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"""Random distribution generator NDArray API of MXNet."""
from ..base import numeric_types, _Null
from ..context import current_context
from . import _internal
from .ndarray import NDArray
__all__ = ['uniform', 'normal', 'randn', 'poisson', 'exponential', 'gamma',
'multinomial', 'negative_binomial', 'generalized_negative_binomial',
'shuffle', 'randint']
def _random_helper(random, sampler, params, shape, dtype, ctx, out, kwargs):
"""Helper function for random generators."""
if isinstance(params[0], NDArray):
for i in params[1:]:
assert isinstance(i, NDArray), \
"Distribution parameters must all have the same type, but got " \
"both %s and %s."%(type(params[0]), type(i))
return sampler(*params, shape=shape, dtype=dtype, out=out, **kwargs)
elif isinstance(params[0], numeric_types):
if ctx is None:
ctx = current_context()
if shape is _Null and out is None:
shape = 1
for i in params[1:]:
assert isinstance(i, numeric_types), \
"Distribution parameters must all have the same type, but got " \
"both %s and %s."%(type(params[0]), type(i))
return random(*params, shape=shape, dtype=dtype, ctx=ctx, out=out, **kwargs)
raise ValueError("Distribution parameters must be either NDArray or numbers, "
"but got %s."%type(params[0]))
[docs]def normal(loc=0, scale=1, shape=_Null, dtype=_Null, ctx=None, out=None, **kwargs):
"""Draw random samples from a normal (Gaussian) distribution.
Samples are distributed according to a normal distribution parametrized
by *loc* (mean) and *scale* (standard deviation).
Parameters
----------
loc : float or NDArray, optional
Mean (centre) of the distribution.
scale : float or NDArray, optional
Standard deviation (spread or width) of the distribution.
shape : int or tuple of ints, optional
The number of samples to draw. If shape is, e.g., `(m, n)` and `loc` and
`scale` are scalars, output shape will be `(m, n)`. If `loc` and `scale`
are NDArrays with shape, e.g., `(x, y)`, then output will have shape
`(x, y, m, n)`, where `m*n` samples are drawn for each `[loc, scale)` pair.
dtype : {'float16', 'float32', 'float64'}, optional
Data type of output samples. Default is 'float32'
ctx : Context, optional
Device context of output. Default is current context. Overridden by
`loc.context` when `loc` is an NDArray.
out : NDArray, optional
Store output to an existing NDArray.
Returns
-------
NDArray
An NDArray of type `dtype`. If input `shape` has shape, e.g., `(m, n)` and
`loc` and `scale` are scalars, output shape will be `(m, n)`. If `loc` and
`scale` are NDArrays with shape, e.g., `(x, y)`, then output will have shape
`(x, y, m, n)`, where `m*n` samples are drawn for each `[loc, scale)` pair.
Examples
--------
>>> mx.nd.random.normal(0, 1)
[ 2.21220636]
>>> mx.nd.random.normal(0, 1, ctx=mx.gpu(0))
[ 0.29253659]
>>> mx.nd.random.normal(-1, 1, shape=(2,))
[-0.2259962 -0.51619542]
>>> loc = mx.nd.array([1,2,3])
>>> scale = mx.nd.array([2,3,4])
>>> mx.nd.random.normal(loc, scale, shape=2)
[[ 0.55912292 3.19566321]
[ 1.91728961 2.47706747]
[ 2.79666662 5.44254589]]
"""
return _random_helper(_internal._random_normal, _internal._sample_normal,
[loc, scale], shape, dtype, ctx, out, kwargs)
[docs]def randn(*shape, **kwargs):
"""Draw random samples from a normal (Gaussian) distribution.
Samples are distributed according to a normal distribution parametrized
by *loc* (mean) and *scale* (standard deviation).
