tfp.math.log_gamma_correction
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Returns the error of the Stirling approximation to lgamma(x) for x >= 8.
tfp.math.log_gamma_correction(
x, name=None
)
This is useful for accurately evaluating ratios between Gamma functions, as
happens when trying to compute Beta functions.
Specifically,
lgamma(x) approx (x - 0.5) * log(x) - x + 0.5 log (2 pi)
+ log_gamma_correction(x)
for x >= 8.
This is the function called Delta in [1], eq (30). We implement it with
the rational minimax approximation given in [1], eq (32).
References:
[1] DiDonato and Morris, "Significant Digit Computation of the Incomplete Beta
Function Ratios", 1988. Technical report NSWC TR 88-365, Naval Surface
Warfare Center (K33), Dahlgren, VA 22448-5000. Section IV, Auxiliary
Functions. https://apps.dtic.mil/dtic/tr/fulltext/u2/a210118.pdf
Args |
|---|
x
|
Floating-point Tensor at which to evaluate the log gamma correction
elementwise. The approximation is accurate when x >= 8.
|
name
|
Optional Python str naming the operation.
|
Returns |
|---|
lgamma_corr
|
Tensor of elementwise log gamma corrections.
|
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Last updated 2023-11-21 UTC.
[null,null,["Last updated 2023-11-21 UTC."],[],[],null,["# tfp.math.log_gamma_correction\n\n\u003cbr /\u003e\n\n|-------------------------------------------------------------------------------------------------------------------------------------------|\n| [View source on GitHub](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/math/special.py#L1854-L1903) |\n\nReturns the error of the Stirling approximation to lgamma(x) for x \\\u003e= 8. \n\n tfp.math.log_gamma_correction(\n x, name=None\n )\n\nThis is useful for accurately evaluating ratios between Gamma functions, as\nhappens when trying to compute Beta functions.\n\nSpecifically, \n\n lgamma(x) approx (x - 0.5) * log(x) - x + 0.5 log (2 pi)\n + log_gamma_correction(x)\n\nfor x \\\u003e= 8.\n\nThis is the function called Delta in \\[1\\], eq (30). We implement it with\nthe rational minimax approximation given in \\[1\\], eq (32).\n\n#### References:\n\n\\[1\\] DiDonato and Morris, \"Significant Digit Computation of the Incomplete Beta\nFunction Ratios\", 1988. Technical report NSWC TR 88-365, Naval Surface\nWarfare Center (K33), Dahlgren, VA 22448-5000. Section IV, Auxiliary\nFunctions. \u003chttps://apps.dtic.mil/dtic/tr/fulltext/u2/a210118.pdf\u003e\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n| Args ---- ||\n|--------|------------------------------------------------------------------------------------------------------------------------------|\n| `x` | Floating-point Tensor at which to evaluate the log gamma correction elementwise. The approximation is accurate when x \\\u003e= 8. |\n| `name` | Optional Python `str` naming the operation. |\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n| Returns ------- ||\n|---------------|----------------------------------------------|\n| `lgamma_corr` | Tensor of elementwise log gamma corrections. |\n\n\u003cbr /\u003e"]]
View source on GitHub