# Source code for mars.tensor.random.standard_cauchy

```
#!/usr/bin/env python
# -*- coding: utf-8 -*-
# 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 ..utils import gen_random_seeds
from .core import TensorRandomOperandMixin, TensorDistribution
class TensorStandardCauchy(TensorDistribution, TensorRandomOperandMixin):
_op_type_ = OperandDef.RAND_STANDARD_CAUCHY
_func_name = "standard_cauchy"
_fields_ = ("size",)
def __call__(self, chunk_size=None):
return self.new_tensor(None, None, raw_chunk_size=chunk_size)
[docs]def standard_cauchy(random_state, size=None, chunk_size=None, gpu=None, dtype=None):
r"""
Draw samples from a standard Cauchy distribution with mode = 0.
Also known as the Lorentz distribution.
Parameters
----------
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. Default is None, in which case a
single value is returned.
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
-------
samples : Tensor or scalar
The drawn samples.
Notes
-----
The probability density function for the full Cauchy distribution is
.. math:: P(x; x_0, \gamma) = \frac{1}{\pi \gamma \bigl[ 1+
(\frac{x-x_0}{\gamma})^2 \bigr] }
and the Standard Cauchy distribution just sets :math:`x_0=0` and
:math:`\gamma=1`
The Cauchy distribution arises in the solution to the driven harmonic
oscillator problem, and also describes spectral line broadening. It
also describes the distribution of values at which a line tilted at
a random angle will cut the x axis.
When studying hypothesis tests that assume normality, seeing how the
tests perform on data from a Cauchy distribution is a good indicator of
their sensitivity to a heavy-tailed distribution, since the Cauchy looks
very much like a Gaussian distribution, but with heavier tails.
References
----------
.. [1] NIST/SEMATECH e-Handbook of Statistical Methods, "Cauchy
Distribution",
http://www.itl.nist.gov/div898/handbook/eda/section3/eda3663.htm
.. [2] Weisstein, Eric W. "Cauchy Distribution." From MathWorld--A
Wolfram Web Resource.
http://mathworld.wolfram.com/CauchyDistribution.html
.. [3] Wikipedia, "Cauchy distribution"
http://en.wikipedia.org/wiki/Cauchy_distribution
Examples
--------
Draw samples and plot the distribution:
>>> import mars.tensor as mt
>>> import matplotlib.pyplot as plt
>>> s = mt.random.standard_cauchy(1000000)
>>> s = s[(s>-25) & (s<25)] # truncate distribution so it plots well
>>> plt.hist(s.execute(), bins=100)
>>> plt.show()
"""
if dtype is None:
dtype = np.random.RandomState().standard_cauchy(size=(0,)).dtype
size = random_state._handle_size(size)
seed = gen_random_seeds(1, random_state.to_numpy())[0]
op = TensorStandardCauchy(size=size, seed=seed, gpu=gpu, dtype=dtype)
return op(chunk_size=chunk_size)
```