Parameters
----------
loc : float or NDArray
Mean (centre) of the distribution.
scale : float or NDArray
Standard deviation (spread or width) of the distribution.
shape : int or tuple of ints
The number of samples to draw. If shape is, e.g., `(m, n)` and `loc` and
`scale` are scalars, output shape will be `(m, n)`. If `loc` and `scale`
are NDArrays with shape, e.g., `(x, y)`, then output will have shape
`(x, y, m, n)`, where `m*n` samples are drawn for each `[loc, scale)` pair.
dtype : {'float16', 'float32', 'float64'}
Data type of output samples. Default is 'float32'
ctx : Context
Device context of output. Default is current context. Overridden by
`loc.context` when `loc` is an NDArray.
out : NDArray
Store output to an existing NDArray.
Returns
-------
NDArray
If input `shape` has shape, e.g., `(m, n)` and `loc` and `scale` are scalars, output
shape will be `(m, n)`. If `loc` and `scale` are NDArrays with shape, e.g., `(x, y)`,
then output will have shape `(x, y, m, n)`, where `m*n` samples are drawn for
each `[loc, scale)` pair.
Examples
--------
>>> mx.nd.random.randn()
2.21220636
>>> mx.nd.random.randn(2, 2)
[[-1.856082 -1.9768796 ]
[-0.20801921 0.2444218 ]]
>>> mx.nd.random.randn(2, 3, loc=5, scale=1)
[[4.19962 4.8311777 5.936328 ]
[5.357444 5.7793283 3.9896927]]
"""
loc = kwargs.pop('loc', 0)
scale = kwargs.pop('scale', 1)
dtype = kwargs.pop('dtype', _Null)
ctx = kwargs.pop('ctx', None)
out = kwargs.pop('out', None)
assert isinstance(loc, (int, float))
assert isinstance(scale, (int, float))
return _random_helper(_internal._random_normal, _internal._sample_normal,
[loc, scale], shape, dtype, ctx, out, kwargs)
[docs]def poisson(lam=1, shape=_Null, dtype=_Null, ctx=None, out=None, **kwargs):
"""Draw random samples from a Poisson distribution.
Samples are distributed according to a Poisson distribution parametrized
by *lambda* (rate). Samples will always be returned as a floating point data type.
Parameters
----------
lam : float or NDArray, optional
Expectation of interval, should be >= 0.
shape : int or tuple of ints, optional
The number of samples to draw. If shape is, e.g., `(m, n)` and `lam` is
a scalar, output shape will be `(m, n)`. If `lam`
is an NDArray with shape, e.g., `(x, y)`, then output will have shape
`(x, y, m, n)`, where `m*n` samples are drawn for each entry in `lam`.
dtype : {'float16', 'float32', 'float64'}, optional
Data type of output samples. Default is 'float32'
ctx : Context, optional
Device context of output. Default is current context. Overridden by
`lam.context` when `lam` is an NDArray.
out : NDArray, optional
Store output to an existing NDArray.
Returns
-------
NDArray
If input `shape` has shape, e.g., `(m, n)` and `lam` is
a scalar, output shape will be `(m, n)`. If `lam`
is an NDArray with shape, e.g., `(x, y)`, then output will have shape
`(x, y, m, n)`, where `m*n` samples are drawn for each entry in `lam`.
Examples
--------
>>> mx.nd.random.poisson(1)
[ 1.]
>>> mx.nd.random.poisson(1, shape=(2,))
[ 0. 2.]
>>> lam = mx.nd.array([1,2,3])
>>> mx.nd.random.poisson(lam, shape=2)
[[ 1. 3.]
[ 3. 2.]
[ 2. 3.]]
"""
return _random_helper(_internal._random_poisson, _internal._sample_poisson,
[lam], shape, dtype, ctx, out, kwargs)
[docs]def exponential(scale=1, shape=_Null, dtype=_Null, ctx=None, out=None, **kwargs):
r"""Draw samples from an exponential distribution.
Its probability density function is
.. math:: f(x; \frac{1}{\beta}) = \frac{1}{\beta} \exp(-\frac{x}{\beta}),
for x > 0 and 0 elsewhere. \beta is the scale parameter, which is the
inverse of the rate parameter \lambda = 1/\beta.
