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#
# 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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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 TensorZipf(TensorDistribution, TensorRandomOperandMixin):
_input_fields_ = ["a"]
_op_type_ = OperandDef.RAND_ZIPF
_fields_ = "a", "size"
a = AnyField("a")
_func_name = "zipf"
def __call__(self, a, chunk_size=None):
return self.new_tensor([a], None, raw_chunk_size=chunk_size)
[docs]def zipf(random_state, a, size=None, chunk_size=None, gpu=None, dtype=None):
r"""
Draw samples from a Zipf distribution.
Samples are drawn from a Zipf distribution with specified parameter
`a` > 1.
The Zipf distribution (also known as the zeta distribution) is a
continuous probability distribution that satisfies Zipf's law: the
frequency of an item is inversely proportional to its rank in a
frequency table.
Parameters
----------
a : float or array_like of floats
Distribution parameter. Should be greater than 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 ``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 Zipf distribution.
See Also
--------
scipy.stats.zipf : probability density function, distribution, or
cumulative density function, etc.
Notes
-----
The probability density for the Zipf distribution is
.. math:: p(x) = \frac{x^{-a}}{\zeta(a)},
where :math:`\zeta` is the Riemann Zeta function.
It is named for the American linguist George Kingsley Zipf, who noted
that the frequency of any word in a sample of a language is inversely
proportional to its rank in the frequency table.
References
----------
.. [1] Zipf, G. K., "Selected Studies of the Principle of Relative
Frequency in Language," Cambridge, MA: Harvard Univ. Press,
1932.
Examples
--------
Draw samples from the distribution:
>>> import mars.tensor as mt
>>> a = 2. # parameter
>>> s = mt.random.zipf(a, 1000)
Display the histogram of the samples, along with
the probability density function:
>>> import matplotlib.pyplot as plt
>>> from scipy import special
Truncate s values at 50 so plot is interesting:
>>> count, bins, ignored = plt.hist(s[s<50].execute(), 50, normed=True)
>>> x = mt.arange(1., 50.)
>>> y = x**(-a) / special.zetac(a)
>>> plt.plot(x.execute(), (y/mt.max(y)).execute(), linewidth=2, color='r')
>>> plt.show()
"""
if dtype is None:
dtype = np.random.RandomState().zipf(handle_array(a), size=(0,)).dtype
size = random_state._handle_size(size)
seed = gen_random_seeds(1, random_state.to_numpy())[0]
op = TensorZipf(size=size, seed=seed, gpu=gpu, dtype=dtype)
return op(a, chunk_size=chunk_size)