tfp.substrates.numpy.math.log1psquare
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Numerically stable calculation of log(1 + x**2) for small or large |x|.
tfp.substrates.numpy.math.log1psquare(
x, name=None
)
For sufficiently large x we use the following observation:
log(1 + x**2) = 2 log(|x|) + log(1 + 1 / x**2)
--> 2 log(|x|) as x --> inf
Numerically, log(1 + 1 / x**2) is 0 when 1 / x**2 is small relative to
machine epsilon.
Args |
|---|
x
|
Float Tensor input.
|
name
|
Python string indicating the name of the TensorFlow operation.
Default value: 'log1psquare'.
|
Returns |
|---|
log1psq
|
Float Tensor representing log(1. + x**2.).
|
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Last updated 2023-11-21 UTC.
[null,null,["Last updated 2023-11-21 UTC."],[],[],null,["# tfp.substrates.numpy.math.log1psquare\n\n\u003cbr /\u003e\n\n|-------------------------------------------------------------------------------------------------------------------------------------------------|\n| [View source on GitHub](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/substrates/numpy/math/numeric.py#L29-L61) |\n\nNumerically stable calculation of `log(1 + x**2)` for small or large `|x|`.\n\n#### View aliases\n\n\n**Main aliases**\n\n[`tfp.experimental.substrates.numpy.math.log1psquare`](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/log1psquare)\n\n\u003cbr /\u003e\n\n tfp.substrates.numpy.math.log1psquare(\n x, name=None\n )\n\nFor sufficiently large `x` we use the following observation: \n\n log(1 + x**2) = 2 log(|x|) + log(1 + 1 / x**2)\n --\u003e 2 log(|x|) as x --\u003e inf\n\nNumerically, `log(1 + 1 / x**2)` is `0` when `1 / x**2` is small relative to\nmachine epsilon.\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n| Args ---- ||\n|--------|------------------------------------------------------------------------------------------------|\n| `x` | Float `Tensor` input. |\n| `name` | Python string indicating the name of the TensorFlow operation. Default value: `'log1psquare'`. |\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n| Returns ------- ||\n|-----------|------------------------------------------------|\n| `log1psq` | Float `Tensor` representing `log(1. + x**2.)`. |\n\n\u003cbr /\u003e"]]
View source on GitHub