Procedures

ProcedureLocationProcedure TypeDescription
alps_error alps_io Subroutine

Error catching subroutine.
alps_error_init alps_io Subroutine

Open a file for the error log.
besselI alps_nhds Function

Calculates the modified Bessel function of argument x and order n.
BESSI alps_nhds Function

Function to calculate the first kind modified Bessel function of integer order N for any real X.
BESSI0 ../../generate_distribution.f90 Function

This function calculates the modified Bessel function of the first kind of order zero for any positive real argument x.
BESSI0 alps_nhds Function

Auxiliary Bessel functions for N=0, N=1
BESSI1 ../../generate_distribution.f90 Function

This function calculates the modified Bessel function of the first kind of order one for any positive real argument x.
BESSI1 alps_nhds Function

Modified Bessel function of order 1.
BESSJ alps_fns_rel Function

This function calculates the first kind Bessel function of integer order N, for any REAL X. We use here the classical recursion formula, when X > N. For X < N, Miller's algorithm is used to avoid overflows. Reference: C.W.Clenshaw, Chebyshev Series for Mathematical Functions, Mathematical Tables, Vol. 5, 1962.
BESSJ0 alps_fns_rel Function

This function calculates the first kind Bessel function of order 0, for any REAL X. The polynomial approximation by series of Chebyshev polynomials is used for 0<X<8 and 0<8/X<1. References: M.Abramowitz, I.A.Stegun, Handbook of Mathematical Functions, 1965. C.W.Clenshaw, Chebyshev Series for Mathematical Functions, Mathematical Tables, Vol. 5, 1962.
BESSJ1 alps_fns_rel Function

This subroutine calculates the First Kind Bessel Function of order 1, for any real number X. The polynomial approximation by series of Chebyshev polynomials is used for 0<X<8 and 0<8/X<1. References: M.Abramowitz, I.A.Stegun, Handbook of Mathematical Functions, 1965. C.W.Clenshaw, Chebyshev Series for Mathematical Functions, Mathematical Tables, Vol. 5, 1962.
BESSK ../../generate_distribution.f90 Function

This function calculates the modified Bessel function of the third kind of integer order N, for any REAL X. The classical recursion formula is used. Reference: C.W.Clenshaw, Chebyshev Series for Mathematical Functions, Mathematical Tables, Vol. 5, 1962.
BESSK0 ../../generate_distribution.f90 Function

This function calculates the modified Bessel function of the third kind of order zero for any positive real argument x.
BESSK1 ../../generate_distribution.f90 Function

This function calculates the modified Bessel function of the third kind of order zero for any positive real argument x.
bM_read alps_io Subroutine

Reads in bi-Maxwellian/cold-plasma parameters.
calc_chi alps_nhds Subroutine

Subroutine that calculates the susceptibility of species j based on NHDS.
calc_chi_cold alps_nhds Subroutine

Subroutine that calculates the susceptibility of species j based on the cold-plasma dispersion relation based on the paper Verscharen & Chandran, ApJ 764, 88, 2013.
calc_eigen alps_fns Subroutine

This subroutine calculates the relative electric and magnetic field amplitudes, the relative fluctuations in the density and velocity of all species, and the heating rates of the given solution. It is based on the calc_eigen routine by Greg Howes and Kris Klein, found in PLUME. The splitting by mechanisms is described in Huang, Howes, and Brown, JPP 2024.
calc_ypsilon alps_nhds Subroutine

Calculates the Y-tensor according to Stix for a bi-Maxwelling, using the NHDS calculation.
CBESSJ alps_fns_rel Subroutine

This subroutine calculates the complex Bessel function. It is based on the CBESSJ function release 1.1 by J-P Moreau, Paris (www.jpmoreau.fr).
derivative_f0 alps_fns Subroutine

This subroutine calculates the perpendicular and parallel derivatives of the background velocity distribution function f0.
derivative_f0_rel alps_fns_rel Subroutine

