int Symm_ru_blk_var6( FLA_Obj A, FLA_Obj B, FLA_Obj C, int nb_alg )
{
FLA_Obj ATL, ATR, A00, A01, A02,
ABL, ABR, A10, A11, A12,
A20, A21, A22;
FLA_Obj BL, BR, B0, B1, B2;
FLA_Obj CL, CR, C0, C1, C2;
int b;
FLA_Part_2x2( A, &ATL, &ATR,
&ABL, &ABR, 0, 0, FLA_BR );
FLA_Part_1x2( B, &BL, &BR, 0, FLA_RIGHT );
FLA_Part_1x2( C, &CL, &CR, 0, FLA_RIGHT );
while ( FLA_Obj_length( ABR ) < FLA_Obj_length( A ) ){
b = min( FLA_Obj_length( ATL ), nb_alg );
FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, &A01, /**/ &A02,
&A10, &A11, /**/ &A12,
/* ************* */ /* ******************** */
ABL, /**/ ABR, &A20, &A21, /**/ &A22,
b, b, FLA_TL );
FLA_Repart_1x2_to_1x3( BL, /**/ BR, &B0, &B1, /**/ &B2,
b, FLA_LEFT );
FLA_Repart_1x2_to_1x3( CL, /**/ CR, &C0, &C1, /**/ &C2,
b, FLA_LEFT );
/*------------------------------------------------------------*/
/*C1 = B0 * A01 + B1 * A11 + B2 * A12' + C1;*/
FLA_Gemm(FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_ONE, B0, A01, FLA_ONE, C1);
FLA_Gemm(FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_ONE, B1, A11, FLA_ONE, C1);
FLA_Gemm(FLA_NO_TRANSPOSE, FLA_TRANSPOSE, FLA_ONE, B2, A12, FLA_ONE, C1);
/*------------------------------------------------------------*/
FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, /**/ A01, A02,
/* ************** */ /* ****************** */
A10, /**/ A11, A12,
&ABL, /**/ &ABR, A20, /**/ A21, A22,
FLA_BR );
FLA_Cont_with_1x3_to_1x2( &BL, /**/ &BR, B0, /**/ B1, B2,
FLA_RIGHT );
FLA_Cont_with_1x3_to_1x2( &CL, /**/ &CR, C0, /**/ C1, C2,
FLA_RIGHT );
}
return FLA_SUCCESS;
}
FLA_Error LU_blk_var4( FLA_Obj A, int nb_alg )
{
FLA_Obj ATL, ATR, A00, A01, A02,
ABL, ABR, A10, A11, A12,
A20, A21, A22;
dim_t b;
FLA_Part_2x2( A, &ATL, &ATR,
&ABL, &ABR, 0, 0, FLA_TL );
while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) ){
b = min( FLA_Obj_length( ABR ), nb_alg );
FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &A01, &A02,
/* ************* */ /* ******************** */
&A10, /**/ &A11, &A12,
ABL, /**/ ABR, &A20, /**/ &A21, &A22,
b, b, FLA_BR );
/*------------------------------------------------------------*/
/* A11 = A11 - A10 * A01 ); */
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
FLA_MINUS_ONE, A10, A01, FLA_ONE, A11 );
/* A11 = LU( A11 ); */
LU_unb_var4( A11 );
/* A12 = A12 - A10 * A02; */
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
FLA_MINUS_ONE, A10, A02, FLA_ONE, A12 );
/* A12 = inv( trilu( A11 ) ) * A12; */
FLA_Trsm( FLA_LEFT, FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_UNIT_DIAG,
FLA_ONE, A11, A12 );
/* A21 = A21 - A20 * A01; */
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
FLA_MINUS_ONE, A20, A01, FLA_ONE, A21 );
/* A21 = A21 * inv( triu( A11 ) ); */
FLA_Trsm( FLA_RIGHT, FLA_UPPER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
FLA_ONE, A11, A21 );
/*------------------------------------------------------------*/
FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, A01, /**/ A02,
A10, A11, /**/ A12,
/* ************** */ /* ****************** */
&ABL, /**/ &ABR, A20, A21, /**/ A22,
FLA_TL );
}
return FLA_SUCCESS;
}
int LU_blk_var3( FLA_Obj A, int nb_alg )
{
FLA_Obj ATL, ATR, A00, A01, A02,
ABL, ABR, A10, A11, A12,
A20, A21, A22;
int b;
FLA_Part_2x2( A, &ATL, &ATR,
&ABL, &ABR, 0, 0, FLA_TL );
while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) ){
b = min( FLA_Obj_length( ABR ), nb_alg );
FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &A01, &A02,
/* ************* */ /* ******************** */
&A10, /**/ &A11, &A12,
ABL, /**/ ABR, &A20, /**/ &A21, &A22,
b, b, FLA_BR );
/*------------------------------------------------------------*/
// A01 := inv(L00) * A01
FLA_Trsm( FLA_LEFT, FLA_LOWER_TRIANGULAR,
FLA_NO_TRANSPOSE, FLA_UNIT_DIAG,
FLA_ONE, A00, A01 );
// A11 := LU(A11 - A10 * A01)
FLA_Gemm(FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
FLA_MINUS_ONE, A10, A01, FLA_ONE, A11);
LU_unb_var3(A11);
// A21 := (A21 - A20 * A01) * inv(U11)
FLA_Gemm(FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
FLA_MINUS_ONE, A20, A01, FLA_ONE, A21);
FLA_Trsm( FLA_RIGHT, FLA_UPPER_TRIANGULAR,
FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
FLA_ONE, A11, A21);
/*------------------------------------------------------------*/
FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, A01, /**/ A02,
A10, A11, /**/ A12,
/* ************** */ /* ****************** */
&ABL, /**/ &ABR, A20, A21, /**/ A22,
FLA_TL );
}
return FLA_SUCCESS;
}
// ============================================================================
void compute_case1( int m, int n, int k, int l,
FLA_Obj cb_A, FLA_Obj cb_B, FLA_Obj C, int print_data ) {
FLA_Obj slice_A, slice_B;
int datatype, h;
double * buff_cb_A, * buff_cb_B;
// Some initializations.
datatype = FLA_Obj_datatype( cb_A );
buff_cb_A = ( double * ) FLA_Obj_buffer_at_view( cb_A );
buff_cb_B = ( double * ) FLA_Obj_buffer_at_view( cb_B );
// Prepare temporal slices.
FLA_Obj_create_without_buffer( datatype, m, k, & slice_A );
FLA_Obj_create_without_buffer( datatype, n, k, & slice_B );
// Initialize matrix C for the result.
MyFLA_Obj_set_to_zero( C );
// Show data.
if( print_data == 1 ) {
FLA_Obj_show( " Ci = [ ", C, "%le", " ];" );
FLA_Obj_show( " cb_A = [ ", cb_A, "%le", " ];" );
FLA_Obj_show( " cb_B = [ ", cb_B, "%le", " ];" );
}
// Perform computation.
for( h = 0; h < l; h++ ) {
FLA_Obj_attach_buffer( buff_cb_A + m * k * h, 1, m, & slice_A );
FLA_Obj_attach_buffer( buff_cb_B + n * k * h, 1, n, & slice_B );
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_TRANSPOSE,
FLA_ONE, slice_A, slice_B, FLA_ONE, C );
}
// Remove temporal slices.
FLA_Obj_free_without_buffer( & slice_A );
FLA_Obj_free_without_buffer( & slice_B );
// Show data.
