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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 itertools
from collections.abc import Iterable
import numpy as np
from ... import opcodes as OperandDef
from ...config import options
from ...serialization.serializables import TupleField
from ..utils import decide_chunk_sizes, gen_random_seeds
from .core import TensorDistribution, TensorRandomOperandMixin
class TensorDirichlet(TensorDistribution, TensorRandomOperandMixin):
_op_type_ = OperandDef.RAND_DIRICHLET
_fields_ = "alpha", "size"
alpha = TupleField("alpha", default=None)
_func_name = "dirichlet"
def _calc_shape(self, shapes):
shape = super()._calc_shape(shapes)
return shape + (len(self.alpha),)
def __call__(self, chunk_size=None):
return self.new_tensor(None, None, raw_chunk_size=chunk_size)
@classmethod
def tile(cls, op):
tensor = op.outputs[0]
chunk_size = tensor.extra_params.raw_chunk_size or options.chunk_size
nsplits = decide_chunk_sizes(
tensor.shape[:-1], chunk_size, tensor.dtype.itemsize
)
nsplits += ((len(op.alpha),),)
idxes = list(itertools.product(*[range(len(s)) for s in nsplits]))
seeds = gen_random_seeds(len(idxes), np.random.RandomState(op.seed))
out_chunks = []
for seed, idx, shape in zip(seeds, idxes, itertools.product(*nsplits)):
inputs = [inp.cix[idx] for inp in op.inputs]
size = shape[:-1]
chunk_op = op.copy().reset_key()
chunk_op._state = None
chunk_op.seed = seed
chunk_op.size = size
out_chunk = chunk_op.new_chunk(inputs, shape=shape, index=idx)
out_chunks.append(out_chunk)
new_op = op.copy()
return new_op.new_tensors(
op.inputs, tensor.shape, chunks=out_chunks, nsplits=nsplits
)
[docs]def dirichlet(random_state, alpha, size=None, chunk_size=None, gpu=None, dtype=None):
r"""
Draw samples from the Dirichlet distribution.
Draw `size` samples of dimension k from a Dirichlet distribution. A
Dirichlet-distributed random variable can be seen as a multivariate
generalization of a Beta distribution. Dirichlet pdf is the conjugate
prior of a multinomial in Bayesian inference.
Parameters
----------
alpha : array
Parameter of the distribution (k dimension for sample of
dimension k).
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
The drawn samples, of shape (size, alpha.ndim).
Raises
-------
ValueError
If any value in alpha is less than or equal to zero
Notes
-----
.. math:: X \approx \prod_{i=1}^{k}{x^{\alpha_i-1}_i}
Uses the following property for computation: for each dimension,
draw a random sample y_i from a standard gamma generator of shape
`alpha_i`, then
:math:`X = \frac{1}{\sum_{i=1}^k{y_i}} (y_1, \ldots, y_n)` is
Dirichlet distributed.
References
----------
.. [1] David McKay, "Information Theory, Inference and Learning
Algorithms," chapter 23,
http://www.inference.phy.cam.ac.uk/mackay/
.. [2] Wikipedia, "Dirichlet distribution",
http://en.wikipedia.org/wiki/Dirichlet_distribution
Examples
--------
Taking an example cited in Wikipedia, this distribution can be used if
one wanted to cut strings (each of initial length 1.0) into K pieces
with different lengths, where each piece had, on average, a designated
average length, but allowing some variation in the relative sizes of
the pieces.
>>> import mars.tensor as mt
>>> s = mt.random.dirichlet((10, 5, 3), 20).transpose()
>>> import matplotlib.pyplot as plt
>>> plt.barh(range(20), s[0].execute())
>>> plt.barh(range(20), s[1].execute(), left=s[0].execute(), color='g')
>>> plt.barh(range(20), s[2].execute(), left=(s[0]+s[1]).execute(), color='r')
>>> plt.title("Lengths of Strings")
"""
if isinstance(alpha, Iterable):
alpha = tuple(alpha)
else:
raise TypeError("`alpha` should be an array")
if dtype is None:
dtype = np.random.RandomState().dirichlet(alpha, size=(0,)).dtype
size = random_state._handle_size(size)
seed = gen_random_seeds(1, random_state.to_numpy())[0]
op = TensorDirichlet(seed=seed, alpha=alpha, size=size, gpu=gpu, dtype=dtype)
return op(chunk_size=chunk_size)