This subroutine calculates the derivatives of the background velocity distribution function f0 for the relativistic calculation.
determine_bessel_array alps_fns Subroutine

This subroutine determines the array of Bessel functions that is used in the T-tensor of Eq. (2.10) of the code paper.
determine_GLLS alps_analyt Subroutine

This subroutine evaluates the General Linear Least Squares fit to the distribution function for component 'is' using the selected polynomial basis functions.
determine_JT alps_analyt Subroutine

This subroutine calculates the transposed Jacobian matrix of the fit function with respect to the fit parameter array.
determine_nmax alps_fns Subroutine

This subroutine determines the maximum required order of the Bessel functions in Eq. (2.9) of the code paper.
determine_param_fit alps_analyt Subroutine

This is the fitting routine for the hybrid analytic continuation. It determines the full field param_fit.
determine_resonances alps_fns Subroutine

This subroutine determines whether any kinetic resonances are located in the integration domain.
determine_sproc_rel alps_fns_rel Subroutine

This subroutine determines sproc_rel for the given process.
disp alps_fns Function

This function returns the determinant of the dispersion tensor for a given frequency om.
dispfunct alps_nhds Function

Calculates the dispersion function based on the complex error function.
display_credits alps_io Subroutine

Writes the opening credits.
distribution_analyt alps_distribution_analyt Function

This function returns the pre-defined function as f0.
eval_fit alps_analyt Function

This function evaluates the fit to f0 at and the complex parallel momentum ppar_valC. It requires the fit parameters that will be determined by the subroutine determine_param_fit.
Fact alps_fns_rel Function

This function returns the factorial k! of its argument k.
factorial alps_analyt Function
find_minima alps_fns Subroutine

This subroutine identifies the minima of the coarse map grid. It is called by map_search. The code is based on a routine by Greg Howes, 2006.
fit_function alps_analyt Function

This function evaluates the fit to f0 at real pperp_val and complex ppar_val, provided that the one-dimensional fit-parameter array params is fed into the function. This is only used during the fitting. For the evaluation in ALPS, use eval_fit.
fit_function_poly alps_analyt Function

This function evaluates the orthogonal polynomical fit to f0 at real pperp_val and complex ppar_val, with the one-dimensional polynomical coefficient array fit_coeffs is fed into the function. For the evaluation in ALPS, use eval_fit. kgk: should this be .gt. or .ge. ?
fit_read alps_io Subroutine

Reads in fit parameters for component is.
full_integrate alps_fns Function

This function returns the full integral expression according to Eq. (2.9) in the code paper.
funct_g alps_fns Function

This function returns the function from Eq. (3.2) of the code paper.
funct_g_rel alps_fns_rel Function

This function returns the function from Eq. (3.2) of the code paper for a relativistic calculation.
Gamma alps_fns_rel Function

This function returns the Gamma-function.
get_indexed_double_namelist_unit alps_io Subroutine

A version of get_indexed_namelist_unit, extended to allow for double indexing in order to read in multiple fits for a single species.
get_indexed_namelist_unit alps_io Subroutine

Determines unused I/O unit.
get_indexed_namelist_unit generate_distribution Subroutine

Determines unused I/O unit.
get_runname alps_io Subroutine

Get runname for output files from input argument.
get_runname generate_distribution Subroutine

Get runname for output files from input argument.
get_runname interpolate Subroutine

Get runname for output files from input argument.
get_unused_unit alps_io Subroutine

Determine unused number for I/O index.
get_unused_unit generate_distribution Subroutine

Determine unused number for I/O index.
get_unused_unit interpolate Subroutine

This subroutine returns an available unit number. It is taken from the AstroGK code.
init_param alps_io Subroutine

Read in system parameters from *.in file. Only processor 0 calls this routine:
input_unit alps_io Function

Assigns input unit for namelist opening.
input_unit generate_distribution Function

Assigns input unit for namelist opening.
input_unit interpolate Function

This function returns a unit number for a namelist. It is taken from the AstroGK code.
input_unit_exist alps_io Function

