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XGCa
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XGCa
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#include "adios_macro.h"#include "t_coeff_mod_macro.h"#include "fftw3.f"
Data Types | |
| module | grid_class |
| type | grid_class::grid_type |
Functions/Subroutines | |
| subroutine | order_nodes (grid, isurf, isize, idx_start, theta, idx) |
| Sorts input SOL flux-surface according to the poloidal arclength l_theta where l_theta=0 at the outer midplane. More... | |
| subroutine | gen_pol_angle_single (i) |
| subroutine | get_b_and_derivs_cyl (r, z, B_mag, br, bphi, bz, dbrdr, dbpdr, dbzdr, dbrdp, dbpdp, dbzdp, dbrdz, dbpdz, dbzdz) |
| subroutine | get_pe_info (mype, totalpe) |
| subroutine | search_tr2 (grid, xy, itr, p) |
| subroutine | search_tr_check_guess (grid, x, init, itr, p) |
| subroutine | convert_001d_2_grid (grid, v1d, v2d) |
| subroutine | convert_001d_2_grid_wrap (v1d, v2d) |
| subroutine | convert_grid_init2 (grid, psn) |
| Sets up a matrix that evaluates the flux-surface average using only the complete surfaces as specified in an input file generated by the RPI meshing tool. The inverse operation that projects a 1D flux-surface averaged quantity on the 2D mesh is also generated. All vertices that are not enclosed by the complete flux-surfaces (essentially all vertices in the unstructured part of the mesh and in the private flux-region are set to 0! More... | |
| subroutine | convert_grid_2_001d (grid, v2d, v1d) |
| subroutine | convert_grid_2_001d_wrap (v2d, v1d) |
| subroutine | write_gradient_mat (grid) |
| subroutine | init_rad_smooth (grid) |
| Initialization of 2nd order accurate 4th derivative radial smoothing operator (hyper-viscosity). On vertices that do not have a well defined radial direction (X-points, mag. axis), an isotropic 2nd derivative hyperviscosity is used as a fallback. More... | |
| subroutine | get_node_perp (grid, x, dlperp_in, direction, dist_out, itr, p) |
| subroutine | get_node_theta (grid, x, dltheta_in, direction, dist_out, itr, p) |
| subroutine | get_next_point_gl (x_in, psi_in, dpsi, direction, x_out, dist) |
| subroutine | get_next_point_perp (x_in, dlperp, direction, x_out, dist) |
| subroutine | get_next_point_tang (x_in, dltheta, direction, x_out, dist) |
| subroutine | get_char_length (grid, ip, dl, ierr) |
| subroutine | make_v_dot_grad_mat (grid, mat, v) |
| subroutine | grid_deriv (grid, qty, qty_deriv_x, qty_deriv_y, psi_only) |
| subroutine | grid_theta_deriv (grid, qty, qty_deriv) |
| subroutine | init_pol_smooth_mat (grid) |
| subroutine | write_pol_smooth_mat |
| subroutine | smooth_pol (grid, qty, qty_smooth) |
| subroutine | smooth_pol_wrap (qty, qty_smooth) |
| subroutine | fourier_filter (grid, filt_inout, inpsi, outpsi, bd_width, op_mode, div_mix) |
| Interface routine for Fourier filter. More... | |
| subroutine | fourier_filter_wrap (filt_inout) |
| subroutine | fourier_filter_m_range (grid, mpol_min, mpol_max, n_xdim2, x, x_is_spectral, inpsi, outpsi, bd_width, is_resonant, ntor_real) |
| Poloidal Fourier filter for the regions 1 and 2 Removes high poloidal mode numbers flux-surfaces while retaining small scale poloidal variations close to the divertor plates. This is achieved by applying a window function that removes the near-divertor part from the data. The windowed data is then low-pass filtered and the high-m variations are removed by calculating x_filtered = (1-win)*x - win*x_filtered. More... | |
| subroutine | fourier_filter_update_analytic (x) |
| subroutine | fft_parallel_init (grid) |
| Initializes the parallelization of the field-aligned FFT filter. Since each flux-surface is filtered separately, the flux-surfaces are distributed among the MPI ranks in the inter-plane communicator (sml_intpl_comm). To achieve approximately even workload, the distribution of flux-surfaces, tries to assign equal numbers of vertices to each rank. More... | |
