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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");
# 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 TensorPoisson(TensorDistribution, TensorRandomOperandMixin):
_input_fields_ = ["lam"]
_op_type_ = OperandDef.RAND_POSSION
_fields_ = "lam", "size"
lam = AnyField("lam")
_func_name = "poisson"
def __call__(self, lam, chunk_size=None):
return self.new_tensor([lam], None, raw_chunk_size=chunk_size)
[docs]def poisson(random_state, lam=1.0, size=None, chunk_size=None, gpu=None, dtype=None):
r"""
Draw samples from a Poisson distribution.
The Poisson distribution is the limit of the binomial distribution
for large N.
Parameters
----------
lam : float or array_like of floats
Expectation of interval, should be >= 0. A sequence of expectation
intervals must be broadcastable over the requested size.
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 ``lam`` is a scalar. Otherwise,
``mt.array(lam).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 Poisson distribution.
Notes
-----
The Poisson distribution
.. math:: f(k; \lambda)=\frac{\lambda^k e^{-\lambda}}{k!}
For events with an expected separation :math:`\lambda` the Poisson
distribution :math:`f(k; \lambda)` describes the probability of
:math:`k` events occurring within the observed
interval :math:`\lambda`.
Because the output is limited to the range of the C long type, a
ValueError is raised when `lam` is within 10 sigma of the maximum
representable value.
References
----------
.. [1] Weisstein, Eric W. "Poisson Distribution."
From MathWorld--A Wolfram Web Resource.
http://mathworld.wolfram.com/PoissonDistribution.html
.. [2] Wikipedia, "Poisson distribution",
http://en.wikipedia.org/wiki/Poisson_distribution
Examples
--------
Draw samples from the distribution:
>>> import mars.tensor as mt
>>> s = mt.random.poisson(5, 10000)
Display histogram of the sample:
>>> import matplotlib.pyplot as plt
>>> count, bins, ignored = plt.hist(s.execute(), 14, normed=True)
>>> plt.show()
Draw each 100 values for lambda 100 and 500:
>>> s = mt.random.poisson(lam=(100., 500.), size=(100, 2))
"""
if dtype is None:
dtype = np.random.RandomState().poisson(handle_array(lam), size=(0,)).dtype
size = random_state._handle_size(size)
seed = gen_random_seeds(1, random_state.to_numpy())[0]
op = TensorPoisson(size=size, seed=seed, gpu=gpu, dtype=dtype)
return op(lam, chunk_size=chunk_size)