Determine if a particular namelist already opened.
input_unit_exist generate_distribution Function

Determine if a particular namelist already opened.
input_unit_exist interpolate Function

This function checks whether a unit number exists. It is taken from the AstroGK code.
int_ee alps_fns Function

This function returns the ee term in Eq. (2.9).
int_ee_rel alps_fns_rel Function

This function returns the ee term in Eq. (2.9) for the relativistic calculation.
int_T alps_fns Function

This function returns the T-tensor according to Eq. (2.10) of the code paper.
int_T_rel alps_fns_rel Function

This function returns the T-tensor according to Eq. (2.10) of the code paper for the relativistic calculation.
int_T_res alps_fns Function

This function returns the T-tensor according to Eq. (2.10) of the code paper for the case in which it is evaluated at the complex resonance momentum.
int_T_res_rel alps_fns_rel Function

This function returns the T-tensor according to Eq. (2.10) of the code paper for the case in which it is evaluated at the complex resonance momentum for the relativistic calculation.
integrate alps_fns Function

This function performs the integral in Eq. (2.9) of the code paper, but without accounting for the Landau contour integral. It is called by full_integrate.
integrate_res alps_fns Function

This function performs the integration near resonances as described in Section 3.1 of the code paper. It is only called if resonances are present in or near the integration domain.
integrate_res_rel alps_fns_rel Function

This function performs the integration near resonances as described in Section 3.1 of the code paper for a relativistic calculation. It is only called if resonances are present in or near the integration domain.
integrate_resU_rel alps_fns_rel Function

This function evaluates the integral with the integrand proportional to in Eq. (2.9) of the code paper for a relativistic calculation.
isnancheck alps_io Function

Checks if double precision number input is NaN.
landau_integrate alps_fns Function

This function evaluates the Landau contour according to Eqs. (3.8) and (3.9) of the code paper.
landau_integrate_rel alps_fns_rel Function

This function evaluates the Landau contour according to Eqs. (3.8) and (3.9) of the code paper for a relativistic calculation.
least_squares_fit alps_analyt Subroutine

Solves General Linear Least Squares Normal Equation
LM_nonlinear_fit alps_analyt Subroutine

This subroutine processes the nonlinear Levenberg-Marquart algorithm and returns the one-dimensional array params at a given iperp. The variable quality is the sum of the squares of all residuals.
map_read alps_io Subroutine

Reads in complex frequency map parameters.
map_search alps_fns Subroutine

This subroutine calculates the map of the determinant of the dispersion tensor in complex frequency space. check

Read more…
normalize ../../interpolation.f90 Subroutine

This subroutine normalises the fine interpolation grid.
om_double_scan alps_fns Subroutine

This subroutine scans along a prescribed plane in wavevector space to map out in this space. It is required that n_scan=2, and is invoked with option =2 KGK: This line causes the solution to (occasionally) smoothly transition to unphysical values. Suppressing until we understand the error.

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om_scan alps_fns Subroutine

This subroutine scans solutions along a single prescribed path in wavevector space. KGK: This line causes the solution to (occasionally) smoothly transition to unphysical values. Suppressing until we understand the error.
output_fit alps_analyt Subroutine

This subroutine outputs the fit parameters for iperp=0 to stdout to monitor the fit.
output_time alps_io Subroutine

Outputs the date and time in a given format using intrinsic FORTRAN function.
pass_distribution alps_com Subroutine

Passes distribution functions and associated parameters.
pass_instructions alps_com Subroutine

Passes information between processes.
poly_read alps_io Subroutine

Reads in Polynomial Basis Function Parameters
polyharmonic_spline ../../interpolation.f90 Subroutine

This soubroutine interpolates the grid with a polyharmonic thin-plate spline. This subroutine needs the LUPACK and BLAS libraries to evoke the dgesv subroutine. The method uses the Thin Plate Spline. We use these resources: http://cseweb.ucsd.edu/~sjb/eccv_tps.pdf http://www.univie.ac.at/nuhag-php/bibtex/open_files/po94_M%20J%20D%20Powell%2003%2093.pdf http://vision.ucsd.edu/sites/default/files/fulltext(4).pdf
polyharmonic_spline alps_fns_rel Subroutine

