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tensorflow_probability/python/math/special.py

Lines changed: 5 additions & 5 deletions
Original file line numberDiff line numberDiff line change
@@ -107,7 +107,7 @@ def _betainc_naive(a, b, x):
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def _betainc_even_partial_numerator(iteration, a, b, x, dtype):
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"""Even partial numerator used in the continued fraction for betainc."""
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# This function computes the partial numerator d_{2m} that is specified
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# here: https://dlmf.nist.gov/8.17#E23
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# here: https://dlmf.nist.gov/8.17.E23
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one = tf.constant(1., dtype=dtype)
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two = tf.constant(2., dtype=dtype)
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@@ -126,7 +126,7 @@ def _betainc_even_partial_numerator(iteration, a, b, x, dtype):
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def _betainc_odd_partial_numerator(iteration, a, b, x, dtype):
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"""Odd partial numerator used in the continued fraction for betainc."""
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# This function computes the partial numerator d_{2m + 1} that is specified
129-
# here: https://dlmf.nist.gov/8.17#E23
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# here: https://dlmf.nist.gov/8.17.E23
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one = tf.constant(1., dtype=dtype)
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two = tf.constant(2., dtype=dtype)
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@@ -283,7 +283,7 @@ def _betainc_der_continued_fraction(a, b, x, dtype, use_continued_fraction):
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# This continued fraction expansion of betainc converges rapidly
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# for x < (a - 1) / (a + b - 2). For x >= (a - 1) / (a + b - 2),
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# we can obtain an equivalent computation by using the symmetry
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# relation given here: https://dlmf.nist.gov/8.17#E4
286+
# relation given here: https://dlmf.nist.gov/8.17.E4
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# betainc(a, b, x) = 1 - betainc(b, a, 1 - x)
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use_symmetry_relation = (x >= (a - one) / (a + b - two))
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a_orig = a
@@ -317,7 +317,7 @@ def _betainc_der_power_series(a, b, x, dtype, use_power_series):
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"""Returns the partial derivatives of betainc with respect to a and b."""
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# This function evaluates betainc(a, b, x) by its series representation:
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# x ** a * 2F1(a, 1 - b; a + 1; x) / (a * B(a, b)) ,
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# where 2F1 is defined here: http://dlmf.nist.gov/15.2.i
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# where 2F1 is the Gauss series as defined here: http://dlmf.nist.gov/15.2.i
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# We apply this function when the input (a, b, x) satisfies at least one
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# of the following conditions:
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# C1: (x < a / (a + b)) & (b * x <= 1) & (x <= 0.95)
@@ -334,7 +334,7 @@ def _betainc_der_power_series(a, b, x, dtype, use_power_series):
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safe_x = tf.where(use_power_series, x, half)
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# When the condition C1 is false, we apply the symmetry relation given
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# here: https://dlmf.nist.gov/8.17#E4
337+
# here: https://dlmf.nist.gov/8.17.E4
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# betainc(a, b, x) = 1 - betainc(b, a, 1 - x)
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use_symmetry_relation = (safe_x >= safe_a / (safe_a + safe_b))
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safe_a_orig = safe_a

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