FLA_Error REF_Svdd_uv_components( FLA_Obj A, FLA_Obj s, FLA_Obj U, FLA_Obj V,
double* dtime_bred, double* dtime_bsvd, double* dtime_appq,
double* dtime_qrfa, double* dtime_gemm )
/*
{
*dtime_bred = 1;
*dtime_bsvd = 1;
*dtime_appq = 1;
*dtime_qrfa = 1;
*dtime_gemm = 1;
return FLA_Svdd_external( FLA_SVD_VECTORS_ALL, A, s, U, V );
}
*/
{
FLA_Datatype dt_A;
FLA_Datatype dt_A_real;
dim_t m_A, n_A;
dim_t min_m_n;
FLA_Obj tq, tu, tv, d, e, Ur, Vr, W;
FLA_Obj eT, epsilonB;
FLA_Uplo uplo = FLA_UPPER_TRIANGULAR;
double crossover_ratio = 16.0 / 10.0;
double dtime_temp;
dt_A = FLA_Obj_datatype( A );
dt_A_real = FLA_Obj_datatype_proj_to_real( A );
m_A = FLA_Obj_length( A );
n_A = FLA_Obj_width( A );
min_m_n = FLA_Obj_min_dim( A );
FLA_Obj_create( dt_A, min_m_n, 1, 0, 0, &tq );
FLA_Obj_create( dt_A, min_m_n, 1, 0, 0, &tu );
FLA_Obj_create( dt_A, min_m_n, 1, 0, 0, &tv );
FLA_Obj_create( dt_A_real, min_m_n, 1, 0, 0, &d );
FLA_Obj_create( dt_A_real, min_m_n, 1, 0, 0, &e );
FLA_Obj_create( dt_A_real, n_A, n_A, 0, 0, &Ur );
FLA_Obj_create( dt_A_real, n_A, n_A, 0, 0, &Vr );
FLA_Part_2x1( e, &eT,
&epsilonB, 1, FLA_BOTTOM );
if ( m_A >= n_A )
{
if ( m_A < crossover_ratio * n_A )
{
dtime_temp = FLA_Clock();
{
// Reduce to bidiagonal form.
FLA_Bidiag_blk_external( A, tu, tv );
FLA_Bidiag_UT_extract_diagonals( A, d, eT );
}
*dtime_bred = FLA_Clock() - dtime_temp;
dtime_temp = FLA_Clock();
{
// Divide-and-conquor algorithm.
FLA_Bsvdd_external( uplo, d, e, Ur, Vr );
}
*dtime_bsvd = FLA_Clock() - dtime_temp;
dtime_temp = FLA_Clock();
{
// Form U.
FLA_Copy_external( Ur, U );
FLA_Bidiag_apply_U_external( FLA_LEFT, FLA_NO_TRANSPOSE, A, tu, U );
// Form V.
FLA_Copy_external( Vr, V );
FLA_Bidiag_apply_V_external( FLA_RIGHT, FLA_CONJ_TRANSPOSE, A, tv, V );
}
*dtime_appq = FLA_Clock() - dtime_temp;
*dtime_qrfa = 0.0;
*dtime_gemm = 0.0;
}
else
{
FLA_Obj AT,
AB;
FLA_Obj UL, UR;
FLA_Part_2x1( A, &AT,
&AB, n_A, FLA_TOP );
FLA_Part_1x2( U, &UL, &UR, n_A, FLA_LEFT );
// Create a temporary n-by-n matrix R.
FLA_Obj_create( dt_A, n_A, n_A, 0, 0, &W );
dtime_temp = FLA_Clock();
{
// Perform a QR factorization.
FLA_QR_blk_external( A, tq );
FLA_Copyr_external( FLA_LOWER_TRIANGULAR, A, UL );
FLA_Setr( FLA_LOWER_TRIANGULAR, FLA_ZERO, A );
}
*dtime_qrfa = FLA_Clock() - dtime_temp;
dtime_temp = FLA_Clock();
{
// Form Q.
FLA_QR_form_Q_external( U, tq );
}
*dtime_appq = FLA_Clock() - dtime_temp;
dtime_temp = FLA_Clock();
{
// Reduce R to bidiagonal form.
FLA_Bidiag_blk_external( AT, tu, tv );
FLA_Bidiag_UT_extract_diagonals( A, d, eT );
}
*dtime_bred = FLA_Clock() - dtime_temp;
dtime_temp = FLA_Clock();
{
// Divide-and-conquor algorithm.
FLA_Bsvdd_external( uplo, d, e, Ur, Vr );
}
*dtime_bsvd = FLA_Clock() - dtime_temp;
dtime_temp = FLA_Clock();
{
// Form U in W.