This soubroutine interpolates the grid with a polyharmonic thin-plate spline. This subroutine needs the LUPACK and BLAS libraries to evoke the dgesv subroutine. The method uses the Thin Plate Spline. We use these resources: http://cseweb.ucsd.edu/~sjb/eccv_tps.pdf http://www.univie.ac.at/nuhag-php/bibtex/open_files/po94_M%20J%20D%20Powell%2003%2093.pdf http://vision.ucsd.edu/sites/default/files/fulltext(4).pdf
principal_integral_rel alps_fns_rel Function

This function performs the integration near resonances as described in Section 3.1 of the code paper for a relativistic calculation. It is only called if resonances are present in or near the integration domain.
read_f0 alps_io Subroutine

Subroutine for reading in background distribution function
read_in_params generate_distribution Subroutine

This subroutine reads in the parameters for the generation of distribution functions for ALPS.
read_in_params interpolate Subroutine

This subroutine reads in system parameters input file (namelist) as argument after executable: ./interpolate input.in
refine_guess alps_fns Subroutine

This subroutine refines the guess at the starting point of the search for solutions to the dispersion relation when scanning. It is also used by map_search to identify the roots on the map.
resU alps_fns Function

This function evaluates the term proportional to in Eq. (2.9) of the code paper.
resU_rel alps_fns_rel Function

This function evaluates the term proportional to in Eq. (2.9) of the code paper for the relativistic calculation.
rtsec alps_fns Function

An alternative implementation of the secant method, adapted from PLUME.
scan_read alps_io Subroutine

The most important subroutine. Reads in wavevector scan parameters. Defines scanner, which controls the behavior of the wavevector scan.
secant alps_fns Subroutine

This subroutine applies the secant method to find the roots of the dispersion tensor.
secant_osc alps_fns Subroutine

Secant method with adaptive damping and Newton search fallback. Ensure we don’t divide by a tiny value Check convergence Detect oscillations over last four iterations Reduce step If oscillation persists, use finite-difference Newton step Regularized Newton step Apply jump limits to prevent large jumps Cap jump at 10% of om If |D| increases, reduce jump Update previous values Apply update
set_polynomial_basis alps_analyt Subroutine

This subroutine evaluates the General Linear Least Squares fit to the distribution function for component 'is' using the selected polynomial basis functions.
solution_read alps_io Subroutine

Reads in initial guesses for dispersion solutions.
spec_read alps_io Subroutine

Subroutine for reading in species parameters
spec_read generate_distribution Subroutine

Subroutine for reading in species parameters.
split_processes alps_fns Subroutine

This subroutine defines the tasks for the individual processes. It uses the number of species and the required orders of the Bessel functions to define the splitting across the MPI processes.
WOFZ alps_nhds Subroutine