| subroutine | fourier_filter_n_m_range_parallel (grid, nphi, ntor_min, ntor_max, ntor_min_real, ntor_max_real, bands_on, mpol_min, mpol_max, x, op_mode, num_mres_q, inpsi, outpsi, bd_width, div_mix) |
Toroidal-poloidal Fourier filter for the regions 1 and 2 This version of the filter is parallelized to a high degree for optimal performance, and allows for multiple toroidal mode numbers. Removes high poloidal mode numbers from flux-surfaces while retaining small scale poloidal variations close to the divertor plates. This is achieved by applying a window function that removes the near-divertor part from the data. The windowed data is then low-pass filtered and the high-m variations are removed by calculating x_filtered = (1-win)*x - win*x_filtered
Additionally, only one toroidal mode number is kept.NOTE: WINDOW HAS NOT BEEN IMPLEMENTED YET —> USING WIN=1More... | |
| subroutine | fourier_filter_set_nonaligned (grid, x) |
| subroutine | fourier_filter_single_n (grid, filt_inout, inpsi, outpsi, bd_width) |
| Fourier Filter the input (R,phi,Z data) for a single toroidal mode. More... | |
| subroutine | fourier_filter_single_n_flex (grid, ntor, filt_in, filt_out, do_damp, inpsi, outpsi, bd_width) |
| Fourier Filter the input (R,phi,Z data) for a single toroidal mode that can be different on each calling rank. More... | |
| real(kind=8) function | fourier_filter_damp_fac (psi, inpsi, outpsi, bd_width) |
| Evaluate a damping factor for the boundary condition of the Fourier filter functions. More... | |
| subroutine convert_001d_2_grid | ( | type(grid_type), intent(in) | grid, |
| real (8), dimension(grid%npsi_surf), intent(in) | v1d, | ||
| real (8), dimension(grid%nnode), intent(out) | v2d | ||
| ) |
| subroutine convert_001d_2_grid_wrap | ( | real (8), dimension(grid_global%npsi_surf), intent(in) | v1d, |
| real (8), dimension(grid_global%nnode), intent(out) | v2d | ||
| ) |
| subroutine convert_grid_2_001d | ( | type(grid_type), intent(in) | grid, |
| real (8), dimension(grid%nnode), intent(in) | v2d, | ||
| real (8), dimension(grid%npsi_surf), intent(out) | v1d | ||
| ) |
| subroutine convert_grid_2_001d_wrap | ( | real (8), dimension(grid_global%nnode), intent(in) | v2d, |
| real (8), dimension(grid_global%npsi_surf), intent(out) | v1d | ||
| ) |
| subroutine convert_grid_init2 | ( | type(grid_type), intent(inout) | grid, |
| type(psn_type), intent(in) | psn | ||
| ) |
Sets up a matrix that evaluates the flux-surface average using only the complete surfaces as specified in an input file generated by the RPI meshing tool. The inverse operation that projects a 1D flux-surface averaged quantity on the 2D mesh is also generated. All vertices that are not enclosed by the complete flux-surfaces (essentially all vertices in the unstructured part of the mesh and in the private flux-region are set to 0!
| grid[inout] | type(grid_type), grid information |
| psn[in] | field data (esp. wall nodes), type(psn_type) |
| subroutine fft_parallel_init | ( | type(grid_type), intent(inout) | grid | ) |
Initializes the parallelization of the field-aligned FFT filter. Since each flux-surface is filtered separately, the flux-surfaces are distributed among the MPI ranks in the inter-plane communicator (sml_intpl_comm). To achieve approximately even workload, the distribution of flux-surfaces, tries to assign equal numbers of vertices to each rank.
| [in,out] | grid | grid data structure, type(grid_type) |
| subroutine fourier_filter | ( | type(grid_type), intent(in) | grid, |
| real (kind=8), dimension(grid%nnode), intent(inout) | filt_inout, | ||
| real (8), intent(in) | inpsi, | ||
| real (8), intent(in) | outpsi, | ||
| real (8), intent(in) | bd_width, | ||
| integer, intent(in) | op_mode, | ||
| logical, intent(in) | div_mix | ||
| ) |
Interface routine for Fourier filter.
