zersolf.f File Reference

The Fortran language bindings for the ZerSol C++ library functions. More...

Functions/Subroutines
subroutine	template_subroutine (z, f, p)
	The template subroutine for complex analytic function f(z) and its derivative f'(z).
subroutine	create_solver (solver, f, df, data, xmin, xmax, ymin, ymax)
	Create a data structure needed for the subsequent calls of the solver functions.
subroutine	find_zeros (solver, N, Z, V, n_zeros, status)
	Run the zeros search procedure.
subroutine	print_status (solver, file_name, length)
	Print the status of the zeros search.
subroutine	print_dump (solver, file_name, length)
	Print the dump of the solver data.
subroutine	free_solver (solver)
	Free the memory allocated by the solver.
subroutine	set_nd_method (solver, method)
	Set a finite difference method for numerical evaluation of the function derivative.
subroutine	set_nd_step (solver, h)
	Set a step size (dz) for numerical evaluation of the function derivative.
subroutine	set_min_rec_lev (solver, min_rec_lev)
	Set the minimum recursion level for the winding number evaluation procedure.
subroutine	set_max_rec_lev (solver, max_rec_lev)
	Set the maximum recursion level for the winding number evaluation procedure.
subroutine	set_interp_err (solver, interp_err)
	Set a tolerance of interpolation for the winding number evaluation procedure.
subroutine	set_jump_err (solver, jump_err)
	Set a tolerance of test for discontinuities for the winding number evaluation procedure.
subroutine	set_n_target (solver, n_target)
	Set a desired number of the function zeros.
subroutine	set_start_array (solver, n_start, start)
	Set the array of a user supplied starting values for the Newton's iterations.
subroutine	set_n_split_x (solver, n_split_x)
	Set the number of automatic starting points along Re{z}.
subroutine	set_n_split_y (solver, n_split_y)
	Set the number of automatic starting points along Im{z}.
subroutine	set_max_iter_num (solver, max_iter_num)
	Set the maximum number of the Newton's iterations for each starting point.
subroutine	set_multiplicity (solver, multiplicity)
	Set the multiplicity of a zero.
subroutine	set_eps_for_arg (solver, abs_eps_z, rel_eps_z)
	Set the absolute and relative tolerances for the convergence condition on z.
subroutine	set_eps_for_func (solver, abs_eps_f, rel_eps_f)
	Set the absolute and relative tolerances for the convergence condition on f(z).
subroutine	set_use_winding (solver, use_winding)
	Set a flag that defines whether the solver will use the winding number evaluation or just Newton iterations.
subroutine	set_max_part_level (solver, max_part_level)
	Set the maximum allowed level of the rectangle partition.
subroutine	set_debug_level (solver, debug_level)
	Set the debug level (determines the amount of internal checks).
subroutine	set_print_level (solver, print_level)
	Set the print level (determines the amount of details printed).
subroutine	get_nd_method (solver, method)
	Get a finite difference method for numerical evaluation of the function derivative.
subroutine	get_nd_step (solver, h)
	Get a step size (dz) for numerical evaluation of the function derivative.
subroutine	get_min_rec_lev (solver, min_rec_lev)
	Get the minimum recursion level for the winding number evaluation procedure.
subroutine	get_max_rec_lev (solver, max_rec_lev)
	Get the maximum recursion level for the winding number evaluation procedure.
subroutine	get_interp_err (solver, interp_err)
	Get a tolerance of interpolation for the winding number evaluation procedure.
subroutine	get_jump_err (solver, jump_err)
	Get a tolerance of test for discontinuities for the winding number evaluation procedure.
subroutine	get_n_target (solver, n_target)
	Get a desired number of the function zeros.
subroutine	get_start_array (solver, n_start, start)
	Get the array of a user supplied starting values for the Newton's iterations.
subroutine	get_n_split_x (solver, n_split_x)
	Get the number of automatic starting points along Re{z}.
subroutine	get_n_split_y (solver, n_split_y)
	Get the number of automatic starting points along Im{z}.
subroutine	get_max_iter_num (solver, max_iter_num)
	Get the maximum number of the Newton's iterations for each starting point.
subroutine	get_multiplicity (solver, multiplicity)
	Get the multiplicity of a zero.
subroutine	get_eps_for_arg (solver, abs_eps_z, rel_eps_z)
	Get the absolute and relative tolerances for the convergence condition on z.
subroutine	get_eps_for_func (solver, abs_eps_f, rel_eps_f)
	Get the absolute and relative tolerances for the convergence condition on f(z).
subroutine	get_use_winding (solver, use_winding)
	Get a flag that defines whether the solver will use the winding number evaluation or just Newton iterations.
subroutine	get_max_part_level (solver, max_part_level)
	Get the maximum allowed level of the rectangle partition.
subroutine	get_debug_level (solver, debug_level)
	Get the debug level (determines the amount of internal checks).
subroutine	get_print_level (solver, print_level)
	Get the print level (determines the amount of details printed).

