Simple implementations of conjugate gradient method for solving linear systems. More...

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "cg_impls.h"

Include dependency graph for cg_impls.c:

Functions
int	rb_dcgsv (int n, Aop A, void ctxt, const double b, double *sol)
	Solves a linear system using conjugate method. More...

void	rb_dscal (int n, double a, double *X, int incx)
	Scales a vector by a constant. $x\leftarrow ax$ . More...

void	rb_daxpy (int n, double a, const double X, int incx, double Y, int incy)
	Scale a vector X by a constant add add it to another vector Y. $y\leftarrow y+ax$ . More...

double	rb_damax (int n, const double *X, int incx)
	Finds the element in X which has the maximum absolute value. More...

double	rb_ddot (int n, const double X, int incx, const double Y, int incy)
	Perform inner product . More...

void	rb_dcopy (int n, const double X, int incx, double Y, int incy)
	Copy a vector to another. More...

void	rb_dsub (int n, const double X, int incx, const double Y, int incy, double *Z, int incz)
	Perform vector substraction, i.e. . More...

Detailed Description

Simple implementations of conjugate gradient method for solving linear systems.

Author: RyanBern

Function Documentation

void rb_damax	(	int	n,
		const double *	X,
		int	incx
	)

Finds the element in X which has the maximum absolute value.

Parameters

n	The length of X.
X	The pointer to the storage of X.
incx	The increment of indices of X.

Returns: The element which has the maximum absolute value

void rb_daxpy	(	int	n,
		double	a,
		const double *	X,
		int	incx,
		double *	Y,
		int	incy
	)

Scale a vector X by a constant add add it to another vector Y. $y\leftarrow y+ax$ .

Parameters

n	The length of X and Y.
a	The scaling constant.
X	The pointer to the storage of X.
incx	The increment of indices of X.
Y	Input/Output. The pointer to the storage of Y.
incy	The increment of indices of Y.

int rb_dcgsv	(	int	n,
		Aop	A,
		void *	ctxt,
		const double *	b,
		double *	sol
	)

Solves a linear system using conjugate method.

Parameters

n	The dimension of A.
A	The function pointer of type Aop.
ctxt	The context needed by A.
b	The right hand side of .
sol	Output. The computed solution of the equation.

Returns: The number of iterations in the conjugate method.

The function rb_dcgsv solves the linear system $Ax=b$ with conjugate gradient method. It requires $A$ to be positive definite.

Conjugate gradient method doesn't need the matrix $A$ to be given explicitly. It only needs $A$ when applying it to a vector. That is, the user only has to tell how to perform $y\leftarrow Ax$ , by providing the parameter of type Aop and all the context needed by the operator.

void rb_dcopy	(	int	n,
		const double *	X,
		int	incx,
		double *	Y,
		int	incy
	)

Copy a vector to another.

Parameters

n	The length of X and Y.
X	The pointer to the storage of X.
incx	The increment of indices of X.
Y	The pointer to the storage of Y.
incy	The increment of indices of Y.

double rb_ddot	(	int	n,
		const double *	X,
		int	incx,
		const double *	Y,
		int	incy
	)

Perform inner product $x^Ty$ .

Parameters

n	The length of X and Y.
X	The pointer to the storage of X.
incx	The increment of indices of X.
Y	The pointer to the storage of Y.
incy	The increment of indices of Y.

Returns: The inner product.

void rb_dscal	(	int	n,
		double	a,
		double *	X,
		int	incx
	)

Scales a vector by a constant. $x\leftarrow ax$ .

Parameters

n	The length of X.
a	The scaling factor.
X	The pointer to the storage of X.
incx	The increment of indices.

void rb_dsub	(	int	n,
		const double *	X,
		int	incx,
		const double *	Y,
		int	incy,
		double *	Z,
		int	incz
	)

Perform vector substraction, i.e. $z=x-y$ .

Parameters

n	The length of X and Y.
X	The pointer to the storage of X.
incx	The increment of indices of X.
Y	The pointer to the storage of Y.
incy	The increment of indices of Y.
Z	Output. The pointer to the storage of Z.
incy	The increment of indices of Z.

Functions

Detailed Description

Function Documentation