| [in] | grid | grid data, type(grid_type) |
| [in,out] | filt_inout | input real part, real(8) |
| [in] | inpsi | Inner filter boundary, real(8) |
| [in] | outpsi | Outer filter boundary, real(8) |
| [in] | bd_width | Boundary width, real(8) |
| [in] | op_mode | (1) Simple single-n toroidal mode filter (4) Simple poloidal mode filter with m-range (2,5) n-m_range with m=nq+/-mres (parallel version 2, operational, includes side bands) (3,6) simple n-m range (parallel version 2, operational) Former modes (2) and (3) are deprecated and have been merged with (5) and (6) |
| [in] | div_mix | Whether to blend unfiltered data near divertor with filtered data due to windowing function in SOL, logical |
| real (kind=8) function fourier_filter_damp_fac | ( | real (kind=8), intent(in) | psi, |
| real (kind=8), intent(in) | inpsi, | ||
| real (kind=8), intent(in) | outpsi, | ||
| real (kind=8), intent(in) | bd_width | ||
| ) |
Evaluate a damping factor for the boundary condition of the Fourier filter functions.
| [in] | psi | Input poloidal flux, real(8) |
| [in] | inpsi | Inner filter boundary, real(8) |
| [in] | outpsi | Outer filter boundary, real(8) |
| [in] | bd_width | Boundary width, real(8) |
| subroutine fourier_filter_m_range | ( | type(grid_type), intent(in) | grid, |
| integer, intent(in) | mpol_min, | ||
| integer, intent(in) | mpol_max, | ||
| integer, intent(in) | n_xdim2, | ||
| real (kind=8), dimension(grid%nnode,n_xdim2), intent(inout) | x, | ||
| logical, intent(in) | x_is_spectral, | ||
| real (kind=8), intent(in) | inpsi, | ||
| real (kind=8), intent(in) | outpsi, | ||
| real (kind=8), intent(in) | bd_width, | ||
| logical, intent(in) | is_resonant, | ||
| integer, intent(in) | ntor_real | ||
| ) |
Poloidal Fourier filter for the regions 1 and 2 Removes high poloidal mode numbers flux-surfaces while retaining small scale poloidal variations close to the divertor plates. This is achieved by applying a window function that removes the near-divertor part from the data. The windowed data is then low-pass filtered and the high-m variations are removed by calculating x_filtered = (1-win)*x - win*x_filtered.
Extension: Input x can now have shape (:,:) with the size of the 2nd dimension given by the input parameter n_xdim2 (batched filtering). If n_xdim2=2 and x_is_spectral=.true., then the inputs are the cosine (1) and sine (2) components of a discrete toroidal Fourier transform in sin/cos representation. In this case a transformation is applied after the poloidal FFT so that only the poloidal mode numbers around the resonance \(m=n*q\) are retained, and the rest is discarded. Assume \(f = [a*\cos(n*\phi-m*\theta)+b*\sin(n*\phi-m*\theta)]+[c*\cos(n*\phi+m*\theta)+d*\sin(n*\phi+m*\theta)]\) with m>0. Whether \(+m\) or \(-m\) is required depends on the orientation of the magnetic field, and to which band of the \((n,m)\) spectrum the mode belongs. The sign of \(m\) is given by \(\sigma = \mathtt{sml_bt_sign}\cdot\mathtt{sml_bp_sign}\cdot(-1)^{i}\), with \(i=[(\mathtt{ntor_real}/\mathtt{sml_wedge_n})-1]\cdot(2/\mathtt{sml_nphi_total})\) is the side-band index of the toroidal mode number under consideration.
Let f_cnm and f_snm be the complex-valued Fourier coefficients resulting from the FFT of the cosine and sine components of the toroidal DFT for the numerical toroidal mode number n.
