Evaluating the Morris test function is very slow

[mbaudin47]

The following code uses vectorized statements and is much faster:

def Morris_function(x):
    delta=np.zeros((20,20,20)); delta[:5,:5,:5].fill(-10)
    	gamma=np.zeros((20,20,20,20)); gamma[:4,:4,:4,:4].fill(5)
    W=np.sum(alpha.reshape(-1,1)*w(x))
    W1=np.sum(beta*(w(x).reshape(1,-1)*w(x))*(np.arange(20).reshape(-1,1)<np.arange(20)))
    W2=np.sum(delta*(w(x).reshape(-1,1,1)*w(x).reshape(1,-1,1)*w(x).reshape(1,1,-1))*(np.arange(20).reshape(-1,1,1)<np.arange(20).reshape(1,-1,1))*(np.arange(20).reshape(1,-1,1)<np.arange(20).reshape(1,1,-1)))
    W3=np.sum(gamma*(w(x).reshape(-1,1,1,1)*w(x).reshape(1,-1,1,1)*w(x).reshape(1,1,-1,1)*w(x).reshape(1,1,1,-1))*(np.arange(20).reshape(-1,1,1,1)<np.arange(20).reshape(1,-1,1,1))*(np.arange(20).reshape(1,-1,1,1)<np.arange(20).reshape(1,1,-1,1))*(np.arange(20).reshape(1,1,-1,1)<np.arange(20).reshape(1,1,1,-1)))
    y=W+W1+W2+W3+float(b0)
    return y

However, the current implementation has no unit tests. This makes changing the implementation unconformable.

[sofianehaddad]

Refer to #7
I do not remember exactly why we decide to drop numpy dependency

I think for unitary tests it is useless to get this vectorized implementation.

[mbaudin47]

• The performance issue make it useless for use-cases where we need lots of evaluations. This is for example the situation where we want to benchmark the Morris method on the Morris function... This is why when we really need to evaluate the Morris function, we finally have to reimplement it.

• Removing numpy because of numpy seems strange: there is no way to use OpenTURNS in Python without having numpy anyway. The correct way to remove numpy would be to implement the code in C++.

• The old implementation relying on numpy was much less efficient than the one I provide.

Please find below a sample working implementation. It is not as fast as I thought.

bench-Morris-function.ipynb.txt

[mbaudin47]

Would a SymbolicFunction be faster ?