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bpo-37798: Add C fastpath for statistics.NormalDist.inv_cdf() (GH-15266)
This commit is contained in:
Dong-hee Na
Raymond Hettinger
parent
5be666010e
commit
0a18ee4be7
9 changed files with 264 additions and 73 deletions
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@ -824,6 +824,81 @@ def pstdev(data, mu=None):
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## Normal Distribution #####################################################
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def _normal_dist_inv_cdf(p, mu, sigma):
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# There is no closed-form solution to the inverse CDF for the normal
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# distribution, so we use a rational approximation instead:
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# Wichura, M.J. (1988). "Algorithm AS241: The Percentage Points of the
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# Normal Distribution". Applied Statistics. Blackwell Publishing. 37
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# (3): 477–484. doi:10.2307/2347330. JSTOR 2347330.
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q = p - 0.5
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if fabs(q) <= 0.425:
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r = 0.180625 - q * q
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# Hash sum: 55.88319_28806_14901_4439
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num = (((((((2.50908_09287_30122_6727e+3 * r +
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3.34305_75583_58812_8105e+4) * r +
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6.72657_70927_00870_0853e+4) * r +
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4.59219_53931_54987_1457e+4) * r +
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1.37316_93765_50946_1125e+4) * r +
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1.97159_09503_06551_4427e+3) * r +
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1.33141_66789_17843_7745e+2) * r +
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3.38713_28727_96366_6080e+0) * q
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den = (((((((5.22649_52788_52854_5610e+3 * r +
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2.87290_85735_72194_2674e+4) * r +
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3.93078_95800_09271_0610e+4) * r +
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2.12137_94301_58659_5867e+4) * r +
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5.39419_60214_24751_1077e+3) * r +
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6.87187_00749_20579_0830e+2) * r +
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4.23133_30701_60091_1252e+1) * r +
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1.0)
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x = num / den
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return mu + (x * sigma)
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r = p if q <= 0.0 else 1.0 - p
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r = sqrt(-log(r))
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if r <= 5.0:
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r = r - 1.6
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# Hash sum: 49.33206_50330_16102_89036
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num = (((((((7.74545_01427_83414_07640e-4 * r +
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2.27238_44989_26918_45833e-2) * r +
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2.41780_72517_74506_11770e-1) * r +
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1.27045_82524_52368_38258e+0) * r +
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3.64784_83247_63204_60504e+0) * r +
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5.76949_72214_60691_40550e+0) * r +
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4.63033_78461_56545_29590e+0) * r +
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1.42343_71107_49683_57734e+0)
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den = (((((((1.05075_00716_44416_84324e-9 * r +
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5.47593_80849_95344_94600e-4) * r +
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1.51986_66563_61645_71966e-2) * r +
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1.48103_97642_74800_74590e-1) * r +
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6.89767_33498_51000_04550e-1) * r +
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1.67638_48301_83803_84940e+0) * r +
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2.05319_16266_37758_82187e+0) * r +
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1.0)
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else:
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r = r - 5.0
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# Hash sum: 47.52583_31754_92896_71629
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num = (((((((2.01033_43992_92288_13265e-7 * r +
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2.71155_55687_43487_57815e-5) * r +
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1.24266_09473_88078_43860e-3) * r +
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2.65321_89526_57612_30930e-2) * r +
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2.96560_57182_85048_91230e-1) * r +
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1.78482_65399_17291_33580e+0) * r +
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5.46378_49111_64114_36990e+0) * r +
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6.65790_46435_01103_77720e+0)
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den = (((((((2.04426_31033_89939_78564e-15 * r +
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1.42151_17583_16445_88870e-7) * r +
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1.84631_83175_10054_68180e-5) * r +
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7.86869_13114_56132_59100e-4) * r +
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1.48753_61290_85061_48525e-2) * r +
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1.36929_88092_27358_05310e-1) * r +
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5.99832_20655_58879_37690e-1) * r +
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1.0)
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x = num / den
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if q < 0.0:
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x = -x
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return mu + (x * sigma)
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class NormalDist:
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"Normal distribution of a random variable"
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# https://en.wikipedia.org/wiki/Normal_distribution
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@ -882,79 +957,7 @@ class NormalDist:
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raise StatisticsError('p must be in the range 0.0 < p < 1.0')
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if self._sigma <= 0.0:
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raise StatisticsError('cdf() not defined when sigma at or below zero')
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# There is no closed-form solution to the inverse CDF for the normal
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# distribution, so we use a rational approximation instead:
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# Wichura, M.J. (1988). "Algorithm AS241: The Percentage Points of the
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# Normal Distribution". Applied Statistics. Blackwell Publishing. 37
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# (3): 477–484. doi:10.2307/2347330. JSTOR 2347330.