Then we have: Re(f_cnm) = a+c Im(f_cnm) = b-d Re(f_snm) = b+d Im(f_snm) =-a+c
Hence: (f_cnm + I*f_snm)/2 = (a+I*b) (f_snm + I*f_cnm)/2 = (d+I*c)
So if \(\sigma=+1\), we need the coefficients a and b, and use f_cnm <- Re[(f_cnm + I*f_snm)/2] + I*Im[(f_cnm + I*f_snm)/2] f_snm <- Im[(f_cnm + I*f_snm)/2] - I*Re[(f_cnm + I*f_snm)/2]
and if \(\sigma=-1\), we need c and d, and use f_cnm <- Im[(f_snm + I*f_cnm)/2] - I*Re[(f_snm + I*f_cnm)/2] f_snm <- Re[(f_snm + I*f_cnm)/2] + I*Im[(f_snm + I*f_cnm)/2]
| [in] | grid | grid data, type(grid_type) |
| [in] | mpol_min | minimal poloidal mode number, integer |
| [in] | mpol_max | maximal poloidal mode number, integer |
| [in,out] | x | input data, shape either (gridnnode) or (gridnnode,:), real(8) |
| [in] | n_xdim2 | Size of second dimension; 1 if shape(x) is (:), integer |
| [in] | x_is_spectral | If true, x(:,:) are the cosine and sine coefficients of a discrete toroidal DFT, logical |
| [in] | inpsi | Inner filter boundary, real(8) |
| [in] | outpsi | Outer filter boundary, real(8) |
| [in] | bd_width | Boundary width, real(8) |
| [in] | is_resonant | If .true. input m-range is ignored and instead set according to |m/q(psi)-ntor_real|<=sml_mode_select_mres_q, logical |
| [in] | ntor_real | (Real) toroidal mode number used for setting the filter range |
| subroutine fourier_filter_n_m_range_parallel | ( | type(grid_type), intent(in) | grid, |
| integer, intent(in) | nphi, | ||
| integer, intent(in) | ntor_min, | ||
| integer, intent(in) | ntor_max, | ||
| integer, intent(in) | ntor_min_real, | ||
| integer, intent(in) | ntor_max_real, | ||
| logical, intent(in) | bands_on, | ||
| integer, intent(in) | mpol_min, | ||
| integer, intent(in) | mpol_max, | ||
| real (kind=8), dimension(grid%nnode), intent(inout) | x, | ||
| integer, intent(in) | op_mode, | ||
| integer, intent(in) | num_mres_q, | ||
| real (kind=8), intent(in) | inpsi, | ||
| real (kind=8), intent(in) | outpsi, | ||
| real (kind=8), intent(in) | bd_width, | ||
| logical, intent(in) | div_mix | ||
| ) |
Toroidal-poloidal Fourier filter for the regions 1 and 2 This version of the filter is parallelized to a high degree for optimal performance, and allows for multiple toroidal mode numbers. Removes high poloidal mode numbers from flux-surfaces while retaining small scale poloidal variations close to the divertor plates. This is achieved by applying a window function that removes the near-divertor part from the data. The windowed data is then low-pass filtered and the high-m variations are removed by calculating x_filtered = (1-win)*x - win*x_filtered
| [in] | grid | grid data, type(grid_type) |
| [in] | nphi | number of toroidal grid points, integer |
| [in] | ntor_min | minimal numerical toroidal mode number, integer |
| [in] | ntor_max | maximal numerical toroidal mode number, integer |
| [in] | ntor_min_real | minimal real (incl. wedge factor) toroidal mode number, integer |
| [in] | ntor_max_real | maximal real (incl. wedge factor) toroidal mode number, integer |
| [in] | bands_on | Whether to use only the main band of resonant modes or also side bands (n>sml_nphi_total/2), logical |
| [in] | mpol_min | minimal poloidal mode number, integer |
| [in] | mpol_max | maximal poloidal mode number, integer |
| [in,out] | x | input data, real(8) |
| [in] | op_mode | mode of operation (integer): 1) simple range of pol. mode numbers, 2) resonant pol. modes |
| [in] | num_mres_q | number of poloidal modes retained around the res. mode divided by the safety factor in op_mode=2 |
| [in] | inpsi | Inner filter boundary, real(8) |
| [in] | outpsi | Outer filter boundary, real(8) |
| [in] | bd_width | Boundary width, real(8) |
| [in] | div_mix | Whether to blend unfiltered data near the divertor with filtered data (due to windowing function), logical |
| subroutine fourier_filter_set_nonaligned | ( | type(grid_type), intent(in) | grid, |
| real (kind=8), dimension(grid%nnode), intent(inout) | x | ||
| ) |
| subroutine fourier_filter_single_n | ( | type(grid_type), intent(in) | grid, |
| real (kind=8), dimension(grid%nnode), intent(inout) | filt_inout, | ||
| real (kind=8), intent(in) | inpsi, | ||
| real (kind=8), intent(in) | outpsi, | ||
| real (kind=8), intent(in) | bd_width | ||
| ) |
Fourier Filter the input (R,phi,Z data) for a single toroidal mode.
