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Minor speed/accuracy improvement for kde() #119910

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Merged
rhettinger merged 3 commits into from
Jun 1, 2024
Merged

Minor speed/accuracy improvement for kde() #119910

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7a4df6d
Minor speed/accuracy improvement for quartic and triweight
rhettinger May 7, 2024
11b3c6f
Add test for the accuracy improvement
rhettinger May 7, 2024
b48e38e
Eliminate local n which shadows a non-local n
rhettinger May 8, 2024
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17 changes: 9 additions & 8 deletions Lib/statistics.py
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Original file line number Diff line number Diff line change
Expand Up @@ -953,12 +953,14 @@ def kde(data, h, kernel='normal', *, cumulative=False):

case 'quartic' | 'biweight':
K = lambda t: 15/16 * (1.0 - t * t) ** 2
W = lambda t: 3/16 * t**5 - 5/8 * t**3 + 15/16 * t + 1/2
W = lambda t: sumprod((3/16, -5/8, 15/16, 1/2),
(t**5, t**3, t, 1.0))
support = 1.0

case 'triweight':
K = lambda t: 35/32 * (1.0 - t * t) ** 3
W = lambda t: 35/32 * (-1/7*t**7 + 3/5*t**5 - t**3 + t) + 1/2
W = lambda t: sumprod((-5/32, 21/32, -35/32, 35/32, 1/2),
(t**7, t**5, t**3, t, 1.0))
support = 1.0

case 'cosine':
Expand All @@ -974,12 +976,10 @@ def kde(data, h, kernel='normal', *, cumulative=False):
if support is None:

def pdf(x):
n = len(data)
return sum(K((x - x_i) / h) for x_i in data) / (n * h)
return sum(K((x - x_i) / h) for x_i in data) / (len(data) * h)

def cdf(x):
n = len(data)
return sum(W((x - x_i) / h) for x_i in data) / n
return sum(W((x - x_i) / h) for x_i in data) / len(data)

else:

Expand Down Expand Up @@ -1732,7 +1732,7 @@ def _quartic_invcdf_estimate(p):

_quartic_invcdf = _newton_raphson(
f_inv_estimate = _quartic_invcdf_estimate,
f = lambda t: 3/16 * t**5 - 5/8 * t**3 + 15/16 * t + 1/2,
f = lambda t: sumprod((3/16, -5/8, 15/16, 1/2), (t**5, t**3, t, 1.0)),
f_prime = lambda t: 15/16 * (1.0 - t * t) ** 2)

def _triweight_invcdf_estimate(p):
Expand All @@ -1742,7 +1742,8 @@ def _triweight_invcdf_estimate(p):

_triweight_invcdf = _newton_raphson(
f_inv_estimate = _triweight_invcdf_estimate,
f = lambda t: 35/32 * (-1/7*t**7 + 3/5*t**5 - t**3 + t) + 1/2,
f = lambda t: sumprod((-5/32, 21/32, -35/32, 35/32, 1/2),
(t**7, t**5, t**3, t, 1.0)),
f_prime = lambda t: 35/32 * (1.0 - t * t) ** 3)

_kernel_invcdfs = {
Expand Down
2 changes: 1 addition & 1 deletion Lib/test/test_statistics.py
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Original file line number Diff line number Diff line change
Expand Up @@ -2444,7 +2444,7 @@ def test_kde_kernel_invcdfs(self):
with self.subTest(kernel=kernel):
cdf = kde([0.0], h=1.0, kernel=kernel, cumulative=True)
for x in xarr:
self.assertAlmostEqual(invcdf(cdf(x)), x, places=5)
self.assertAlmostEqual(invcdf(cdf(x)), x, places=6)

@support.requires_resource('cpu')
def test_kde_random(self):
Expand Down