Parameters
----------
scale : float or NDArray, optional
The scale parameter, \beta = 1/\lambda.
shape : int or tuple of ints, optional
The number of samples to draw. If shape is, e.g., `(m, n)` and `scale` is
a scalar, output shape will be `(m, n)`. If `scale`
is an NDArray with shape, e.g., `(x, y)`, then output will have shape
`(x, y, m, n)`, where `m*n` samples are drawn for each entry in `scale`.
dtype : {'float16', 'float32', 'float64'}, optional
Data type of output samples. Default is 'float32'
ctx : Context, optional
Device context of output. Default is current context. Overridden by
`scale.context` when `scale` is an NDArray.
out : NDArray, optional
Store output to an existing NDArray.
Returns
-------
NDArray
If input `shape` has shape, e.g., `(m, n)` and `scale` is a scalar, output shape will
be `(m, n)`. If `scale` is an NDArray with shape, e.g., `(x, y)`, then `output`
will have shape `(x, y, m, n)`, where `m*n` samples are drawn for each entry in scale.
Examples
--------
>>> mx.nd.random.exponential(1)
[ 0.79587454]
>>> mx.nd.random.exponential(1, shape=(2,))
[ 0.89856035 1.25593066]
>>> scale = mx.nd.array([1,2,3])
>>> mx.nd.random.exponential(scale, shape=2)
[[ 0.41063145 0.42140478]
[ 2.59407091 10.12439728]
[ 2.42544937 1.14260709]]
"""
return _random_helper(_internal._random_exponential, _internal._sample_exponential,
[1.0/scale], shape, dtype, ctx, out, kwargs)
[docs]def gamma(alpha=1, beta=1, shape=_Null, dtype=_Null, ctx=None, out=None, **kwargs):
"""Draw random samples from a gamma distribution.
Samples are distributed according to a gamma distribution parametrized
by *alpha* (shape) and *beta* (scale).
Parameters
----------
alpha : float or NDArray, optional
The shape of the gamma distribution. Should be greater than zero.
beta : float or NDArray, optional
The scale of the gamma distribution. Should be greater than zero.
Default is equal to 1.
shape : int or tuple of ints, optional
The number of samples to draw. If shape is, e.g., `(m, n)` and `alpha` and
`beta` are scalars, output shape will be `(m, n)`. If `alpha` and `beta`
are NDArrays with shape, e.g., `(x, y)`, then output will have shape
`(x, y, m, n)`, where `m*n` samples are drawn for each `[alpha, beta)` pair.
dtype : {'float16', 'float32', 'float64'}, optional
Data type of output samples. Default is 'float32'
ctx : Context, optional
Device context of output. Default is current context. Overridden by
`alpha.context` when `alpha` is an NDArray.
out : NDArray, optional
Store output to an existing NDArray.
Returns
-------
NDArray
If input `shape` has shape, e.g., `(m, n)` and `alpha` and `beta` are scalars, output
shape will be `(m, n)`. If `alpha` and `beta` are NDArrays with shape, e.g.,
`(x, y)`, then output will have shape `(x, y, m, n)`, where `m*n` samples are
drawn for each `[alpha, beta)` pair.
Examples
--------
>>> mx.nd.random.gamma(1, 1)
[ 1.93308783]
>>> mx.nd.random.gamma(1, 1, shape=(2,))
[ 0.48216391 2.09890771]
>>> alpha = mx.nd.array([1,2,3])
>>> beta = mx.nd.array([2,3,4])
>>> mx.nd.random.gamma(alpha, beta, shape=2)
[[ 3.24343276 0.94137681]
[ 3.52734375 0.45568955]
[ 14.26264095 14.0170126 ]]
"""
return _random_helper(_internal._random_gamma, _internal._sample_gamma,
[alpha, beta], shape, dtype, ctx, out, kwargs)
[docs]def negative_binomial(k=1, p=1, shape=_Null, dtype=_Null, ctx=None,
out=None, **kwargs):
"""Draw random samples from a negative binomial distribution.
