int phonopy_pinv_libflame(double *matrix,
double *eigvals,
const int size,
const double cutoff)
{
FLA_Obj A, B, l;
/* FLA_Obj C; */
double *inv_eigvals;
int i;
inv_eigvals = (double*)malloc(sizeof(double) * size);
FLA_Init();
FLA_Obj_create_without_buffer(FLA_DOUBLE, size, size, &A);
FLA_Obj_attach_buffer(matrix, 0, 0, &A);
FLA_Obj_create_without_buffer(FLA_DOUBLE, size, 1, &l);
FLA_Obj_attach_buffer(eigvals, 0, 0, &l);
/* Eigensolver */
FLA_Obj_create_copy_of(FLA_NO_TRANSPOSE, A, &B);
FLA_Hevd(FLA_EVD_WITH_VECTORS, FLA_LOWER_TRIANGULAR, B, l);
/* SVD */
/* FLA_Obj_create(FLA_DOUBLE, size, size, 0, 0, &B); */
/* use U */
/* FLA_Svd(FLA_SVD_VECTORS_ALL, FLA_SVD_VECTORS_NONE, A, l, B, C); */
/* use V */
/* FLA_Svd(FLA_SVD_VECTORS_NONE, FLA_SVD_VECTORS_ALL, A, l, C, B); */
FLA_Obj_free_without_buffer(&l);
for (i = 0; i < size; i++) {
if (eigvals[i] < cutoff) {
inv_eigvals[i] = 0;
} else {
inv_eigvals[i] = 1.0 / sqrt(eigvals[i]);
}
}
FLA_Obj_create_without_buffer(FLA_DOUBLE, size, 1, &l);
FLA_Obj_attach_buffer(inv_eigvals, 0, 0, &l);
FLA_Apply_diag_matrix(FLA_RIGHT, FLA_NO_CONJUGATE, l, B);
FLA_Syrk(FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_ONE, B, FLA_ZERO, A);
FLA_Symmetrize(FLA_LOWER_TRIANGULAR, A);
FLA_Obj_free_without_buffer(&A);
FLA_Obj_free_without_buffer(&l);
FLA_Obj_free(&B);
FLA_Finalize();
free(inv_eigvals);
return 0;
}
// ============================================================================
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", " ];" );
}
}
void FLA_Gemm_pack_andor_scale_A( FLA_Trans transA, FLA_Obj alpha,
FLA_Obj A, FLA_Obj* packed_A )
{
int m, n, ldim_A;
double *buff_packed_A, *buff_packed_aligned_A, *buff_A;
m = FLA_Obj_length( A );
n = FLA_Obj_width ( A );
ldim_A = FLA_Obj_ldim ( A );
buff_A = ( double* ) FLA_Obj_buffer_at_view( A );
dgemm_itcopy( m, n, buff_A, ldim_A, FLA_Work_buffer_aligned_A );
FLA_Obj_create_without_buffer( FLA_DOUBLE, m, n, packed_A );
// FLA_Obj_attach_buffer( buff_packed_A, n, packed_A );
}
void FLA_Gemm_pack_andor_scale_B( FLA_Trans transB, FLA_Obj alpha,
FLA_Obj B, FLA_Obj* packed_B )
{
int m, n, ldim_B;
double *buff_packed_B, *buff_packed_aligned_B, *buff_B;
m = FLA_Obj_length( B );
n = FLA_Obj_width ( B );
ldim_B = FLA_Obj_ldim ( B );
buff_B = ( double* ) FLA_Obj_buffer_at_view( B );
dgemm_oncopy( m, n, buff_B, ldim_B, FLA_Work_buffer_aligned_B );
FLA_Obj_create_without_buffer( FLA_DOUBLE, m, n, packed_B );
// FLA_Obj_attach_buffer( buff_packed_B, m, packed_B );
}
void F77_fla_obj_show( char* prefix, int* m, int* n, void* buffer, int* ldim )
{
FLA_Error init_result;
FLA_Datatype datatype;
FLA_Obj A;
switch( *prefix ) {
case 'i':
case 'I':
datatype = FLA_INT;
break;
case 's':
case 'S':
datatype = FLA_FLOAT;
break;
case 'd':
case 'D':
datatype = FLA_DOUBLE;
break;
case 'c':
case 'C':
datatype = FLA_COMPLEX;
break;
case 'z':
case 'Z':
datatype = FLA_DOUBLE_COMPLEX;
break;
default:
fprintf(stderr, "Invalid prefix %c, where i,s,d,c,z are allowed.\n", *prefix);
FLA_Abort();
}
FLA_Init_safe( &init_result );
FLA_Obj_create_without_buffer( datatype, *m, *n, &A );
FLA_Obj_attach_buffer( buffer, 1, *ldim, &A );
FLA_Obj_fshow( stdout,
"= F77_FLA_OBJ_SHOW =", A, "% 6.4e",
"=-=-=-=-=-=-=-=-=-=-\n");
FLA_Obj_free_without_buffer( &A );
FLA_Finalize_safe( init_result );
}
FLA_Error FLA_Copy_object_to_buffer( FLA_Trans trans, dim_t i, dim_t j, FLA_Obj A, dim_t m, dim_t n, void* B_buffer, dim_t rs, dim_t cs )
{
FLA_Obj B;
FLA_Obj ATL, ATR,
ABL, Aij;
if ( FLA_Check_error_level() >= FLA_MIN_ERROR_CHECKING )
FLA_Copy_object_to_buffer_check( trans, i, j, A, m, n, B_buffer, rs, cs );
FLA_Part_2x2( A, &ATL, &ATR,
&ABL, &Aij, i, j, FLA_TL );
FLA_Obj_create_without_buffer( FLA_Obj_datatype( A ), m, n, &B );
FLA_Obj_attach_buffer( B_buffer, rs, cs, &B );
FLA_Copyt_external( trans, Aij, B );
FLA_Obj_free_without_buffer( &B );
return FLA_SUCCESS;
}
