def integ(alpha, b):
"""
:param alpha:
:param b:
:return: integral of -alpha * b * e^(-x) * x ^(-alpha-1), from b to infty
That is the integral of e^-W+ from b to infty
That is E[e^[-W+]]
"""
result = integrate(sp_exp(-x) * x**(-alpha - 1), (x, b, float("inf")))
result *= -alpha * b**alpha
return result
###########################################################
from pathlib import Path
reproduced_results = Path("reproduced-results")
from sympy import exp as sp_exp
from sympy import symbols as sp_symbols
from sympy import Rational as sp_Rational
from sympy import lambdify as sp_lambdify
from IPython.display import display
import numpy as np
from collections import defaultdict
n = sp_symbols('n')
psis = [sp_exp(-1 / n), 1 - sp_exp(-n)]
psi_codes = {
psis[0]: 'exp((NType)(-1./ln))',
psis[1]: '1. - exp(-(NType)ln)',
}
Gs = {psis[0]: [-3.6], psis[1]: [-1.4, -1.6]}
Ls = [255]
E6_P2F6_sym = sp_symbols("\\boldsymbol{E}^{(6)}_{P2\,F6}")
E8_P2F8_sym = sp_symbols("\\boldsymbol{E}^{(8)}_{P2\,F8}")
E6_P4F6_sym = sp_symbols("\\boldsymbol{E}^{(6)}_{P4\,F6}")
E8_P4F6_sym = sp_symbols("\\boldsymbol{E}^{(8)}_{P4\,F6}")
stencil_string = {
