLA_malloc( n_trials * sizeof( double ) );
FLASH_Queue_set_num_threads( n_threads );
FLASH_Queue_set_sorting( sorting );
FLASH_Queue_set_caching( caching );
FLASH_Queue_set_work_stealing( work_stealing );
FLASH_Queue_set_data_affinity( data_affinity );
for ( i = 0; i < n_trials; i++ )
{
size = begin + i * increment;
FLA_Obj_create( datatype, size, size, 0, 0, &A );
FLA_Obj_create( datatype, size, size, 0, 0, &B );
FLA_Obj_create( datatype, size, 1, 0, 0, &x );
FLA_Obj_create( datatype, size, 1, 0, 0, &b );
FLA_Obj_create( datatype, 1, 1, 0, 0, &b_norm );
for ( j = 0; j < n_repeats; j++ )
{
FLA_Random_matrix( A );
FLA_Random_matrix( B );
FLA_Random_matrix( x );
FLA_Random_matrix( b );
FLA_Symmetrize( uplo, A );
FLA_Symmetrize( uplo, B );
length = ( double ) FLA_Obj_length( B );
FLA_Add_to_diag( &length, B );
FLA_Symv_external( uplo, FLA_ONE, B, x, FLA_ZERO, b );
FLASH_Obj_create_hier_copy_of_flat( A, 1, &nb_alg, &AH );
FLASH_Obj_create_hier_copy_of_flat( B, 1, &nb_alg, &BH );
FLASH_Chol( uplo, BH );
dtime = FLA_Clock();
FLASH_Eig_gest( inv, uplo, AH, BH );
dtime = FLA_Clock() - dtime;
dtimes[j] = dtime;
FLASH_Obj_free( &AH );
FLASH_Obj_free( &BH );
}
dtime = dtimes[0];
for ( j = 1; j < n_repeats; j++ )
dtime = min( dtime, dtimes[j] );
flops[i] = 1.0 * size * size * size / dtime / 1e9;
#ifdef FLA_ENABLE_WINDOWS_BUILD
fprintf( stdout, " %d %6.3f %le\n", size, flops[i], b_norm_value );
#else
fprintf( fpp, " %d %6.3f\n", size, flops[i] );
fprintf( stdout, "Time: %e | GFlops: %6.3f\n", dtime, flops[i] );
fprintf( stdout, "Matrix size: %u x %u | nb_alg: %u\n",
size, size, nb_alg );
fprintf( stdout, "Norm of difference: %le\n\n", b_norm_value );
#endif
FLA_Obj_free( &A );
FLA_Obj_free( &B );
FLA_Obj_free( &x );
FLA_Obj_free( &b );
FLA_Obj_free( &b_norm );
}
#ifdef FLA_ENABLE_WINDOWS_BUILD
fprintf( stdout, "];\n\n" );
#else
fprintf( fpp, "];\n" );
fflush( fpp );
fclose( fpp );
#endif
FLA_free( dtimes );
FLA_free( flops );
FLA_Finalize();
return 0;
}
FLA_Error FLA_Symv( FLA_Uplo uplo, FLA_Obj alpha, FLA_Obj A, FLA_Obj x, FLA_Obj beta, FLA_Obj y )
{
return FLA_Symv_external( uplo, alpha, A, x, beta, y );
}
