scipy.linalg.expm does not give the expected result

Hi all,

I have the following example and it gives the correct results when my matrix elements are not integers, however it does not work when they are integers:

Reproducing code example:

import numpy as np
import scipy

Q = np.array([[-500,500,0,0],[0,-550,360,190],[0,630,-630,0],[0,0,0,0]])   # Rate Matrix
pi = scipy.linalg.expm(Q*10) 

np.sum(pi,axis=1)
array([-0.63612061, -0.2620967 , -0.53480159,  1.        ])

But it works for the following case:

Q = np.array([[-500,500,0,0],[0,-550,360,190],[0,630,-630,0],[0,0,0,0]])   # Rate Matrix
pi = scipy.linalg.expm(Q*10.5) 

np.sum(pi,axis=1)
array([1., 1., 1., 1.])

Error message:

I do not get any error but the results are wrong.

Scipy/Numpy/Python version information:

scipy.__version__
'1.1.0'

Does anyone know why this is the case and why I am getting this error?

[WarrenWeckesser]

Thanks for reporting the problem. This looks like a bug.

The expm code computes several even matrix powers of the input A while maintaining the data type of A. Q*10 is an integer array, and the values in it are large enough that the values in the matrix power A**6 overflow (using 64 bit integers). Once that happens, the result of the computation is garbage.

The work-around (as you discovered) is to be sure that the input array is floating point.

[ilayn]

Strange. I can’t replicate it on 1.2.0.dev0+c79b48d. Must have installed from one of my branches.