#!/usr/bin/env python3
import math
import numpy as np
A=3.3; s_fine=1/6; s_coarse=2.0
def R(A,s): return A*math.exp(-0.5)/(1+s*s)
print('R_fine',R(A,s_fine))
print('R_coarse',R(A,s_coarse))
for aa in [3.0,3.3,3.6]:
    for sf in [0.10,1/6,0.25]:
        for sc in [1.8,2.0,2.2]:
            rf=R(aa,sf); rc=R(aa,sc)
            assert rf>1 and rc<1
print('27/27 sensitivity combinations PASS')