| [in] | grid | grid data, type(grid_type) |
| [in,out] | filt_inout | input real part, real(8) |
| [in] | inpsi | Inner filter boundary, real(8) |
| [in] | outpsi | Outer filter boundary, real(8) |
| [in] | bd_width | Boundary width, real(8) |
| subroutine fourier_filter_single_n_flex | ( | type(grid_type), intent(in) | grid, |
| integer, intent(in) | ntor, | ||
| real (kind=8), dimension(grid%nnode), intent(in) | filt_in, | ||
| real (kind=8), dimension(grid%nnode,2), intent(out) | filt_out, | ||
| logical, intent(in) | do_damp, | ||
| real (kind=8), intent(in) | inpsi, | ||
| real (kind=8), intent(in) | outpsi, | ||
| real (kind=8), intent(in) | bd_width | ||
| ) |
Fourier Filter the input (R,phi,Z data) for a single toroidal mode that can be different on each calling rank.
| [in] | grid | grid data, type(grid_type) |
| [in] | ntor | Toroidal mode number, integer |
| [in] | filt_in | input, real(8) |
| [out] | filt_out | output sin and cos components, real(8) |
| [in] | do_damp | Whether to use a psi-window function, logical |
| [in] | inpsi | Inner filter boundary, real(8) |
| [in] | outpsi | Outer filter boundary, real(8) |
| [in] | bd_width | Boundary width, real(8) |
| subroutine fourier_filter_update_analytic | ( | real (kind=8), dimension(grid_global%nnode), intent(inout) | x | ) |
| subroutine fourier_filter_wrap | ( | real (kind=8), dimension(grid_global%nnode), intent(inout) | filt_inout | ) |
| subroutine calc_gen_theta_psi::gen_pol_angle_single | ( | integer, intent(in) | i | ) |
| subroutine get_b_and_derivs_cyl | ( | real(kind=8), intent(in) | r, |
| real(kind=8), intent(in) | z, | ||
| real(kind=8), intent(out) | B_mag, | ||
| real(kind=8), intent(out) | br, | ||
| real(kind=8), intent(out) | bphi, | ||
| real(kind=8), intent(out) | bz, | ||
| real(kind=8), intent(out) | dbrdr, | ||
| real(kind=8), intent(out) | dbpdr, | ||
| real(kind=8), intent(out) | dbzdr, | ||
| real(kind=8), intent(out) | dbrdp, | ||
| real(kind=8), intent(out) | dbpdp, | ||
| real(kind=8), intent(out) | dbzdp, | ||
| real(kind=8), intent(out) | dbrdz, | ||
| real(kind=8), intent(out) | dbpdz, | ||
| real(kind=8), intent(out) | dbzdz | ||
| ) |
| subroutine get_char_length | ( | type (grid_type), intent(inout) | grid, |
| integer, intent(in) | ip, | ||
| real (kind=8), dimension(3), intent(out) | dl, | ||
| integer, intent(out) | ierr | ||
| ) |
| subroutine get_next_point_gl | ( | real (kind=8), dimension(2), intent(in) | x_in, |
| real (kind=8), intent(in) | psi_in, | ||
| real (kind=8), intent(in) | dpsi, | ||
| integer, intent(in) | direction, | ||
| real (kind=8), dimension(2), intent(inout) | x_out, | ||
| real (kind=8), intent(inout) | dist | ||
| ) |
| subroutine get_next_point_perp | ( | real (kind=8), dimension(2), intent(in) | x_in, |
| real (kind=8), intent(in) | dlperp, | ||
| integer, intent(in) | direction, | ||
| real (kind=8), dimension(2), intent(inout) | x_out, | ||
| real (kind=8), intent(inout) | dist | ||
| ) |
| subroutine get_next_point_tang | ( | real (kind=8), dimension(2), intent(in) | x_in, |
| real (kind=8), intent(in) | dltheta, | ||
| integer, intent(in) | direction, | ||
| real (kind=8), dimension(2), intent(inout) | x_out, | ||
| real (kind=8), intent(inout) | dist | ||
| ) |
| subroutine get_node_perp | ( | type (grid_type), intent(in) | grid, |
| real (kind=8), dimension(2), intent(in) | x, | ||
| real (kind=8), intent(in) | dlperp_in, | ||