Samples are distributed according to a negative binomial distribution
parametrized by *k* (limit of unsuccessful experiments) and *p* (failure
probability in each experiment). Samples will always be returned as a
floating point data type.
Parameters
----------
k : float or NDArray, optional
Limit of unsuccessful experiments, > 0.
p : float or NDArray, optional
Failure probability in each experiment, >= 0 and <=1.
shape : int or tuple of ints, optional
The number of samples to draw. If shape is, e.g., `(m, n)` and `k` and
`p` are scalars, output shape will be `(m, n)`. If `k` and `p`
are NDArrays with shape, e.g., `(x, y)`, then output will have shape
`(x, y, m, n)`, where `m*n` samples are drawn for each `[k, p)` pair.
dtype : {'float16', 'float32', 'float64'}, optional
Data type of output samples. Default is 'float32'
ctx : Context, optional
Device context of output. Default is current context. Overridden by
`k.context` when `k` is an NDArray.
out : NDArray, optional
Store output to an existing NDArray.
Returns
-------
NDArray
If input `shape` has shape, e.g., `(m, n)` and `k` and `p` are scalars, output shape
will be `(m, n)`. If `k` and `p` are NDArrays with shape, e.g., `(x, y)`, then
output will have shape `(x, y, m, n)`, where `m*n` samples are drawn for each `[k, p)` pair.
Examples
--------
>>> mx.nd.random.negative_binomial(10, 0.5)
[ 4.]
>>> mx.nd.random.negative_binomial(10, 0.5, shape=(2,))
[ 3. 4.]
>>> k = mx.nd.array([1,2,3])
>>> p = mx.nd.array([0.2,0.4,0.6])
>>> mx.nd.random.negative_binomial(k, p, shape=2)
[[ 3. 2.]
[ 4. 4.]
[ 0. 5.]]
"""
return _random_helper(_internal._random_negative_binomial,
_internal._sample_negative_binomial,
[k, p], shape, dtype, ctx, out, kwargs)
[docs]def generalized_negative_binomial(mu=1, alpha=1, shape=_Null, dtype=_Null, ctx=None,
out=None, **kwargs):
"""Draw random samples from a generalized negative binomial distribution.
Samples are distributed according to a generalized negative binomial
distribution parametrized by *mu* (mean) and *alpha* (dispersion).
*alpha* is defined as *1/k* where *k* is the failure limit of the
number of unsuccessful experiments (generalized to real numbers).
Samples will always be returned as a floating point data type.
Parameters
----------
mu : float or NDArray, optional
Mean of the negative binomial distribution.
alpha : float or NDArray, optional
Alpha (dispersion) parameter of the negative binomial distribution.
shape : int or tuple of ints, optional
The number of samples to draw. If shape is, e.g., `(m, n)` and `mu` and
`alpha` are scalars, output shape will be `(m, n)`. If `mu` and `alpha`
are NDArrays with shape, e.g., `(x, y)`, then output will have shape
`(x, y, m, n)`, where `m*n` samples are drawn for each `[mu, alpha)` pair.
dtype : {'float16', 'float32', 'float64'}, optional
Data type of output samples. Default is 'float32'
ctx : Context, optional
Device context of output. Default is current context. Overridden by
`mu.context` when `mu` is an NDArray.
out : NDArray, optional
Store output to an existing NDArray.
Returns
-------
NDArray
If input `shape` has shape, e.g., `(m, n)` and `mu` and `alpha` are scalars, output
shape will be `(m, n)`. If `mu` and `alpha` are NDArrays with shape, e.g., `(x, y)`,
then output will have shape `(x, y, m, n)`, where `m*n` samples are drawn for
each `[mu, alpha)` pair.
Examples
--------
>>> mx.nd.random.generalized_negative_binomial(10, 0.5)
[ 19.]
>>> mx.nd.random.generalized_negative_binomial(10, 0.5, shape=(2,))
[ 30. 21.]
>>> mu = mx.nd.array([1,2,3])
>>> alpha = mx.nd.array([0.2,0.4,0.6])
>>> mx.nd.random.generalized_negative_binomial(mu, alpha, shape=2)
[[ 4. 0.]
