def FixedResGlobal(nsigma):
n_levels = len(nsigma)
q_perlevel = np.empty(n_levels, dtype=object)
for l, lev in enumerate(nsigma):
q_total = 0
nQs = len(lev)
for j, sig in enumerate(lev):
pval = mp.erfc(abs(sig)/mp.sqrt(2))
q = -2*mp.log(pval)
q_total += q
q_perlevel[l] = [q_total, nQs]
nsigma_fixedres = np.zeros(n_levels)
for i, entry in enumerate(q_perlevel):
qT = entry[0]
nQ = entry[1]
Dchi2 = mp.gammainc(nQ, 0, 0.5*qT)/mp.gamma(nQ)
nsigma_ell = mp.sqrt(2)*mp.erfinv(Dchi2)
nsigma_fixedres[i] = nsigma_ell
return nsigma_fixedres
def norm_q(prob):
r"""
A multi-precision calculation of the
standard normal quantile function:
.. math::
\int_{-\infty}^{q(p)} \frac{e^{-z^2/2}}{\sqrt{2\pi}} \; dz = p
where $p$ is `prob`.
Parameters
----------
prob : float
Returns
-------
quantile : float
"""
return np.array(mp.erfinv(2*prob-1)*mp.sqrt(2))
def _nsigma(pLessX):
return mp.sqrt(2) * mp.erfinv(pLessX)
def Phi_inv(x):
return( -mp.sqrt(2)*mp.erfinv(mp.mpf(1)-mp.mpf(2)*x) )