Source code for mars.tensor.random.dirichlet

#!/usr/bin/env python
# -*- coding: utf-8 -*-
# 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.
# You may obtain a copy of the License at
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# See the License for the specific language governing permissions and
# limitations under the License.

import itertools
from import Iterable

import numpy as np

from ... import opcodes as OperandDef
from ...serialization.serializables import TupleField
from ...config import options
from ..utils import decide_chunk_sizes, gen_random_seeds
from .core import TensorRandomOperandMixin, TensorDistribution

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)

    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)

        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, .. [2] Wikipedia, "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)