#!/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 from ..array_utils import get_array_module, is_sparse_module @arithmetic_operand(sparse_mode='unary') class TensorI0(TensorUnaryOp): _op_type_ = OperandDef.I0 _func_name = 'i0' @classmethod def execute(cls, ctx, op): x = ctx[op.inputs[0].key] xp = get_array_module(x) res = xp.i0(x) if not is_sparse_module(xp): res = res.reshape(op.outputs[0].shape) ctx[op.outputs[0].key] = res [文档]@infer_dtype(np.i0) def i0(x, **kwargs): """ Modified Bessel function of the first kind, order 0. Usually denoted :math:`I_0`. This function does broadcast, but will *not* "up-cast" int dtype arguments unless accompanied by at least one float or complex dtype argument (see Raises below). Parameters ---------- x : array_like, dtype float or complex Argument of the Bessel function. Returns ------- out : Tensor, shape = x.shape, dtype = x.dtype The modified Bessel function evaluated at each of the elements of `x`. Raises ------ TypeError: array cannot be safely cast to required type If argument consists exclusively of int dtypes. See Also -------- scipy.special.iv, scipy.special.ive Notes ----- We use the algorithm published by Clenshaw [1]_ and referenced by Abramowitz and Stegun [2]_, for which the function domain is partitioned into the two intervals [0,8] and (8,inf), and Chebyshev polynomial expansions are employed in each interval. Relative error on the domain [0,30] using IEEE arithmetic is documented [3]_ as having a peak of 5.8e-16 with an rms of 1.4e-16 (n = 30000). References ---------- .. [1] C. W. Clenshaw, "Chebyshev series for mathematical functions", in *National Physical Laboratory Mathematical Tables*, vol. 5, London: Her Majesty's Stationery Office, 1962. .. [2] M. Abramowitz and I. A. Stegun, *Handbook of Mathematical Functions*, 10th printing, New York: Dover, 1964, pp. 379. http://www.math.sfu.ca/~cbm/aands/page_379.htm .. [3] http://kobesearch.cpan.org/htdocs/Math-Cephes/Math/Cephes.html Examples -------- >>> import mars.tensor as mt >>> mt.i0([0.]).execute() array([1.]) >>> mt.i0([0., 1. + 2j]).execute() array([ 1.00000000+0.j , 0.18785373+0.64616944j]) """ op = TensorI0(**kwargs) return op(x)