Header of periodic invariant curve. More...

#include "newton.h"

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Data Structures
struct	pic
	Periodic Invariant Curve. More...
Defines
#define	PIC_AUTONOMOUS
	The dynamic system is autonomous.
#define	PIC_NAUTONOMOUS
	The dynamic system is not autonomous.
Typedefs
typedef struct pic	pic
Functions
unsigned int	pic_get_max_iterations ()
	Get maximum number of iterations.
unsigned int	pic_set_max_iterations (unsigned int max_iter)
	Set maximum number of iterations.
size_t	pic_get_n (struct pic *const)
size_t	pic_get_N (struct pic *const)
double *	pic_get_x (struct pic *const)
double *	pic_get_X (struct pic *const)
double **	pic_get_DF (struct pic *const)
double	pic_get_w (struct pic *const)
size_t	pic_get_mesh_size (struct pic *const)
size_t	pic_get_dimension_size (struct pic *const)
int	pic_set_mesh_size (struct pic *const p, size_t N)
	Set the mesh size.
int	pic_set_dimension_size (struct pic *const p, size_t n)
	Set the dimension.
int	pic_set_function_pointer (struct pic *const p, _FUNCTION_PROTOTYPE)
int	pic_set_function_solve (struct pic *const p, _SOLVE_PROTOTYPE)
struct pic *	pic_create (size_t n, size_t N, double w, double *const X, _FUNCTION_PROTOTYPE, _SOLVE_PROTOTYPE)
	Function that initializes a struct pic.
void *	pic_execute (struct pic *const p, double tol)
	Function that compute the Discrete Fourier Transform.
double **	pic_differential (struct pic const p, size_t const m, size_t *const n)
	Return a differential matrix for the current pic struct's values.
double *	pic_load_fourier_coef (size_t n, size_t N, FILE *const f)
	Function that load the Fourier coefficients from a given file.
double *	pic_loadas_fourier_coef (size_t n, size_t N, char *const name)
	Function that load the Fourier coefficients from a given file by name.
int	pic_save_fourier_coef (struct pic const p, FILE const f)
	Function that saves the Fourier coefficients in a given file.
int	pic_saveas_fourier_coef (struct pic const p, char const name)
	Function that saves the Fourier coefficients in a given file by name.
int	pic_save_curve (struct pic const p, FILE const f)
	Function that saves the values of the solution curve in a given file.
int	pic_saveas_curve (struct pic const p, char const name)
	Function that saves the values of the solution curve in a given file by name.
int	pic_saveas_differential (struct pic const p, char const name)
	Function that saves the values of the differential of Newton method in a given file by name.
int	pic_save_differential (struct pic const p, FILE const f)
	Function that saves the values of the differential of Newton method in a given file.
int	pic_saveas_differential_indexs (struct pic const p, char const name)
	Function that saves the values of the differential of Newton method in a given file by name from its indexs.
int	pic_save_differential_indexs (struct pic const p, FILE const f)
	Function that saves the values of the differential of Newton method in a given file from its indexs.
void	pic_destroy (struct pic *const p)
	Function that frees the memory space pointed to by the differents pointers of struct pic.

Detailed Description

Header of periodic invariant curve.

Author:: Joan Gimeno

Date:: 22/01/2014 (start)

Version:: 1.0

Define Documentation

#define PIC_AUTONOMOUS

The dynamic system is autonomous.

#define PIC_NAUTONOMOUS

The dynamic system is not autonomous.

Typedef Documentation

pic

Function Documentation

struct pic * pic_create	(	size_t	n,
		size_t	N,
		double	w,
		double *const	X,
		_FUNCTION_PROTOTYPE	,
		_SOLVE_PROTOTYPE
	)		`[read]`

Function that initializes a struct pic.

Parameters:

[in]	n	Space's dimension of the function $f \colon \mathbb{R}^n \rightarrow \mathbb{R}^n$
[in]	N	Mesh size of the $\mathbb{T}^1$ , 2N+1
[in]	w	Real number densely filling the circumference
[in]	X	Seed of the newton method. The size has to be n(2N+1)
[in]	f	Function pointer
[in]	solve	Function pointer for solves a linear system equations

Return values:

NULL	If memory space has not been allocated
p	Pointer to struct pic

Precondition:: The space's dimension is not zero

Postcondition:: The struct pic has been initialized

Note:: If the seed of newton method is NULL, the default seed will be the vector zero

References pic::autonomous, pic::DF, pic::f, pic::n, pic::N, PIC_NAUTONOMOUS, pic::solve, solve(), SOLVE_WITH_LU, pic::w, pic::x, and pic::X.

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void pic_destroy ( struct pic *const p )

Function that frees the memory space pointed to by the differents pointers of struct pic.

Parameters:

[in] p Pointer to periodic invariant curve

Postcondition:: The memory space has been freed

References pic::autonomous, pic::DF, pic::n, pic::N, pic::x, and pic::X.

double ** pic_differential	(	struct pic *const	p,
		size_t *const	m,
		size_t *const	n
	)

Return a differential matrix for the current pic struct's values.