Detailed Description

The Fortran language bindings for the ZerSol C++ library functions.

The following subroutines demonstrate the Fortran interface of the ZerSol library functions. Make sure that precision of floating point numbers in your Fortran code

integer, parameter :: prec = 8  ! prec = 4 for single precision and prec = 8 for double precision

is consistent with that used in the ZerSol Fortran bindings. You can change the type of floating point numbers used in the ZerSol interface in the file zersolf.cpp in line:

#define _Real double /* float, double (recommended) */

Don't forget to rebuild the ZerSol Fortran bindings after that!

Please note, that pp parameter defined in a user Fortran code (see test cases) must conform the architecture of your machine:

integer, parameter :: pp = 8    ! pp = 4 for 32-bit machines and pp = 8 for 64-bit machines

Function/Subroutine Documentation

subroutine template_subroutine	(	complex(prec)	z,
		complex(prec)	f,
			p
	)

The template subroutine for complex analytic function f(z) and its derivative f'(z).

Parameters

z	value of independent complex variable
f	the function value at z
p	any additional parameter: a number, an array, etc...

subroutine create_solver	(	integer(pp)	solver,
		integer(pp)	f,
		integer(pp)	df,
			data,
		real(prec)	xmin,
		real(prec)	xmax,
		real(prec)	ymin,
		real(prec)	ymax
	)

Create a data structure needed for the subsequent calls of the solver functions.

Parameters

solver	address of the solver structure
f	address of a Fortran subroutine that evaluates the complex function value
df	address of a Fortran subroutine that evaluates the complex function derivative
data	a structure (a number, an array, etc) that can be used to pass any data into the function and its derivative
xmin	minimum x-coordinate of the rectangular region
xmax	maximum x-coordinate of the rectangular region
ymin	minimum y-coordinate of the rectangular region
ymax	maximum y-coordinate of the rectangular region

subroutine find_zeros	(	integer(pp)	solver,
		integer	N,
		complex(prec), dimension(n)	Z,
		complex(prec), dimension(n)	V,
		integer	n_zeros,
		integer	status
	)

Run the zeros search procedure.

Parameters

solver	address of the solver structure
N	length of the passed Z and V arrays
Z	array for the function zeros
V	array for the function values V = F(Z)
n_zeros	number of the zeros found
status	search status

subroutine print_status	(	integer(pp)	solver,
		character(length+1)	file_name,
		integer	length
	)

Print the status of the zeros search.

Parameters

solver	address of the solver structure
file_name	name of a file to store the search status
length	length of the trimmed file_name character array

subroutine print_dump	(	integer(pp)	solver,
		character(length+1)	file_name,
		integer	length
	)

Print the dump of the solver data.

Parameters

solver	address of the solver structure
file_name	name of a file to store the solver dump
length	length of the trimmed file_name character array

subroutine free_solver

(

integer(pp)

solver

)

Free the memory allocated by the solver.

Parameters

solver

address of the solver structure

subroutine set_nd_method	(	integer(pp)	solver,
		integer	method
	)

Set a finite difference method for numerical evaluation of the function derivative.

Parameters

solver	address of the solver structure
method	finite difference method: pass method = 0 for 3-point stencil approximation (second order) and method = 1 for 5-point stencil approximation (fourth order)

subroutine set_nd_step	(	integer(pp)	solver,
		real(prec)	h
	)

Set a step size (dz) for numerical evaluation of the function derivative.

