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Minor code beautifications in statistics.py (gh-124866)
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@rhettinger
rhettinger authored Oct 1, 2024
1 parent 04bfea2 commit 120729d
Showing 1 changed file with 95 additions and 85 deletions.
180 changes: 95 additions & 85 deletions Lib/statistics.py
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Original file line number Diff line number Diff line change
Expand Up @@ -248,6 +248,7 @@ def count_positive(iterable):
found_zero = True
else:
raise StatisticsError('No negative inputs allowed', x)

total = fsum(map(log, count_positive(data)))

if not n:
Expand Down Expand Up @@ -710,6 +711,7 @@ def correlation(x, y, /, *, method='linear'):
start = (n - 1) / -2 # Center rankings around zero
x = _rank(x, start=start)
y = _rank(y, start=start)

else:
xbar = fsum(x) / n
ybar = fsum(y) / n
Expand Down Expand Up @@ -1213,91 +1215,6 @@ def quantiles(data, *, n=4, method='exclusive'):

## Normal Distribution #####################################################

def _normal_dist_inv_cdf(p, mu, sigma):
# There is no closed-form solution to the inverse CDF for the normal
# distribution, so we use a rational approximation instead:
# Wichura, M.J. (1988). "Algorithm AS241: The Percentage Points of the
# Normal Distribution". Applied Statistics. Blackwell Publishing. 37
# (3): 477–484. doi:10.2307/2347330. JSTOR 2347330.
q = p - 0.5

if fabs(q) <= 0.425:
r = 0.180625 - q * q
# Hash sum: 55.88319_28806_14901_4439
num = (((((((2.50908_09287_30122_6727e+3 * r +
3.34305_75583_58812_8105e+4) * r +
6.72657_70927_00870_0853e+4) * r +
4.59219_53931_54987_1457e+4) * r +
1.37316_93765_50946_1125e+4) * r +
1.97159_09503_06551_4427e+3) * r +
1.33141_66789_17843_7745e+2) * r +
3.38713_28727_96366_6080e+0) * q
den = (((((((5.22649_52788_52854_5610e+3 * r +
2.87290_85735_72194_2674e+4) * r +
3.93078_95800_09271_0610e+4) * r +
2.12137_94301_58659_5867e+4) * r +
5.39419_60214_24751_1077e+3) * r +
6.87187_00749_20579_0830e+2) * r +
4.23133_30701_60091_1252e+1) * r +
1.0)
x = num / den
return mu + (x * sigma)

r = p if q <= 0.0 else 1.0 - p
r = sqrt(-log(r))
if r <= 5.0:
r = r - 1.6
# Hash sum: 49.33206_50330_16102_89036
num = (((((((7.74545_01427_83414_07640e-4 * r +
2.27238_44989_26918_45833e-2) * r +
2.41780_72517_74506_11770e-1) * r +
1.27045_82524_52368_38258e+0) * r +
3.64784_83247_63204_60504e+0) * r +
5.76949_72214_60691_40550e+0) * r +
4.63033_78461_56545_29590e+0) * r +
1.42343_71107_49683_57734e+0)
den = (((((((1.05075_00716_44416_84324e-9 * r +
5.47593_80849_95344_94600e-4) * r +
1.51986_66563_61645_71966e-2) * r +
1.48103_97642_74800_74590e-1) * r +
6.89767_33498_51000_04550e-1) * r +
1.67638_48301_83803_84940e+0) * r +
2.05319_16266_37758_82187e+0) * r +
1.0)
else:
r = r - 5.0
# Hash sum: 47.52583_31754_92896_71629
num = (((((((2.01033_43992_92288_13265e-7 * r +
2.71155_55687_43487_57815e-5) * r +
1.24266_09473_88078_43860e-3) * r +
2.65321_89526_57612_30930e-2) * r +
2.96560_57182_85048_91230e-1) * r +
1.78482_65399_17291_33580e+0) * r +
5.46378_49111_64114_36990e+0) * r +
6.65790_46435_01103_77720e+0)
den = (((((((2.04426_31033_89939_78564e-15 * r +
1.42151_17583_16445_88870e-7) * r +
1.84631_83175_10054_68180e-5) * r +
7.86869_13114_56132_59100e-4) * r +
1.48753_61290_85061_48525e-2) * r +
1.36929_88092_27358_05310e-1) * r +
5.99832_20655_58879_37690e-1) * r +
1.0)

x = num / den
if q < 0.0:
x = -x

return mu + (x * sigma)


# If available, use C implementation
try:
from _statistics import _normal_dist_inv_cdf
except ImportError:
pass


class NormalDist:
"Normal distribution of a random variable"
# https://en.wikipedia.org/wiki/Normal_distribution
Expand Down Expand Up @@ -1561,11 +1478,13 @@ def _sum(data):
types_add = types.add
partials = {}
partials_get = partials.get

for typ, values in groupby(data, type):
types_add(typ)
for n, d in map(_exact_ratio, values):
count += 1
partials[d] = partials_get(d, 0) + n

if None in partials:
# The sum will be a NAN or INF. We can ignore all the finite
# partials, and just look at this special one.
Expand All @@ -1574,6 +1493,7 @@ def _sum(data):
else:
# Sum all the partial sums using builtin sum.
total = sum(Fraction(n, d) for d, n in partials.items())

