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(git:5e7fe52)
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(git:5e7fe52)
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Block-circulant inverse operators for replicated-cell OT preconditioners. More...
Functions/Subroutines | |
| subroutine, public | lattice_grid (lattice_dims, index_to_cell, xkp) |
| Enumerate a regular direct/reciprocal lattice with the first direction varying fastest. | |
| subroutine, public | build_lattice_inverse (operator_matrix, lattice_dims, inverse_k, projection_error, used_fft, info) |
| Project a cell-major SPD operator onto lattice translations and invert its Fourier blocks. | |
| subroutine, public | build_lattice_inverse_from_blocks (blocks, lattice_dims, inverse_k, used_fft, info) |
| Transform and invert already projected real-space lattice blocks. | |
| subroutine, public | build_lattice_local_correction (operator_matrix, lattice_dims, local_cell_count, correction_indices, operator_columns, coarse_inverse, corrected_projection_error, info) |
| Build a balanced local correction for selected non-circulant cell blocks. | |
| pure real(kind=dp) function, public | lattice_fft_cost_ratio (lattice_dims, block_size, rhs_count, num_pe) |
| Estimate lattice-FFT application work relative to a dense inverse application. | |
| pure real(kind=dp) function, public | lattice_fft_storage_ratio (lattice_dims, operator_count) |
| Estimate reciprocal-block storage relative to one dense real operator. | |
| pure real(kind=dp) function, public | lattice_local_cost_ratio (lattice_dims, local_cell_count) |
| Estimate balanced-local-correction work relative to a dense inverse application. | |
| pure real(kind=dp) function, public | lattice_local_storage_ratio (lattice_dims, operator_count, local_cell_count) |
| Estimate balanced-local-correction storage relative to one dense real operator. | |
| pure logical function, public | lattice_fft_auto_select (lattice_dims, block_size, rhs_count, operator_count, num_pe, projection_error, used_fft, info) |
| Conservative error-, work-, and storage-aware AUTO selector. | |
| subroutine, public | apply_lattice_inverse_dense (inverse_k, lattice_dims, matrix_in, matrix_out, used_fft, imaginary_residual) |
| Apply inverse Fourier blocks to a dense cell-major real matrix. | |
| subroutine, public | apply_lattice_state_inverse_dense (inverse_k, lattice_dims, matrix_in, matrix_out, used_fft, imaginary_residual, state_indices) |
| Apply one inverse Fourier operator to every column of a dense real matrix. | |
Variables | |
| integer, parameter, public | lattice_fft_auto_min_cells = 8 |
| real(kind=dp), parameter, public | lattice_fft_auto_max_error = 1.0E-3_dp |
| real(kind=dp), parameter, public | lattice_fft_auto_max_cost_ratio = 0.8_dp |
| real(kind=dp), parameter, public | lattice_fft_auto_max_storage_ratio = 4.0_dp |
Block-circulant inverse operators for replicated-cell OT preconditioners.
| subroutine, public lattice_preconditioner_operator::lattice_grid | ( | integer, dimension(3), intent(in) | lattice_dims, |
| integer, dimension(:, :), intent(out) | index_to_cell, | ||
| real(kind=dp), dimension(:, :), intent(out) | xkp ) |
Enumerate a regular direct/reciprocal lattice with the first direction varying fastest.
| lattice_dims | number of cells in every lattice direction |
| index_to_cell | integer direct-lattice coordinates |
| xkp | fractional reciprocal-lattice coordinates |
Definition at line 54 of file lattice_preconditioner_operator.F.
| subroutine, public lattice_preconditioner_operator::build_lattice_inverse | ( | real(kind=dp), dimension(:, :), intent(in) | operator_matrix, |
| integer, dimension(3), intent(in) | lattice_dims, | ||
| complex(kind=dp), dimension(:, :, :), intent(out), allocatable | inverse_k, | ||
| real(kind=dp), intent(out) | projection_error, | ||
| logical, intent(out) | used_fft, | ||
| integer, intent(out) | info ) |
Project a cell-major SPD operator onto lattice translations and invert its Fourier blocks.