Parameters:

[in]	p	Pointer to a pic struct
[out]	m	Number of differential matrix's rows
[out]	n	Number of differential matrix's columns

Returns:: Pointer to initial position of the matrix differential or NULL if some problem occurred

Precondition:: The pointer to a pic struct is not NULL

Note:: The pointers for rows and columns can be NULL

References pic::autonomous, pic::DF, pic::f, pic::n, pic::N, newton_differential(), pic::w, pic::x, and pic::X.

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void * pic_execute	(	struct pic *const	p,
		double	tol
	)

Function that compute the Discrete Fourier Transform.

Parameters:

[in]	p	Pointer to the pic struct
[in]	tol	Tolerance for the result

Returns:: NULL if some problem ocurrer. Otherwise the number of iterations performed until the result (minimum 1)

Note:: The mesh size of pic struct can have been changed. Use

See also:: pic_get_mesh_size

Precondition:: The pointers are not NULL

Postcondition:: The vector p->x has the solution

References _init_pic(), pic::autonomous, pic::DF, pic::f, pic::n, pic::N, newton_execute(), pic_error(), pic_estimate_mesh_size(), pic_set_mesh_size(), pic_x(), pic::solve, pic::w, pic::x, and pic::X.

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double ** pic_get_DF ( struct pic * const p )

Parameters:

[in] p Pointer to a pic struct

Returns:: The pointer to the differential of the pic struct

Precondition:: The pointer is not NULL

References pic::DF.

size_t pic_get_dimension_size ( struct pic * const p )

Parameters:

[in] p Pointer to a pic struct

Returns:: Space's dimension of the pic struct

Precondition:: The pointer is not NULL

References pic::n.

unsigned int pic_get_max_iterations ( )

Get maximum number of iterations.

Returns:: Maximum iterations that increase the mesh size

size_t pic_get_mesh_size ( struct pic * const p )

Parameters:

[in] p Pointer to a pic struct

Returns:: Mesh size of the pic struct

Precondition:: The pointer is not NULL

References pic::N.

size_t pic_get_n ( struct pic * const p )

Parameters:

[in] p Pointer to a pic struct

Returns:: Space's dimension of the pic struct

Precondition:: The pointer is not NULL

References pic::n.

size_t pic_get_N ( struct pic * const p )

Parameters:

[in] p Pointer to a pic struct

Returns:: The mesh size of the pic struct

Precondition:: The pointer is not NULL

References pic::N.

double pic_get_w ( struct pic * const p )

Parameters:

[in] p Pointer to a pic struct

Returns:: The real number of the pic struct

Precondition:: The pointer is not NULL

References pic::w.

double * pic_get_x ( struct pic * const p )

Parameters:

[in] p Pointer to a pic struct

Returns:: The value table of the curve solution of the pic struct

Precondition:: The pointer is not NULL

References pic::x.

double * pic_get_X ( struct pic * const p )

Parameters:

[in] p Pointer to a pic struct

Returns:: The Fourier's coefficients of the pic struct

Precondition:: The pointer is not NULL

References pic::X.

double * pic_load_fourier_coef	(	size_t	n,
		size_t	N,
		FILE *const	f
	)

Function that load the Fourier coefficients from a given file.

Parameters:

[in]	n	Dimension of each coefficient
[in]	N	Number of coefficient
[in]	f	Pointer to a file

Returns:: n*(2N+1)-dimensional vector with the Fourier coefficients saved

Precondition:: The pointer is not NULL

Postcondition:: The user has to free the memory for the pointer returned

Note:: The structure of the vector is a_0, a_1, b_1, ..., a_N, b_N where each element is a n-dimensional vector

References _MAX_LENGTH_STRING_INPUT, and pic::n.

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double * pic_loadas_fourier_coef	(	size_t	n,
		size_t	N,
		char *const	name
	)

Function that load the Fourier coefficients from a given file by name.

Parameters:

[in]	n	Dimension of each coefficient
[in]	N	Number of coefficient
[in]	f	Pointer to a file

Returns:: n*(2N+1)-dimensional vector with the Fourier coefficients saved

Postcondition:: The user has to free the memory for the pointer returned

Precondition:: The pointer is not NULL

Note:: The structure of the vector is a_0, a_1, b_1, ..., a_N, b_N where each element is a n-dimensional vector

References pic::f, and pic_load_fourier_coef().

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int pic_save_curve	(	struct pic *const	p,
		FILE *const	f
	)

Function that saves the values of the solution curve in a given file.

Parameters:

[in]	p	Pointer to struct pic
[in]	f	Output file

Return values:

0	If some error has occurred in some moment of the process
1	Otherwise

Precondition:: The pointers are not NULL

Postcondition:: The file with name has been created or modified with the result

References pic::n, pic::N, and pic::x.

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int pic_save_differential	(	struct pic *const	p,
		FILE *const	f
	)

Function that saves the values of the differential of Newton method in a given file.

