tfp.substrates.numpy.math.bessel_iv_ratio
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Computes I_{v} (z) / I_{v - 1} (z) in a numerically stable way.
tfp.substrates.numpy.math.bessel_iv_ratio(
v, z, name=None
)
Let I(v, z) be the modified bessel function of the first kind. This computes
the ratio of I(v, z) / I(v - 1, z). This can be more numerically stable
and faster than computing the ratio directly.
This uses a continued fraction approximation attributed to Gauss for
computing this quantity in the limit where z <= v, and a continued fraction
approximation attributed to Perron for z > v.
Args |
|---|
v
|
value for which I_{v}(z) / I_{v - 1}(z) should be computed. Expect
v > 0.
|
z
|
value for which I_{v}(z) / I_{v - 1}(z) should be computed. Expect
z > 0.
|
name
|
A name for the operation (optional).
Default value: None (i.e., 'bessel_iv_ratio').
|
Returns |
|---|
|
I(v, z) / I(v - 1, z).
|
References
[1]: Walter Gautschi and Josef Slavik. On the Computation of Modified
Bessel Function Ratios. http://www.jstor.com/stable/2006491
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Last updated 2023-11-21 UTC.
[null,null,["Last updated 2023-11-21 UTC."],[],[],null,["# tfp.substrates.numpy.math.bessel_iv_ratio\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/bessel.py#L349-L379) |\n\nComputes `I_{v} (z) / I_{v - 1} (z)` in a numerically stable way.\n\n#### View aliases\n\n\n**Main aliases**\n\n[`tfp.experimental.substrates.numpy.math.bessel_iv_ratio`](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/bessel_iv_ratio)\n\n\u003cbr /\u003e\n\n tfp.substrates.numpy.math.bessel_iv_ratio(\n v, z, name=None\n )\n\nLet I(v, z) be the modified bessel function of the first kind. This computes\nthe ratio of I(v, z) / I(v - 1, z). This can be more numerically stable\nand faster than computing the ratio directly.\n\nThis uses a continued fraction approximation attributed to Gauss for\ncomputing this quantity in the limit where z \\\u003c= v, and a continued fraction\napproximation attributed to Perron for z \\\u003e v.\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n| Args ---- ||\n|--------|---------------------------------------------------------------------------------------|\n| `v` | value for which `I_{v}(z) / I_{v - 1}(z)` should be computed. Expect v \\\u003e 0. |\n| `z` | value for which `I_{v}(z) / I_{v - 1}(z)` should be computed. Expect z \\\u003e 0. |\n| `name` | A name for the operation (optional). Default value: `None` (i.e., 'bessel_iv_ratio'). |\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n| Returns ------- ||\n|---|---|\n| I(v, z) / I(v - 1, z). ||\n\n\u003cbr /\u003e\n\n#### References\n\n\\[1\\]: Walter Gautschi and Josef Slavik. On the Computation of Modified\nBessel Function Ratios. \u003chttp://www.jstor.com/stable/2006491\u003e"]]
View source on GitHub