FLA_Error FLA_Copy_buffer_to_object( FLA_Trans trans, dim_t m, dim_t n, void* A_buffer, dim_t rs, dim_t cs, dim_t i, dim_t j, FLA_Obj B )
{
FLA_Obj A;
FLA_Obj BTL, BTR,
BBL, Bij;
if ( FLA_Check_error_level() >= FLA_MIN_ERROR_CHECKING )
FLA_Copy_buffer_to_object_check( trans, m, n, A_buffer, rs, cs, i, j, B );
FLA_Part_2x2( B, &BTL, &BTR,
&BBL, &Bij, i, j, FLA_TL );
FLA_Obj_create_without_buffer( FLA_Obj_datatype( B ), m, n, &A );
FLA_Obj_attach_buffer( A_buffer, rs, cs, &A );
FLA_Copyt_external( trans, A, Bij );
FLA_Obj_free_without_buffer( &A );
return FLA_SUCCESS;
}
FLA_Error FLASH_Axpy_hier_to_buffer( FLA_Obj alpha, dim_t i, dim_t j, FLA_Obj H, dim_t m, dim_t n, void* buffer, dim_t rs, dim_t cs )
{
FLA_Obj flat_matrix;
FLA_Datatype datatype;
FLA_Error e_val;
if ( FLA_Check_error_level() >= FLA_MIN_ERROR_CHECKING )
{
e_val = FLA_Check_if_scalar( alpha );
FLA_Check_error_code( e_val );
e_val = FLA_Check_consistent_object_datatype( alpha, H );
FLA_Check_error_code( e_val );
e_val = FLA_Check_matrix_strides( m, n, rs, cs );
FLA_Check_error_code( e_val );
e_val = FLA_Check_submatrix_dims_and_offset( m, n, i, j, H );
FLA_Check_error_code( e_val );
}
// Acquire the datatype from the hierarchical matrix object.
datatype = FLASH_Obj_datatype( H );
// Create a temporary conventional matrix object of the requested datatype
// and dimensions and attach the given buffer containing the incoming data.
FLA_Obj_create_without_buffer( datatype, m, n, &flat_matrix );
FLA_Obj_attach_buffer( buffer, rs, cs, &flat_matrix );
// Recurse through H, adding in the corresponding elements of flat_matrix,
// starting at the (i,j) element offset.
FLASH_Axpy_hier_to_flat( alpha, i, j, H, flat_matrix );
// Free the object (but don't free the buffer!).
FLA_Obj_free_without_buffer( &flat_matrix );
return FLA_SUCCESS;
}
// ============================================================================
void compute_case4b( 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_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, ldim_slice_C;
size_t idx_A, idx_B, idx_C;
double * buff_cb_A, * buff_cb_B, * buff_cb_C, * buff_slice_C, d_one = 1.0;
// 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_a, size_c, & slice_C );
#if 0
FLA_Obj_create_without_buffer( datatype, size_a, 1, & slice_A );
FLA_Obj_create_without_buffer( datatype, size_c, 1, & slice_B );
#endif
// Perform computation.
for( iter_b = 0; iter_b < size_b; iter_b++ ) {
for( iter_d = 0; iter_d < size_d; iter_d++ ) {
// Define slice_C.
iter_a = 0;
iter_c = 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_ab, & slice_C );
buff_slice_C = ( double * ) FLA_Obj_buffer_at_view( slice_C );
ldim_slice_C = FLA_Obj_col_stride( slice_C );
// Initialize slice_C.
MyFLA_Obj_set_to_zero( slice_C );
for( iter_i = 0; iter_i < size_i; iter_i++ ) {
for( iter_j = 0; iter_j < size_j; iter_j++ ) {
#if 0
// Define slice_A.
FLA_Obj_attach_buffer(
& buff_cb_A[ iter_i + 0 * size_i + iter_j * size_ia +
iter_b * size_iaj ],
size_i, 1, & slice_A );
// Define slice_B.
FLA_Obj_attach_buffer(
& buff_cb_B[ iter_j + 0 * size_j + iter_i * size_jc +
iter_d * size_jci ],
size_j, 1, & slice_B );
// Compute DGER operation.
FLA_Ger( FLA_ONE, slice_A, slice_B, slice_C );
#endif
idx_A = ( ( size_t ) iter_i ) +
( ( size_t ) 0 * size_i ) +
( ( size_t ) iter_j * size_ia ) +
( ( size_t ) iter_b * size_iaj );
idx_B = ( ( size_t ) iter_j ) +
( ( size_t ) 0 * size_j ) +
( ( size_t ) iter_i * size_jc ) +
( ( size_t ) iter_d * size_jci );
dger_( & size_a, & size_c,
& d_one,
& buff_cb_A[ idx_A ], & size_i,
& buff_cb_B[ idx_B ], & size_j,
buff_slice_C, & ldim_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_C );
#if 0
FLA_Obj_free_without_buffer( & slice_A );
FLA_Obj_free_without_buffer( & slice_B );
#endif
}
// ============================================================================
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 );
}