#!/usr/bin/env python # -*- coding: utf-8 -*- # Copyright 1999-2020 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 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)