if( print_data == 1 ) {
FLA_Obj_show( " Cf = [ ", C, "%le", " ];" );
}
}
int main(int argc, char *argv[])
{
int
m_input,
m,
p_first, p_last, p_inc,
p,
k_accum,
b_alg,
n_iter_max,
variant,
n_repeats,
i,
n_variants = 2;
char *colors = "brkgmcbrkg";
char *ticks = "o+*xso+*xs";
char m_dim_desc[14];
char m_dim_tag[10];
double max_gflops=6.0;
double
dtime,
gflops,
diff1, diff2;
FLA_Datatype datatype, dt_real;
FLA_Obj
A, l, Q, Ql, TT, r, d, e, A_orig, G, R, W2, de, alpha;
FLA_Init();
fprintf( stdout, "%c number of repeats:", '%' );
scanf( "%d", &n_repeats );
fprintf( stdout, "%c %d\n", '%', n_repeats );
fprintf( stdout, "%c enter n_iter_max (per eigenvalue): ", '%' );
scanf( "%d", &n_iter_max );
fprintf( stdout, "%c %d\n", '%', n_iter_max );
fprintf( stdout, "%c enter number of sets of Givens rotations to accumulate:", '%' );
scanf( "%d", &k_accum );
fprintf( stdout, "%c %d\n", '%', k_accum );
fprintf( stdout, "%c enter blocking size for application of G:", '%' );
scanf( "%d", &b_alg );
fprintf( stdout, "%c %d\n", '%', b_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 (-1 means bind to problem size): ", '%' );
scanf( "%d", &m_input );
fprintf( stdout, "%c %d\n", '%', m_input );
fprintf( stdout, "\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 );
}
for ( p = p_first, i = 1; p <= p_last; p += p_inc, i += 1 )
{
m = m_input;
if( m < 0 ) m = p / abs(m_input);
//datatype = FLA_FLOAT;
//datatype = FLA_DOUBLE;
//datatype = FLA_COMPLEX;
datatype = FLA_DOUBLE_COMPLEX;
FLA_Obj_create( datatype, m, m, 0, 0, &A );
FLA_Obj_create( datatype, m, m, 0, 0, &A_orig );
FLA_Obj_create( datatype, m, m, 0, 0, &Q );
FLA_Obj_create( datatype, m, m, 0, 0, &Ql );
FLA_Obj_create( datatype, m, 1, 0, 0, &r );
FLA_Obj_create( datatype, m, m, 0, 0, &W2 );
FLA_Obj_create( datatype, m-1, k_accum, 0, 0, &G );
dt_real = FLA_Obj_datatype_proj_to_real( A );
FLA_Obj_create( dt_real, m, 1, 0, 0, &l );
FLA_Obj_create( dt_real, m, 1, 0, 0, &d );
FLA_Obj_create( dt_real, m-1, 1, 0, 0, &e );
FLA_Obj_create( dt_real, m, m, 0, 0, &R );
FLA_Obj_create( dt_real, 1, 1, 0, 0, &alpha );
*FLA_DOUBLE_PTR( alpha ) = 1.0 / ( sqrt( sqrt( (double) m ) ) );
FLA_Random_unitary_matrix( Q );
//FLA_Fill_with_uniform_dist( FLA_ONE, l );
//FLA_Fill_with_inverse_dist( FLA_ONE, l );
FLA_Fill_with_geometric_dist( alpha, l );
{
FLA_Copy( Q, Ql );
FLA_Apply_diag_matrix( FLA_RIGHT, FLA_NO_CONJUGATE, l, Ql );
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
FLA_ONE, Ql, Q, FLA_ZERO, A );
FLA_Triangularize( FLA_LOWER_TRIANGULAR, FLA_NONUNIT_DIAG, A );
FLA_Copy( A, A_orig );
}
FLA_Set( FLA_ZERO, l );
FLA_Set( FLA_ZERO, Q );
FLA_Tridiag_UT_create_T( A, &TT );
FLA_Tridiag_UT( FLA_LOWER_TRIANGULAR, A, TT );
FLA_Tridiag_UT_realify( FLA_LOWER_TRIANGULAR, A, r );
FLA_Tridiag_UT_extract_diagonals( FLA_LOWER_TRIANGULAR, A, d, e );
FLA_Tridiag_UT_form_Q( FLA_LOWER_TRIANGULAR, A, TT );
FLA_Apply_diag_matrix( FLA_RIGHT, FLA_CONJUGATE, r, A );
FLA_Obj_free( &TT );
time_Tevd_v( 0, FLA_ALG_REFERENCE, n_repeats, m, k_accum, b_alg, n_iter_max,
A_orig, d, e, G, R, W2, A, l, &dtime, &diff1, &diff2, &gflops );
fprintf( stdout, "data_REFq( %d, 1:3 ) = [ %d %6.3lf %9.2e %6.2le %6.2le ]; \n", i, p, gflops, dtime, diff1, diff2 );
fflush( stdout );
for ( variant = 1; variant <= n_variants; variant++ ){
fprintf( stdout, "data_var%d( %d, 1:3 ) = [ %d ", variant, i, p );
fflush( stdout );
time_Tevd_v( variant, FLA_ALG_UNB_OPT, n_repeats, m, k_accum, b_alg, n_iter_max,
A_orig, d, e, G, R, W2, A, l, &dtime, &diff1, &diff2, &gflops );
fprintf( stdout, "%6.3lf %9.2e %6.2le %6.2le ", gflops, dtime, diff1, diff2 );
fflush( stdout );
fprintf( stdout, "];\n" );
fflush( stdout );
}
fprintf( stdout, "\n" );
FLA_Obj_free( &A );
FLA_Obj_free( &A_orig );
FLA_Obj_free( &Q );
FLA_Obj_free( &Ql );
FLA_Obj_free( &G );
FLA_Obj_free( &W2 );
FLA_Obj_free( &r );
FLA_Obj_free( &l );
FLA_Obj_free( &d );
FLA_Obj_free( &e );
FLA_Obj_free( &R );
FLA_Obj_free( &alpha );
}
/*
fprintf( stdout, "figure;\n" );
fprintf( stdout, "plot( data_REF( :,1 ), data_REF( :, 2 ), '-' ); \n" );
fprintf( stdout, "hold on;\n" );
for ( i = 1; i <= n_variants; i++ ) {
fprintf( stdout, "plot( data_var%d( :,1 ), data_var%d( :, 2 ), '%c:%c' ); \n",
i, i, colors[ i-1 ], ticks[ i-1 ] );
fprintf( stdout, "plot( data_var%d( :,1 ), data_var%d( :, 4 ), '%c-.%c' ); \n",
i, i, colors[ i-1 ], ticks[ i-1 ] );
}
fprintf( stdout, "legend( ... \n" );
fprintf( stdout, "'Reference', ... \n" );
for ( i = 1; i < n_variants; i++ )
fprintf( stdout, "'unb\\_var%d', 'blk\\_var%d', ... \n", i, i );
fprintf( stdout, "'unb\\_var%d', 'blk\\_var%d' ); \n", i, i );
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 Hevd_lv performance (%s, %s)' );\n",
m_dim_desc, n_dim_desc );
fprintf( stdout, "print -depsc tridiag_%s_%s.eps\n", m_dim_tag, n_dim_tag );
fprintf( stdout, "hold off;\n");
fflush( stdout );
*/
FLA_Finalize( );
return 0;
}
FLA_Error FLA_Svd_uv_unb_var1( dim_t n_iter_max, FLA_Obj A, FLA_Obj s, FLA_Obj U, FLA_Obj V, dim_t k_accum, dim_t b_alg )
{
FLA_Error r_val = FLA_SUCCESS;
FLA_Datatype dt;
FLA_Datatype dt_real;
FLA_Datatype dt_comp;
FLA_Obj scale, T, S, rL, rR, d, e, G, H;
dim_t m_A, n_A;
dim_t min_m_n;
dim_t n_GH;
double crossover_ratio = 17.0 / 9.0;
n_GH = k_accum;
m_A = FLA_Obj_length( A );
n_A = FLA_Obj_width( A );
min_m_n = FLA_Obj_min_dim( A );
dt = FLA_Obj_datatype( A );
dt_real = FLA_Obj_datatype_proj_to_real( A );
dt_comp = FLA_Obj_datatype_proj_to_complex( A );
// Create matrices to hold block Householder transformations.
FLA_Bidiag_UT_create_T( A, &T, &S );
// Create vectors to hold the realifying scalars.
FLA_Obj_create( dt, min_m_n, 1, 0, 0, &rL );
FLA_Obj_create( dt, min_m_n, 1, 0, 0, &rR );
// Create vectors to hold the diagonal and sub-diagonal.
FLA_Obj_create( dt_real, min_m_n, 1, 0, 0, &d );
FLA_Obj_create( dt_real, min_m_n-1, 1, 0, 0, &e );
// Create matrices to hold the left and right Givens scalars.
FLA_Obj_create( dt_comp, min_m_n-1, n_GH, 0, 0, &G );
FLA_Obj_create( dt_comp, min_m_n-1, n_GH, 0, 0, &H );
// Create a real scaling factor.
FLA_Obj_create( dt_real, 1, 1, 0, 0, &scale );
// Compute a scaling factor; If none is needed, sigma will be set to one.
FLA_Svd_compute_scaling( A, scale );
// Scale the matrix if scale is non-unit.
if ( !FLA_Obj_equals( scale, FLA_ONE ) )
FLA_Scal( scale, A );
if ( m_A < crossover_ratio * n_A )
{
// Reduce the matrix to bidiagonal form.
// Apply scalars to rotate elements on the superdiagonal to the real domain.
// Extract the diagonal and superdiagonal from A.
FLA_Bidiag_UT( A, T, S );
FLA_Bidiag_UT_realify( A, rL, rR );
FLA_Bidiag_UT_extract_real_diagonals( A, d, e );
// Form U and V.
FLA_Bidiag_UT_form_U( A, T, U );
FLA_Bidiag_UT_form_V( A, S, V );
// Apply the realifying scalars in rL and rR to U and V, respectively.
{
FLA_Obj UL, UR;
FLA_Obj VL, VR;
FLA_Part_1x2( U, &UL, &UR, min_m_n, FLA_LEFT );
FLA_Part_1x2( V, &VL, &VR, min_m_n, FLA_LEFT );
FLA_Apply_diag_matrix( FLA_RIGHT, FLA_CONJUGATE, rL, UL );
FLA_Apply_diag_matrix( FLA_RIGHT, FLA_NO_CONJUGATE, rR, VL );
}
// Perform a singular value decomposition on the bidiagonal matrix.
r_val = FLA_Bsvd_v_opt_var1( n_iter_max, d, e, G, H, U, V, b_alg );
}
else // if ( crossover_ratio * n_A <= m_A )
{
FLA_Obj TQ, R;
FLA_Obj AT,
AB;
FLA_Obj UL, UR;
// Perform a QR factorization on A and form Q in U.
FLA_QR_UT_create_T( A, &TQ );
FLA_QR_UT( A, TQ );
FLA_QR_UT_form_Q( A, TQ, U );
FLA_Obj_free( &TQ );
// Set the lower triangle of R to zero and then copy the upper
// triangle of A to R.
FLA_Part_2x1( A, &AT,
&AB, n_A, FLA_TOP );
FLA_Obj_create( dt, n_A, n_A, 0, 0, &R );
FLA_Setr( FLA_LOWER_TRIANGULAR, FLA_ZERO, R );
FLA_Copyr( FLA_UPPER_TRIANGULAR, AT, R );
// Reduce the matrix to bidiagonal form.
// Apply scalars to rotate elements on the superdiagonal to the real domain.
// Extract the diagonal and superdiagonal from A.
FLA_Bidiag_UT( R, T, S );
FLA_Bidiag_UT_realify( R, rL, rR );
FLA_Bidiag_UT_extract_real_diagonals( R, d, e );
// Form V from right Householder vectors in upper triangle of R.
FLA_Bidiag_UT_form_V( R, S, V );
// Form U in R.
FLA_Bidiag_UT_form_U( R, T, R );
// Apply the realifying scalars in rL and rR to U and V, respectively.
FLA_Apply_diag_matrix( FLA_RIGHT, FLA_CONJUGATE, rL, R );
FLA_Apply_diag_matrix( FLA_RIGHT, FLA_NO_CONJUGATE, rR, V );
// Perform a singular value decomposition on the bidiagonal matrix.
r_val = FLA_Bsvd_v_opt_var1( n_iter_max, d, e, G, H, R, V, b_alg );
// Multiply R into U, storing the result in A and then copying back
// to U.
FLA_Part_1x2( U, &UL, &UR, n_A, FLA_LEFT );
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
FLA_ONE, UL, R, FLA_ZERO, A );
FLA_Copy( A, UL );
FLA_Obj_free( &R );
}
// Copy the converged eigenvalues to the output vector.
FLA_Copy( d, s );
// Sort the singular values and singular vectors in descending order.
