Source code for mars.tensor.random.vonmises

#!/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
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# See the License for the specific language governing permissions and
# limitations under the License.

import numpy as np

from ... import opcodes as OperandDef
from ...serialize import AnyField
from .core import TensorRandomOperandMixin, handle_array, TensorDistribution

class TensorVonmises(TensorDistribution, TensorRandomOperandMixin):
    _input_fields_ = ['_mu', '_kappa']
    _op_type_ = OperandDef.RAND_VONMISES

    _fields_ = '_mu', '_kappa', '_size'
    _mu = AnyField('mu')
    _kappa = AnyField('kappa')
    _func_name = 'vonmises'

    def __init__(self, size=None, state=None, dtype=None, **kw):
        dtype = np.dtype(dtype) if dtype is not None else dtype
        super().__init__(_size=size, _state=state, dtype=dtype, **kw)

    def mu(self):
        return self._mu

    def kappa(self):
        return self._kappa

    def __call__(self, mu, kappa, chunk_size=None):
        return self.new_tensor([mu, kappa], None, raw_chunk_size=chunk_size)

[docs]def vonmises(random_state, mu, kappa, size=None, chunk_size=None, gpu=None, dtype=None): r""" Draw samples from a von Mises distribution. Samples are drawn from a von Mises distribution with specified mode (mu) and dispersion (kappa), on the interval [-pi, pi]. The von Mises distribution (also known as the circular normal distribution) is a continuous probability distribution on the unit circle. It may be thought of as the circular analogue of the normal distribution. Parameters ---------- mu : float or array_like of floats Mode ("center") of the distribution. kappa : float or array_like of floats Dispersion of the distribution, has to be >=0. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``mu`` and ``kappa`` are both scalars. Otherwise, ``np.broadcast(mu, kappa).size`` samples are drawn. chunk_size : int or tuple of int or tuple of ints, optional Desired chunk size on each dimension gpu : bool, optional Allocate the tensor on GPU if True, False as default dtype : data-type, optional Data-type of the returned tensor. Returns ------- out : Tensor or scalar Drawn samples from the parameterized von Mises distribution. See Also -------- scipy.stats.vonmises : probability density function, distribution, or cumulative density function, etc. Notes ----- The probability density for the von Mises distribution is .. math:: p(x) = \frac{e^{\kappa cos(x-\mu)}}{2\pi I_0(\kappa)}, where :math:`\mu` is the mode and :math:`\kappa` the dispersion, and :math:`I_0(\kappa)` is the modified Bessel function of order 0. The von Mises is named for Richard Edler von Mises, who was born in Austria-Hungary, in what is now the Ukraine. He fled to the United States in 1939 and became a professor at Harvard. He worked in probability theory, aerodynamics, fluid mechanics, and philosophy of science. References ---------- .. [1] Abramowitz, M. and Stegun, I. A. (Eds.). "Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing," New York: Dover, 1972. .. [2] von Mises, R., "Mathematical Theory of Probability and Statistics", New York: Academic Press, 1964. Examples -------- Draw samples from the distribution: >>> import mars.tensor as mt >>> mu, kappa = 0.0, 4.0 # mean and dispersion >>> s = mt.random.vonmises(mu, kappa, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> from scipy.special import i0 >>> plt.hist(s.execute(), 50, normed=True) >>> x = mt.linspace(-mt.pi, mt.pi, num=51) >>> y = mt.exp(kappa*mt.cos(x-mu))/(2*mt.pi*i0(kappa)) >>> plt.plot(x.execute(), y.execute(), linewidth=2, color='r') >>> """ if dtype is None: dtype = np.random.RandomState().vonmises( handle_array(mu), handle_array(kappa), size=(0,)).dtype size = random_state._handle_size(size) op = TensorVonmises(size=size, state=random_state.to_numpy(), gpu=gpu, dtype=dtype) return op(mu, kappa, chunk_size=chunk_size)