rlp.h File Reference

Implementation of linear programming functions. More...

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Functions
int	simplex (double *a, int n, int m, FILE *file)
	Applies the Simplex Algorithm to an optimization problem.
int	simplexp (double *a, int n, int m, int pos, FILE *file)
	Applies the Simplex algorithm to a primal optimization problem.
int	simplexd (double *a, int n, int m, int pos, FILE *file)
	Applies the Simplex algorithm to a dual optimization problem.

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Detailed Description

Implementation of linear programming functions.

Author:

Rui Carlos Gonçalves

Version:

3.0

Date:

07/2012

Definition in file rlp.h.

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Function Documentation

int simplex	(	double *	a,
		int	n,
		int	m,
		FILE *	file
	)

Applies the Simplex Algorithm to an optimization problem.

Given a problem with n variables (x₁, ..., x_n) and m conditions (c₁ = b₁, ..., c_m = b_m), the function must receive a matrix a of size (m+1)*(n+m+2), containing:

• at a[0][i-1] (for i in [1, n]) the coefficient of variable x_i in the expression to minimize;
• at a[0][i] (for i in [n, n+m+1]) the value 0;
• at a[i][j-1] (for i in [1, m], and for j in [1, n]) the coefficient of variable x_j in condition c_i;
• at a[i][j] (for i in [1, m], and for j in [n, n+m-1]) the identity matrix;
• at a[i][n+m] (for i in [1, m]) the value of b_i;
• at a[i][n+m+1] (for i in [1, m]) the value of n+i.

Allows to specify the file where the table resulting from the application of the algorithm (using the parameter file).

Parameters:

a	matrix that represents the problem
n	number of variable of the function
m	number restrictions
file	file where the tables will be saved (or NULL)

Returns:

0 if it is possible to solve the problem
1 otherwise

Definition at line 118 of file rlp.c.

int simplexd	(	double *	a,
		int	n,
		int	m,
		int	pos,
		FILE *	file
	)

Applies the Simplex algorithm to a dual optimization problem.

The input matrix (a) must follow the format defined in function <ref>simplex</ref>.

Allows to specify the file where the table resulting from the application of the algorithm (using the parameter file).

Parameters:

a	matrix that represents the problem
n	number of variables of the function
m	number restrictions
pos	position of the minimum value of the first row (it must be a negative value)
file	file where the tables will be saved (or NULL)

Returns:

0 if it is possible to solve the problem
1 otherwise

Definition at line 198 of file rlp.c.

int simplexp	(	double *	a,
		int	n,
		int	m,
		int	pos,
		FILE *	file
	)

Applies the Simplex algorithm to a primal optimization problem.

The input matrix (a) must follow the format defined in function <ref>simplex</ref>.

Allows to specify the file where the table resulting from the application of the algorithm (using the parameter file).

Parameters:

a	matrix that represents the problem
n	number of variables of the function
m	number restrictions
pos	position of the minimum value of the restrictions' column (it must be a negative value)
file	file where the tables will be saved (or NULL)

Returns:

0 if it is possible to solve the problem
1 otherwise

Definition at line 137 of file rlp.c.