Given a complex number Z = (XI,YI), this subroutine computes the value of the Faddeeva function W(Z) = exp(-Z2)erfc(-IZ), where erfc is the complex complementary error function and I is the imaginary unit.
call~~graph~~CallGraph proc~alps_error alps_error proc~output_time output_time proc~alps_error->proc~output_time mpi_abort mpi_abort proc~alps_error->mpi_abort proc~alps_error_init alps_error_init proc~get_runname get_runname proc~alps_error_init->proc~get_runname proc~get_unused_unit get_unused_unit proc~alps_error_init->proc~get_unused_unit proc~besseli besselI proc~bessi BESSI proc~besseli->proc~bessi proc~bessi0~2 BESSI0 proc~bessi->proc~bessi0~2 proc~bessi1~2 BESSI1 proc~bessi->proc~bessi1~2 dfloat dfloat proc~bessi->dfloat float float proc~bessi->float proc~bessi0 BESSI0 proc~bessi1 BESSI1 proc~bessj BESSJ proc~bessj0 BESSJ0 proc~bessj->proc~bessj0 proc~bessj1 BESSJ1 proc~bessj->proc~bessj1 proc~bessj->float proc~bessk BESSK proc~bessk->dfloat proc~bessk0 BESSK0 proc~bessk1 BESSK1 proc~bm_read bM_read proc~calc_chi calc_chi proc~calc_chi->proc~besseli proc~calc_chi_cold calc_chi_cold proc~calc_chi->proc~calc_chi_cold proc~calc_ypsilon calc_ypsilon proc~calc_chi->proc~calc_ypsilon proc~calc_eigen calc_eigen proc~disp disp proc~calc_eigen->proc~disp proc~calc_ypsilon->proc~besseli proc~dispfunct dispfunct proc~calc_ypsilon->proc~dispfunct proc~cbessj CBESSJ proc~fact Fact proc~cbessj->proc~fact proc~derivative_f0 derivative_f0 proc~derivative_f0_rel derivative_f0_rel proc~derivative_f0->proc~derivative_f0_rel proc~derivative_f0->proc~get_unused_unit proc~derivative_f0_rel->proc~get_unused_unit proc~polyharmonic_spline polyharmonic_spline proc~derivative_f0_rel->proc~polyharmonic_spline proc~determine_bessel_array determine_bessel_array proc~determine_bessel_array->proc~bessj proc~determine_glls determine_GLLS proc~least_squares_fit least_squares_fit proc~determine_glls->proc~least_squares_fit proc~determine_jt determine_JT proc~determine_nmax determine_nmax proc~determine_nmax->proc~bessj mpi_barrier mpi_barrier proc~determine_nmax->mpi_barrier proc~determine_param_fit determine_param_fit proc~determine_param_fit->proc~determine_glls proc~lm_nonlinear_fit LM_nonlinear_fit proc~determine_param_fit->proc~lm_nonlinear_fit proc~output_fit output_fit proc~determine_param_fit->proc~output_fit proc~set_polynomial_basis set_polynomial_basis proc~determine_param_fit->proc~set_polynomial_basis proc~determine_resonances determine_resonances proc~determine_sproc_rel determine_sproc_rel proc~disp->proc~calc_chi proc~disp->proc~determine_resonances proc~full_integrate full_integrate proc~disp->proc~full_integrate proc~int_ee int_ee proc~disp->proc~int_ee proc~int_ee_rel int_ee_rel proc~disp->proc~int_ee_rel proc~disp->mpi_barrier mpi_bcast mpi_bcast proc~disp->mpi_bcast mpi_reduce mpi_reduce proc~disp->mpi_reduce proc~wofz WOFZ proc~dispfunct->proc~wofz proc~display_credits display_credits proc~distribution_analyt distribution_analyt proc~eval_fit eval_fit proc~eval_fit->proc~distribution_analyt proc~fit_function fit_function proc~eval_fit->proc~fit_function proc~fit_function_poly fit_function_poly proc~eval_fit->proc~fit_function_poly proc~factorial factorial proc~find_minima find_minima proc~fit_read fit_read proc~integrate integrate proc~full_integrate->proc~integrate proc~integrate_res integrate_res proc~full_integrate->proc~integrate_res proc~integrate_res_rel integrate_res_rel proc~full_integrate->proc~integrate_res_rel proc~landau_integrate landau_integrate proc~full_integrate->proc~landau_integrate