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118 lines
3.7 KiB
Python
118 lines
3.7 KiB
Python
# -*- coding: utf-8 -*-
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from typing import Tuple
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from numpy import array as npArray
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from numpy import infty as npInfty
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from numpy import log as npLog
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from numpy import nan as npNaN
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from numpy import pi as npPi
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from numpy import sqrt as npSqrt
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from pandas_ta import Imports
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from ._math import hpoly
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def _gaussian_poly_coefficients():
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"""Three pairs of Polynomial Approximation Coefficients
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for the Gaussian Normal CDF"""
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p0 = npArray([
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-5.99633501014107895267E1, 9.80010754185999661536E1,
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-5.66762857469070293439E1, 1.39312609387279679503E1,
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-1.23916583867381258016E0
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])
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q0 = npArray([
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1.00000000000000000000E0, 1.95448858338141759834E0,
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4.67627912898881538453E0, 8.63602421390890590575E1,
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-2.25462687854119370527E2, 2.00260212380060660359E2,
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-8.20372256168333339912E1, 1.59056225126211695515E1,
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-1.18331621121330003142E0
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])
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p1 = npArray([
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4.05544892305962419923E0, 3.15251094599893866154E1,
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5.71628192246421288162E1, 4.40805073893200834700E1,
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1.46849561928858024014E1, 2.18663306850790267539E0,
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-1.40256079171354495875E-1, -3.50424626827848203418E-2,
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-8.57456785154685413611E-4
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])
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q1 = npArray([
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1.00000000000000000000E0, 1.57799883256466749731E1,
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4.53907635128879210584E1, 4.13172038254672030440E1,
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1.50425385692907503408E1, 2.50464946208309415979E0,
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-1.42182922854787788574E-1, -3.80806407691578277194E-2,
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-9.33259480895457427372E-4
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])
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p2 = npArray([
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3.23774891776946035970E0, 6.91522889068984211695E0,
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3.93881025292474443415E0, 1.33303460815807542389E0,
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2.01485389549179081538E-1, 1.23716634817820021358E-2,
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3.01581553508235416007E-4, 2.65806974686737550832E-6,
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6.23974539184983293730E-9
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])
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q2 = npArray([
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1.00000000000000000000E0, 6.02427039364742014255E0,
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3.67983563856160859403E0, 1.37702099489081330271E0,
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2.16236993594496635890E-1, 1.34204006088543189037E-2,
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3.28014464682127739104E-4, 2.89247864745380683936E-6,
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6.79019408009981274425E-9
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])
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return p0, q0, p1, q1, p2, q2
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def inv_norm(value: Tuple[float, int]) -> Tuple[float, None]:
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"""Inverse Normal (inv_norm)
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Calculates the 'x' in which the area under the Gaussian PDF is
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equal to value.
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If the user has package "statsmodels" installed, the method will call and
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return norm().ppf(value)
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Source: https://github.com/scipy/scipy/blob/701ffcc8a6f04509d115aac5e5681c538b5265a2/scipy/special/cephes/ndtri.c
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"""
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if Imports["statsmodels"]:
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from scipy.stats import norm
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return norm().ppf(value)
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negate = True
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v = value
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if v == 0.0: return -npInfty
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if v == 1.0: return npInfty
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if v < 0.0 or value > 1.0: return npNaN
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p0, q0, p1, q1, p2, q2 = _gaussian_poly_coefficients()
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sqrt2pi = npSqrt(2 * npPi)
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threshold = 0.13533528323661269189
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if v > 1.0 - threshold:
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v, negate = 1.0 - v, False
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# 0 <= |x0 - 0.5| <= 3/8
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if v > threshold:
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v -= 0.5
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v2 = v * v
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y = v + v * (v2 * hpoly(p0, v2) / hpoly(q0, v2))
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y *= sqrt2pi
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return y
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y = npSqrt(-2.0 * npLog(v))
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y0 = y - npLog(y) / y
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z = 1.0 / y
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if y < 8.0:
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# Approximation for interval z = sqrt(-2 log y ) between 2 and 8
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# i.e., x between exp(-2) = .135 and exp(-32) = 1.27e-14.
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y1 = z * hpoly(p1, z) / hpoly(q1, z)
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else:
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# Approximation for interval z = sqrt(-2 log y ) between 8 and 64
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# i.e., x between exp(-32) = 1.27e-14 and exp(-2048) = 3.67e-890.
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y1 = z * hpoly(p2, z) / hpoly(q2, z)
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y = y0 - y1
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if negate: y = -y
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return y |