src/include/newton.h File Reference

Header of compute a solutions of an equation with Newton method. More...

#include "linear_solve.h"

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Defines
#define	_OPENMP_NEWTON_METHOD   1e2
#define	_FUNCTION_PROTOTYPE
	Function prototype of a pic struct.
Functions
unsigned int	get_newton_max_iterations ()
	Get the maximum number of newton iterations.
unsigned int	set_newton_max_iterations (unsigned int newton_max_iter)
	Set the maximum number of newton iterations.
void *	newton_execute (size_t n, size_t N, double *const x, double *const X, double **const DF, double w, double tol, void(*f)(size_t, size_t, double *const, double *const, double **const, double, double), void *(*solve)(size_t, size_t, double **const, double *const, double *const, double), short unsigned int autonomous)
	Implement the execution of a Newton's method.
void	newton_differential (size_t n, size_t N, double *const x, double *const X, double **const DF, void(*f)(size_t, size_t, double *const, double *const, double **const, double, double), double w, double *h)
	Compute the differential for the Newton's method.
void	dft_r2r_1d (size_t n, size_t N, double *const dft, double *const x, double theta)
	Compute the Discrete Fourier Transform.
int	newton (size_t m, size_t n, double *const x, double *const f, double **const df, void *(*solve)(size_t, size_t, double **const, double *const, double *const, double), double tol)
	Implements the compute of a newton method's iteration.

---

Detailed Description

Header of compute a solutions of an equation with Newton method.

Author:

Joan Gimeno

Date:

22/02/2014 (start)

Version:

1.0

---

Define Documentation

#define _FUNCTION_PROTOTYPE

Function prototype of a pic struct.

#define _OPENMP_NEWTON_METHOD   1e2

---

Function Documentation

void dft_r2r_1d	(	size_t	n,
		size_t	N,
		double *const	dft,
		double *const	x,
		double	theta
	)

Compute the Discrete Fourier Transform.

Parameters:

[in]	n	Space's dimension
[in]	N	Mesh size
[out]	x	Discrete Fourier Transform
[in]	X	Fourier coefficients
[in]	theta	Angle evaluation

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unsigned int get_newton_max_iterations

(

)

Get the maximum number of newton iterations.

Returns:

Maximum number iterations for Newton's method

int newton	(	size_t	m,
		size_t	n,
		double *const	x,
		double *const	f,
		double **const	df,
		void *(*)(size_t, size_t, double **const, double *const, double *const, double)	solve,
		double	tol
	)

Implements the compute of a newton method's iteration.

Parameters:

[in]	m	Rows of the matrix
[in]	n	Columns of the matrix
[in]	x	Current iteration value
[out]	x	Next iteration value
[in]	f	Constant terms
[in]	df	Matrix of the linear system
[in]	*solve	Pointer to solver linear systems of equations
[in]	tol	Tolerance

Return values:

0	Some problem has ocurred
1	When the solution x is accepted by the tolerance given

References solve().

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void newton_differential	(	size_t	n,
		size_t	N,
		double *const	x,
		double *const	X,
		double **const	DF,
		void(*)(size_t, size_t, double *const, double *const, double **const, double, double)	f,
		double	w,
		double *	h
	)

Compute the differential for the Newton's method.

Parameters:

[in]	n	Space's dimension
[in]	N	Mesh size
[in,out]	x	Discrete Fourier Transform for each mesh's element, that is, n(2N+1) components
[in]	X	Fourier coefficients
[in]	DF	Matrix of the linear system
[in]	f	Pointer to function given by the user
[in]	w	Parameter
[in]	h	Auxiliar vector

Returns:

Number of iterations have been performed or NULL if some problem has ocurred

References dft_r2r_1d(), malloc_vector(), and newton_differential_block().

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void * newton_execute	(	size_t	n,
		size_t	N,
		double *const	x,
		double *const	X,
		double **const	DF,
		double	w,
		double	tol,
		void(*)(size_t, size_t, double *const, double *const, double **const, double, double)	f,
		void *(*)(size_t, size_t, double **const, double *const, double *const, double)	solve,
		short unsigned int	autonomous
	)

Implement the execution of a Newton's method.

Parameters:

[in]	n	Space's dimension
[in]	N	Mesh size
[in,out]	x	Discrete Fourier Transform for each mesh's element, that is, n(2N+1) components
[in]	X	Fourier coefficients
[in]	DF	Matrix of the linear system
[in]	w	Parameter
[in]	tol	Tolerance
[in]	f	Pointer to function given by the user
[in]	solve	Pointer to solver linear systems of equations

Returns:

Number of iterations have been performed or NULL if some problem has ocurred

See also:

newton_max_iterations

References newton(), newton_differential(), and solve().

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unsigned int set_newton_max_iterations

(

unsigned int

newton_max_iter

)

Set the maximum number of newton iterations.

Parameters:

[in]

newton_max_iter

New value

Returns:

The old maximum number iterations for Newton's method