| operator_matrix | dense SPD matrix with identical cell blocks stored consecutively |
| lattice_dims | number of replicated cells in every lattice direction |
| inverse_k | inverse Hermitian operator block at every reciprocal-grid point |
| projection_error | relative Frobenius error of the block-circulant projection |
| used_fft | reports whether construction used the FFT path |
| info | zero on success; otherwise the failing Cholesky factorization index |
Definition at line 93 of file lattice_preconditioner_operator.F.
| subroutine, public lattice_preconditioner_operator::build_lattice_inverse_from_blocks | ( | real(kind=dp), dimension(:, :, :), intent(in) | blocks, |
| integer, dimension(3), intent(in) | lattice_dims, | ||
| complex(kind=dp), dimension(:, :, :), intent(out), allocatable | inverse_k, | ||
| logical, intent(out) | used_fft, | ||
| integer, intent(out) | info ) |
Transform and invert already projected real-space lattice blocks.
| blocks | translation-averaged real-space blocks |
| lattice_dims | number of replicated cells in every lattice direction |
| inverse_k | inverse Hermitian operator block at every reciprocal-grid point |
| used_fft | reports whether construction used the FFT path |
| info | zero on success; otherwise the failing Cholesky factorization index |
Definition at line 130 of file lattice_preconditioner_operator.F.
| subroutine, public lattice_preconditioner_operator::build_lattice_local_correction | ( | real(kind=dp), dimension(:, :), intent(in) | operator_matrix, |
| integer, dimension(3), intent(in) | lattice_dims, | ||
| integer, intent(in) | local_cell_count, | ||
| integer, dimension(:), intent(out), allocatable | correction_indices, | ||
| real(kind=dp), dimension(:, :), intent(out), allocatable | operator_columns, | ||
| real(kind=dp), dimension(:, :), intent(out), allocatable | coarse_inverse, | ||
| real(kind=dp), intent(out) | corrected_projection_error, | ||
| integer, intent(out) | info ) |
Build a balanced local correction for selected non-circulant cell blocks.
| operator_matrix | dense SPD operator |
| lattice_dims | number of replicated cells in every lattice direction |
| local_cell_count | number of cell blocks retained in the correction |
| correction_indices | selected global AO indices |
| operator_columns | columns A U for the selected coordinate basis U |
| coarse_inverse | inverse of U^T A U |
| corrected_projection_error | residual projection error after removing selected rows/columns |
| info | zero on success; otherwise the failing Cholesky factorization index |
Definition at line 170 of file lattice_preconditioner_operator.F.
| pure real(kind=dp) function, public lattice_preconditioner_operator::lattice_fft_cost_ratio | ( | integer, dimension(3), intent(in) | lattice_dims, |
| integer, intent(in) | block_size, | ||
| integer, intent(in) | rhs_count, | ||
| integer, intent(in) | num_pe ) |
Estimate lattice-FFT application work relative to a dense inverse application.
| lattice_dims | number of explicitly replicated cells |
| block_size | number of orbitals in the reference cell |
| rhs_count | number of orbital columns transformed together |
| num_pe | number of message-passing ranks sharing the operator |
Definition at line 354 of file lattice_preconditioner_operator.F.
| pure real(kind=dp) function, public lattice_preconditioner_operator::lattice_fft_storage_ratio | ( | integer, dimension(3), intent(in) | lattice_dims, |
| integer, intent(in) | operator_count ) |
Estimate reciprocal-block storage relative to one dense real operator.
| lattice_dims | number of explicitly replicated cells |
| operator_count | number of distinct state-dependent reciprocal operators |
Definition at line 396 of file lattice_preconditioner_operator.F.
| pure real(kind=dp) function, public lattice_preconditioner_operator::lattice_local_cost_ratio | ( | integer, dimension(3), intent(in) | lattice_dims, |
| integer, intent(in) | local_cell_count ) |
Estimate balanced-local-correction work relative to a dense inverse application.
| lattice_dims | number of replicated cells |
| local_cell_count | number of cell blocks retained in the correction |
Definition at line 416 of file lattice_preconditioner_operator.F.
| pure real(kind=dp) function, public lattice_preconditioner_operator::lattice_local_storage_ratio | ( | integer, dimension(3), intent(in) | lattice_dims, |
| integer, intent(in) | operator_count, | ||
| integer, intent(in) | local_cell_count ) |
Estimate balanced-local-correction storage relative to one dense real operator.