Parameters

solver	address of the solver structure
h	step size

subroutine set_min_rec_lev	(	integer(pp)	solver,
		integer	min_rec_lev
	)

Set the minimum recursion level for the winding number evaluation procedure.

Parameters

solver	address of the solver structure
min_rec_lev	minimum recursion level

subroutine set_max_rec_lev	(	integer(pp)	solver,
		integer	max_rec_lev
	)

Set the maximum recursion level for the winding number evaluation procedure.

Parameters

solver	address of the solver structure
max_rec_lev	maximum recursion level

subroutine set_interp_err	(	integer(pp)	solver,
		real(prec)	interp_err
	)

Set a tolerance of interpolation for the winding number evaluation procedure.

Parameters

solver	address of the solver structure
interp_err	tolerance of interpolation

subroutine set_jump_err	(	integer(pp)	solver,
		real(prec)	jump_err
	)

Set a tolerance of test for discontinuities for the winding number evaluation procedure.

Parameters

solver	address of the solver structure
jump_err	tolerance of test for discontinuities

subroutine set_n_target	(	integer(pp)	solver,
		integer	n_target
	)

Set a desired number of the function zeros.

Parameters

solver	address of the solver structure
n_target	target number of zeros

subroutine set_start_array	(	integer(pp)	solver,
		integer	n_start,
		complex(prec), dimension(n_start)	start
	)

Set the array of a user supplied starting values for the Newton's iterations.

Parameters

solver	address of the solver structure
n_start	number of starting values
start	array of starting values

subroutine set_n_split_x	(	integer(pp)	solver,
		integer	n_split_x
	)

Set the number of automatic starting points along Re{z}.

Parameters

solver	address of the solver structure
n_split_x	number of starting points

subroutine set_n_split_y	(	integer(pp)	solver,
		integer	n_split_y
	)

Set the number of automatic starting points along Im{z}.

Parameters

solver	address of the solver structure
n_split_y	number of starting points

subroutine set_max_iter_num	(	integer(pp)	solver,
		integer	max_iter_num
	)

Set the maximum number of the Newton's iterations for each starting point.

Parameters

solver	address of the solver structure
max_iter_num	maximum number of iterations

subroutine set_multiplicity	(	integer(pp)	solver,
		integer	multiplicity
	)

Set the multiplicity of a zero.

Parameters

solver	address of the solver structure
multiplicity	expected multiplicity of a zero

subroutine set_eps_for_arg	(	integer(pp)	solver,
		real(prec)	abs_eps_z,
		real(prec)	rel_eps_z
	)

Set the absolute and relative tolerances for the convergence condition on z.

Parameters

solver	address of the solver structure
abs_eps_z	absolute tolerance
rel_eps_z	relative tolerance

subroutine set_eps_for_func	(	integer(pp)	solver,
		real(prec)	abs_eps_f,
		real(prec)	rel_eps_f
	)

Set the absolute and relative tolerances for the convergence condition on f(z).

Parameters

solver	address of the solver structure
abs_eps_f	absolute tolerance
rel_eps_f	relative tolerance

subroutine set_use_winding	(	integer(pp)	solver,
		integer	use_winding
	)

Set a flag that defines whether the solver will use the winding number evaluation or just Newton iterations.

Parameters

solver	address of the solver structure
use_winding	flag: true - use the winding number evaluation, false - use the Newton's iterations only

subroutine set_max_part_level	(	integer(pp)	solver,
		integer	max_part_level
	)

Set the maximum allowed level of the rectangle partition.

Parameters

solver	address of the solver structure
max_part_level	partition level

subroutine set_debug_level	(	integer(pp)	solver,
		integer	debug_level
	)

Set the debug level (determines the amount of internal checks).

Parameters

solver	address of the solver structure
debug_level	debug level

subroutine set_print_level	(	integer(pp)	solver,
		integer	print_level
	)

Set the print level (determines the amount of details printed).

Parameters

solver	address of the solver structure
print_level	print level

subroutine get_nd_method	(	integer(pp)	solver,
		integer	method
	)

Get a finite difference method for numerical evaluation of the function derivative.

