function y=nma_ForwardSub(L,w)
%function y=nma_ForwardSub(L,w)
%
%Forward substitution that solves the lower triangular system
%Ly=w for y
%
%
%INPUT:
%  L:  an nxn L, lower tirangular square matrix
%  w:  vector of size n
%
%OUTPUT:
%  y: the solution to L*y=w

% By Nasser M. Abbasi
% HW 4, MATH 501, CSUF
%
% LU decomposition with threshold support.
% Copyright (C) 2007  Nasser Abbasi
% 
% This program is free software; you can redistribute it and/or
% modify it under the terms of the GNU General Public License
% as published by the Free Software Foundation; either version 2
% of the License, or (at your option) any later version.
% 
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
% GNU General Public License for more details.
% 
% You should have received a copy of the GNU General Public License
% along with this program; if not, write to the Free Software
% Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
% 02110-1301, USA.


%EXAMPLE RUN
% >> [L,U,P]=nma_LU(A,0);
% >> nma_ForwardSub(L,b)
% 
% ans =
% 
%    0.83849604493808
%    0.36727512318587
%    0.12405626870025
%   -0.14539724685973
%    0.17813906538571
%   -0.19809655526705
% % >> 

    if nargin ~= 2
       error 'Only two inputs are required'
    end

    if ~(isnumeric(L)&isnumeric(w))
        error 'input must be numeric'
    end

    [nRow,nCol]=size(w);
    if nRow>1 & nCol>1
        error 'w must be a vector not a matrix'
    end
    
    [nRow,nCol]=size(L);
    if nRow ~= nCol
        error 'Matrix L must be square'
    end       
    
    if length(w) ~= nRow
        error 'w length does not match L matrix dimension'        
    end

    y=zeros(nRow,1);
    y(1)=w(1)/L(1,1);
    
    w=w(:);
    
    for n=2:nRow
        y(n)=( w(n) - L(n,1:n-1)*y(1:n-1) ) / L(n,n);
    end
   
end