Numpy Creates

from scipy.sparse import diags
def standard(n):
    offsets = np.arange(-(n+1)//2,(n+1)//2+2)
    values = 1/offsets
    values[n//2+1] = 8
    return diags(values,offsets,shape=(n-1,n-1)).toarray()

def selectmgrid(n):
    fill = lambda x, y: np.select([x==y, x!=5], [8, 1/(x+y)])
    return fill(*np.mgrid[1:n, 1:n])

def vectmgrid(n):
    fill_array = np.vectorize(lambda x, y: 1/(x+y) if x!=y else 8.0)
    return fill_array(*np.mgrid[1:n, 1:n])

def mixedmgrid(n):
    fill_it = lambda x, y: 1/(x+y)   # removing the if else statement
    likelihood = fill_it(*np.mgrid[1:n, 1:n])
    np.fill_diagonal(likelihood, 8)
    return likelihood

n = 100
# print(standard(n),'\n')
# print(selectmgrid(n),'\n')
# print(vectmgrid(n),'\n')
# print(mixedmgrid(n),'\n')

print('standard    ', end='')
%timeit(standard(n))
print('selectmgrid ', end='')
%timeit(selectmgrid(n))
print('vectmgrid   ', end='')
%timeit(vectmgrid(n))
print('mixedmgrid  ', end='')
%timeit(mixedmgrid(n))

standard    1000 loops, best of 3: 1.73 ms per loop
selectmgrid 1000 loops, best of 3: 319 µs per loop
vectmgrid   100 loops, best of 3: 2.58 ms per loop
mixedmgrid  1000 loops, best of 3: 209 µs per loop