FLA_Sort_svd( FLA_BACKWARD, s, U, V );
// If the matrix was scaled, rescale the singular values.
if ( !FLA_Obj_equals( scale, FLA_ONE ) )
FLA_Inv_scal( scale, s );
FLA_Obj_free( &scale );
FLA_Obj_free( &T );
FLA_Obj_free( &S );
FLA_Obj_free( &rL );
FLA_Obj_free( &rR );
FLA_Obj_free( &d );
FLA_Obj_free( &e );
FLA_Obj_free( &G );
FLA_Obj_free( &H );
return r_val;
}
FLA_Error FLA_Svd_uv_var2_components( dim_t n_iter_max, dim_t k_accum, dim_t b_alg,
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 )
{
FLA_Error r_val = FLA_SUCCESS;
FLA_Datatype dt;
FLA_Datatype dt_real;
FLA_Datatype dt_comp;
FLA_Obj T, S, rL, rR, d, e, G, H, RG, RH, W;
dim_t m_A, n_A;
dim_t min_m_n;
dim_t n_GH;
double crossover_ratio = 17.0 / 9.0;
double dtime_temp;
n_GH = k_accum;
m_A = FLA_Obj_length( A );
n_A = FLA_Obj_width( A );
min_m_n = FLA_Obj_min_dim( A );
dt = FLA_Obj_datatype( A );
dt_real = FLA_Obj_datatype_proj_to_real( A );
dt_comp = FLA_Obj_datatype_proj_to_complex( A );
// If the matrix is a scalar, then the SVD is easy.
if ( min_m_n == 1 )
{
FLA_Copy( A, s );
FLA_Set_to_identity( U );
FLA_Set_to_identity( V );
return FLA_SUCCESS;
}
// Create matrices to hold block Householder transformations.
FLA_Bidiag_UT_create_T( A, &T, &S );
// Create vectors to hold the realifying scalars.
FLA_Obj_create( dt, min_m_n, 1, 0, 0, &rL );
FLA_Obj_create( dt, min_m_n, 1, 0, 0, &rR );
// Create vectors to hold the diagonal and sub-diagonal.
FLA_Obj_create( dt_real, min_m_n, 1, 0, 0, &d );
FLA_Obj_create( dt_real, min_m_n-1, 1, 0, 0, &e );
// Create matrices to hold the left and right Givens scalars.
FLA_Obj_create( dt_comp, min_m_n-1, n_GH, 0, 0, &G );
FLA_Obj_create( dt_comp, min_m_n-1, n_GH, 0, 0, &H );
// Create matrices to hold the left and right Givens matrices.
FLA_Obj_create( dt_real, min_m_n, min_m_n, 0, 0, &RG );
FLA_Obj_create( dt_real, min_m_n, min_m_n, 0, 0, &RH );
FLA_Obj_create( dt, m_A, n_A, 0, 0, &W );
if ( m_A >= n_A )
{
if ( m_A < crossover_ratio * n_A )
{
dtime_temp = FLA_Clock();
{
// Reduce the matrix to bidiagonal form.
// Apply scalars to rotate elements on the sub-diagonal to the real domain.
// Extract the diagonal and sub-diagonal from A.
FLA_Bidiag_UT( A, T, S );
FLA_Bidiag_UT_realify( A, rL, rR );
FLA_Bidiag_UT_extract_diagonals( A, d, e );
}
*dtime_bred = FLA_Clock() - dtime_temp;
dtime_temp = FLA_Clock();
{
// Form U and V.
FLA_Bidiag_UT_form_U( A, T, U );
FLA_Bidiag_UT_form_V( A, S, V );
}
*dtime_appq = FLA_Clock() - dtime_temp;
// Apply the realifying scalars in rL and rR to U and V, respectively.
{
FLA_Obj UL, UR;
FLA_Obj VL, VR;
FLA_Part_1x2( U, &UL, &UR, min_m_n, FLA_LEFT );
FLA_Part_1x2( V, &VL, &VR, min_m_n, FLA_LEFT );
FLA_Apply_diag_matrix( FLA_RIGHT, FLA_CONJUGATE, rL, UL );
FLA_Apply_diag_matrix( FLA_RIGHT, FLA_NO_CONJUGATE, rR, VL );
}
dtime_temp = FLA_Clock();
{
// Perform a singular value decomposition on the bidiagonal matrix.
r_val = FLA_Bsvd_v_opt_var2( n_iter_max, d, e, G, H, RG, RH, W, U, V, b_alg );
}
*dtime_bsvd = FLA_Clock() - dtime_temp;
}
else // if ( crossover_ratio * n_A <= m_A )
{
FLA_Obj TQ, R;
FLA_Obj AT,
AB;
FLA_Obj UL, UR;
//FLA_QR_UT_create_T( A, &TQ );
FLA_Obj_create( dt, 32, n_A, 0, 0, &TQ );
dtime_temp = FLA_Clock();
{
// Perform a QR factorization on A and form Q in U.
FLA_QR_UT( A, TQ );
}
*dtime_qrfa = FLA_Clock() - dtime_temp;
dtime_temp = FLA_Clock();
{
FLA_QR_UT_form_Q( A, TQ, U );
}
*dtime_appq = FLA_Clock() - dtime_temp;
FLA_Obj_free( &TQ );
// Set the lower triangle of R to zero and then copy the upper
// triangle of A to R.
FLA_Part_2x1( A, &AT,
&AB, n_A, FLA_TOP );
FLA_Obj_create( dt, n_A, n_A, 0, 0, &R );
FLA_Setr( FLA_LOWER_TRIANGULAR, FLA_ZERO, R );
FLA_Copyr( FLA_UPPER_TRIANGULAR, AT, R );
dtime_temp = FLA_Clock();
{
// Reduce the matrix to bidiagonal form.
// Apply scalars to rotate elements on the superdiagonal to the real domain.
// Extract the diagonal and superdiagonal from A.
FLA_Bidiag_UT( R, T, S );
FLA_Bidiag_UT_realify( R, rL, rR );
FLA_Bidiag_UT_extract_diagonals( R, d, e );
}
*dtime_bred = FLA_Clock() - dtime_temp;
dtime_temp = FLA_Clock();
{
// Form V from right Householder vectors in upper triangle of R.
FLA_Bidiag_UT_form_V( R, S, V );
// Form U in R.
FLA_Bidiag_UT_form_U( R, T, R );
}
*dtime_appq += FLA_Clock() - dtime_temp;
// Apply the realifying scalars in rL and rR to U and V, respectively.
FLA_Apply_diag_matrix( FLA_RIGHT, FLA_CONJUGATE, rL, R );
FLA_Apply_diag_matrix( FLA_RIGHT, FLA_NO_CONJUGATE, rR, V );
dtime_temp = FLA_Clock();
{
// Perform a singular value decomposition on the bidiagonal matrix.
r_val = FLA_Bsvd_v_opt_var2( n_iter_max, d, e, G, H, RG, RH, W, R, V, b_alg );
}
*dtime_bsvd = FLA_Clock() - dtime_temp;
dtime_temp = FLA_Clock();
{
// Multiply R into U, storing the result in A and then copying back
// to U.
FLA_Part_1x2( U, &UL, &UR, n_A, FLA_LEFT );
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
FLA_ONE, UL, R, FLA_ZERO, A );
FLA_Copy( A, UL );
}
*dtime_gemm = FLA_Clock() - dtime_temp;
FLA_Obj_free( &R );
}
}
else // if ( m_A < n_A )
{
FLA_Check_error_code( FLA_NOT_YET_IMPLEMENTED );
}
// Copy the converged eigenvalues to the output vector.
FLA_Copy( d, s );
// Sort the singular values and singular vectors in descending order.
