Subroutines for equation parsing in case of an analytic trajectory or luminosity mode. More...

Functions/Subroutines
logical function, private	is_digit (str_in)
	Function to decide whether a character is a number or not (i.e., 0-9). More...

logical function, private	is_operator (str_in)
	Function to decide whether a character is a mathematical operator or not. Functions (as e.g., sin) are not defined here! More...

logical function, private	is_dot_operator (str_in)
	Function to decide whether a character is "*" or "/". More...

logical function, private	is_line_operator (str_in)
	Function to decide whether a character is a "+" or "-". More...

logical function, private	is_power_operator (str_in)
	Function to decide whether a character is a "^". More...

logical function, private	is_separator (str_in)
	Function to decide whether a character can be associated with a number. More...

real(r_kind) function, private	operation (number_1, number_2, str_in)
	Function to perform a simple mathematical operation. More...

real(r_kind) function, private	eval_function (number, str_in)
	Function to perform a function operations. More...

subroutine, private	make_pars_str_consistent
	Subroutine to check the parsing string for consistency and correct it. More...

real(r_kind) function, private	common_variables (inp_str)
	Function to define constants. More...

subroutine, private	store_digits_operator
	Store mathematical operators (+-*/) and numbers in arrays. More...

subroutine, private	get_simple_result
	Evaluate a simple string expression, without brackets and functions. More...

subroutine, private	evaluate
	Evaluate a complex string expression. More...

real(r_kind) function, public	parse_string (input_string, var_value)
	Takes a string and evaluates the expression. More...

subroutine, public	find_start_value (input_string, eq_value, initial_guess, converged, result)
	Finds a value of the variable for a given y-value. More...

Variables
character(max_fname_len), private	parsing_string
	Current substring to parse. More...

character(max_fname_len), private	complete_string
	Complete input string. More...

integer, private	operator_count

integer, private	number_count

character(1), dimension(:), allocatable, private	operators
	Array containing the operations of the equation as a character (e.g., ["*","+"]) More...

real(r_kind), dimension(:), allocatable, private	numbers
	Array containing the numbers of the equation (e.g., [1, 2, 3]) More...

real(r_kind), private	variable_value
	Input variable, set by parse_string. More...

character(1), parameter, private	variable_name ='x'
	Name of the variable that is replaced by parse_string. More...

Detailed Description

Subroutines for equation parsing in case of an analytic trajectory or luminosity mode.

The subroutine can calculate equations from a string, e.g., "5.1+3d-2*(2-1)*sin(pi)/x". A variable name (in the upper example "x") can be given, which will be filled with a value. Everything in this function is private with the exception of the function "parse_string" which serves as a interface to parse the given string. The return value of this function is a real (i.e., not a string).

Author: Moritz Reichert

Date: 20.12.20

Function/Subroutine Documentation

◆ common_variables()

real(r_kind) function, private parser_module::common_variables ( character(len=*), intent(in) inp_str )

private

Function to define constants.

This function translates names of constants to numbers (real). For example, "pi" is translated to 3.1415. Define new constants (names and values) in this function.

Example

b = common_variables("pi")

After this, will be 3.141592653589793

Note: New variables can be defined here.

Author: Moritz Reichert

Date: 20.12.20

Parameters

[in] inp_str Input character, defining the constant

Returns: A value of a given constant

Definition at line 441 of file parser_module.f90.

◆ eval_function()

real(r_kind) function, private parser_module::eval_function	(	real(r_kind), intent(in)	number,
		character(max_fname_len), intent(in)	str_in
	)

private

Function to perform a function operations.

Depending on the input it will calculate, e.g., the square root (sqrt) or the sinus (sin). To add a function to the functionality of the parser, add the translation in this function here.

Example

b = eval_function(4, "sqrt")

b will be 2.

Note: New parsing functions can be defined here.

Author: Moritz Reichert

Date: 20.12.20

Parameters

[in]	str_in	Name of the function
[in]	number	input to the function

Returns: function(number), where function is defined by the input string.

Definition at line 314 of file parser_module.f90.

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◆ evaluate()

subroutine, private parser_module::evaluate

private

Evaluate a complex string expression.

Evaluate expressions with brackets ( i.e., "(" and ")" ) and function names (i.e., "sin(5)" ).

Example

parsing_string = "2+sin(pi)-5*(1+1)"

call evaluate()

After this, the array numbers will have -8 on its first entry.

Author: Moritz Reichert

Date: 20.12.20

Definition at line 713 of file parser_module.f90.

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◆ find_start_value()

subroutine, public parser_module::find_start_value	(	character(300), intent(in)	input_string,
		real(r_kind), intent(in)	eq_value,
		real(r_kind), intent(in)	initial_guess,
		logical, intent(out)	converged,
		real(r_kind), intent(out)	result
	)

Finds a value of the variable for a given y-value.

