# Source code for mars.tensor.arithmetic.arcsin

#!/usr/bin/env python
# -*- coding: utf-8 -*-
# Copyright 1999-2018 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
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# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
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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 TensorArcsin(TensorUnaryOp):
_op_type_ = OperandDef.ARCSIN
_func_name = 'arcsin'

[docs]@infer_dtype(np.arcsin)
def arcsin(x, out=None, where=None, **kwargs):
"""
Inverse sine, element-wise.

Parameters
----------
x : array_like
y-coordinate on the unit circle.
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
-------
angle : Tensor
The inverse sine of each element in x, in radians and in the
closed interval [-pi/2, pi/2].  If x is a scalar, a scalar
is returned, otherwise a tensor.

--------
sin, cos, arccos, tan, arctan, arctan2, emath.arcsin

Notes
-----
arcsin is a multivalued function: for each x there are infinitely
many numbers z such that :math:sin(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, *arcsin* 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, arcsin is a complex analytic function that
has, by convention, the branch cuts [-inf, -1] and [1, inf]  and is
continuous from above on the former and from below on the latter.

The inverse sine is also known as asin or sin^{-1}.

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

Examples
--------
>>> import mars.tensor as mt
>>> mt.arcsin(1).execute()     # pi/2
1.5707963267948966
>>> mt.arcsin(-1).execute()    # -pi/2
-1.5707963267948966
>>> mt.arcsin(0).execute()
0.0
"""
op = TensorArcsin(**kwargs)
return op(x, out=out, where=where)