Code covered by the BSD License

### Highlights fromNumerical Methods Using MATLAB, 2e

lusolv(A,B,row)
function  [X,Y] = lusolv(A,B,row)
%---------------------------------------------------------------------------
%LUSOLV   Forward substitution followed by back substitution is used.
% Sample call
%   [X,Y] = lufact(A,B,row)
% Remark
%   The matrix A must be in factored LU form.
%   It is the output from the function  lufact.
% Inputs
%   A     matrix obtained from  lufact
%   row   row permutation information obtained from  lufact
%   B     right hand side vector
% Return
%   X     solution: to AX=B
%   Y     solution: to LY=PB
%
% NUMERICAL METHODS: MATLAB Programs, (c) John H. Mathews 1995
% To accompany the text:
% NUMERICAL METHODS for Mathematics, Science and Engineering, 2nd Ed, 1992
% Prentice Hall, Englewood Cliffs, New Jersey, 07632, U.S.A.
% Prentice Hall, Inc.; USA, Canada, Mexico ISBN 0-13-624990-6
% Prentice Hall, International Editions:   ISBN 0-13-625047-5
% This free software is compliments of the author.
%
% Algorithm 3.3 (PA = LU Factorization with Pivoting).
% Section	3.6, Triangular Factorizaton, Page 175
%---------------------------------------------------------------------------

[n n] = size(A);
Y = zeros(n,1);
Y(1) = B(row(1));
for k = 2:n,
Y(k) = B(row(k)) - A(row(k),1:k-1)*Y(1:k-1);
end
X = zeros(n,1);
X(n) = Y(n)/A(row(n),n);
for k = n-1:-1:1,
X(k) = (Y(k) - A(row(k),k+1:n)*X(k+1:n))/A(row(k),k);
end