This function solves an equation, i.e., finds the value of variable "x" for expressions as, for example, "3*x+2+x^2 = 10" returns 1.701562. This works with a newton raphson to find the root of f(x) - 10.

Example

input_string  = "3*x+2+x^2"
eq_value      = 10
initial_guess = 0.0
converged     = .false.
result        = 0.0
call find_start_value(input_string,eq_value,initial_guess,converged,result)

After this, result will be 1.701562 and converged will be .True.

Author: Moritz Reichert

Date: 20.12.20

Parameters

[in]	input_string	String to parse
[in]	eq_value	Value of the equation
[in]	initial_guess	Initial guess for the variable
[out]	converged	Flag that indicates a success
[out]	result	Time at which the expression is equal to eq_value.

Definition at line 855 of file parser_module.f90.

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◆ get_simple_result()

subroutine, private parser_module::get_simple_result

private

Evaluate a simple string expression, without brackets and functions.

This subroutine is able to evaluate simply expressions without brackets or functions. Only +- * / and ^ is allowed here. In addition a variable name or constant names may be given. For example "2+3-1" will store the result (4) in the first entry of the "numbers" array.

Example

parsing_string = "0-2-3^2"

call get_simple_result()

After this, the array numbers will have -11 on its first entry.

Author: Moritz Reichert

Date: 20.12.20

Definition at line 594 of file parser_module.f90.

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◆ is_digit()

logical function, private parser_module::is_digit ( character(1), intent(in) str_in )

private

Function to decide whether a character is a number or not (i.e., 0-9).

Example

b = is_digit("5")

c = is_digit("a")

b will be .True. and c will be .False.

Author: Moritz Reichert

Date: 20.12.20

Parameters

[in] str_in Input character

Returns: True in case of a digit and False in case of another character

Definition at line 73 of file parser_module.f90.

◆ is_dot_operator()

logical function, private parser_module::is_dot_operator ( character(1), intent(in) str_in )

private

Function to decide whether a character is "*" or "/".

Example

b = is_dot_operator("+")

c = is_dot_operator("*")

b will be .False. and c will be .True.

See also: is_line_operator, is_power_operator, is_separator, is_operator

Author: Moritz Reichert

Date: 20.12.20

Parameters

[in] str_in Input character

Returns: True in case of a * or / input string and False otherwise

Definition at line 141 of file parser_module.f90.

◆ is_line_operator()

logical function, private parser_module::is_line_operator ( character(1), intent(in) str_in )

private

Function to decide whether a character is a "+" or "-".

Example

b = is_line_operator("+")

c = is_line_operator("*")

b will be .True. and c will be .False.

See also: is_dot_operator, is_power_operator, is_separator, is_operator

Author: Moritz Reichert

Date: 20.12.20

Parameters

[in] str_in Input character

Returns: True in case of a + or - input string and False otherwise

Definition at line 172 of file parser_module.f90.

◆ is_operator()

logical function, private parser_module::is_operator ( character(1), intent(in) str_in )

private

Function to decide whether a character is a mathematical operator or not. Functions (as e.g., sin) are not defined here!

Example

b = is_operator("+")

c = is_operator("5")

b will be .True. and c will be .False.

See also: is_line_operator, is_power_operator, is_separator, is_dot_operator

Author: Moritz Reichert

Date: 20.12.20

Parameters

[in] str_in Input character

Returns: True in case of an operator (+,-,*,/,^) and False otherwise

Definition at line 104 of file parser_module.f90.

◆ is_power_operator()

logical function, private parser_module::is_power_operator ( character(1), intent(in) str_in )

private

Function to decide whether a character is a "^".

Example

b = is_power_operator("^")

c = is_power_operator("-")

b will be .True. and c will be .False.

See also: is_dot_operator, is_line_operator, is_separator, is_operator

Author: Moritz Reichert

Date: 20.12.20

Parameters

[in] str_in Input character

Returns: True in case of a ^ input string and False otherwise

Definition at line 203 of file parser_module.f90.

◆ is_separator()

logical function, private parser_module::is_separator ( character(1), intent(in) str_in )

private

Function to decide whether a character can be associated with a number.

Allowed characters are ".", "d", and "e" (for scientific format of a number).

Example

b = is_separator(",")

c = is_separator("-")

b will be .True. and c will be .False.

See also: is_dot_operator, is_line_operator, is_separator, is_operator, is_power_operator

Author: Moritz Reichert

Date: 20.12.20

Parameters

[in] str_in Input character

Returns: True in case of a ",", "d", and "e" input string and False otherwise

Definition at line 235 of file parser_module.f90.

