Simple implementations of PLU factorization. More...

#include <stdio.h>
#include <math.h>
#include "lu_impls.h"

Include dependency graph for lu_impls.c:

Functions
int	rb_dgetrf (int m, int n, double A, int lda, int ipiv)
	Computes the PLU factorization of an m by n matrix A, i.e. . More...

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

void	rb_dswap (int n, double X, int incx, double Y, int incy)
	Swaps the value of vector X and Y. 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...

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

Detailed Description

Simple implementations of PLU factorization.

Author: RyanBern

Function Documentation

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_dgetrf	(	int	m,
		int	n,
		double *	A,
		int	lda,
		int *	ipiv
	)

Computes the PLU factorization of an m by n matrix A, i.e. $ PA=LU $ .

Parameters

m	The number of rows of A.
n	The number of columns of A.
A	Input/Output. Pointer to the storage of A.
lda	The leading dimension of A.
ipiv	Output. The integer array that stores the pivoting indices. That is, row i exchanges with row ipiv[i].

Returns: The function returns 0 when it exits normally. When it returns with a positive integer i, it means that lu stops at i-th row because A may be singular or ill-conditioned.

On exit, R is stored at the upper triangular/trapezoidal part of A, L is stored at the strictly lower triangular/trapezoidal part of A, the diagonal of L is not stored.

For example, suppose A is 4 by 3

$A = \left(\begin{array}{ccc} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \\ a_{41} & a_{42} & a_{43} \\ \end{array}\right)$

Then after LU is completed, A is overwritten by

$A = \left(\begin{array}{ccc} u_{11} & u_{12} & u_{13} \\ l_{21} & u_{22} & u_{23} \\ l_{31} & l_{32} & u_{33} \\ l_{41} & l_{42} & l_{43} \\ \end{array}\right)$

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_dswap	(	int	n,
		double *	X,
		int	incx,
		double *	Y,
		int	incy
	)

Swaps the value of vector X and 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.

int rb_idamax	(	int	n,
		double *	X,
		int	incx
	)

Finds the index of 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.

Functions

Detailed Description

Function Documentation