T = reduce(_coerce, types, int) # or raise TypeError
return (T, total, count)

Expand All @@ -1596,6 +1516,7 @@ def _ss(data, c=None):
types_add = types.add
sx_partials = defaultdict(int)
sxx_partials = defaultdict(int)

for typ, values in groupby(data, type):
types_add(typ)
for n, d in map(_exact_ratio, values):
Expand All @@ -1605,11 +1526,13 @@ def _ss(data, c=None):

if not count:
ssd = c = Fraction(0)

elif None in sx_partials:
# The sum will be a NAN or INF. We can ignore all the finite
# partials, and just look at this special one.
ssd = c = sx_partials[None]
assert not _isfinite(ssd)

else:
sx = sum(Fraction(n, d) for d, n in sx_partials.items())
sxx = sum(Fraction(n, d*d) for d, n in sxx_partials.items())
Expand Down Expand Up @@ -1693,8 +1616,10 @@ def _convert(value, T):
# This covers the cases where T is Fraction, or where value is
# a NAN or INF (Decimal or float).
return value

if issubclass(T, int) and value.denominator != 1:
T = float

try:
# FIXME: what do we do if this overflows?
return T(value)
Expand Down Expand Up @@ -1857,3 +1782,88 @@ def _sqrtprod(x: float, y: float) -> float:
# https://www.wolframalpha.com/input/?i=Maclaurin+series+sqrt%28h**2+%2B+x%29+at+x%3D0
d = sumprod((x, h), (y, -h))
return h + d / (2.0 * h)


def _normal_dist_inv_cdf(p, mu, sigma):
# There is no closed-form solution to the inverse CDF for the normal
# distribution, so we use a rational approximation instead:
# Wichura, M.J. (1988). "Algorithm AS241: The Percentage Points of the
# Normal Distribution". Applied Statistics. Blackwell Publishing. 37
# (3): 477–484. doi:10.2307/2347330. JSTOR 2347330.
q = p - 0.5

if fabs(q) <= 0.425:
r = 0.180625 - q * q
# Hash sum: 55.88319_28806_14901_4439
num = (((((((2.50908_09287_30122_6727e+3 * r +
3.34305_75583_58812_8105e+4) * r +
6.72657_70927_00870_0853e+4) * r +
4.59219_53931_54987_1457e+4) * r +
1.37316_93765_50946_1125e+4) * r +
1.97159_09503_06551_4427e+3) * r +
1.33141_66789_17843_7745e+2) * r +
3.38713_28727_96366_6080e+0) * q
den = (((((((5.22649_52788_52854_5610e+3 * r +
2.87290_85735_72194_2674e+4) * r +
3.93078_95800_09271_0610e+4) * r +
2.12137_94301_58659_5867e+4) * r +
5.39419_60214_24751_1077e+3) * r +
6.87187_00749_20579_0830e+2) * r +
4.23133_30701_60091_1252e+1) * r +
1.0)
x = num / den
return mu + (x * sigma)

r = p if q <= 0.0 else 1.0 - p
r = sqrt(-log(r))
if r <= 5.0:
r = r - 1.6
# Hash sum: 49.33206_50330_16102_89036
num = (((((((7.74545_01427_83414_07640e-4 * r +
2.27238_44989_26918_45833e-2) * r +
2.41780_72517_74506_11770e-1) * r +
1.27045_82524_52368_38258e+0) * r +
3.64784_83247_63204_60504e+0) * r +
5.76949_72214_60691_40550e+0) * r +
4.63033_78461_56545_29590e+0) * r +
1.42343_71107_49683_57734e+0)
den = (((((((1.05075_00716_44416_84324e-9 * r +
5.47593_80849_95344_94600e-4) * r +
1.51986_66563_61645_71966e-2) * r +
1.48103_97642_74800_74590e-1) * r +
6.89767_33498_51000_04550e-1) * r +
1.67638_48301_83803_84940e+0) * r +
2.05319_16266_37758_82187e+0) * r +
1.0)
else:
r = r - 5.0
# Hash sum: 47.52583_31754_92896_71629
num = (((((((2.01033_43992_92288_13265e-7 * r +
2.71155_55687_43487_57815e-5) * r +
1.24266_09473_88078_43860e-3) * r +
2.65321_89526_57612_30930e-2) * r +
2.96560_57182_85048_91230e-1) * r +
1.78482_65399_17291_33580e+0) * r +
5.46378_49111_64114_36990e+0) * r +
6.65790_46435_01103_77720e+0)
den = (((((((2.04426_31033_89939_78564e-15 * r +
1.42151_17583_16445_88870e-7) * r +
1.84631_83175_10054_68180e-5) * r +
7.86869_13114_56132_59100e-4) * r +
1.48753_61290_85061_48525e-2) * r +
1.36929_88092_27358_05310e-1) * r +
5.99832_20655_58879_37690e-1) * r +
1.0)

x = num / den
if q < 0.0:
x = -x

return mu + (x * sigma)


# If available, use C implementation
try:
from _statistics import _normal_dist_inv_cdf
except ImportError:
pass

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