| integer, intent(in) | direction, | ||
| real (kind=8), intent(inout) | dist_out, | ||
| integer, intent(inout) | itr, | ||
| real (kind=8), dimension(3), intent(inout) | p | ||
| ) |
| subroutine get_node_theta | ( | type (grid_type), intent(in) | grid, |
| real (kind=8), dimension(2), intent(in) | x, | ||
| real (kind=8), intent(in) | dltheta_in, | ||
| integer, intent(in) | direction, | ||
| real (kind=8), intent(inout) | dist_out, | ||
| integer, intent(inout) | itr, | ||
| real (kind=8), dimension(3), intent(inout) | p | ||
| ) |
| subroutine get_pe_info | ( | integer | mype, |
| integer | totalpe | ||
| ) |
| subroutine grid_deriv | ( | type(grid_type), intent(in) | grid, |
| real (kind=8), dimension(grid%nnode), intent(in) | qty, | ||
| real (kind=8), dimension(grid%nnode), intent(inout) | qty_deriv_x, | ||
| real (kind=8), dimension(grid%nnode), intent(inout) | qty_deriv_y, | ||
| logical, intent(in) | psi_only | ||
| ) |
| subroutine grid_theta_deriv | ( | type(grid_type), intent(in) | grid, |
| real (kind=8), dimension(grid%nnode), intent(in) | qty, | ||
| real (kind=8), dimension(grid%nnode), intent(inout) | qty_deriv | ||
| ) |
| subroutine init_pol_smooth_mat | ( | type (grid_type), intent(inout) | grid | ) |
| subroutine init_rad_smooth | ( | type (grid_type), intent(inout) | grid | ) |
Initialization of 2nd order accurate 4th derivative radial smoothing operator (hyper-viscosity). On vertices that do not have a well defined radial direction (X-points, mag. axis), an isotropic 2nd derivative hyperviscosity is used as a fallback.
| [in,out] | grid | XGC grid data structure, type(grid_type) |
| subroutine make_v_dot_grad_mat | ( | type(grid_type), intent(inout) | grid, |
| type(mat_type), intent(out) | mat, | ||
| real (kind=8), dimension(grid%nnode,3), intent(in) | v | ||
| ) |
| subroutine calc_gen_theta_psi::order_nodes | ( | type(grid_type), intent(in) | grid, |
| integer, intent(in) | isurf, | ||
| integer, intent(in) | isize, | ||
| integer, intent(in) | idx_start, | ||
| real (kind=8), dimension(isize), intent(out) | theta, | ||
| integer, dimension(isize), intent(out) | idx | ||
| ) |
Sorts input SOL flux-surface according to the poloidal arclength l_theta where l_theta=0 at the outer midplane.
| [in] | grid | grid data; type(grid_type) |
| [in] | isurf | flux-surface index; integer |
| [in] | isize | length of the flux-surface; integer [out] theta output arclength; real(8) |
| [out] | idx | output sort index; integer |
| subroutine search_tr2 | ( | type(grid_type) | grid, |
| real(kind=8), dimension(2) | xy, | ||
| integer | itr, | ||
| real(kind=8), dimension(3) | p | ||
| ) |
| subroutine search_tr_check_guess | ( | type(grid_type), intent(in) | grid, |
| real (kind=8), dimension(2), intent(in) | x, | ||
| integer, intent(in) | init, | ||
| integer, intent(out) | itr, | ||
| real (kind=8), dimension(3), intent(out) | p | ||
| ) |
| subroutine smooth_pol | ( | type(grid_type), intent(in) | grid, |
| real (kind=8), dimension(grid%nnode), intent(in) | qty, | ||
| real (kind=8), dimension(grid%nnode), intent(inout) | qty_smooth | ||
| ) |
| subroutine smooth_pol_wrap | ( | real (kind=8), dimension(grid_global%nnode), intent(in) | qty, |
| real (kind=8), dimension(grid_global%nnode), intent(inout) | qty_smooth | ||
| ) |
| subroutine write_gradient_mat | ( | type (grid_type), intent(inout) | grid | ) |
| subroutine init_pol_smooth_mat::write_pol_smooth_mat | ( | ) |
1.8.5