# Copyright 2022-2023 XProbe Inc.
# derived from 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
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import numpy as np
from ... import opcodes as OperandDef
from ...serialization.serializables import FieldTypes, Int64Field, TupleField
from ..utils import gen_random_seeds
from .core import TensorDistribution, TensorRandomOperandMixin
class TensorMultinomial(TensorDistribution, TensorRandomOperandMixin):
_op_type_ = OperandDef.RAND_MULTINOMIAL
_fields_ = "n", "pvals", "size"
n = Int64Field("n")
pvals = TupleField("pvals", FieldTypes.float64)
_func_name = "multinomial"
def __call__(self, chunk_size=None):
if self.size is None:
shape = (len(self.pvals),)
else:
try:
shape = tuple(self.size) + (len(self.pvals),)
except TypeError:
shape = (self.size, len(self.pvals))
return self.new_tensor(None, shape, raw_chunk_size=chunk_size)
[docs]def multinomial(
random_state, n, pvals, size=None, chunk_size=None, gpu=None, dtype=None
):
"""
Draw samples from a multinomial distribution.
The multinomial distribution is a multivariate generalisation of the
binomial distribution. Take an experiment with one of ``p``
possible outcomes. An example of such an experiment is throwing a dice,
where the outcome can be 1 through 6. Each sample drawn from the
distribution represents `n` such experiments. Its values,
``X_i = [X_0, X_1, ..., X_p]``, represent the number of times the
outcome was ``i``.
Parameters
----------
n : int
Number of experiments.
pvals : sequence of floats, length p
Probabilities of each of the ``p`` different outcomes. These
should sum to 1 (however, the last element is always assumed to
account for the remaining probability, as long as
``sum(pvals[:-1]) <= 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. 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
-------
out : Tensor
The drawn samples, of shape *size*, if that was provided. If not,
the shape is ``(N,)``.
In other words, each entry ``out[i,j,...,:]`` is an N-dimensional
value drawn from the distribution.
Examples
--------
Throw a dice 20 times:
>>> import mars.tensor as mt
>>> mt.random.multinomial(20, [1/6.]*6, size=1).execute()
array([[4, 1, 7, 5, 2, 1]])
It landed 4 times on 1, once on 2, etc.
Now, throw the dice 20 times, and 20 times again:
>>> mt.random.multinomial(20, [1/6.]*6, size=2).execute()
array([[3, 4, 3, 3, 4, 3],
[2, 4, 3, 4, 0, 7]])
For the first run, we threw 3 times 1, 4 times 2, etc. For the second,
we threw 2 times 1, 4 times 2, etc.
A loaded die is more likely to land on number 6:
>>> mt.random.multinomial(100, [1/7.]*5 + [2/7.]).execute()
array([11, 16, 14, 17, 16, 26])
The probability inputs should be normalized. As an implementation
detail, the value of the last entry is ignored and assumed to take
up any leftover probability mass, but this should not be relied on.
A biased coin which has twice as much weight on one side as on the
other should be sampled like so:
>>> mt.random.multinomial(100, [1.0 / 3, 2.0 / 3]).execute() # RIGHT
array([38, 62])
not like:
>>> mt.random.multinomial(100, [1.0, 2.0]).execute() # WRONG
array([100, 0])
"""
n = int(n)
pvals = tuple(pvals)
if dtype is None:
dtype = np.random.RandomState().multinomial(n, pvals, size=(0,)).dtype
size = random_state._handle_size(size)
seed = gen_random_seeds(1, random_state.to_numpy())[0]
op = TensorMultinomial(n=n, pvals=pvals, seed=seed, size=size, gpu=gpu, dtype=dtype)
return op(chunk_size=chunk_size)