# Source code for mars.tensor.arithmetic.sinc

#!/usr/bin/env python
# -*- coding: utf-8 -*-
# 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
#
#
# 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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# See the License for the specific language governing permissions and
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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 TensorSinc(TensorUnaryOp):
_op_type_ = OperandDef.SINC
_func_name = "sinc"

[docs]@infer_dtype(np.sinc)
def sinc(x, **kwargs):
r"""
Return the sinc function.

The sinc function is :math:\\sin(\\pi x)/(\\pi x).

Parameters
----------
x : Tensor
Tensor (possibly multi-dimensional) of values for which to to
calculate sinc(x).

Returns
-------
out : Tensor
sinc(x), which has the same shape as the input.

Notes
-----
sinc(0) is the limit value 1.

The name sinc is short for "sine cardinal" or "sinus cardinalis".

The sinc function is used in various signal processing applications,
including in anti-aliasing, in the construction of a Lanczos resampling
filter, and in interpolation.

For bandlimited interpolation of discrete-time signals, the ideal
interpolation kernel is proportional to the sinc function.

References
----------
.. [1] Weisstein, Eric W. "Sinc Function." From MathWorld--A Wolfram Web
Resource. http://mathworld.wolfram.com/SincFunction.html
.. [2] Wikipedia, "Sinc function",
http://en.wikipedia.org/wiki/Sinc_function

Examples
--------
>>> import mars.tensor as mt

>>> x = mt.linspace(-4, 4, 41)
>>> mt.sinc(x).execute()
array([ -3.89804309e-17,  -4.92362781e-02,  -8.40918587e-02,
-8.90384387e-02,  -5.84680802e-02,   3.89804309e-17,
6.68206631e-02,   1.16434881e-01,   1.26137788e-01,
8.50444803e-02,  -3.89804309e-17,  -1.03943254e-01,
-1.89206682e-01,  -2.16236208e-01,  -1.55914881e-01,
3.89804309e-17,   2.33872321e-01,   5.04551152e-01,
7.56826729e-01,   9.35489284e-01,   1.00000000e+00,
9.35489284e-01,   7.56826729e-01,   5.04551152e-01,
2.33872321e-01,   3.89804309e-17,  -1.55914881e-01,
-2.16236208e-01,  -1.89206682e-01,  -1.03943254e-01,
-3.89804309e-17,   8.50444803e-02,   1.26137788e-01,
1.16434881e-01,   6.68206631e-02,   3.89804309e-17,
-5.84680802e-02,  -8.90384387e-02,  -8.40918587e-02,
-4.92362781e-02,  -3.89804309e-17])

>>> import matplotlib.pyplot as plt
>>> plt.plot(x.execute(), np.sinc(x).execute())
[<matplotlib.lines.Line2D object at 0x...>]
>>> plt.title("Sinc Function")
<matplotlib.text.Text object at 0x...>
>>> plt.ylabel("Amplitude")
<matplotlib.text.Text object at 0x...>
>>> plt.xlabel("X")
<matplotlib.text.Text object at 0x...>
>>> plt.show()
"""
op = TensorSinc(**kwargs)
return op(x)