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# 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.
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# http://www.apache.org/licenses/LICENSE-2.0
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# Unless required by applicable law or agreed to in writing, software
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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 TensorRandomPower(TensorDistribution, TensorRandomOperandMixin):
_input_fields_ = ["a"]
_op_type_ = OperandDef.RAND_POWER
_fields_ = "a", "size"
a = AnyField("a")
_func_name = "power"
def __call__(self, a, chunk_size=None):
return self.new_tensor([a], None, raw_chunk_size=chunk_size)
[docs]def power(random_state, a, size=None, chunk_size=None, gpu=None, dtype=None):
r"""
Draws samples in [0, 1] from a power distribution with positive
exponent a - 1.
Also known as the power function distribution.
Parameters
----------
a : float or array_like of floats
Parameter of the distribution. Should be greater than zero.
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 ``a`` is a scalar. Otherwise,
``mt.array(a).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 power distribution.
Raises
------
ValueError
If a < 1.
Notes
-----
The probability density function is
.. math:: P(x; a) = ax^{a-1}, 0 \le x \le 1, a>0.
The power function distribution is just the inverse of the Pareto
distribution. It may also be seen as a special case of the Beta
distribution.
It is used, for example, in modeling the over-reporting of insurance
claims.
References
----------
.. [1] Christian Kleiber, Samuel Kotz, "Statistical size distributions
in economics and actuarial sciences", Wiley, 2003.
.. [2] Heckert, N. A. and Filliben, James J. "NIST Handbook 148:
Dataplot Reference Manual, Volume 2: Let Subcommands and Library
Functions", National Institute of Standards and Technology
Handbook Series, June 2003.
http://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/powpdf.pdf
Examples
--------
Draw samples from the distribution:
>>> import mars.tensor as mt
>>> a = 5. # shape
>>> samples = 1000
>>> s = mt.random.power(a, samples)
Display the histogram of the samples, along with
the probability density function:
>>> import matplotlib.pyplot as plt
>>> count, bins, ignored = plt.hist(s.execute(), bins=30)
>>> x = mt.linspace(0, 1, 100)
>>> y = a*x**(a-1.)
>>> normed_y = samples*mt.diff(bins)[0]*y
>>> plt.plot(x.execute(), normed_y.execute())
>>> plt.show()
Compare the power function distribution to the inverse of the Pareto.
>>> from scipy import stats
>>> rvs = mt.random.power(5, 1000000)
>>> rvsp = mt.random.pareto(5, 1000000)
>>> xx = mt.linspace(0,1,100)
>>> powpdf = stats.powerlaw.pdf(xx.execute(),5)
>>> plt.figure()
>>> plt.hist(rvs.execute(), bins=50, normed=True)
>>> plt.plot(xx.execute(),powpdf,'r-')
>>> plt.title('np.random.power(5)')
>>> plt.figure()
>>> plt.hist((1./(1.+rvsp)).execute(), bins=50, normed=True)
>>> plt.plot(xx.execute(),powpdf,'r-')
>>> plt.title('inverse of 1 + np.random.pareto(5)')
>>> plt.figure()
>>> plt.hist((1./(1.+rvsp)).execute(), bins=50, normed=True)
>>> plt.plot(xx.execute(),powpdf,'r-')
>>> plt.title('inverse of stats.pareto(5)')
"""
if dtype is None:
dtype = np.random.RandomState().power(handle_array(a), size=(0,)).dtype
size = random_state._handle_size(size)
seed = gen_random_seeds(1, random_state.to_numpy())[0]
op = TensorRandomPower(size=size, seed=seed, gpu=gpu, dtype=dtype)
return op(a, chunk_size=chunk_size)