FLA_Copy_external( Ur, W );
FLA_Bidiag_apply_U_external( FLA_LEFT, FLA_NO_TRANSPOSE, AT, tu, W );
// Form V.
FLA_Copy_external( Vr, V );
FLA_Bidiag_apply_V_external( FLA_RIGHT, FLA_CONJ_TRANSPOSE, AT, tv, V );
}
*dtime_appq += FLA_Clock() - dtime_temp;
dtime_temp = FLA_Clock();
{
// Multiply R into U, storing the result in A and then copying
// back to U.
FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
FLA_ONE, UL, W, FLA_ZERO, A );
FLA_Copy( A, UL );
}
*dtime_gemm = FLA_Clock() - dtime_temp;
// Free R.
FLA_Obj_free( &W );
}
}
else
{
FLA_Check_error_code( FLA_NOT_YET_IMPLEMENTED );
}
// Copy singular values to output vector.
FLA_Copy( d, s );
// Sort singular values and vectors.
FLA_Sort_svd( FLA_BACKWARD, s, U, V );
FLA_Obj_free( &tq );
FLA_Obj_free( &tu );
FLA_Obj_free( &tv );
FLA_Obj_free( &d );
FLA_Obj_free( &e );
FLA_Obj_free( &Ur );
FLA_Obj_free( &Vr );
return FLA_SUCCESS;
}
int main(int argc, char *argv[])
{
int
datatype,
precision,
nb_alg, bm, bn,
m_input, n_input,
m, n,
p_first, p_last, p_inc,
p,
n_repeats,
param_combo,
i,
n_param_combos = N_PARAM_COMBOS;
char *colors = "brkgmcbrkgmcbrkgmc";
char *ticks = "o+*xso+*xso+*xso+*xs";
char m_dim_desc[14];
char n_dim_desc[14];
char m_dim_tag[10];
char n_dim_tag[10];
double max_gflops=6.0;
double
dtime,
gflops,
diff;
FLA_Obj
A, A_save, A_flat, B, B_ref, T, T_flat, W, t;
FLA_Init( );
fprintf( stdout, "%c number of repeats: ", '%' );
scanf( "%d", &n_repeats );
fprintf( stdout, "%c %d\n", '%', n_repeats );
fprintf( stdout, "%c enter FLASH blocksize: ", '%' );
scanf( "%d", &nb_alg );
fprintf( stdout, "%c %d\n", '%', nb_alg );
fprintf( stdout, "%c enter problem size first, last, inc: ", '%' );
scanf( "%d%d%d", &p_first, &p_last, &p_inc );
fprintf( stdout, "%c %d %d %d\n", '%', p_first, p_last, p_inc );
fprintf( stdout, "%c enter m n (-1 means bind to problem size): ", '%' );
scanf( "%d%d", &m_input, &n_input );
fprintf( stdout, "%c %d %d\n", '%', m_input, n_input );
fprintf( stdout, "\nclear all;\n\n" );
if ( m_input > 0 ) {
sprintf( m_dim_desc, "m = %d", m_input );
sprintf( m_dim_tag, "m%dc", m_input);
}
else if( m_input < -1 ) {
sprintf( m_dim_desc, "m = p/%d", -m_input );
sprintf( m_dim_tag, "m%dp", -m_input );
}
else if( m_input == -1 ) {
sprintf( m_dim_desc, "m = p" );
sprintf( m_dim_tag, "m%dp", 1 );
}
if ( n_input > 0 ) {
sprintf( n_dim_desc, "n = %d", n_input );
sprintf( n_dim_tag, "n%dc", n_input);
}
else if( n_input < -1 ) {
sprintf( n_dim_desc, "n = p/%d", -n_input );
sprintf( n_dim_tag, "n%dp", -n_input );
}
else if( n_input == -1 ) {
sprintf( n_dim_desc, "n = p" );
sprintf( n_dim_tag, "n%dp", 1 );
}
//precision = FLA_SINGLE_PRECISION;
precision = FLA_DOUBLE_PRECISION;
FLASH_Queue_disable();
for ( p = p_first, i = 1; p <= p_last; p += p_inc, i += 1 )
{
m = m_input;
n = n_input;
if( m < 0 ) m = p / abs(m_input);
if( n < 0 ) n = p / abs(n_input);
for ( param_combo = 0; param_combo < n_param_combos; param_combo++ ){
// Determine datatype based on trans argument.
