%
% subroutine for solving a linear system with A=LU
% given, but the k-th column in A is incorrect and
% the correct column is stored in akt. Output:
% the solution z in At z = b where At is the matrix
% obtained by replacing the kth column in A by akt.
% 
%
% l   = lower triangular matrix in A=LU
% u   = upper triangular matrix in A=LU
% b   = right-hand side in the linear system
% akt = correct column
% k   = number of the incorrect column in A
% n   = dimension of the matrix
%

function z=smartsolve(l,u,b,akt,k,n)