% This program is used in simplex programs to perform the pivoting in the
% simplex tableau.
% The problem is to minimize z=c*x+d, subject to constraints Ax=b and x>=0.
% The input data are d, c, A, b, the size of A, as well as the row and column 
% number identifying the pivot position.

% Written by helga schaffrin, oct. 2003


function [d,c,A,b]=pivot(d,c,A,b,m,n,row,column)

% Starting the pivoting: A(row,column) should be 1.

b(row)=b(row)/A(row,column);
A(row,:)=A(row,:)/A(row,column);

% Continuing with the pivoting: All other rows should have entry 0
% in that column...

b([1:row-1 row+1:m])=b([1:row-1 row+1:m])-(b(row)*A([1:row-1 row+1:m],column));
A([1:row-1 row+1:m],:)=A([1:row-1 row+1:m],:)-A([1:row-1 row+1:m],column)*A(row,:);

% ...including c.

d=d-b(row)*c(column);
c=c-c(column)*A(row,:);