function Problem04()
  %  I'm writing this as a function so you can include
  %  subfunctions below, which have been started for you.  The parts for you 
  %  to fill in are marked with ???
  %
  %  To run this, in the command window type: testques4
  
  % Step 1:  Randomly initialize trainging parameters and other constants
  %   Nothing to change here.
  x=randn; y=randn;    % Variables to minimize E.
  MaxIters=100;        % Max number of times to run.
  alpha=0.01;          % Step size for gradient descent.
  
  % Step 2:  Calculate the error and gradient using the subroutine below. 
  %    Please change the function below, you don't need to change the two
  %    lines below.
  
  [E, gradE]=ErrorCalculation([x;y]);
  ErrToPlot(1)=E;
  
  % Step 3:  Main loop
  for i=1:MaxIters
    
    % Gradient Descent:  Finish these two expressions using the step size and gradient.
    x=x ???
    y=y ???
    

    %Get ready for the next iteration:
    %  No changes here or to the end of this "for" loop.
    [E,gradE]=ErrorCalculation([x;y]);
    ErrToPlot(i+1)=E;
    
    % Check to see if we can exit:
    if norm(gradE)<1e-8
      break
    end
    
  end % End of the for loop.
  
  % Visualization:
  %  No changes needed here.
  figure(1)
  plot(ErrToPlot);
  
  fprintf('Finished on iteration %d\n',i);
  fprintf('Final error was %f\n',ErrToPlot(end));
  fprintf('Solution is %f, %f\n',x,y);
  
 end

function [E,gradE]=ErrorCalculation(vecx)
  x=vecx(1); y=vecx(2);
  
  % This section is where you'll want to make changes as noted:
  
  % What is the error you wrote down in 4(a).  The unknowns are x, y like on the exam.
 
  E=???
  
  % What is the gradient you wrote down in 4(b):
  Ex=???
  Ey=??
  
  % You don't have to change anything else; notice the vector gradE will
  %   contain BOTH partial derivatives.
  gradE=[Ex;Ey];
  
end