FLA_Sort_svd( FLA_BACKWARD, s, U, V );
FLA_Obj_free( &T );
FLA_Obj_free( &S );
FLA_Obj_free( &rL );
FLA_Obj_free( &rR );
FLA_Obj_free( &d );
FLA_Obj_free( &e );
FLA_Obj_free( &G );
FLA_Obj_free( &H );
FLA_Obj_free( &RG );
FLA_Obj_free( &RH );
FLA_Obj_free( &W );
return r_val;
}
int Symm_blk_var5( FLA_Obj A, FLA_Obj B, FLA_Obj C, int nb_alg )
{
FLA_Obj ATL, ATR, A00, A01, A02,
ABL, ABR, A10, A11, A12,
A20, A21, A22;
FLA_Obj BT, B0,
BB, B1,
B2;
FLA_Obj CT, C0,
CB, C1,
C2;
int b;
FLA_Part_2x2( A, &ATL, &ATR,
&ABL, &ABR, 0, 0, FLA_TL );
FLA_Part_2x1( B, &BT,
&BB, 0, FLA_TOP );
FLA_Part_2x1( C, &CT,
&CB, 0, FLA_TOP );
while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) ){
b = min( FLA_Obj_length( ABR ), nb_alg );
FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &A01, &A02,
/* ************* */ /* ******************** */
&A10, /**/ &A11, &A12,
ABL, /**/ ABR, &A20, /**/ &A21, &A22,
b, b, FLA_BR );
FLA_Repart_2x1_to_3x1( BT, &B0,
/* ** */ /* ** */
&B1,
BB, &B2, b, FLA_BOTTOM );
FLA_Repart_2x1_to_3x1( CT, &C0,
/* ** */ /* ** */
&C1,
CB, &C2, b, FLA_BOTTOM );
/*------------------------------------------------------------*/
// C2 = C2 + A21*B1;
FLA_Gemm(FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_ONE, A21, B1, FLA_ONE, C2);
// C1 = C1 + A11*B1 + A21^T*B2;
// FLA_Gemm(FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_ONE, A11, B1, FLA_ONE, C1);
FLA_Symm(FLA_LEFT, FLA_LOWER_TRIANGULAR, FLA_ONE, A11, B1, FLA_ONE, C1);
FLA_Gemm(FLA_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_ONE, A21, B2, FLA_ONE, C1);
/*------------------------------------------------------------*/
FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, A01, /**/ A02,
A10, A11, /**/ A12,
/* ************** */ /* ****************** */
&ABL, /**/ &ABR, A20, A21, /**/ A22,
FLA_TL );
FLA_Cont_with_3x1_to_2x1( &BT, B0,
B1,
/* ** */ /* ** */
&BB, B2, FLA_TOP );
FLA_Cont_with_3x1_to_2x1( &CT, C0,
C1,
/* ** */ /* ** */
&CB, C2, FLA_TOP );
}
return FLA_SUCCESS;
}
void FLA_Gemm_kernel( FLA_Obj alpha, FLA_Obj packed_A,
FLA_Obj packed_B, FLA_Obj packed_C )
{
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, alpha, packed_A, packed_B,
FLA_ONE, packed_C );
}
void time_Gemm(
int param_combo, int type, int nrepeats, int m, int k, int n,
FLA_Obj A, FLA_Obj B, FLA_Obj C, FLA_Obj C_ref,
double *dtime, double *diff, double *gflops )
{
int
irep;
double
dtime_old = 1.0e9;
FLA_Obj
C_old;
if ( param_combo != 4 )
{
*gflops = 0.0;
*diff = 0.0;
return;
}
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, C, &C_old );
FLA_Copy_external( C, C_old );
for ( irep = 0 ; irep < nrepeats; irep++ ){
FLA_Copy_external( C_old, C );
*dtime = FLA_Clock();
switch( param_combo ){
// Time parameter combination 0
case 0:{
switch( type ){
case FLA_ALG_REFERENCE:
REF_Gemm( FLA_CONJ_TRANSPOSE, FLA_CONJ_TRANSPOSE, FLA_ONE, A, B, FLA_ZERO, C );
break;
case FLA_ALG_FRONT:
FLA_Gemm( FLA_CONJ_TRANSPOSE, FLA_CONJ_TRANSPOSE, FLA_ONE, A, B, FLA_ZERO, C );
break;
default:
printf("trouble\n");
}
break;
}
// Time parameter combination 1
case 1:{
switch( type ){
case FLA_ALG_REFERENCE:
REF_Gemm( FLA_CONJ_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_ONE, A, B, FLA_ZERO, C );
break;
case FLA_ALG_FRONT:
FLA_Gemm( FLA_CONJ_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_ONE, A, B, FLA_ZERO, C );
break;
default:
printf("trouble\n");
}
break;
}
// Time parameter combination 2
case 2:{
switch( type ){
case FLA_ALG_REFERENCE:
REF_Gemm( FLA_CONJ_TRANSPOSE, FLA_TRANSPOSE, FLA_ONE, A, B, FLA_ZERO, C );
break;
case FLA_ALG_FRONT:
FLA_Gemm( FLA_CONJ_TRANSPOSE, FLA_TRANSPOSE, FLA_ONE, A, B, FLA_ZERO, C );
break;
default:
printf("trouble\n");
}
break;
}
// Time parameter combination 3
case 3:{
switch( type ){
case FLA_ALG_REFERENCE:
REF_Gemm( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE, FLA_ONE, A, B, FLA_ZERO, C );
break;
case FLA_ALG_FRONT:
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE, FLA_ONE, A, B, FLA_ZERO, C );
break;
default:
printf("trouble\n");
}
break;
}
// Time parameter combination 4
case 4:{
switch( type ){
case FLA_ALG_REFERENCE:
REF_Gemm( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_ONE, A, B, FLA_ZERO, C );
break;
case FLA_ALG_FRONT:
//FLA_Gemm( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_ONE, A, B, FLA_ZERO, C );
//FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_ONE, A, B, FLA_ZERO, C );
FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_ONE, A, B, FLA_ONE, C );
break;
default:
printf("trouble\n");
}
break;
}
// Time parameter combination 5
case 5:{
switch( type ){
case FLA_ALG_REFERENCE:
REF_Gemm( FLA_NO_TRANSPOSE, FLA_TRANSPOSE, FLA_ONE, A, B, FLA_ZERO, C );
break;
case FLA_ALG_FRONT:
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_TRANSPOSE, FLA_ONE, A, B, FLA_ZERO, C );
break;
default:
printf("trouble\n");
}
break;
}
// Time parameter combination 6
case 6:{
switch( type ){
case FLA_ALG_REFERENCE:
REF_Gemm( FLA_TRANSPOSE, FLA_CONJ_TRANSPOSE, FLA_ONE, A, B, FLA_ZERO, C );
break;
case FLA_ALG_FRONT:
FLA_Gemm( FLA_TRANSPOSE, FLA_CONJ_TRANSPOSE, FLA_ONE, A, B, FLA_ZERO, C );
break;
default:
printf("trouble\n");
}
break;
}
// Time parameter combination 7
case 7:{
switch( type ){
case FLA_ALG_REFERENCE:
REF_Gemm( FLA_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_ONE, A, B, FLA_ZERO, C );
break;
case FLA_ALG_FRONT:
FLA_Gemm( FLA_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_ONE, A, B, FLA_ZERO, C );
break;
default:
printf("trouble\n");
}
break;
}
// Time parameter combination 8
case 8:{
switch( type ){
case FLA_ALG_REFERENCE:
REF_Gemm( FLA_TRANSPOSE, FLA_TRANSPOSE, FLA_ONE, A, B, FLA_ZERO, C );
break;
case FLA_ALG_FRONT:
FLA_Gemm( FLA_TRANSPOSE, FLA_TRANSPOSE, FLA_ONE, A, B, FLA_ZERO, C );
break;
default:
printf("trouble\n");
}
break;
}
}
*dtime = FLA_Clock() - *dtime;
dtime_old = min( *dtime, dtime_old );
}
/*
if ( type == FLA_ALG_REFERENCE )
{
FLA_Copy_external( C, C_ref );
*diff = 0.0;
}
else
{
*diff = FLA_Max_elemwise_diff( C, C_ref );
}
*/
*gflops = 2.0 * m * k * n /
dtime_old /
1.0e9;
if ( param_combo == 0 ||
param_combo == 1 ||
param_combo == 2 ||
param_combo == 3 ||
param_combo == 6 )
*gflops *= 4.0;
*dtime = dtime_old;
FLA_Copy_external( C_old, C );
FLA_Obj_free( &C_old );
}
void time_Tevd_v(
int variant, int type, int n_repeats, int m, int k_accum, int b_alg, int n_iter_max,
FLA_Obj A_orig, FLA_Obj d, FLA_Obj e, FLA_Obj G, FLA_Obj R, FLA_Obj W, FLA_Obj A, FLA_Obj l,
double *dtime, double *diff1, double* diff2, double *gflops )
{
int irep;
double
k, dtime_old = 1.0e9;
FLA_Obj
A_save, G_save, d_save, e_save;
if (
//( variant == 0 ) ||
//( variant == 1 && type == FLA_ALG_UNB_OPT ) ||
//( variant == 2 && type == FLA_ALG_UNB_OPT ) ||
FALSE
)
{
*dtime = 0.0;
*gflops = 0.0;
*diff1 = 0.0;
*diff2 = 0.0;
return;
}
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &A_save );
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, G, &G_save );
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, d, &d_save );
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, e, &e_save );
FLA_Copy_external( A, A_save );
FLA_Copy_external( G, G_save );
FLA_Copy_external( d, d_save );
FLA_Copy_external( e, e_save );
for ( irep = 0 ; irep < n_repeats; irep++ ){
FLA_Copy_external( A_save, A );
FLA_Copy_external( G_save, G );
FLA_Copy_external( d_save, d );
FLA_Copy_external( e_save, e );
*dtime = FLA_Clock();
switch( variant ){
case 0:
REF_Tevd_v( d, e, A );
break;
// Time variant 1
case 1:
{
switch( type ){
case FLA_ALG_UNB_OPT:
FLA_Tevd_v_opt_var1( n_iter_max, d, e, G, A, b_alg );
break;
}
break;
}
// Time variant 2
case 2:
{
switch( type ){
case FLA_ALG_UNB_OPT:
FLA_Tevd_v_opt_var2( n_iter_max, d, e, G, R, W, A, b_alg );
break;
}
break;
}
}
*dtime = FLA_Clock() - *dtime;
dtime_old = min( *dtime, dtime_old );
}
{
FLA_Obj V, A_rev_evd, norm, eye;
FLA_Copy( d, l );
//FLA_Obj_show( "A_save", A_save, "%9.2e + %9.2e ", "" );
//FLA_Obj_show( "A_evd", A, "%9.2e + %9.2e ", "" );
FLA_Sort_evd( FLA_FORWARD, l, A );
FLA_Obj_create_copy_of( FLA_NO_TRANSPOSE, A, &V );
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &A_rev_evd );
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &eye );
FLA_Obj_create( FLA_Obj_datatype_proj_to_real( A ), 1, 1, 0, 0, &norm );
FLA_Apply_diag_matrix( FLA_RIGHT, FLA_NO_CONJUGATE, l, A );
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
FLA_ONE, A, V, FLA_ZERO, A_rev_evd );
FLA_Triangularize( FLA_LOWER_TRIANGULAR, FLA_NONUNIT_DIAG, A_rev_evd );
/*
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
FLA_ONE, A, D, FLA_ZERO, A_rev_evd );
FLA_Copy( A_rev_evd, D );
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
FLA_ONE, D, V, FLA_ZERO, A_rev_evd );
FLA_Triangularize( FLA_LOWER_TRIANGULAR, FLA_NONUNIT_DIAG, A_rev_evd );
*/
//FLA_Obj_show( "A_rev_evd", A_rev_evd, "%9.2e + %9.2e ", "" );
FLA_Axpy( FLA_MINUS_ONE, A_orig, A_rev_evd );
FLA_Norm_frob( A_rev_evd, norm );
FLA_Obj_extract_real_scalar( norm, diff1 );
//*diff = FLA_Max_elemwise_diff( A_orig, A_rev_evd );
FLA_Set_to_identity( eye );
FLA_Copy( V, A_rev_evd );
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
FLA_ONE, V, A_rev_evd, FLA_MINUS_ONE, eye );
FLA_Norm_frob( eye, norm );
FLA_Obj_extract_real_scalar( norm, diff2 );
/*
FLA_Obj_free( &EL );
FLA_Obj_free( &EU );
FLA_Obj_free( &D );
FLA_Obj_free( &dc );
FLA_Obj_free( &ec );
*/
FLA_Obj_free( &V );
FLA_Obj_free( &A_rev_evd );
FLA_Obj_free( &eye );
FLA_Obj_free( &norm );
}
k = 2.00;
if ( FLA_Obj_is_complex( A ) )
{
*gflops = (
( 4.5 * k * m * m ) +
2.0 * ( 3.0 * k * m * m * m ) ) /
dtime_old / 1e9;
}
else
{
*gflops = (
( 4.5 * k * m * m ) +
1.0 * ( 3.0 * k * m * m * m ) ) /
dtime_old / 1e9;
}
*dtime = dtime_old;
FLA_Copy_external( A_save, A );
FLA_Copy_external( G_save, G );
FLA_Copy_external( d_save, d );
FLA_Copy_external( e_save, e );
FLA_Obj_free( &A_save );
FLA_Obj_free( &G_save );
FLA_Obj_free( &d_save );
FLA_Obj_free( &e_save );
}
void libfla_test_hessut_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_alg_flat = params.b_alg_flat;
double time_min = 1e9;
double time;
unsigned int i;
unsigned int m;
signed int m_input = -1;
FLA_Obj A, T, W, Qh, AQ, QhAQ, norm;
FLA_Obj AT, AB;
FLA_Obj QhT, QhB;
FLA_Obj A_save;
// Determine the dimensions.