proc~landau_integrate_rel landau_integrate_rel proc~full_integrate->proc~landau_integrate_rel proc~funct_g funct_g proc~int_t int_T proc~funct_g->proc~int_t proc~funct_g_rel funct_g_rel proc~int_t_rel int_T_rel proc~funct_g_rel->proc~int_t_rel proc~gamma Gamma proc~get_indexed_double_namelist_unit get_indexed_double_namelist_unit proc~get_indexed_double_namelist_unit->proc~alps_error proc~get_indexed_double_namelist_unit->proc~get_unused_unit proc~input_unit input_unit proc~get_indexed_double_namelist_unit->proc~input_unit proc~input_unit_exist input_unit_exist proc~get_indexed_double_namelist_unit->proc~input_unit_exist proc~get_indexed_namelist_unit get_indexed_namelist_unit proc~get_indexed_namelist_unit->proc~alps_error proc~get_indexed_namelist_unit->proc~get_unused_unit proc~get_indexed_namelist_unit->proc~input_unit proc~get_indexed_namelist_unit->proc~input_unit_exist proc~get_indexed_namelist_unit~2 get_indexed_namelist_unit proc~get_unused_unit~2 get_unused_unit proc~get_indexed_namelist_unit~2->proc~get_unused_unit~2 proc~input_unit_exist~2 input_unit_exist proc~get_indexed_namelist_unit~2->proc~input_unit_exist~2 proc~input_unit~2 input_unit proc~get_indexed_namelist_unit~2->proc~input_unit~2 proc~get_runname~2 get_runname proc~get_runname~3 get_runname proc~get_unused_unit~3 get_unused_unit proc~init_param init_param proc~init_param->proc~alps_error proc~init_param->proc~bm_read proc~init_param->proc~fit_read proc~init_param->proc~get_indexed_double_namelist_unit proc~init_param->proc~get_indexed_namelist_unit proc~init_param->proc~get_unused_unit proc~map_read map_read proc~init_param->proc~map_read proc~poly_read poly_read proc~init_param->proc~poly_read proc~scan_read scan_read proc~init_param->proc~scan_read proc~solution_read solution_read proc~init_param->proc~solution_read proc~spec_read spec_read proc~init_param->proc~spec_read proc~input_unit_exist~3 input_unit_exist proc~input_unit~3 input_unit proc~int_ee_rel->proc~determine_sproc_rel proc~int_t_rel->proc~bessj proc~int_t_res int_T_res proc~int_t_res_rel int_T_res_rel proc~int_t_res_rel->proc~cbessj proc~integrate->proc~int_t proc~resu resU proc~integrate->proc~resu proc~integrate_res->proc~funct_g proc~integrate_res->proc~integrate proc~integrate_res_rel->proc~determine_sproc_rel proc~integrate_resu_rel integrate_resU_rel proc~integrate_res_rel->proc~integrate_resu_rel proc~integrate_resu_rel->proc~alps_error proc~integrate_resu_rel->proc~int_t_rel proc~principal_integral_rel principal_integral_rel proc~integrate_resu_rel->proc~principal_integral_rel proc~resu_rel resU_rel proc~integrate_resu_rel->proc~resu_rel proc~isnancheck isnancheck proc~landau_integrate->proc~eval_fit proc~landau_integrate->proc~int_t_res proc~landau_integrate_rel->proc~determine_sproc_rel proc~landau_integrate_rel->proc~eval_fit proc~landau_integrate_rel->proc~int_t_res_rel dgemm dgemm proc~least_squares_fit->dgemm dgemv dgemv proc~least_squares_fit->dgemv dgesv dgesv proc~least_squares_fit->dgesv proc~lm_nonlinear_fit->proc~alps_error proc~lm_nonlinear_fit->proc~determine_jt proc~lm_nonlinear_fit->proc~fit_function dgetrf dgetrf proc~lm_nonlinear_fit->dgetrf dgetri dgetri proc~lm_nonlinear_fit->dgetri proc~map_search map_search proc~map_search->proc~disp proc~map_search->proc~find_minima proc~map_search->proc~get_unused_unit proc~refine_guess refine_guess proc~map_search->proc~refine_guess proc~map_search->mpi_bcast proc~normalize normalize proc~om_double_scan om_double_scan proc~om_double_scan->proc~alps_error proc~om_double_scan->proc~calc_eigen