Newton's Method for Mat 4010

function [ AnsVec, TracF ]  = NewtonMethod ( A, x )
# Matthew Graham
# Mat 4010
# Newton'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 = length(x)-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];

    NormF = sqrt(F'*F);

    TracF = [F];

    while NormF > 1e-6

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

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

        for i = 1: n

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

        endfor

      F(n+1) = .5*(v'*v);

      F = F + [-lambda*v; -1];
      NormF = sqrt(F'*F);

      TracF = [TracF, F];

      endwhile

    AnsVec = x;

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

endfunction