if ( m_input < 0 ) m = p_cur * abs(m_input);
else m = p_cur;
// Create the matrices for the current operation.
libfla_test_obj_create( datatype, FLA_NO_TRANSPOSE, sc_str[0], m, m, &A );
if ( impl == FLA_TEST_FLAT_FRONT_END ||
impl == FLA_TEST_FLAT_BLK_VAR )
{
libfla_test_obj_create( datatype, FLA_NO_TRANSPOSE, sc_str[1], b_alg_flat, m, &T );
libfla_test_obj_create( datatype, FLA_NO_TRANSPOSE, sc_str[1], b_alg_flat, m, &W );
}
else
{
libfla_test_obj_create( datatype, FLA_NO_TRANSPOSE, sc_str[1], m, m, &T );
libfla_test_obj_create( datatype, FLA_NO_TRANSPOSE, sc_str[1], m, m, &W );
}
// Initialize the test matrices.
FLA_Random_matrix( A );
// Save the original object contents in a temporary object.
FLA_Obj_create_copy_of( FLA_NO_TRANSPOSE, A, &A_save );
// Create auxiliary matrices to be used when checking the result.
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &Qh );
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &AQ );
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &QhAQ );
// Create a real scalar object to hold the norm of A.
FLA_Obj_create( FLA_Obj_datatype_proj_to_real( A ), 1, 1, 0, 0, &norm );
// 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 )
libfla_test_hessut_cntl_create( var, b_alg_flat );
// Repeat the experiment n_repeats times and record results.
for ( i = 0; i < n_repeats; ++i )
{
FLA_Copy_external( A_save, A );
time = FLA_Clock();
libfla_test_hessut_impl( impl, A, T );
time = FLA_Clock() - time;
time_min = min( time_min, time );
}
// 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 )
libfla_test_hessut_cntl_free();
// Compute the performance of the best experiment repeat.
*perf = ( 10.0 / 3.0 * m * m * m ) / time_min / FLOPS_PER_UNIT_PERF;
if ( FLA_Obj_is_complex( A ) ) *perf *= 4.0;
// Check the result by computing R - Q' A_orig Q.
FLA_Set_to_identity( Qh );
FLA_Part_2x1( Qh, &QhT,
&QhB, 1, FLA_TOP );
FLA_Part_2x1( A, &AT,
&AB, 1, FLA_TOP );
FLA_Apply_Q_UT( FLA_LEFT, FLA_CONJ_TRANSPOSE, FLA_FORWARD, FLA_COLUMNWISE,
AB, T, W, QhB );
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
FLA_ONE, A_save, Qh, FLA_ZERO, AQ );
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
FLA_ONE, Qh, AQ, FLA_ZERO, QhAQ );
FLA_Triangularize( FLA_UPPER_TRIANGULAR, FLA_NONUNIT_DIAG, AB );
*residual = FLA_Max_elemwise_diff( A, QhAQ );
// Free the supporting flat objects.
FLA_Obj_free( &W );
FLA_Obj_free( &Qh );
FLA_Obj_free( &AQ );
FLA_Obj_free( &QhAQ );
FLA_Obj_free( &norm );
FLA_Obj_free( &A_save );
// Free the flat test matrices.
FLA_Obj_free( &A );
FLA_Obj_free( &T );
}
FLA_Error REF_Gemm( FLA_Trans transa, FLA_Trans transb, FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C )
{
FLA_Gemm( transa, transb, alpha, A, B, beta, C );
return 0;
}
void time_Lyap_h(
int variant, int type, int n_repeats, int m, int nb_alg,
FLA_Obj isgn, FLA_Obj A, FLA_Obj C, FLA_Obj C_ref, FLA_Obj scale,
double *dtime, double *diff, double *gflops )
{
int irep;
double dtime_old = 1.0e9;
FLA_Obj C_save, norm;
fla_blocksize_t* bp;
fla_lyap_t* cntl_lyap_unb;
fla_lyap_t* cntl_lyap_opt;
fla_lyap_t* cntl_lyap_blk;
if ( type == FLA_ALG_UNB_OPT && variant > 4 )
{
*gflops = 0.0;
*diff = 0.0;
return;
}
bp = FLA_Blocksize_create( nb_alg, nb_alg, nb_alg, nb_alg );
cntl_lyap_unb = FLA_Cntl_lyap_obj_create( FLA_FLAT,
FLA_UNB_VAR_OFFSET + variant,
NULL,
NULL,
NULL,
NULL,
NULL,
NULL,
NULL,
NULL );
cntl_lyap_opt = FLA_Cntl_lyap_obj_create( FLA_FLAT,
FLA_OPT_VAR_OFFSET + variant,
NULL,
NULL,
NULL,
NULL,
NULL,
NULL,
NULL,
NULL );
cntl_lyap_blk = FLA_Cntl_lyap_obj_create( FLA_FLAT,
FLA_BLK_VAR_OFFSET + variant,
bp,
fla_scal_cntl_blas,
fla_lyap_cntl_leaf,
fla_sylv_cntl,
fla_gemm_cntl_blas,
fla_gemm_cntl_blas,
fla_hemm_cntl_blas,
fla_her2k_cntl_blas );
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, C, &C_save );
FLA_Obj_create( FLA_Obj_datatype_proj_to_real( C ), 1, 1, 0, 0, &norm );
FLA_Copy_external( C, C_save );
for ( irep = 0 ; irep < n_repeats; irep++ )
{
FLA_Copy_external( C_save, C );
*dtime = FLA_Clock();
switch( variant )
{
case 0:
REF_Lyap_h( isgn, A, C, scale );
break;
case 1:
{
switch( type )
{
case FLA_ALG_UNBLOCKED:
FLA_Lyap_h_unb_var1( isgn, A, C );
break;
case FLA_ALG_UNB_OPT:
FLA_Lyap_h_opt_var1( isgn, A, C );
break;
case FLA_ALG_BLOCKED:
FLA_Lyap_h_blk_var1( isgn, A, C, scale, cntl_lyap_blk );
break;
}
break;
}
case 2:
{
switch( type )
{
case FLA_ALG_UNBLOCKED:
FLA_Lyap_h_unb_var2( isgn, A, C );
break;
case FLA_ALG_UNB_OPT:
FLA_Lyap_h_opt_var2( isgn, A, C );
break;
case FLA_ALG_BLOCKED:
FLA_Lyap_h_blk_var2( isgn, A, C, scale, cntl_lyap_blk );
break;
}
break;
}
case 3:
{
switch( type )
{
case FLA_ALG_UNBLOCKED:
FLA_Lyap_h_unb_var3( isgn, A, C );
break;
case FLA_ALG_UNB_OPT:
FLA_Lyap_h_opt_var3( isgn, A, C );
break;
case FLA_ALG_BLOCKED:
FLA_Lyap_h_blk_var3( isgn, A, C, scale, cntl_lyap_blk );
break;
}
break;
}
case 4:
{
switch( type )
{
case FLA_ALG_UNBLOCKED:
FLA_Lyap_h_unb_var4( isgn, A, C );
break;
case FLA_ALG_UNB_OPT:
FLA_Lyap_h_opt_var4( isgn, A, C );
break;
case FLA_ALG_BLOCKED:
FLA_Lyap_h_blk_var4( isgn, A, C, scale, cntl_lyap_blk );
break;
}
break;
}
}
*dtime = FLA_Clock() - *dtime;
dtime_old = min( *dtime, dtime_old );
}
FLA_Blocksize_free( bp );
FLA_Cntl_obj_free( cntl_lyap_unb );
FLA_Cntl_obj_free( cntl_lyap_opt );
FLA_Cntl_obj_free( cntl_lyap_blk );
/*
if ( variant == 0 )
{
FLA_Copy_external( C, C_ref );
*diff = 0.0;
}
else
{
FLA_Hermitianize( FLA_UPPER_TRIANGULAR, C );
*diff = FLA_Max_elemwise_diff( C, C_ref );
}
*/
{
FLA_Obj X, W;
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, C, &X );
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, C, &W );
FLA_Copy( C, X );
FLA_Hermitianize( FLA_UPPER_TRIANGULAR, X );
FLA_Gemm( FLA_CONJ_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_ONE, A, X, FLA_ZERO, W );
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_ONE, X, A, FLA_ONE, W );
FLA_Scal( isgn, W );
/*
if ( variant == 3 && type == FLA_ALG_UNBLOCKED )
{
FLA_Obj_show( "W", W, "%10.3e + %10.3e ", "" );
FLA_Obj_show( "C_save", C_save, "%10.3e + %10.3e ", "" );
}
*/
FLA_Axpy( FLA_MINUS_ONE, C_save, W );
FLA_Norm1( W, norm );
FLA_Obj_extract_real_scalar( norm, diff );
FLA_Obj_free( &X );
FLA_Obj_free( &W );
}
*gflops = ( 2.0 / 3.0 ) * ( m * m * m ) /
dtime_old / 1e9;
if ( FLA_Obj_is_complex( C ) )
*gflops *= 4.0;
*dtime = dtime_old;
FLA_Copy_external( C_save, C );
FLA_Obj_free( &C_save );
FLA_Obj_free( &norm );
}
void time_Hevd_lv_components(
int variant, int type, int n_repeats, int m, int n_iter_max, int k_accum, int b_alg,
FLA_Obj A, FLA_Obj l,
double* dtime, double* diff1, double* diff2, double* gflops,
double* dtime_tred, double* gflops_tred,
double* dtime_tevd, double* gflops_tevd,
