Module is part of the LIBSTELL. This modules contains code to define and integrate along an arbitray path. More...

Data Types
interface	check
	Interface for checking the results of the unit tests. More...

interface	path_construct
	Construction interface using either path_construct_int or path_construct_vertex. More...

interface	path_destruct
	Destruct interface using either path_destruct_int or path_destruct_vertex. More...

type	path_int_class
	Class containing the parameters of the integration method to use. More...

type	vertex
	A single point in space defined by an z, y, z coordinate. A vertex is structured as a singly linked list. More...

Functions/Subroutines
type(path_int_class) function, pointer	path_construct_int (method, npoints, length)
	Construct a single path_int_class. More...

type(vertex) function, pointer	path_construct_vertex (position)
	Construct a single vertex. More...

subroutine	path_destruct_int (this)
	Deconstruct a path_int_class object. More...

recursive subroutine	path_destruct_vertex (this)
	Deconstruct a vertex object. More...

recursive subroutine	path_append_vertex (this, position)
	Append a vertex to a path. More...

recursive real(rprec) function	path_integrate (this, path, integration_function, context)
	Integrate along the path. More...

recursive real(rprec) function, dimension(3)	path_search (path, search_function, context, found)
	Search along the path. More...

real(rprec) function, private	integrate (this, context, vertex1, vertex2, integration_function)
	Line integrate between to points. More...

real(rprec) function, private	integrate_add (this, context, vertex1, vertex2, integration_function)
	Line integrate between to points. More...

real(rprec) function, private	integrate_gleg (this, context, vertex1, vertex2, integration_function)
	Integrate between to points using Guass-Legendre quadrature. More...

real(rprec) function, private	integrate_hp_gleg (this, context, vertex1, vertex2, integration_function)
	Integrate between to points using hp Guass-Legendre quadrature method. More...

logical function, private	search (context, vertex1, vertex2, search_function, xcart)
	Search line between to points. More...

subroutine	path_get_gaussqad_weights (a, b, abscissas, weights)
	@breif Calculate the weights and abscissas for Gauss-Legendre integration. More...

logical function	path_test ()
	Path unit test function. More...

logical function, private	check_log (expected, received, testNum, name)
	Check a logical value. More...

logical function, private	check_real (expected, received, testNum, name)
	Check a real value. More...

logical function, private	check_int (expected, received, testNum, name)
	Check an integer value. More...

real(rprec) function, private	test_function (context, xcart, dxcart, length, dx)
	Call back function to test the integration. More...

Variables
integer, parameter	path_none_type = -1
	No qaudrature type.

integer, parameter	path_add_type = 0
	Integrate the length in addition.

integer, parameter	path_gleg_type = 1
	Integrate the path using Gauss Legendre Quadrature.

integer, parameter	path_hp_glep_type = 2
	Integrate the path using a hp approch.

real(rprec), parameter	path_default_dx = 0.0025
	Default step size of the integration.

Detailed Description

Module is part of the LIBSTELL. This modules contains code to define and integrate along an arbitray path.

Function/Subroutine Documentation

◆ check_int()

logical function, private integration_path::check_int	(	integer, intent(in)	expected,
		integer, intent(in)	received,
		integer, intent(in)	testNum,
		character (len=*), intent(in)	name
	)

private

Check an integer value.

Checks that the expected value matches the recieved. Otherwise report an error.

Parameters

[in]	expected	The known value.
[in]	received	The known test value.
[in]	testNum	The number of the test.
[in]	name	The name of the test.

Returns: True if the check passes and false otherwise.

Definition at line 1066 of file integration_path.f.

◆ check_log()

logical function, private integration_path::check_log	(	logical, intent(in)	expected,
		logical, intent(in)	received,
		integer, intent(in)	testNum,
		character (len=*), intent(in)	name
	)

private

Check a logical value.

Checks that the expected value matches the recieved. Otherwise report an error.

Parameters

[in]	expected	The known value.
[in]	received	The known test value.
[in]	testNum	The number of the test.
[in]	name	The name of the test.

Returns: True if the check passes and false otherwise.

Definition at line 997 of file integration_path.f.

◆ check_real()

logical function, private integration_path::check_real	(	real(rprec), intent(in)	expected,
		real(rprec), intent(in)	received,
		integer, intent(in)	testNum,
		character (len=*), intent(in)	name
	)

private

Check a real value.

Checks that the expected value matches the recieved. Otherwise report an error.

Parameters

[in]	expected	The known value.
[in]	received	The known test value.
[in]	testNum	The number of the test.
[in]	name	The name of the test.

Returns: True if the check passes and false otherwise.

Definition at line 1030 of file integration_path.f.

