# Source code for mars.tensor.arithmetic.arctan

#!/usr/bin/env python
# -*- coding: utf-8 -*-
# Copyright 1999-2020 Alibaba Group Holding Ltd.
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# you may not use this file except in compliance with the License.
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import numpy as np

from ... import opcodes as OperandDef
from ..utils import infer_dtype
from .core import TensorUnaryOp
from .utils import arithmetic_operand

@arithmetic_operand(sparse_mode='unary')
class TensorArctan(TensorUnaryOp):
_op_type_ = OperandDef.ARCTAN
_func_name = 'arctan'

[docs]@infer_dtype(np.arctan)
def arctan(x, out=None, where=None, **kwargs):
"""
Trigonometric inverse tangent, element-wise.

The inverse of tan, so that if y = tan(x) then x = arctan(y).

Parameters
----------
x : array_like
out : Tensor, None, or tuple of Tensor and 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 tensor is returned. A tuple (possible only as a
keyword argument) must have length equal to the number of outputs.
where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values
of False indicate to leave the value in the output alone.
**kwargs

Returns
-------
out : Tensor
Out has the same shape as x.  Its real part is in
[-pi/2, pi/2] (arctan(+/-inf) returns +/-pi/2).
It is a scalar if x is a scalar.

--------
arctan2 : The "four quadrant" arctan of the angle formed by (x, y)
and the positive x-axis.
angle : Argument of complex values.

Notes
-----
arctan is a multi-valued function: for each x there are infinitely
many numbers z such that tan(z) = x.  The convention is to return
the angle z whose real part lies in [-pi/2, pi/2].

For real-valued input data types, arctan always returns real output.
For each value that cannot be expressed as a real number or infinity,
it yields nan and sets the invalid floating point error flag.

For complex-valued input, arctan is a complex analytic function that
has [1j, infj] and [-1j, -infj] as branch cuts, and is continuous
from the left on the former and from the right on the latter.

The inverse tangent is also known as atan or tan^{-1}.

References
----------
Abramowitz, M. and Stegun, I. A., *Handbook of Mathematical Functions*,
10th printing, New York: Dover, 1964, pp. 79.
http://www.math.sfu.ca/~cbm/aands/

Examples
--------
We expect the arctan of 0 to be 0, and of 1 to be pi/4:
>>> import mars.tensor as mt

>>> mt.arctan([0, 1]).execute()
array([ 0.        ,  0.78539816])

>>> mt.pi/4
0.78539816339744828

Plot arctan:

>>> import matplotlib.pyplot as plt
>>> x = mt.linspace(-10, 10)
>>> plt.plot(x.execute(), mt.arctan(x).execute())
>>> plt.axis('tight')
>>> plt.show()
"""
op = TensorArctan(**kwargs)
return op(x, out=out, where=where)