◆ make_pars_str_consistent()

subroutine, private parser_module::make_pars_str_consistent

private

Subroutine to check the parsing string for consistency and correct it.

This subroutine will convert all characters to lower case characters (e.g., 4E-1 -> 4e-1) and will add a leading "0" in case the string starts with a mathematical operator (i.e., + or -, e.g., "-3+5" -> "0-3+5"). Furthermore, it checks for "+-" (and "++", "--" and all combinations) and will correct it to "-". Additionally "**" is corrected to "^", in this way the power can be written by both (**, and ^).

Example

parsing_string = "-2+-3**2"

call make_pars_str_consistent()

After this, parsing_string will be "0-2-3^2"

Returns: A corrected string that can be parsed by other functions

Author: Moritz Reichert

Date: 20.12.20

Definition at line 372 of file parser_module.f90.

◆ operation()

real(r_kind) function, private parser_module::operation	(	real(r_kind)	number_1,
		real(r_kind)	number_2,
		character(1), intent(in)	str_in
	)

private

Function to perform a simple mathematical operation.

Depending on the input character, the function performs "+". "-", "*", "/", or "^". In case of a different character, an error is raised.

Example

b = operation(10.3, 2.7, "+")

b will be 13.

Author: Moritz Reichert

Date: 20.12.20

Parameters

[in] str_in Input character (containing "+","-","*","/","^".)

Returns: Result of a certain operation of number_1 and number_2, determined by the input string.

Parameters

number_2 Input numbers on which the operation is performed

Definition at line 269 of file parser_module.f90.

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◆ parse_string()

real(r_kind) function, public parser_module::parse_string	(	character(300), intent(in)	input_string,
		real(r_kind), intent(in)	var_value
	)

Takes a string and evaluates the expression.

This function is accessible to the outside of the module. It serves as interface between other modules and this one. Also replaces variable_name with variable_value.

Example

b = parse_string("-8+3*(2-1)-x",10)

After this, b will be -15.

Author: Moritz Reichert

Date: 20.12.20

Parameters

[in]	input_string	String to parse
[in]	var_value	Value of the variable that will be stored in variable_value

Returns: Value of the evaluated expression

Definition at line 806 of file parser_module.f90.

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◆ store_digits_operator()

subroutine, private parser_module::store_digits_operator

private

Store mathematical operators (+-*/) and numbers in arrays.

The result of this subroutine are two arrays, one containing all operators (e.g., for "3+2*2+1-1": ['+','*','+','-']) and one array containing all numbers (as real type, [3,2,2,1,1]).

Example

parsing_string = "0-2-3^2"

call store_digits_operator()

After this, the array operators will contain ("-","-","^"), and the array numbers will contain (0, 2, 3, 2).

Author: Moritz Reichert

Date: 20.12.20

Definition at line 480 of file parser_module.f90.

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Variable Documentation

◆ complete_string

character(max_fname_len), private parser_module::complete_string

private

Complete input string.

Definition at line 29 of file parser_module.f90.

◆ number_count

integer, private parser_module::number_count

private

Definition at line 32 of file parser_module.f90.

◆ numbers

real(r_kind), dimension(:), allocatable, private parser_module::numbers

private

Array containing the numbers of the equation (e.g., [1, 2, 3])

Definition at line 34 of file parser_module.f90.

◆ operator_count

integer, private parser_module::operator_count

private

Definition at line 32 of file parser_module.f90.

◆ operators

character(1), dimension(:), allocatable, private parser_module::operators

private

Array containing the operations of the equation as a character (e.g., ["*","+"])

Definition at line 33 of file parser_module.f90.

◆ parsing_string

character(max_fname_len), private parser_module::parsing_string

private

Current substring to parse.

Definition at line 28 of file parser_module.f90.

◆ variable_name

character(1), parameter, private parser_module::variable_name ='x'

private

Name of the variable that is replaced by parse_string.

Definition at line 38 of file parser_module.f90.

◆ variable_value

real(r_kind), private parser_module::variable_value

private

Input variable, set by parse_string.

Definition at line 37 of file parser_module.f90.

Functions/Subroutines

Variables

Detailed Description

Function/Subroutine Documentation

◆ common_variables()

Example

◆ eval_function()

Example

◆ evaluate()

Example

◆ find_start_value()

Example

◆ get_simple_result()

Example

◆ is_digit()

Example

◆ is_dot_operator()

Example

◆ is_line_operator()

Example

◆ is_operator()

Example

◆ is_power_operator()

Example

◆ is_separator()

Example

◆ make_pars_str_consistent()

Example

◆ operation()

Example

◆ parse_string()

Example

◆ store_digits_operator()

Example

Variable Documentation

◆ complete_string

◆ number_count

◆ numbers

◆ operator_count

◆ operators

◆ parsing_string

◆ variable_name

◆ variable_value