◆ integrate()

real (rprec) function, private integration_path::integrate	(	type (path_int_class), intent(in)	this,
		character(len=1), dimension(:), intent(in)	context,
		type (vertex), intent(in)	vertex1,
		type (vertex), intent(in)	vertex2,
			integration_function
	)

private

Line integrate between to points.

This chooses the specific integration method.

Parameters

[in]	this	In instance of a path_int_class instance.
[in]	context	Generic object that contains data for the integration function.
[in]	vertex1	Starting point.
[in]	vertex2	Ending point.
[in]	dxinput	optional input allowing user to define dx
	integration_function	Function pointer that defines the integrand.

Returns: The path integrated value between the vertex1 and vertex2.

Definition at line 396 of file integration_path.f.

◆ integrate_add()

real (rprec) function, private integration_path::integrate_add	(	type (path_int_class), intent(in)	this,
		character(len=1), dimension(:), intent(in)	context,
		type (vertex), intent(in)	vertex1,
		type (vertex), intent(in)	vertex2,
			integration_function
	)

private

Line integrate between to points.

This divids the straight line path defined by two vertices and line integrates the function. The integrand is proveded by means of call back function.

Parameters

[in]	this	In instance of a path_int_class instance.
[in]	context	Generic object that contains data for the integration function.
[in]	vertex1	Starting point.
[in]	vertex2	Ending point.
	integration_function	Function pointer that defines the integrand.

Returns: The path integrated value between the vertex1 and vertex2.

Definition at line 460 of file integration_path.f.

◆ integrate_gleg()

real (rprec) function, private integration_path::integrate_gleg	(	type (path_int_class), intent(in)	this,
		character(len=1), dimension(:), intent(in)	context,
		type (vertex), intent(in)	vertex1,
		type (vertex), intent(in)	vertex2,
			integration_function
	)

private

Integrate between to points using Guass-Legendre quadrature.

This divids the straight line path defined by two vertices and line integrates the function. The integrand is proveded by means of call back function.

Parameters

[in]	this	In instance of a path_int_class instance.
[in]	context	Generic object that contains data for the integration function.
[in]	vertex1	Starting point.
[in]	vertex2	Ending point.
	integration_function	Function pointer that defines the integrand.

Returns: The path integrated value between the vertex1 and vertex2.

Definition at line 531 of file integration_path.f.

◆ integrate_hp_gleg()

real (rprec) function, private integration_path::integrate_hp_gleg	(	type (path_int_class), intent(in)	this,
		character(len=1), dimension(:), intent(in)	context,
		type (vertex), intent(in)	vertex1,
		type (vertex), intent(in)	vertex2,
			integration_function
	)

private

Integrate between to points using hp Guass-Legendre quadrature method.

This divids the straight line path defined by two vertices into a set of intergval of length len. Then Gauss-Legendre quadrature is used to integrate the function across each interval. The integrand is provided by means of call back function.

Parameters

[in]	this	In instance of a path_int_class instance.
[in]	context	Generic object that contains data for the integration function.
[in]	vertex1	Starting point.
[in]	vertex2	Ending point.
	integration_function	Function pointer that defines the integrand.

Returns: The path integrated value between the vertex1 and vertex2.

Definition at line 607 of file integration_path.f.

◆ path_append_vertex()

recursive subroutine integration_path::path_append_vertex	(	type (vertex), pointer	this,
		real (rprec), dimension(3), intent(in)	position
	)

Append a vertex to a path.

Recursively runs through the next vertex to find the last vertex. Once the last vertex is found, a new vertex is allocated and appended to the path. This allow works as a constructer and allocates the first vertex if needed.

Parameters

[in,out]	this	Vertex to append path to.
[in]	position	Cartesian position of the vertex object.

Definition at line 253 of file integration_path.f.

◆ path_construct_int()

type (path_int_class) function, pointer integration_path::path_construct_int	(	character (len=*), intent(in)	method,
		integer, intent(in)	npoints,
		real (rprec), intent(in)	length
	)

Construct a single path_int_class.

Allocates memory and initializes a path_int_class object.

Parameters

[in]	method	Integartion method to use.
[in]	npoints	Number of quadrature points to use.
[in]	length	Length of the interval.

Returns: A pointer to a constructed path_int_class object.

Definition at line 116 of file integration_path.f.

◆ path_construct_vertex()

type (vertex) function, pointer integration_path::path_construct_vertex ( real (rprec), dimension(3), intent(in) position )

Construct a single vertex.

Allocates memory and initializes a vertex object.

Parameters

[in] position Cartesian position of the vertex object.

Returns: A pointer to a constructed vertex object.

Definition at line 167 of file integration_path.f.

◆ path_destruct_int()

subroutine integration_path::path_destruct_int ( type (path_int_class), pointer this )

Deconstruct a path_int_class object.

Deallocates memory and uninitializes a path_int_class object.

Parameters

[in,out] this A path_int_class instance.

Definition at line 192 of file integration_path.f.