if ( pc_str[param_combo][1] == 'c' )
{
if ( precision == FLA_SINGLE_PRECISION )
datatype = FLA_COMPLEX;
else
datatype = FLA_DOUBLE_COMPLEX;
}
else
{
if ( precision == FLA_SINGLE_PRECISION )
datatype = FLA_FLOAT;
else
datatype = FLA_DOUBLE;
}
bm = nb_alg / 4;
bn = nb_alg;
// If multiplying Q on the left, A is m x m; ...on the right, A is n x n.
if ( pc_str[param_combo][0] == 'l' )
{
FLA_Obj_create( datatype, nb_alg, nb_alg, &A_flat );
FLASH_Obj_create( datatype, nb_alg, nb_alg, 1, &nb_alg, &A );
FLASH_Obj_create( datatype, nb_alg, nb_alg, 1, &nb_alg, &A_save );
FLA_Obj_create( datatype, bm, bn, &T_flat );
FLASH_Obj_create_ext( datatype, bm, bn, 1, &bm, &bn, &T );
FLASH_Obj_create_ext( datatype, bm, n, 1, &bm, &bn, &W );
}
else
{
FLASH_Obj_create( datatype, n, n, 1, &nb_alg, &A );
}
FLASH_Obj_create( datatype, nb_alg, n, 1, &nb_alg, &B );
FLASH_Obj_create( datatype, nb_alg, n, 1, &nb_alg, &B_ref );
FLA_Obj_create( datatype, nb_alg, 1, &t );
FLASH_Random_matrix( A );
FLASH_Random_matrix( B );
fprintf( stdout, "data_applyq_%s( %d, 1:5 ) = [ %d ", pc_str[param_combo], i, p );
fflush( stdout );
FLASH_Copy( A, A_save );
FLASH_Obj_flatten( A, A_flat );
FLA_QR_blk_external( A_flat, t );
FLASH_Obj_hierarchify( A_flat, A );
time_Apply_Q( param_combo, FLA_ALG_REFERENCE, n_repeats, m, n,
A, B, B_ref, t, T, W, &dtime, &diff, &gflops );
fprintf( stdout, "%6.3lf %6.2le ", gflops, diff );
fflush( stdout );
FLASH_Copy( A_save, A );
FLASH_Obj_flatten( A, A_flat );
FLA_QR_UT( A_flat, t, T_flat );
FLASH_Obj_hierarchify( A_flat, A );
FLASH_Obj_hierarchify( T_flat, T );
time_Apply_Q( param_combo, FLA_ALG_FRONT, n_repeats, m, n,
A, B, B_ref, t, T, W, &dtime, &diff, &gflops );
fprintf( stdout, "%6.3lf %6.2le ", gflops, diff );
fflush( stdout );
fprintf( stdout, " ]; \n" );
fflush( stdout );
FLASH_Obj_free( &A );
FLA_Obj_free( &A_flat );
FLASH_Obj_free( &B );
FLASH_Obj_free( &B_ref );
FLA_Obj_free( &t );
FLASH_Obj_free( &T );
FLA_Obj_free( &T_flat );
FLASH_Obj_free( &W );
}
fprintf( stdout, "\n" );
}
fprintf( stdout, "figure;\n" );
fprintf( stdout, "hold on;\n" );
for ( i = 0; i < n_param_combos; i++ ) {
fprintf( stdout, "plot( data_applyq_%s( :,1 ), data_applyq_%s( :, 2 ), '%c:%c' ); \n",
pc_str[i], pc_str[i], colors[ i ], ticks[ i ] );
fprintf( stdout, "plot( data_applyq_%s( :,1 ), data_applyq_%s( :, 4 ), '%c-.%c' ); \n",
pc_str[i], pc_str[i], colors[ i ], ticks[ i ] );
}
fprintf( stdout, "legend( ... \n" );
for ( i = 0; i < n_param_combos; i++ )
fprintf( stdout, "'ref\\_applyq\\_%s', 'fla\\_applyq\\_%s', ... \n", pc_str[i], pc_str[i] );
fprintf( stdout, "'Location', 'SouthEast' ); \n" );
fprintf( stdout, "xlabel( 'problem size p' );\n" );
fprintf( stdout, "ylabel( 'GFLOPS/sec.' );\n" );
fprintf( stdout, "axis( [ 0 %d 0 %.2f ] ); \n", p_last, max_gflops );
fprintf( stdout, "title( 'FLAME applyq front-end performance (%s, %s)' );\n",
m_dim_desc, n_dim_desc );
fprintf( stdout, "print -depsc applyq_front_%s_%s.eps\n", m_dim_tag, n_dim_tag );
fprintf( stdout, "hold off;\n");
fflush( stdout );
FLA_Finalize( );
return 0;
}
FLA_Error REF_QR_UT( FLA_Obj A, FLA_Obj t )
{
return FLA_QR_blk_external( A, t );
}