double* dtime_appq, double* gflops_appq, int* k_perf )
{
int i;
double k;
double dtime_save = 1.0e9;
double dtime_tred_save = 1.0e9;
double dtime_tevd_save = 1.0e9;
double dtime_appq_save = 1.0e9;
double flops_tred;
double flops_tevd;
double flops_appq;
double mult_tred;
double mult_tevd;
double mult_appq;
FLA_Obj A_save, Z;
if (
( variant == -3 ) ||
( variant == -4 ) ||
( variant == -5 ) ||
//( variant == 0 ) ||
//( variant == -1 ) ||
//( variant == -2 ) ||
//( variant == 1 ) ||
//( variant == 2 ) ||
//( variant == 3 ) ||
//( variant == 4 ) ||
FALSE
)
{
*gflops = 0.0;
*dtime = 0.0;
*diff1 = 0.0;
*diff2 = 0.0;
*dtime_tred = 0.0;
*dtime_tevd = 0.0;
*dtime_appq = 0.0;
*gflops_tred = 0.0;
*gflops_tevd = 0.0;
*gflops_appq = 0.0;
*k_perf = 0;
return;
}
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &A_save );
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &Z );
FLA_Copy_external( A, A_save );
for ( i = 0 ; i < n_repeats; i++ ){
FLA_Copy_external( A_save, A );
*dtime = FLA_Clock();
switch( variant ){
case -3:
{
*k_perf = 0;
REF_Hevd_lv( A, l,
dtime_tred, dtime_tevd, dtime_appq );
break;
}
case -4:
{
*k_perf = 0;
REF_Hevdd_lv( A, l,
dtime_tred, dtime_tevd, dtime_appq );
break;
}
case -5:
{
*k_perf = 0;
REF_Hevdr_lv( A, l, Z,
dtime_tred, dtime_tevd, dtime_appq );
break;
}
case 0:
{
*k_perf = 0;
REF_Hevd_lv_components( A, l,
dtime_tred, dtime_tevd, dtime_appq );
break;
}
case -1:
{
*k_perf = 0;
REF_Hevdd_lv_components( A, l,
dtime_tred, dtime_tevd, dtime_appq );
break;
}
case -2:
{
*k_perf = 0;
REF_Hevdr_lv_components( A, l, Z,
dtime_tred, dtime_tevd, dtime_appq );
break;
}
// Time variant 1
case 1:
{
*k_perf = FLA_Hevd_lv_var1_components( n_iter_max, A, l, k_accum, b_alg,
dtime_tred, dtime_tevd, dtime_appq );
break;
}
// Time variant 2
case 2:
{
*k_perf = FLA_Hevd_lv_var2_components( n_iter_max, A, l, k_accum, b_alg,
dtime_tred, dtime_tevd, dtime_appq );
break;
}
}
*dtime = FLA_Clock() - *dtime;
if ( *dtime < dtime_save )
{
dtime_save = *dtime;
dtime_tred_save = *dtime_tred;
dtime_tevd_save = *dtime_tevd;
dtime_appq_save = *dtime_appq;
}
}
*dtime = dtime_save;
*dtime_tred = dtime_tred_save;
*dtime_tevd = dtime_tevd_save;
*dtime_appq = dtime_appq_save;
//if ( variant == -3 || variant == 0 )
//printf( "\ndtime is %9.3e\n", *dtime );
{
FLA_Obj V, A_rev_evd, norm, eye;
if ( variant == -2 || variant == -5 ) FLA_Copy( Z, A );
FLA_Obj_create_copy_of( FLA_NO_TRANSPOSE, A, &V );
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &A_rev_evd );
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &eye );
FLA_Obj_create( FLA_Obj_datatype_proj_to_real( A ), 1, 1, 0, 0, &norm );
FLA_Apply_diag_matrix( FLA_RIGHT, FLA_NO_CONJUGATE, l, A );
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
FLA_ONE, A, V, FLA_ZERO, A_rev_evd );
FLA_Triangularize( FLA_LOWER_TRIANGULAR, FLA_NONUNIT_DIAG, A_rev_evd );
//FLA_Obj_show( "A_rev_evd", A_rev_evd, "%9.2e + %9.2e ", "" );
FLA_Axpy( FLA_MINUS_ONE, A_save, A_rev_evd );
FLA_Norm_frob( A_rev_evd, norm );
FLA_Obj_extract_real_scalar( norm, diff1 );
FLA_Set_to_identity( eye );
FLA_Copy( V, A_rev_evd );
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
FLA_ONE, V, A_rev_evd, FLA_MINUS_ONE, eye );
FLA_Norm_frob( eye, norm );
FLA_Obj_extract_real_scalar( norm, diff2 );
FLA_Obj_free( &V );
FLA_Obj_free( &A_rev_evd );
FLA_Obj_free( &eye );
FLA_Obj_free( &norm );
}
k = 2.00;
flops_tred = ( ( 4.0 / 3.0 ) * m * m * m );
flops_tevd = ( 4.5 * k * m * m +
3.0 * k * m * m * m );
if ( variant == -1 || variant == -2 ||
variant == -4 || variant == -5 )
flops_appq = ( 2.0 * m * m * m );
else
flops_appq = ( 4.0 / 3.0 * m * m * m );
/*
if ( FLA_Obj_is_complex( A ) )
{
*gflops = ( 4.0 * flops_tred +
2.0 * flops_tevd +
4.0 * flops_appq ) / *dtime / 1e9;
*gflops_tred = ( 4.0 * flops_tred ) / *dtime_tred / 1e9;
*gflops_tevd = ( 2.0 * flops_tevd ) / *dtime_tevd / 1e9;
*gflops_appq = ( 4.0 * flops_appq ) / *dtime_appq / 1e9;
}
else
{
*gflops = ( 1.0 * flops_tred +
1.0 * flops_tevd +
1.0 * flops_appq ) / *dtime / 1e9;
*gflops_tred = ( 1.0 * flops_tred ) / *dtime_tred / 1e9;
*gflops_tevd = ( 1.0 * flops_tevd ) / *dtime_tevd / 1e9;
*gflops_appq = ( 1.0 * flops_appq ) / *dtime_appq / 1e9;
}
*/
if ( FLA_Obj_is_complex( A ) )
{
mult_tred = 4.0;
mult_tevd = 2.0;
mult_appq = 4.0;
}
else
{
mult_tred = 1.0;
mult_tevd = 1.0;
mult_appq = 1.0;
}
*gflops = ( mult_tred * flops_tred +
mult_tevd * flops_tevd +
mult_appq * flops_appq ) / *dtime / 1e9;
*gflops_tred = ( mult_tred * flops_tred ) / *dtime_tred / 1e9;
*gflops_tevd = ( mult_tevd * flops_tevd ) / *dtime_tevd / 1e9;
*gflops_appq = ( mult_appq * flops_appq ) / *dtime_appq / 1e9;
FLA_Copy_external( A_save, A );
FLA_Obj_free( &A_save );
FLA_Obj_free( &Z );
}
void time_Bidiag_UT(
int param_combo, int type, int nrepeats, int m, int n,
FLA_Obj A, FLA_Obj tu, FLA_Obj tv, FLA_Obj TU, FLA_Obj TV,
double *dtime, double *diff, double *gflops )
{
int
irep;
double
dtime_old = 1.0e9;
FLA_Obj
A_save, norm;
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &A_save );
FLA_Obj_create( FLA_Obj_datatype_proj_to_real( A ), 1, 1, 0, 0, &norm );
FLA_Copy_external( A, A_save );
for ( irep = 0 ; irep < nrepeats; irep++ ){
FLA_Copy_external( A_save, A );
*dtime = FLA_Clock();
switch( param_combo ){
case 0:
{
switch( type )
{
case FLA_ALG_REFERENCE:
REF_Bidiag_UT( A, tu, tv );
break;
case FLA_ALG_FRONT:
FLA_Bidiag_UT( A, TU, TV );
break;
}
break;
}
}
*dtime = FLA_Clock() - *dtime;
dtime_old = min( *dtime, dtime_old );
}
{
FLA_Obj AL, AR;
FLA_Obj ATL, ATR,
ABL, ABR;
FLA_Obj QU;
FLA_Obj QV, QVL, QVR;
FLA_Obj E, EL, ER;
FLA_Obj F;
FLA_Obj WU, WV, eye;
FLA_Obj tvT,
tvB;
dim_t m_A, n_A, m_TU;
//FLA_Obj_show( "A_save", A_save, "%10.3e", "" );
m_A = FLA_Obj_length( A );
n_A = FLA_Obj_width( A );
m_TU = FLA_Obj_length( TU );
FLA_Obj_create( FLA_Obj_datatype( A ), m_A, m_A, 0, 0, &QU );
FLA_Obj_create( FLA_Obj_datatype( A ), n_A, n_A, 0, 0, &QV );
FLA_Obj_create( FLA_Obj_datatype( A ), m_TU, m_A, 0, 0, &WU );
FLA_Obj_create( FLA_Obj_datatype( A ), m_TU, n_A, 0, 0, &WV );
FLA_Set_to_identity( QU );
FLA_Set_to_identity( QV );
FLA_Part_1x2( QV, &QVL, &QVR, 1, FLA_LEFT );
FLA_Part_1x2( A, &AL, &AR, 1, FLA_LEFT );
FLA_Part_2x2( A, &ATL, &ATR,
&ABL, &ABR, 1, 1, FLA_BL );
FLA_Part_2x1( tv, &tvT,
&tvB, 1, FLA_BOTTOM );
if ( type == FLA_ALG_REFERENCE )
{
if ( FLA_Obj_is_real( A ) )
FLA_Apply_Q_blk_external( FLA_LEFT, FLA_TRANSPOSE, FLA_COLUMNWISE, A, tu, QU );
else
FLA_Apply_Q_blk_external( FLA_LEFT, FLA_CONJ_TRANSPOSE, FLA_COLUMNWISE, A, tu, QU );
//FLA_Apply_Q_blk_external( FLA_RIGHT, FLA_NO_TRANSPOSE, FLA_ROWWISE, AR, tv, QVR );
//
// Need to apply backwards transformation, since vectors are stored columnwise.
