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I know this was asked many times, but, I am still having trouble with the following problem. I defined my own functions for mean and stdev, but stdev takes too long to calculate std(Wapproxlist). So, I need a solution for the issue.

import numpy as np
def Taylor_Integration(a, b, mu):
    import sympy as sy
    A, B, rho = sy.symbols('A B rho', real=True)
    Wapp = (A + B*rho - rho/(2*mu*(1 - rho)))**2
    eq1 = sy.diff(sy.integrate(Wapp, (rho, a, b)),A)
    eq2 = sy.diff(sy.integrate(Wapp, (rho, a, b)),B)
    sol = sy.solve([eq1,eq2], [A,B])
    return sol[A], sol[B]
def Wapprox(rho, A, B):
    return A + B*rho
def W(mu, rho):
    return rho/(2*mu*(1-rho))
Wapproxlist = []
Wlist = []
alist = np.linspace(0, 0.98, 10)
for a in alist:
    b = a+0.01; mu = 1
    A, B = Taylor_Integration(a, b, mu)
    rholist = np.linspace(a, b, 100)
    for rho in rholist:
        Wapproxlist.append(Wapprox(rho, A, B))
        Wlist.append(W(mu, rho))
print('mean=%.3f stdv=%.3f' % (np.mean(Wapproxlist), np.std(Wapproxlist)))
print('mean=%.3f stdv=%.3f' % (np.mean(Wlist), np.std(Wlist)))
Output:
AttributeError                            Traceback (most recent call last)
<ipython-input-83-468c8e1a9f89> in <module>()
----> 1 print('mean=%.3f stdv=%.3f' % (np.mean(Wapproxlist), np.std(Wapproxlist)))
      2 print('mean=%.3f stdv=%.3f' % (np.mean(Wlist), np.std(Wlist)))
C:\Users\2tc\.julia\v0.6\Conda\deps\usr\lib\site-packages\numpy\core\fromnumeric.pyc in std(a, axis, dtype, out, ddof, keepdims)
   3074     return _methods._std(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
-> 3075                          **kwargs)
C:\Users\2tc\.julia\v0.6\Conda\deps\usr\lib\site-packages\numpy\core\_methods.pyc in _std(a, axis, dtype, out, ddof, keepdims)
    140         ret = ret.dtype.type(um.sqrt(ret))
    141     else:
--> 142         ret = um.sqrt(ret)
    144     return ret
AttributeError: 'Float' object has no attribute 'sqrt'
Convert it to a numpy array before calling np.mean and np.std.
Wapproxlist = np.array(Wapproxlist, dtype=np.float64) # can use np.float32 as well
print('mean=%.3f stdv=%.3f' % (np.mean(Wapproxlist), np.std(Wapproxlist)))
print('mean=%.3f stdv=%.3f' % (np.mean(Wlist), np.std(Wlist)))
output:
mean=4.177 stdv=10.283
mean=4.180 stdv=10.300
Note: If you're looking to speed this up, you'll want to avoid sympy. Symbolic solvers are pretty cool, but they're also very slow compared to floating point computations.
        
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