Parameters

solver	address of the solver structure
method	finite difference method: method = 0 for 3-point stencil approximation (second order) and method = 1 for 5-point stencil approximation (fourth order)

subroutine get_nd_step	(	integer(pp)	solver,
		real(prec)	h
	)

Get a step size (dz) for numerical evaluation of the function derivative.

Parameters

solver	address of the solver structure
h	step size

subroutine get_min_rec_lev	(	integer(pp)	solver,
		integer	min_rec_lev
	)

Get the minimum recursion level for the winding number evaluation procedure.

Parameters

solver	address of the solver structure
min_rec_lev	minimum recursion level

subroutine get_max_rec_lev	(	integer(pp)	solver,
		integer	max_rec_lev
	)

Get the maximum recursion level for the winding number evaluation procedure.

Parameters

solver	address of the solver structure
max_rec_lev	maximum recursion level

subroutine get_interp_err	(	integer(pp)	solver,
		real(prec)	interp_err
	)

Get a tolerance of interpolation for the winding number evaluation procedure.

Parameters

solver	address of the solver structure
interp_err	tolerance of interpolation

subroutine get_jump_err	(	integer(pp)	solver,
		real(prec)	jump_err
	)

Get a tolerance of test for discontinuities for the winding number evaluation procedure.

Parameters

solver	address of the solver structure
jump_err	tolerance of test for discontinuities

subroutine get_n_target	(	integer(pp)	solver,
		integer	n_target
	)

Get a desired number of the function zeros.

Parameters

solver	address of the solver structure
n_target	target number of zeros

subroutine get_start_array	(	integer(pp)	solver,
		integer	n_start,
		complex(prec)	start
	)

Get the array of a user supplied starting values for the Newton's iterations.

Parameters

solver	address of the solver structure
n_start	number of starting values
start	array of starting values to be filled in

subroutine get_n_split_x	(	integer(pp)	solver,
		integer	n_split_x
	)

Get the number of automatic starting points along Re{z}.

Parameters

solver	address of the solver structure
n_split_x	number of starting points

subroutine get_n_split_y	(	integer(pp)	solver,
		integer	n_split_y
	)

Get the number of automatic starting points along Im{z}.

Parameters

solver	address of the solver structure
n_split_y	number of starting points

subroutine get_max_iter_num	(	integer(pp)	solver,
		integer	max_iter_num
	)

Get the maximum number of the Newton's iterations for each starting point.

Parameters

solver	address of the solver structure
max_iter_num	maximum number of iterations

subroutine get_multiplicity	(	integer(pp)	solver,
		integer	multiplicity
	)

Get the multiplicity of a zero.

Parameters

solver	address of the solver structure
multiplicity	expected multiplicity of a zero

subroutine get_eps_for_arg	(	integer(pp)	solver,
		real(prec)	abs_eps_z,
		real(prec)	rel_eps_z
	)

Get the absolute and relative tolerances for the convergence condition on z.

Parameters

solver	address of the solver structure
abs_eps_z	absolute tolerance
rel_eps_z	relative tolerance

subroutine get_eps_for_func	(	integer(pp)	solver,
		real(prec)	abs_eps_f,
		real(prec)	rel_eps_f
	)

Get the absolute and relative tolerances for the convergence condition on f(z).

Parameters

solver	address of the solver structure
abs_eps_f	absolute tolerance
rel_eps_f	relative tolerance

subroutine get_use_winding	(	integer(pp)	solver,
		integer	use_winding
	)

Get a flag that defines whether the solver will use the winding number evaluation or just Newton iterations.

Parameters

solver	address of the solver structure
use_winding	flag: true - use the winding number evaluation, false - use the Newton's iterations only

subroutine get_max_part_level	(	integer(pp)	solver,
		integer	max_part_level
	)

Get the maximum allowed level of the rectangle partition.

Parameters

solver	address of the solver structure
max_part_level	maximum partition level

subroutine get_debug_level	(	integer(pp)	solver,
		integer	debug_level
	)

Get the debug level (determines the amount of internal checks).

Parameters

solver	address of the solver structure
debug_level	debug level

subroutine get_print_level	(	integer(pp)	solver,
		integer	print_level
	)

Get the print level (determines the amount of details printed).

Parameters

solver	address of the solver structure
print_level	print level