Shakemap functions

[schmidni]

My results of trying to improve performance of the correlation calculations for shakemaps.

• changes in cross_corr_matrix are mostlya changing of the if/else orders
• spatial_covariance_array had a matrix multiplication using for loops, doing a proper matmul using np had a major improvement in performance
• cholesky function is the one that takes now the longest. I tried switching out all loops with matrix manipulations but could not get a noticeable improvement. Apart from the cholesky decomposition, the L * L.T obviously just takes a fixed amount of time.

[schmidni]

Also, there are two more "direct" ways to calculate the LLT matrix in the cholesky function, which however give no performance improvement:

using:
L = numpy.array([numpy.linalg.cholesky(spatial_cov[i]) for i in range(M)]).reshape(N*M, N)

it is possible to get LLT

LLT = (numpy.matmul(L, L.T).reshape(M, N, M, N) * cross_corr[:, None, :, None]).reshape(N*M, N*M)

or

LLT = numpy.multiply( L@L.T, numpy.kron(cross_corr, numpy.ones((N, N))))

Without any direct performance or readability improvement I didn't see a reason to include those changes. I can include them however if you want.

[micheles]

I like this.

[micheles]

We would need a comment here explaining the magic number 0.99999

[schmidni]

Took the magic number from line 214 of the original code.

I can only guess that there is some numerical reason? "Not quite 1"

[micheles]

You are right, it was there from the beginning. Let's me accept the PR as it is, then.