Question

Assume that I have an affinity matrix A and a diagonal matrix D. How can I compute the Laplacian matrix in Python with nympy?

L = D^(-1/2) A D^(1/2)

Currently, I use L = D**(-1/2) * A * D**(1/2). Is this a right way?

Thank you.

Answer 1

Numpy allows you to exponentiate a diagonal "matrix" with positive elements and a positive exponent directly:

m = diag(range(1, 11))
print m**0.5

The result is what you expect in this case because NumPy actually applies the exponentiation to each element of the NumPy array individually.

However, it indeed does not allow you to exponentiate any NumPy matrix directly:

m = matrix([[1, 1], [1, 2]])
print m**0.5

produces the TypeError that you have observed (the exception says that the exponent must be an integer–even for matrices that can be diagonalized with positive coefficients).

So, as long as your matrix D is diagonal and your exponent is positive, you should be able to directly use your formula.