function [W,b,err]=wid_hoff1(X,Y,lr,iters)
%FUNCTION [W,b,err]=wid_hoff1(X,Y,lr,iters)
%This function trains a linear neural network
%using the Widrow-Hoff training algorithm. This
%is a steepest descent method, and so will need
%a learning rate, lr (for example, lr=0.1)
%
% Input: Data sets X, Y (for input, output)
% Dimensions: number of points x dimension
% 
% lr: Learning rate
% iters: Number of times to run through the data
%
% Output: Weight matrix W and bias vector b so that Wx+b approximates y.
%
% err: Training record for the error
%
%It’s convenient to work with X and Y as dimension by number of points

X=X'; Y=Y';
[m1,m2]=size(X);
[n1,n2]=size(Y);

%Initialize W and b to zero
W=zeros(n1,m1);
b=zeros(n1,1);
err=zeros(iters,m2);  %Storage for all errors

for i=1:iters %Number of times through data
    for j=1:m2 %Go through every data point
        e=(Y(:,j)-(W*X(:,j)+b)); %Target - Network Output
        dW=lr*e*X(:,j)';
        W=W+dW;
        b=b+lr*e;
        err(i,j)=norm(e); %Store error for later
    end
end