◆ path_destruct_vertex()

recursive subroutine integration_path::path_destruct_vertex ( type (vertex), pointer this )

Deconstruct a vertex object.

Deallocates memory and uninitializes a vertex object. This recursively deconstructed the next vertex until the last in the linked list is found.

Parameters

[in,out] this A vertex instance.

Definition at line 222 of file integration_path.f.

◆ path_get_gaussqad_weights()

subroutine integration_path::path_get_gaussqad_weights	(	real (rprec), intent(in)	a,
		real (rprec), intent(in)	b,
		real(rprec), dimension(:), intent(out)	abscissas,
		real(rprec), dimension(:), intent(out)	weights
	)

@breif Calculate the weights and abscissas for Gauss-Legendre integration.

This suprogram calculated the weights and abscissas for Gauss-Legendre integration. The subroutine is adapted from NIMROD which was adapted from Numerical Recipies, 2ed., Cambridge Press.

Parameters

[in]	a	Start point for integration.
[in]	b	End point for integration.
[out]	abscissas	Array of abscissas.
[out]	weights	Array of weights.

Definition at line 770 of file integration_path.f.

◆ path_integrate()

recursive real (rprec) function integration_path::path_integrate	(	type (path_int_class), intent(in)	this,
		type (vertex), intent(in)	path,
			integration_function,
		character (len=1), dimension(:), intent(in)	context
	)

Integrate along the path.

Recursively runs through the next vertex to find the last vertex. Once the last vertex is found, integrate alone that path. The integrand is proveded by means of call back function.

Parameters

[in]	this	In instance of a path_int_class instance.
[in]	path	Starting vertex to of the path to integrate.
	integration_function	Function pointer that defines the integrand.
[in]	context	Generic object that contains data for the integration function.

Returns: The total integrated path to the end.

Definition at line 293 of file integration_path.f.

◆ path_search()

recursive real (rprec) function, dimension(3) integration_path::path_search	(	type (vertex), intent(in)	path,
			search_function,
		character (len=1), dimension(:), intent(in)	context,
		logical, intent(out)	found
	)

Search along the path.

Recursively runs through the next vertex to find the last vertex. Once the last vertex is found, a new vertex is allocated and appended to the path. The integrand is proveded by means of call back function.

Parameters

[in]	path	Starting vertex to begin search.
	search_function	Function pointer that defines the search criteria.
[in]	context	Generic object that contains data for the integration function.
[out]	found	Signals if the condition was met.

Returns: The vertex position along the path where the search condition was found.

Definition at line 344 of file integration_path.f.

◆ path_test()

logical function integration_path::path_test

Path unit test function.

This runs the associated unit tests and returns the result.

Returns: True if the tests pass and false otherwise.

Definition at line 851 of file integration_path.f.

◆ search()

logical function, private integration_path::search	(	character(len=1), dimension(:), intent(in)	context,
		type (vertex), intent(in)	vertex1,
		type (vertex), intent(in)	vertex2,
			search_function,
		real (rprec), dimension(3), intent(out)	xcart
	)

private

Search line between to points.

This divides the straight line path defined by two vertices and searched for a condition. The search criteria is proveded by means of call back function.

Parameters

[in]	context	Generic object that contains data for the search function.
[in]	vertex1	Starting point.
[in]	vertex2	Ending point.
	search_function	Function pointer that defines the search criteria.
[out]	xcart	Point where the search criteria was found.

Returns: True if the criteria was met between vertex1 and vertex2.

Definition at line 691 of file integration_path.f.

◆ test_function()

real (rprec) function, private integration_path::test_function	(	character (len=1), dimension(:), intent(in)	context,
		real (rprec), dimension(3), intent(in)	xcart,
		real (rprec), dimension(3), intent(in)	dxcart,
		real (rprec), intent(in)	length,
		real (rprec), intent(in)	dx
	)

private

Call back function to test the integration.

This defined a function of f(x) = 1.

Parameters

[in]	context	Generic object that contains data for the integration function.
[in]	xcart	Current point in the integration.
[in]	dxcart	Vector direction of the current integration path.
[in]	length	Length along the current integration.
[in]	dx	Scaler length of the current integration path.

Returns: One

Definition at line 1100 of file integration_path.f.

Data Types

Functions/Subroutines

Variables

Detailed Description

Function/Subroutine Documentation

◆ check_int()

◆ check_log()

◆ check_real()

◆ integrate()

◆ integrate_add()

◆ integrate_gleg()

◆ integrate_hp_gleg()

◆ path_append_vertex()

◆ path_construct_int()

◆ path_construct_vertex()

◆ path_destruct_int()

◆ path_destruct_vertex()

◆ path_get_gaussqad_weights()

◆ path_integrate()

◆ path_search()

◆ path_test()

◆ search()

◆ test_function()