Parameters:

[in]	p	Pointer to struct pic
[in]	f	Output file

Return values:

0	If some error has occurred in some moment of the process
1	Otherwise

Precondition:: The pointers are not NULL

Postcondition:: The file with name has been created or modified with the result

References pic::DF, pic::n, pic::N, and save_matrix().

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int pic_save_differential_indexs	(	struct pic *const	p,
		FILE *const	f
	)

Function that saves the values of the differential of Newton method in a given file from its indexs.

Parameters:

[in]	p	Pointer to struct pic
[in]	f	Output file

Return values:

0	If some error has occurred in some moment of the process
1	Otherwise

Precondition:: The pointers are not NULL

Postcondition:: The file with name has been created or modified with the result

References pic::DF, pic::n, pic::N, and save_matrix_indexs().

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int pic_save_fourier_coef	(	struct pic *const	p,
		FILE *const	f
	)

Function that saves the Fourier coefficients in a given file.

Parameters:

[in]	p	Pointer to struct pic
[in]	f	Output file

Return values:

0	If some error has occurred in some moment of the process
1	Otherwise

Precondition:: The pointers are not NULL

Postcondition:: The file has been created or modified with the result

References pic::n, pic::N, and pic::X.

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int pic_saveas_curve	(	struct pic *const	p,
		char *const	name
	)

Function that saves the values of the solution curve in a given file by name.

Parameters:

[in]	p	Pointer to struct pic
[in]	name	Name of the output file

Return values:

0	If some error has occurred in some moment of the process
1	Otherwise

Precondition:: The struct pointer is not NULL

Postcondition:: The file with name has been created or modified with the result

References pic::f, and pic_save_curve().

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int pic_saveas_differential	(	struct pic *const	p,
		char *const	name
	)

Function that saves the values of the differential of Newton method in a given file by name.

Parameters:

[in]	p	Pointer to struct pic
[in]	name	Name of the output file

Return values:

0	If some error has occurred in some moment of the process
1	Otherwise

Precondition:: The struct pointer is not NULL

Postcondition:: The file with name has been created or modified with the result

References pic::DF, pic::n, pic::N, and saveas_matrix().

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int pic_saveas_differential_indexs	(	struct pic *const	p,
		char *const	name
	)

Function that saves the values of the differential of Newton method in a given file by name from its indexs.

Parameters:

[in]	p	Pointer to struct pic
[in]	name	Name of the output file

Return values:

0	If some error has occurred in some moment of the process
1	Otherwise

Precondition:: The struct pointer is not NULL

Postcondition:: The file with name has been created or modified with the result

References pic::DF, pic::n, pic::N, and saveas_matrix_indexs().

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int pic_saveas_fourier_coef	(	struct pic *const	p,
		char *const	name
	)

Function that saves the Fourier coefficients in a given file by name.

Parameters:

[in]	p	Pointer to struct pic
[in]	f	Output file

Return values:

0	If some error has occurred in some moment of the process
1	Otherwise

Precondition:: The pointers are not NULL

Postcondition:: The file has been created or modified with the result

References pic::f, and pic_save_fourier_coef().

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int pic_set_dimension_size	(	struct pic *const	p,
		size_t	n
	)

Set the dimension.

Parameters:

[in]	p	Pointer to a pic struct
[in]	N	New dimension

Returns:: 0 if some error occurred or the old dimension

Precondition:: The new mesh size is not 0 and the pointer is not NULL

Postcondition:: The pointer memory has been reallocated with the new dimension

References _pic_realloc(), pic::autonomous, pic::n, and pic::N.

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int pic_set_function_pointer	(	struct pic *const	p,
		_FUNCTION_PROTOTYPE
	)

Parameters:

[in]	p	Pointer to a pic struct
[in]	f	Pointer to a function pointer

Return values:

0	if some argument is NULL
1	Otherwise

int pic_set_function_solve	(	struct pic *const	p,
		_SOLVE_PROTOTYPE
	)

Parameters:

[in]	p	Pointer to a pic struct
[in]	f	Pointer to a function pointer

Return values:

0	if some argument is NULL
1	Otherwise

References pic::solve, and solve().

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unsigned int pic_set_max_iterations ( unsigned int max_iter )

Set maximum number of iterations.

Parameters:

[in] max_iter New value

Returns:: The old maximum iterations that increase the mesh size

int pic_set_mesh_size	(	struct pic *const	p,
		size_t	N
	)

Set the mesh size.

Parameters:

[in]	p	Pointer to a pic struct
[in]	N	New mesh size

Returns:: 0 if some error occurred or the old mesh size

Precondition:: The new mesh size is not 0 and the pointer is not NULL

Postcondition:: The pointer memory has been reallocated with the new mesh size

References _pic_realloc(), pic::autonomous, pic::n, and pic::N.

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Data Structures

Defines

Typedefs

Functions

Detailed Description

Define Documentation

Typedef Documentation

Function Documentation