# xarray.ufuncs.atan2

### xarray.ufuncs.atan2 *= <xarray.ufuncs._binary_ufunc object>*

xarray specific variant of `numpy.atan2()`. Handles xarray objects by dispatching to the appropriate function for the underlying array type.

Documentation from numpy:

Element-wise arc tangent of `x1/x2` choosing the quadrant correctly.

The quadrant (i.e., branch) is chosen so that `arctan2(x1, x2)` is
the signed angle in radians between the ray ending at the origin and
passing through the point (1,0), and the ray ending at the origin and
passing through the point (x2, x1).  (Note the role reversal: the
“y-coordinate” is the first function parameter, the “x-coordinate”
is the second.)  By IEEE convention, this function is defined for
x2 = +/-0 and for either or both of x1 and x2 = +/-inf (see
Notes for specific values).

This function is not defined for complex-valued arguments; for the
so-called argument of complex values, use angle.

* **Parameters:**
  * **x1** ([array_like](https://numpy.org/doc/stable/glossary.html#term-array_like), `real-valued`) – y-coordinates.
  * **x2** ([array_like](https://numpy.org/doc/stable/glossary.html#term-array_like), `real-valued`) – x-coordinates.
    If `x1.shape != x2.shape`, they must be broadcastable to a common
    shape (which becomes the shape of the output).
  * **out** ([`ndarray`](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray), [`None`](https://docs.python.org/3/builtins/constants.html#None), or [`tuple`](https://docs.python.org/3/builtins/stdtypes.html#tuple) of [`ndarray`](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray) and [`None`](https://docs.python.org/3/builtins/constants.html#None), *optional*) – A location into which the result is stored. If provided, it must have
    a shape that the inputs broadcast to. If not provided or None,
    a freshly-allocated array is returned. A tuple (possible only as a
    keyword argument) must have length equal to the number of outputs.
  * **where** ([array_like](https://numpy.org/doc/stable/glossary.html#term-array_like), *optional*) – This condition is broadcast over the input. At locations where the
    condition is True, the out array will be set to the ufunc result.
    Elsewhere, the out array will retain its original value.
    Note that if an uninitialized out array is created via the default
    `out=None`, locations within it where the condition is False will
    remain uninitialized.
  * **\*\*kwargs** – For other keyword-only arguments, see the
    [ufunc docs](https://numpy.org/doc/stable/reference/ufuncs.html#ufuncs-kwargs).
* **Returns:**
  **angle** ([`ndarray`](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray)) – Array of angles in radians, in the range `[-pi, pi]`.
  This is a scalar if both x1 and x2 are scalars.

#### SEE ALSO
[`arctan`](xarray.ufuncs.arctan.html.md#xarray.ufuncs.arctan), [`tan`](xarray.ufuncs.tan.html.md#xarray.ufuncs.tan), [`angle`](xarray.ufuncs.angle.html.md#xarray.ufuncs.angle)

### Notes

*arctan2* is identical to the atan2 function of the underlying
C library.  The following special values are defined in the C
standard: <sup>[1](#id2)</sup>

| x1     | x2     | arctan2(x1,x2)   |
|--------|--------|------------------|
| +/- 0  | +0     | +/- 0            |
| +/- 0  | -0     | +/- pi           |
| > 0    | +/-inf | +0 / +pi         |
| < 0    | +/-inf | -0 / -pi         |
| +/-inf | +inf   | +/- (pi/4)       |
| +/-inf | -inf   | +/- (3\*pi/4)    |

Note that +0 and -0 are distinct floating point numbers, as are +inf
and -inf.

### References

* <a id='id2'>**[1]**</a> ISO/IEC standard 9899:1999, “Programming language C.”

### Examples

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Consider four points in different quadrants:

```pycon
>>> import numpy as np
>>> x = np.array([-1, +1, +1, -1])
>>> y = np.array([-1, -1, +1, +1])
>>> np.arctan2(y, x) * 180 / np.pi
array([-135.,  -45.,   45.,  135.])
```

Note the order of the parameters. arctan2 is defined also when x2 = 0
and at several other special points, obtaining values in
the range `[-pi, pi]`:

```pycon
>>> np.arctan2([1., -1.], [0., 0.])
array([ 1.57079633, -1.57079633])
>>> np.arctan2([0., 0., np.inf], [+0., -0., np.inf])
array([0.        , 3.14159265, 0.78539816])
```

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