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 libfla_test_eig_gest_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;
FLA_Uplo inv;
FLA_Uplo uplo;
FLA_Obj A, B, Y, norm;
FLA_Obj A_save, B_save;
FLA_Obj A_test, B_test, Y_test;
// Determine the dimensions.
if ( m_input < 0 ) m = p_cur / abs(m_input);
else m = p_cur;
// Translate parameter characters to libflame constants.
FLA_Param_map_char_to_flame_inv( &pc_str[pci][0], &inv );
FLA_Param_map_char_to_flame_uplo( &pc_str[pci][1], &uplo );
if ( inv == FLA_NO_INVERSE &&
( ( impl == FLA_TEST_FLAT_UNB_VAR && var == 3 ) ||
( impl == FLA_TEST_FLAT_OPT_VAR && var == 3 ) ||
( impl == FLA_TEST_FLAT_BLK_VAR && var == 3 ) )
)
{
*perf = 0.0;
*residual = 0.0;
return;
}
// Create the matrices for the current operation.
libfla_test_obj_create( datatype, FLA_NO_TRANSPOSE, sc_str[0], m, m, &A );
libfla_test_obj_create( datatype, FLA_NO_TRANSPOSE, sc_str[1], m, m, &Y );
libfla_test_obj_create( datatype, FLA_NO_TRANSPOSE, sc_str[2], m, m, &B );
// Initialize the test matrices.
FLA_Random_spd_matrix( uplo, A );
FLA_Scalr( uplo, FLA_TWO, A );
FLA_Hermitianize( uplo, A );
FLA_Random_spd_matrix( uplo, B );
FLA_Scalr( uplo, FLA_TWO, B );
FLA_Chol( uplo, B );
// Save the original object contents in a temporary object.
FLA_Obj_create_copy_of( FLA_NO_TRANSPOSE, A, &A_save );
FLA_Obj_create_copy_of( FLA_NO_TRANSPOSE, B, &B_save );
// 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 );
// 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( Y, 1, &b_flash, &Y_test );
FLASH_Obj_create_hier_copy_of_flat( B, 1, &b_flash, &B_test );
}
else
{
A_test = A;
Y_test = Y;
B_test = B;
}
// 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_eig_gest_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( A_save, A_test );
FLASH_Obj_hierarchify( B_save, B_test );
}
else
{
FLA_Copy_external( A_save, A_test );
FLA_Copy_external( B_save, B_test );
}
time = FLA_Clock();
libfla_test_eig_gest_impl( impl, inv, uplo, A_test, Y_test, B_test );
time = FLA_Clock() - time;
time_min = min( time_min, time );
}
// Check our solution.
if ( impl == FLA_TEST_HIER_FRONT_END )
{
FLA_Trans trans_left, trans_right;
FLASH_Hermitianize( uplo, A_test );
if ( ( inv == FLA_NO_INVERSE && uplo == FLA_LOWER_TRIANGULAR ) ||
( inv == FLA_INVERSE && uplo == FLA_UPPER_TRIANGULAR ) )
{
trans_left = FLA_CONJ_TRANSPOSE;
trans_right = FLA_NO_TRANSPOSE;
}
else
{
trans_left = FLA_NO_TRANSPOSE;
trans_right = FLA_CONJ_TRANSPOSE;
}
if ( inv == FLA_NO_INVERSE )
{
FLASH_Trsm( FLA_LEFT, uplo, trans_left, FLA_NONUNIT_DIAG,
FLA_ONE, B_test, A_test );
FLASH_Trsm( FLA_RIGHT, uplo, trans_right, FLA_NONUNIT_DIAG,
FLA_ONE, B_test, A_test );
}
else // if ( inv == FLA_INVERSE )
{
FLASH_Trmm( FLA_LEFT, uplo, trans_left, FLA_NONUNIT_DIAG,
FLA_ONE, B_test, A_test );
FLASH_Trmm( FLA_RIGHT, uplo, trans_right, FLA_NONUNIT_DIAG,
FLA_ONE, B_test, A_test );
}
FLASH_Obj_flatten( A_test, A );
}
else
{
FLA_Trans trans_left, trans_right;
FLA_Hermitianize( uplo, A_test );
if ( ( inv == FLA_NO_INVERSE && uplo == FLA_LOWER_TRIANGULAR ) ||
( inv == FLA_INVERSE && uplo == FLA_UPPER_TRIANGULAR ) )
{
trans_left = FLA_CONJ_TRANSPOSE;
trans_right = FLA_NO_TRANSPOSE;
}
else
{
trans_left = FLA_NO_TRANSPOSE;
trans_right = FLA_CONJ_TRANSPOSE;
}
if ( inv == FLA_NO_INVERSE )
{
FLA_Trsm( FLA_LEFT, uplo, trans_left, FLA_NONUNIT_DIAG,
FLA_ONE, B_test, A_test );
FLA_Trsm( FLA_RIGHT, uplo, trans_right, FLA_NONUNIT_DIAG,
FLA_ONE, B_test, A_test );
}
else // if ( inv == FLA_INVERSE )
{
FLA_Trmm( FLA_LEFT, uplo, trans_left, FLA_NONUNIT_DIAG,
FLA_ONE, B_test, A_test );
FLA_Trmm( FLA_RIGHT, uplo, trans_right, FLA_NONUNIT_DIAG,
FLA_ONE, B_test, A_test );
}
}
// 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( &Y_test );
FLASH_Obj_free( &B_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 )
libfla_test_eig_gest_cntl_free();
// Compute the performance of the best experiment repeat.
*perf = 1.0 * m * m * m / time_min / FLOPS_PER_UNIT_PERF;
if ( FLA_Obj_is_complex( A ) ) *perf *= 4.0;
// Compute the residual.
FLA_Axpy_external( FLA_MINUS_ONE, A_save, A );
FLA_Norm1( A, norm );
FLA_Obj_extract_real_scalar( norm, residual );
// Free the supporting flat objects.
FLA_Obj_free( &norm );
FLA_Obj_free( &A_save );
FLA_Obj_free( &B_save );
// Free the flat test matrices.
FLA_Obj_free( &A );
FLA_Obj_free( &Y );
FLA_Obj_free( &B );
}
