def __init__(self, npts):
# Legendre poly
lp = lambda x: mp.legendre(npts - 1, x)
# Coefficients of lp
cf = mp.taylor(lp, 0, npts - 1)
# Coefficients of dlp/dx
dcf = [i*c for i, c in enumerate(cf[1:], start=1)]
self.points = [mp.mpf(-1)] + mp.polyroots(dcf[::-1]) + [mp.mpf(1)]
self.weights = [2/(npts*(npts - 1)*lp(p)**2) for p in self.points]
# NOTE: This file implements an slightly different version of li_criter. # It finds the taylor expansion coefficients of log(xi(z/(z-1)), instead if its derivative, # which is in the original li_criterion # # the following code is from # http://fredrikj.net/blog/2013/03/testing-lis-criterion/ # It uses mpmath to calculate taylor expansion of xi function # # It will produce the 1st 21 coefficients for Li-criter # [-0.69315, 0.023096, 0.046173, 0.069213, 0.092198, 0.11511, 0.13793, 0.16064, 0.18322, 0.20566, # 0.22793, 0.25003, 0.27194, 0.29363, 0.31511, 0.33634, 0.35732, 0.37803, 0.39847, 0.41862, 0.43846] # # More information about mpmath can be found at: mpmath.org # http://mpmath.org/ from mpmath import mp mp.dps = 5 mp.pretty = True xi = lambda s: (s - 1) * mp.pi ** (-0.5 * s) * mp.gamma(1 + 0.5 * s) * mp.zeta(s) # calculate 1st 21 coefficients of taylor expansion of log(xi(z/(z-1)) tmp = mp.taylor(lambda z: mp.log(xi(z / (z - 1))), 0, 20) print tmp
def __init__(self, npts):
# Legendre poly
lp = lambda x: mp.legendre(npts, x)
self.points = mp.polyroots(mp.taylor(lp, 0, npts)[::-1])
self.weights = [2/((1 - p*p)*mp.diff(lp, p)**2) for p in self.points]