// QL? RQ?
//
//FLA_Apply_Q_blk_external( FLA_RIGHT, FLA_NO_TRANSPOSE, FLA_ROWWISE, ATR, tvT, QVR );
//FLA_Apply_Q_blk_external( FLA_RIGHT, FLA_CONJ_TRANSPOSE, FLA_ROWWISE, ATR, tvT, QVR );
//FLA_Apply_Q_blk_external( FLA_RIGHT, FLA_CONJ_TRANSPOSE, FLA_ROWWISE, AR, tvT, QVR );
}
else
{
FLA_Apply_Q_UT( FLA_LEFT, FLA_CONJ_TRANSPOSE, FLA_FORWARD, FLA_COLUMNWISE, A, TU, WU, QU );
FLA_Apply_Q_UT( FLA_RIGHT, FLA_NO_TRANSPOSE, FLA_FORWARD, FLA_ROWWISE, AR, TV, WV, QVR );
}
/*
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &eye );
FLA_Set_to_identity( eye );
//FLA_Gemm( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
// FLA_ONE, QV, QV, FLA_MINUS_ONE, eye );
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
FLA_ONE, QU, QU, FLA_MINUS_ONE, eye );
FLA_Obj_show( "eye", eye, "%10.3e", "" );
FLA_Norm_frob( eye, norm );
FLA_Obj_extract_real_scalar( norm, diff );
FLA_Obj_free( &eye );
*/
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &E );
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &F );
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
FLA_ONE, A_save, QV, FLA_ZERO, E );
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
FLA_ONE, QU, E, FLA_ZERO, F );
//FLA_Obj_show( "A_save", A_save, "%10.3e", "" );
FLA_Copy( A, E );
FLA_Triangularize( FLA_UPPER_TRIANGULAR, FLA_NONUNIT_DIAG, E );
FLA_Part_1x2( E, &EL, &ER, 1, FLA_LEFT );
FLA_Triangularize( FLA_LOWER_TRIANGULAR, FLA_NONUNIT_DIAG, ER );
//FLA_Obj_show( "B", E, "%10.3e", "" );
//FLA_Obj_show( "Q'AV", F, "%10.3e", "" );
//FLA_Obj_show( "B", E, "%10.3e + %10.3e ", "" );
//FLA_Obj_show( "Q'AV", F, "%10.3e + %10.3e ", "" );
*diff = FLA_Max_elemwise_diff( E, F );
FLA_Obj_free( &E );
FLA_Obj_free( &F );
FLA_Obj_free( &QU );
FLA_Obj_free( &QV );
FLA_Obj_free( &WU );
FLA_Obj_free( &WV );
}
*gflops = 4.0 * n * n * ( m - n / 3.0 ) /
dtime_old / 1e9;
if ( FLA_Obj_is_complex( A ) )
*gflops *= 4.0;
*dtime = dtime_old;
FLA_Copy_external( A_save, A );
FLA_Obj_free( &A_save );
FLA_Obj_free( &norm );
}
// ============================================================================
void compute_case2b( int size_a, int size_b, int size_c, int size_d,
int size_i, int size_j, FLA_Obj cb_A, FLA_Obj cb_B, FLA_Obj cb_C,
int print_data ) {
FLA_Obj slice_A, slice_B, slice_C;
int datatype, size_ab, size_abc, size_ia, size_iaj, size_jc, size_jci,
iter_a, iter_b, iter_c, iter_d, iter_i, iter_j,
ii, jj, ldim_slice_B;
size_t idx_A, idx_B, idx_C;
double * buff_cb_A, * buff_cb_B, * buff_cb_C, * buff_slice_B;
// Some initializations.
datatype = FLA_Obj_datatype( cb_A );
buff_cb_A = ( double * ) FLA_Obj_buffer_at_view( cb_A );
buff_cb_B = ( double * ) FLA_Obj_buffer_at_view( cb_B );
buff_cb_C = ( double * ) FLA_Obj_buffer_at_view( cb_C );
size_ab = size_a * size_b;
size_abc = size_a * size_b * size_c;
size_ia = size_i * size_a;
size_iaj = size_i * size_a * size_j;
size_jc = size_j * size_c;
size_jci = size_j * size_c * size_i;
// Show data.
if( print_data == 1 ) {
FLA_Obj_show( " cb_A_i = [ ", cb_A, "%le", " ];" );
FLA_Obj_show( " cb_B_i = [ ", cb_B, "%le", " ];" );
FLA_Obj_show( " cb_C_i = [ ", cb_C, "%le", " ];" );
}
// Prepare temporal slices without buffer.
FLA_Obj_create_without_buffer( datatype, size_i, size_a, & slice_A );
FLA_Obj_create( datatype, size_i, size_d, 0, 0, & slice_B );
FLA_Obj_create_without_buffer( datatype, size_a, size_d, & slice_C );
// Perform computation.
for( iter_b = 0; iter_b < size_b; iter_b++ ) {
for( iter_c = 0; iter_c < size_c; iter_c++ ) {
iter_a = 0;
iter_d = 0;
iter_i = 0;
idx_C = ( ( size_t ) iter_a ) +
( ( size_t ) iter_b * size_a ) +
( ( size_t ) iter_c * size_ab ) +
( ( size_t ) iter_d * size_abc ),
FLA_Obj_attach_buffer( & buff_cb_C[ idx_C ], 1, size_abc, & slice_C );
MyFLA_Obj_set_to_zero( slice_C );
for( iter_j = 0; iter_j < size_j; iter_j++ ) {
// Define Ai.
idx_A = ( ( size_t ) iter_i ) +
( ( size_t ) iter_a * size_i ) +
( ( size_t ) iter_j * size_ia ) +
( ( size_t ) iter_b * size_iaj );
FLA_Obj_attach_buffer( & buff_cb_A[ idx_A ], 1, size_i, & slice_A );
// Define Bi.
buff_slice_B = ( double * ) FLA_Obj_buffer_at_view( slice_B );
ldim_slice_B = FLA_Obj_col_stride( slice_B );
for( jj = 0; jj < size_d; jj++ ) {
for( ii = 0; ii < size_i; ii++ ) {
idx_B = ( ( size_t ) iter_j ) +
( ( size_t ) iter_c * size_j ) +
( ( size_t ) ii * size_jc ) +
( ( size_t ) jj * size_jci );
buff_slice_B[ ii + jj * ldim_slice_B ] = buff_cb_B[ idx_B ];
}
}
// Compute Ai' * Bi.
FLA_Gemm( FLA_TRANSPOSE, FLA_NO_TRANSPOSE,
FLA_ONE, slice_A, slice_B, FLA_ONE, slice_C );
}
}
}
// Show data.
if( print_data == 1 ) {
FLA_Obj_show( " cb_A_f = [ ", cb_A, "%le", " ];" );
FLA_Obj_show( " cb_B_f = [ ", cb_B, "%le", " ];" );
FLA_Obj_show( " cb_C_f = [ ", cb_C, "%le", " ];" );
}
// Remove temporal slices.
FLA_Obj_free_without_buffer( & slice_A );
FLA_Obj_free( & slice_B );
FLA_Obj_free_without_buffer( & slice_C );
}
int Trsm_blk_var1( FLA_Obj L, FLA_Obj B, int nb_alg )
{
FLA_Obj LTL, LTR, L00, L01, L02,
LBL, LBR, L10, L11, L12,
L20, L21, L22;
FLA_Obj BT, B0,
BB, B1,
B2;
int b;
FLA_Part_2x2( L, <L, <R,
&LBL, &LBR, 0, 0, FLA_TL );
FLA_Part_2x1( B, &BT,
&BB, 0, FLA_TOP );
while ( FLA_Obj_length( LTL ) < FLA_Obj_length( L ) ){
b = min( FLA_Obj_length( LBR ), nb_alg );
FLA_Repart_2x2_to_3x3( LTL, /**/ LTR, &L00, /**/ &L01, &L02,
/* ************* */ /* ******************** */
&L10, /**/ &L11, &L12,
LBL, /**/ LBR, &L20, /**/ &L21, &L22,
b, b, FLA_BR );
FLA_Repart_2x1_to_3x1( BT, &B0,
/* ** */ /* ** */
&B1,
BB, &B2, b, FLA_BOTTOM );
/*------------------------------------------------------------*/
/* B1 = B1 - L10 * B0 */
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
FLA_MINUS_ONE, L10, B0, FLA_ONE, B1 );
/* B1 = inv( L11 ) B1 */
Trsm_unb_var1( L11, B1 );
//Alternatively, try
// FLA_Trsm( FLA_LEFT, FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
// FLA_ONE, L11, B1 );
/*------------------------------------------------------------*/
FLA_Cont_with_3x3_to_2x2( <L, /**/ <R, L00, L01, /**/ L02,
L10, L11, /**/ L12,
/* ************** */ /* ****************** */
&LBL, /**/ &LBR, L20, L21, /**/ L22,
FLA_TL );
FLA_Cont_with_3x1_to_2x1( &BT, B0,
B1,
/* ** */ /* ** */
&BB, B2, FLA_TOP );
}
return FLA_SUCCESS;
}
FLA_Error FLA_Svd_ext_u_unb_var1( FLA_Svd_type jobu, FLA_Svd_type jobv,
dim_t n_iter_max,
FLA_Obj A, FLA_Obj s, FLA_Obj U, FLA_Obj V,
dim_t k_accum,
dim_t b_alg )
{
FLA_Error r_val = FLA_SUCCESS;
FLA_Datatype dt;
FLA_Datatype dt_real;
FLA_Datatype dt_comp;
FLA_Obj scale, T, S, rL, rR, d, e, G, H, C; // C is dummy.
dim_t m_A, n_A, min_m_n;
dim_t n_GH;
double crossover_ratio = 17.0 / 9.0;
FLA_Bool u_is_formed = FALSE,
v_is_formed = FALSE;
int apply_scale;
n_GH = k_accum;
m_A = FLA_Obj_length( A );
n_A = FLA_Obj_width( A );
min_m_n = min( m_A, n_A );
dt = FLA_Obj_datatype( A );
dt_real = FLA_Obj_datatype_proj_to_real( A );
dt_comp = FLA_Obj_datatype_proj_to_complex( A );
// Create matrices to hold block Householder transformations.