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q = p - 0.5
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if fabs(q) <= 0.425:
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r = 0.180625 - q * q
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# Hash sum: 55.88319_28806_14901_4439
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num = (((((((2.50908_09287_30122_6727e+3 * r +
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3.34305_75583_58812_8105e+4) * r +
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6.72657_70927_00870_0853e+4) * r +
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4.59219_53931_54987_1457e+4) * r +
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1.37316_93765_50946_1125e+4) * r +
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1.97159_09503_06551_4427e+3) * r +
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1.33141_66789_17843_7745e+2) * r +
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3.38713_28727_96366_6080e+0) * q
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den = (((((((5.22649_52788_52854_5610e+3 * r +
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2.87290_85735_72194_2674e+4) * r +
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3.93078_95800_09271_0610e+4) * r +
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2.12137_94301_58659_5867e+4) * r +
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5.39419_60214_24751_1077e+3) * r +
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6.87187_00749_20579_0830e+2) * r +
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4.23133_30701_60091_1252e+1) * r +
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1.0)
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x = num / den
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return self._mu + (x * self._sigma)
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r = p if q <= 0.0 else 1.0 - p
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r = sqrt(-log(r))
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if r <= 5.0:
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r = r - 1.6
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# Hash sum: 49.33206_50330_16102_89036
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num = (((((((7.74545_01427_83414_07640e-4 * r +
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2.27238_44989_26918_45833e-2) * r +
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2.41780_72517_74506_11770e-1) * r +
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1.27045_82524_52368_38258e+0) * r +
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3.64784_83247_63204_60504e+0) * r +
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5.76949_72214_60691_40550e+0) * r +
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4.63033_78461_56545_29590e+0) * r +
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1.42343_71107_49683_57734e+0)
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den = (((((((1.05075_00716_44416_84324e-9 * r +
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5.47593_80849_95344_94600e-4) * r +
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1.51986_66563_61645_71966e-2) * r +
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1.48103_97642_74800_74590e-1) * r +
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6.89767_33498_51000_04550e-1) * r +
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1.67638_48301_83803_84940e+0) * r +
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2.05319_16266_37758_82187e+0) * r +
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1.0)
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else:
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r = r - 5.0
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# Hash sum: 47.52583_31754_92896_71629
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num = (((((((2.01033_43992_92288_13265e-7 * r +
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2.71155_55687_43487_57815e-5) * r +
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1.24266_09473_88078_43860e-3) * r +
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2.65321_89526_57612_30930e-2) * r +
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2.96560_57182_85048_91230e-1) * r +
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1.78482_65399_17291_33580e+0) * r +
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5.46378_49111_64114_36990e+0) * r +
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6.65790_46435_01103_77720e+0)
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den = (((((((2.04426_31033_89939_78564e-15 * r +
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1.42151_17583_16445_88870e-7) * r +
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1.84631_83175_10054_68180e-5) * r +
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7.86869_13114_56132_59100e-4) * r +
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1.48753_61290_85061_48525e-2) * r +
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1.36929_88092_27358_05310e-1) * r +
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5.99832_20655_58879_37690e-1) * r +
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1.0)
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x = num / den
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if q < 0.0:
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x = -x
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return self._mu + (x * self._sigma)
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return _normal_dist_inv_cdf(p, self._mu, self._sigma)
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def overlap(self, other):
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"""Compute the overlapping coefficient (OVL) between two normal distributions.
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@ -1078,6 +1081,12 @@ class NormalDist:
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def __repr__(self):
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return f'{type(self).__name__}(mu={self._mu!r}, sigma={self._sigma!r})'
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# If available, use C implementation
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try:
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from _statistics import _normal_dist_inv_cdf
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except ImportError:
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pass
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if __name__ == '__main__':
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