Broyden's Method for Mat 4010

function [ AnsVec, TracF  ] = BroydenMethod ( A, x )
# Matthew Graham
# Mat 4010
# Broyden's Method
# A is the matrix in which we are trying to find the eigenvalues and eigenvectors
# x is the initial guess for the eigenvector with the eigenvalue as the last entry
# work in progress as far as comments are concerned
# rest of the code is good to go

  if (size(A, 1) == size(A, 2))
    n = size(A,1);
    v = x(1:n);
    lambda = x(n+1);

    for i = 1: n

       F(i) = [A(i,:)*v];
       i = i+1;

    endfor

    F = F';
    F = [F; .5*(v'*v)] + [-lambda*v; -1];

    TracF = [F];

    J = [A-lambda*eye(n), -v; v', 0];
    d = -J\F;

    x = [x, x(:, columns(x))+d];
    delta = x(:, columns(x)-1) - x(:, columns(x));

    v = x(1:n, columns(x));
    lambda = x(n+1, columns(x));

      for i = 1: n

        F(i) = [A(i,:)*v];
        i = i+1;

      endfor

    F(n+1) = .5*(v'*v);
    F = F + [-lambda*v; -1];

    TracF = [TracF, F];
    y = TracF(:, columns(TracF)-1) - TracF(:, columns	(TracF));

    J = J + ((y - J*delta)/(delta'*delta))*delta';

    while abs((sqrt(delta'*delta))/sqrt((x(:, columns(x))'*x(:, columns(x)))))>1e-6

      d = -J\F;

      x = [x, x(:, columns(x))+d];
      delta = x(:, columns(x)-1) - x(:, columns(x));

      v = x(1:n, columns(x));
      lambda = x(n+1, columns(x));

        for i = 1: n

          F(i) = [A(i,:)*v];
          i = i+1;

        endfor

      F(n+1) = .5*(v'*v);
      F = F + [-lambda*v; -1];

      TracF = [TracF, F];
      y = TracF(:, columns(TracF)-1) - TracF(:, columns	(TracF));

      J = J + ((y - J*delta)/(delta'*delta))*delta';

    endwhile

    AnsVec = x(:, columns(x));

  else
    printf("Matrix A is not square \n")
  endif

endfunction