Dot products in exercise 2

The vectors described in the notes on minimization correspond to vectors in 3N-dimensional space. Therefore, the dot products for the conjugate gradient formulas indicate the multidimensional dot product in 3N-dimensional space. In other words

f^N . f^N = fx,1^2 + fy,1^2 + fz,1^2 + fx,2^2 + ... + fz,N^2

The result should be a scalar.

You will be working with (N,3) arrays in NumPy. For these kinds of arrays, NumPy's dot product will not give you the behavior above, since this function is a generalized matrix multiplication and NumPy will think your two-dimensional array is intended as a matrix, not a 3N-dimensional vector.

Instead you want to use something like:

np.sum(Forces**2)

Or,

np.sum((Forces - OldForces) * Forces)

Here, this code indicates that the Forces array will be squared on an element-by-element basis, and then these 3N elements will be summed.

Cheers,
MSS