Source code for mars.tensor.arithmetic.i0

#!/usr/bin/env python
# -*- coding: utf-8 -*-
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# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
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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
from ..array_utils import get_array_module, is_sparse_module

class TensorI0(TensorUnaryOp):
    _op_type_ = OperandDef.I0
    _func_name = "i0"

    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

[docs]@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. .. [3] 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)