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# derived from copyright 1999-2021 Alibaba Group Holding Ltd.
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# Licensed under the Apache License, Version 2.0 (the "License");
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# http://www.apache.org/licenses/LICENSE-2.0
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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 TensorLogseries(TensorDistribution, TensorRandomOperandMixin):
_input_fields_ = ["p"]
_op_type_ = OperandDef.RAND_LOGSERIES
_fields_ = "p", "size"
p = AnyField("p")
_func_name = "logseries"
def __call__(self, p, chunk_size=None):
return self.new_tensor([p], None, raw_chunk_size=chunk_size)
[docs]def logseries(random_state, p, size=None, chunk_size=None, gpu=None, dtype=None):
r"""
Draw samples from a logarithmic series distribution.
Samples are drawn from a log series distribution with specified
shape parameter, 0 < ``p`` < 1.
Parameters
----------
p : float or array_like of floats
Shape parameter for the distribution. Must be in the range (0, 1).
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 ``p`` is a scalar. Otherwise,
``np.array(p).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 logarithmic series distribution.
See Also
--------
scipy.stats.logser : probability density function, distribution or
cumulative density function, etc.
Notes
-----
The probability density for the Log Series distribution is
.. math:: P(k) = \frac{-p^k}{k \ln(1-p)},
where p = probability.
The log series distribution is frequently used to represent species
richness and occurrence, first proposed by Fisher, Corbet, and
Williams in 1943 [2]. It may also be used to model the numbers of
occupants seen in cars [3].
References
----------
.. [1] Buzas, Martin A.; Culver, Stephen J., Understanding regional
species diversity through the log series distribution of
occurrences: BIODIVERSITY RESEARCH Diversity & Distributions,
Volume 5, Number 5, September 1999 , pp. 187-195(9).
.. [2] Fisher, R.A,, A.S. Corbet, and C.B. Williams. 1943. The
relation between the number of species and the number of
individuals in a random sample of an animal population.
Journal of Animal Ecology, 12:42-58.
.. [3] D. J. Hand, F. Daly, D. Lunn, E. Ostrowski, A Handbook of Small
Data Sets, CRC Press, 1994.
.. [4] Wikipedia, "Logarithmic distribution",
http://en.wikipedia.org/wiki/Logarithmic_distribution
Examples
--------
Draw samples from the distribution:
>>> import mars.tensor as mt
>>> import matplotlib.pyplot as plt
>>> a = .6
>>> s = mt.random.logseries(a, 10000)
>>> count, bins, ignored = plt.hist(s.execute())
# plot against distribution
>>> def logseries(k, p):
... return -p**k/(k*mt.log(1-p))
>>> plt.plot(bins, (logseries(bins, a)*count.max()/
... logseries(bins, a).max()).execute(), 'r')
>>> plt.show()
"""
if dtype is None:
dtype = np.random.RandomState().logseries(handle_array(p), size=(0,)).dtype
size = random_state._handle_size(size)
seed = gen_random_seeds(1, random_state.to_numpy())[0]
op = TensorLogseries(seed=seed, size=size, gpu=gpu, dtype=dtype)
return op(p, chunk_size=chunk_size)