Source code for xorbits._mars.tensor.arithmetic.arctan

# Copyright 2022-2023 XProbe Inc.
# derived from copyright 1999-2021 Alibaba Group Holding Ltd.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#      http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

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"


@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.

    See Also
    --------
    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)