proc~om_double_scan->proc~determine_bessel_array proc~om_double_scan->proc~determine_nmax proc~om_double_scan->proc~disp proc~om_double_scan->proc~get_unused_unit proc~om_double_scan->proc~isnancheck proc~rtsec rtsec proc~om_double_scan->proc~rtsec proc~secant secant proc~om_double_scan->proc~secant proc~secant_osc secant_osc proc~om_double_scan->proc~secant_osc proc~split_processes split_processes proc~om_double_scan->proc~split_processes proc~om_double_scan->mpi_barrier proc~om_double_scan->mpi_bcast proc~om_scan om_scan proc~om_scan->proc~alps_error proc~om_scan->proc~calc_eigen proc~om_scan->proc~determine_bessel_array proc~om_scan->proc~determine_nmax proc~om_scan->proc~disp proc~om_scan->proc~get_unused_unit proc~om_scan->proc~isnancheck proc~om_scan->proc~rtsec proc~om_scan->proc~secant proc~om_scan->proc~secant_osc proc~om_scan->proc~split_processes proc~om_scan->mpi_barrier proc~om_scan->mpi_bcast proc~output_fit->proc~alps_error proc~output_fit->proc~eval_fit proc~output_fit->proc~isnancheck proc~pass_distribution pass_distribution proc~pass_distribution->mpi_bcast proc~pass_instructions pass_instructions proc~pass_instructions->mpi_bcast proc~polyharmonic_spline->dgesv proc~polyharmonic_spline~2 polyharmonic_spline proc~polyharmonic_spline~2->dgesv proc~principal_integral_rel->proc~funct_g_rel proc~read_f0 read_f0 proc~read_f0->proc~get_unused_unit proc~read_in_params read_in_params proc~read_in_params->proc~get_indexed_namelist_unit~2 proc~read_in_params->proc~get_runname~2 proc~read_in_params->proc~get_unused_unit~2 proc~spec_read~2 spec_read proc~read_in_params->proc~spec_read~2 proc~read_in_params~2 read_in_params proc~read_in_params~2->proc~get_runname~3 proc~read_in_params~2->proc~get_unused_unit~3 proc~refine_guess->proc~disp proc~refine_guess->proc~get_unused_unit proc~refine_guess->proc~rtsec proc~refine_guess->proc~secant proc~refine_guess->proc~secant_osc proc~refine_guess->mpi_barrier proc~secant->proc~disp proc~secant->mpi_barrier proc~secant_osc->proc~disp proc~secant_osc->mpi_barrier proc~set_polynomial_basis->proc~alps_error proc~split_processes->mpi_barrier dcos dcos proc~wofz->dcos dexp dexp proc~wofz->dexp dsin dsin proc~wofz->dsin idint idint proc~wofz->idint idnint idnint proc~wofz->idnint program~alps alps program~alps->proc~alps_error program~alps->proc~alps_error_init program~alps->proc~derivative_f0 program~alps->proc~determine_bessel_array program~alps->proc~determine_nmax program~alps->proc~determine_param_fit program~alps->proc~display_credits program~alps->proc~init_param program~alps->proc~map_search program~alps->proc~om_double_scan program~alps->proc~om_scan program~alps->proc~output_time program~alps->proc~pass_distribution program~alps->proc~pass_instructions program~alps->proc~read_f0 program~alps->proc~refine_guess program~alps->proc~split_processes program~alps->mpi_barrier mpi_comm_rank mpi_comm_rank program~alps->mpi_comm_rank mpi_comm_size mpi_comm_size program~alps->mpi_comm_size mpi_finalize mpi_finalize program~alps->mpi_finalize mpi_init mpi_init program~alps->mpi_init program~generate_distribution generate_distribution program~generate_distribution->proc~distribution_analyt program~generate_distribution->proc~read_in_params dgamma dgamma program~generate_distribution->dgamma program~interpolate interpolate program~interpolate->proc~read_in_params~2 normalize normalize program~interpolate->normalize polyharmonic_spline polyharmonic_spline program~interpolate->polyharmonic_spline
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