# Copyright 2022-2023 XProbe Inc.
# derived from 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
#
# 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 ...serialization.serializables import AnyField
from ..utils import gen_random_seeds
from .core import TensorDistribution, TensorRandomOperandMixin, handle_array
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 __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')
>>> plt.show()
"""
if dtype is None:
dtype = (
np.random.RandomState()
.vonmises(handle_array(mu), handle_array(kappa), size=(0,))
.dtype
)
size = random_state._handle_size(size)
seed = gen_random_seeds(1, random_state.to_numpy())[0]
op = TensorVonmises(size=size, seed=seed, gpu=gpu, dtype=dtype)
return op(mu, kappa, chunk_size=chunk_size)