tfp.math.atan_difference
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Difference of arctan(x) and arctan(y).
tfp.math.atan_difference(
x, y, name=None
)
Computes arctan(x) - arctan(y) avoiding catastrophic cancellation. This is
by resorting to the identity:
arctan(x) - arctan(y) = arctan((x - y) / (1 + x * y)) +
pi * sign(x) * 1_{x * y < -1)
where 1_A is the indicator function on the set A.
For a derivation of this fact, see [1].
References
[1] De Stefano, Sum of Arctangents
https://sites.google.com/site/micdestefano/mathematics/trigonometry/sum-of-arctangents
Args |
|---|
x
|
Floating-point Tensor. Should be broadcastable with y.
|
y
|
Floating-point Tensor. Should be broadcastable with x.
|
name
|
Optional Python str naming the operation.
|
Returns |
|---|
z
|
Tensor of same shape and dtype as x and y.
|
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Last updated 2023-11-21 UTC.
[null,null,["Last updated 2023-11-21 UTC."],[],[],null,["# tfp.math.atan_difference\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#L52-L91) |\n\nDifference of arctan(x) and arctan(y). \n\n tfp.math.atan_difference(\n x, y, name=None\n )\n\nComputes arctan(x) - arctan(y) avoiding catastrophic cancellation. This is\nby resorting to the identity: \n\n arctan(x) - arctan(y) = arctan((x - y) / (1 + x * y)) +\n pi * sign(x) * 1_{x * y \u003c -1)\n\nwhere `1_A` is the indicator function on the set `A`.\n\nFor a derivation of this fact, see \\[1\\].\n\n#### References\n\n\\[1\\] De Stefano, Sum of Arctangents\n\u003chttps://sites.google.com/site/micdestefano/mathematics/trigonometry/sum-of-arctangents\u003e\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n| Args ---- ||\n|--------|----------------------------------------------------------|\n| `x` | Floating-point Tensor. Should be broadcastable with `y`. |\n| `y` | Floating-point Tensor. Should be broadcastable with `x`. |\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| `z` | Tensor of same shape and dtype as `x` and `y`. |\n\n\u003cbr /\u003e"]]
View source on GitHub