| lattice_dims | number of replicated cells |
| operator_count | number of distinct state-dependent local corrections |
| local_cell_count | number of cell blocks retained in each correction |
Definition at line 443 of file lattice_preconditioner_operator.F.
| pure logical function, public lattice_preconditioner_operator::lattice_fft_auto_select | ( | integer, dimension(3), intent(in) | lattice_dims, |
| integer, intent(in) | block_size, | ||
| integer, intent(in) | rhs_count, | ||
| integer, intent(in) | operator_count, | ||
| integer, intent(in) | num_pe, | ||
| real(kind=dp), intent(in) | projection_error, | ||
| logical, intent(in) | used_fft, | ||
| integer, intent(in) | info ) |
Conservative error-, work-, and storage-aware AUTO selector.
| lattice_dims | number of explicitly replicated cells |
| block_size | number of orbitals in the reference cell |
| rhs_count | number of orbital columns transformed together |
| operator_count | number of distinct reciprocal operators stored |
| num_pe | number of message-passing ranks sharing the operator |
| projection_error | relative Frobenius projection error |
| used_fft | whether construction used the FFT path |
| info | zero when all projected Fourier blocks were positive definite |
Definition at line 474 of file lattice_preconditioner_operator.F.
| subroutine, public lattice_preconditioner_operator::apply_lattice_inverse_dense | ( | complex(kind=dp), dimension(:, :, :), intent(in) | inverse_k, |
| integer, dimension(3), intent(in) | lattice_dims, | ||
| real(kind=dp), dimension(:, :), intent(in) | matrix_in, | ||
| real(kind=dp), dimension(:, :), intent(out) | matrix_out, | ||
| logical, intent(out) | used_fft, | ||
| real(kind=dp), intent(out), optional | imaginary_residual ) |
Apply inverse Fourier blocks to a dense cell-major real matrix.
| inverse_k | inverse overlap blocks on a complete reciprocal grid |
| lattice_dims | number of replicated cells in every lattice direction |
| matrix_in | matrix to precondition |
| matrix_out | preconditioned matrix |
| used_fft | reports whether both transforms used the FFT path |
| imaginary_residual | largest discarded imaginary component |
Definition at line 504 of file lattice_preconditioner_operator.F.
| subroutine, public lattice_preconditioner_operator::apply_lattice_state_inverse_dense | ( | complex(kind=dp), dimension(:, :, :, :), intent(in) | inverse_k, |
| integer, dimension(3), intent(in) | lattice_dims, | ||
| real(kind=dp), dimension(:, :), intent(in) | matrix_in, | ||
| real(kind=dp), dimension(:, :), intent(out) | matrix_out, | ||
| logical, intent(out) | used_fft, | ||
| real(kind=dp), intent(out), optional | imaginary_residual, | ||
| integer, dimension(:), intent(in), optional | state_indices ) |
Apply one inverse Fourier operator to every column of a dense real matrix.
| inverse_k | state-dependent inverse blocks on a complete reciprocal grid |
| lattice_dims | number of replicated cells in every lattice direction |
| matrix_in | matrix to precondition, with one state per column |
| matrix_out | preconditioned matrix |
| used_fft | reports whether both transforms used the FFT path |
| imaginary_residual | largest discarded imaginary component |
| state_indices | optional global operator index for every input column |
Definition at line 564 of file lattice_preconditioner_operator.F.
| integer, parameter, public lattice_preconditioner_operator::lattice_fft_auto_min_cells = 8 |
Definition at line 29 of file lattice_preconditioner_operator.F.
| real(kind=dp), parameter, public lattice_preconditioner_operator::lattice_fft_auto_max_error = 1.0E-3_dp |
Definition at line 30 of file lattice_preconditioner_operator.F.
| real(kind=dp), parameter, public lattice_preconditioner_operator::lattice_fft_auto_max_cost_ratio = 0.8_dp |
Definition at line 31 of file lattice_preconditioner_operator.F.
| real(kind=dp), parameter, public lattice_preconditioner_operator::lattice_fft_auto_max_storage_ratio = 4.0_dp |
Definition at line 32 of file lattice_preconditioner_operator.F.
1.15.0