FLA_Bidiag_UT_create_T( A, &T, &S );
// Create vectors to hold the realifying scalars.
if ( FLA_Obj_is_complex( A ) )
{
FLA_Obj_create( dt, min_m_n, 1, 0, 0, &rL );
FLA_Obj_create( dt, min_m_n, 1, 0, 0, &rR );
}
// Create vectors to hold the diagonal and sub-diagonal.
FLA_Obj_create( dt_real, min_m_n, 1, 0, 0, &d );
FLA_Obj_create( dt_real, min_m_n-1, 1, 0, 0, &e );
// Create matrices to hold the left and right Givens scalars.
FLA_Obj_create( dt_comp, min_m_n-1, n_GH, 0, 0, &G );
FLA_Obj_create( dt_comp, min_m_n-1, n_GH, 0, 0, &H );
// Create a real scaling factor.
FLA_Obj_create( dt_real, 1, 1, 0, 0, &scale );
// Scale matrix A if necessary.
FLA_Max_abs_value( A, scale );
apply_scale =
( FLA_Obj_gt( scale, FLA_OVERFLOW_SQUARE_THRES ) == TRUE ) -
( FLA_Obj_lt( scale, FLA_UNDERFLOW_SQUARE_THRES ) == TRUE );
if ( apply_scale )
FLA_Scal( apply_scale > 0 ? FLA_SAFE_MIN : FLA_SAFE_INV_MIN, A );
if ( m_A < crossover_ratio * n_A )
{
// Reduce the matrix to bidiagonal form.
// Apply scalars to rotate elements on the superdiagonal to the real domain.
// Extract the diagonal and superdiagonal from A.
FLA_Bidiag_UT( A, T, S );
if ( FLA_Obj_is_complex( A ) )
FLA_Bidiag_UT_realify( A, rL, rR );
FLA_Bidiag_UT_extract_real_diagonals( A, d, e );
// Form U and V.
if ( u_is_formed == FALSE )
{
switch ( jobu )
{
case FLA_SVD_VECTORS_MIN_OVERWRITE:
if ( jobv != FLA_SVD_VECTORS_NONE )
FLA_Bidiag_UT_form_V_ext( FLA_UPPER_TRIANGULAR, A, S, FLA_NO_TRANSPOSE, V );
v_is_formed = TRUE; // For this case, V should be formed here.
U = A;
case FLA_SVD_VECTORS_ALL:
case FLA_SVD_VECTORS_MIN_COPY:
FLA_Bidiag_UT_form_U_ext( FLA_UPPER_TRIANGULAR, A, T, FLA_NO_TRANSPOSE, U );
u_is_formed = TRUE;
break;
case FLA_SVD_VECTORS_NONE:
// Do nothing
break;
}
}
if ( v_is_formed == FALSE )
{
if ( jobv == FLA_SVD_VECTORS_MIN_OVERWRITE )
{
FLA_Bidiag_UT_form_V_ext( FLA_UPPER_TRIANGULAR, A, S, FLA_CONJ_TRANSPOSE, A );
v_is_formed = TRUE; /* and */
V = A; // This V is actually V^H.
// V^H -> V
FLA_Obj_flip_base( &V );
FLA_Obj_flip_view( &V );
if ( FLA_Obj_is_complex( A ) )
FLA_Conjugate( V );
}
else if ( jobv != FLA_SVD_VECTORS_NONE )
{
FLA_Bidiag_UT_form_V_ext( FLA_UPPER_TRIANGULAR, A, S, FLA_NO_TRANSPOSE, V );
v_is_formed = TRUE;
}
}
// For complex matrices, apply realification transformation.
if ( FLA_Obj_is_complex( A ) && jobu != FLA_SVD_VECTORS_NONE )
{
FLA_Obj UL, UR;
FLA_Part_1x2( U, &UL, &UR, min_m_n, FLA_LEFT );
FLA_Apply_diag_matrix( FLA_RIGHT, FLA_CONJUGATE, rL, UL );
}
if ( FLA_Obj_is_complex( A ) && jobv != FLA_SVD_VECTORS_NONE )
{
FLA_Obj VL, VR;
FLA_Part_1x2( V, &VL, &VR, min_m_n, FLA_LEFT );
FLA_Apply_diag_matrix( FLA_RIGHT, FLA_NO_CONJUGATE, rR, VL );
}
// Perform a singular value decomposition on the upper bidiagonal matrix.
r_val = FLA_Bsvd_ext_opt_var1( n_iter_max,
d, e, G, H,
jobu, U, jobv, V,
FALSE, C, // C is not referenced
b_alg );
}
else // if ( crossover_ratio * n_A <= m_A )
{
FLA_Obj TQ, R;
FLA_Obj AT,
AB;
// Perform a QR factorization on A.
FLA_QR_UT_create_T( A, &TQ );
FLA_QR_UT( A, TQ );
// Set the lower triangle of R to zero and then copy the upper
// triangle of A to R.
FLA_Part_2x1( A, &AT,
&AB, n_A, FLA_TOP );
FLA_Obj_create( dt, n_A, n_A, 0, 0, &R );
FLA_Setr( FLA_LOWER_TRIANGULAR, FLA_ZERO, R );
FLA_Copyr( FLA_UPPER_TRIANGULAR, AT, R );
// Form U; if necessary overwrite on A.
if ( u_is_formed == FALSE )
{
switch ( jobu )
{
case FLA_SVD_VECTORS_MIN_OVERWRITE:
U = A;
case FLA_SVD_VECTORS_ALL:
case FLA_SVD_VECTORS_MIN_COPY:
FLA_QR_UT_form_Q( A, TQ, U );
u_is_formed = TRUE;
break;
case FLA_SVD_VECTORS_NONE:
// Do nothing
break;
}
}
FLA_Obj_free( &TQ );
// Reduce the matrix to bidiagonal form.
// Apply scalars to rotate elements on the superdiagonal to the real domain.
// Extract the diagonal and superdiagonal from A.
FLA_Bidiag_UT( R, T, S );
if ( FLA_Obj_is_complex( R ) )
FLA_Bidiag_UT_realify( R, rL, rR );
FLA_Bidiag_UT_extract_real_diagonals( R, d, e );
if ( v_is_formed == FALSE )
{
if ( jobv == FLA_SVD_VECTORS_MIN_OVERWRITE )
{
FLA_Bidiag_UT_form_V_ext( FLA_UPPER_TRIANGULAR, R, S, FLA_CONJ_TRANSPOSE, AT );
v_is_formed = TRUE; /* and */
V = AT; // This V is actually V^H.
// V^H -> V
FLA_Obj_flip_base( &V );
FLA_Obj_flip_view( &V );
if ( FLA_Obj_is_complex( A ) )
FLA_Conjugate( V );
}
else if ( jobv != FLA_SVD_VECTORS_NONE )
{
FLA_Bidiag_UT_form_V_ext( FLA_UPPER_TRIANGULAR, R, S, FLA_NO_TRANSPOSE, V );
v_is_formed = TRUE;
}
}
// Apply householder vectors U in R.
FLA_Bidiag_UT_form_U_ext( FLA_UPPER_TRIANGULAR, R, T, FLA_NO_TRANSPOSE, R );
// Apply the realifying scalars in rL and rR to U and V, respectively.
if ( FLA_Obj_is_complex( A ) && jobu != FLA_SVD_VECTORS_NONE )
{
FLA_Obj RL, RR;
FLA_Part_1x2( R, &RL, &RR, min_m_n, FLA_LEFT );
FLA_Apply_diag_matrix( FLA_RIGHT, FLA_CONJUGATE, rL, RL );
}
if ( FLA_Obj_is_complex( A ) && jobv != FLA_SVD_VECTORS_NONE )
{
FLA_Obj VL, VR;
FLA_Part_1x2( V, &VL, &VR, min_m_n, FLA_LEFT );
FLA_Apply_diag_matrix( FLA_RIGHT, FLA_NO_CONJUGATE, rR, VL );
}
// Perform a singular value decomposition on the bidiagonal matrix.
r_val = FLA_Bsvd_ext_opt_var1( n_iter_max,
d, e, G, H,
jobu, R, jobv, V,
FALSE, C,
b_alg );
// Multiply R into U, storing the result in A and then copying back
// to U.
if ( jobu != FLA_SVD_VECTORS_NONE )
{
FLA_Obj UL, UR;
FLA_Part_1x2( U, &UL, &UR, min_m_n, FLA_LEFT );
if ( jobu == FLA_SVD_VECTORS_MIN_OVERWRITE ||
jobv == FLA_SVD_VECTORS_MIN_OVERWRITE )
{
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, UL, &C );
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
FLA_ONE, UL, R, FLA_ZERO, C );
FLA_Copy( C, UL );
FLA_Obj_free( &C );
}
else
{
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
FLA_ONE, UL, R, FLA_ZERO, A );
FLA_Copy( A, UL );
}
}
FLA_Obj_free( &R );
}
// Copy the converged eigenvalues to the output vector.
FLA_Copy( d, s );
// No sort is required as it is applied on FLA_Bsvd.
if ( apply_scale )
FLA_Scal( apply_scale < 0 ? FLA_SAFE_MIN : FLA_SAFE_INV_MIN, s );
// When V is overwritten, flip it again.
if ( jobv == FLA_SVD_VECTORS_MIN_OVERWRITE )
{
// Always apply conjugation first wrt dimensions used; then, flip base.
if ( FLA_Obj_is_complex( V ) )
FLA_Conjugate( V );
FLA_Obj_flip_base( &V );
}
FLA_Obj_free( &scale );
FLA_Obj_free( &T );
FLA_Obj_free( &S );
if ( FLA_Obj_is_complex( A ) )
{
FLA_Obj_free( &rL );
FLA_Obj_free( &rR );
}
FLA_Obj_free( &d );
FLA_Obj_free( &e );
FLA_Obj_free( &G );
FLA_Obj_free( &H );
return r_val;
}
