Implementation

Using the value alphat=1e-5 for , put code which implements Eq. (1) at the location indicated in the code for this problem.

Hints:

• Eq. (1) requires , the value of the gradient evaluated for the vector . You may wish to define a pvector ut=u+alphat*dir, and then replicate the code your wrote previously for computing N, D and the gradient, calling the new result gradt instead of grad.
• Dot products like are equal to the real part of the ``dagger product'', . So your code will have fragments that look something like ``real(dir^gradt)-real(dir^grad)''.