[ 3. 2.]
[ 6. 2.]]
"""
return _random_helper(_internal._random_generalized_negative_binomial,
_internal._sample_generalized_negative_binomial,
[mu, alpha], shape, dtype, ctx, out, kwargs)
[docs]def multinomial(data, shape=_Null, get_prob=False, out=None, dtype='int32', **kwargs):
"""Concurrent sampling from multiple multinomial distributions.
.. note:: The input distribution must be normalized, i.e. `data` must sum to
1 along its last dimension.
Parameters
----------
data : NDArray
An *n* dimensional array whose last dimension has length `k`, where
`k` is the number of possible outcomes of each multinomial distribution.
For example, data with shape `(m, n, k)` specifies `m*n` multinomial
distributions each with `k` possible outcomes.
shape : int or tuple of ints, optional
The number of samples to draw from each distribution. If shape is empty
one sample will be drawn from each distribution.
get_prob : bool, optional
If true, a second array containing log likelihood of the drawn
samples will also be returned.
This is usually used for reinforcement learning, where you can provide
reward as head gradient w.r.t. this array to estimate gradient.
out : NDArray, optional
Store output to an existing NDArray.
dtype : str or numpy.dtype, optional
Data type of the sample output array. The default is int32.
Note that the data type of the log likelihood array is the same with that of `data`.
Returns
-------
List, or NDArray
For input `data` with `n` dimensions and shape `(d1, d2, ..., dn-1, k)`, and input
`shape` with shape `(s1, s2, ..., sx)`, returns an NDArray with shape
`(d1, d2, ... dn-1, s1, s2, ..., sx)`. The `s1, s2, ... sx` dimensions of the
returned NDArray consist of 0-indexed values sampled from each respective multinomial
distribution provided in the `k` dimension of `data`.
For the case `n`=1, and `x`=1 (one shape dimension), returned NDArray has shape `(s1,)`.
If `get_prob` is set to True, this function returns a list of format:
`[ndarray_output, log_likelihood_output]`, where `log_likelihood_output` is an NDArray of the
same shape as the sampled outputs.
Examples
--------
>>> probs = mx.nd.array([0, 0.1, 0.2, 0.3, 0.4])
>>> mx.nd.random.multinomial(probs)
[3]
>>> probs = mx.nd.array([[0, 0.1, 0.2, 0.3, 0.4], [0.4, 0.3, 0.2, 0.1, 0]])
>>> mx.nd.random.multinomial(probs)
[3 1]
>>> mx.nd.random.multinomial(probs, shape=2)
[[4 4]
[1 2]]
>>> mx.nd.random.multinomial(probs, get_prob=True)
[3 2]
[-1.20397282 -1.60943794]
"""
return _internal._sample_multinomial(data, shape, get_prob, out=out, dtype=dtype, **kwargs)
[docs]def shuffle(data, **kwargs):
"""Shuffle the elements randomly.
This shuffles the array along the first axis.
The order of the elements in each subarray does not change.
For example, if a 2D array is given, the order of the rows randomly changes,
but the order of the elements in each row does not change.
Parameters
----------
data : NDArray
Input data array.
out : NDArray, optional
Array to store the result.
Returns
-------
NDArray
A new NDArray with the same shape and type as input `data`, but
with items in the first axis of the returned NDArray shuffled randomly.
The original input `data` is not modified.
Examples
--------
>>> data = mx.nd.array([[0, 1, 2], [3, 4, 5], [6, 7, 8]])
>>> mx.nd.random.shuffle(data)
[[ 0. 1. 2.]
[ 6. 7. 8.]
[ 3. 4. 5.]]
>>> mx.nd.random.shuffle(data)
[[ 3. 4. 5.]
[ 0. 1. 2.]
[ 6. 7. 8.]]
"""
return _internal._shuffle(data, **kwargs)
[docs]def randint(low, high, shape=_Null, dtype=_Null, ctx=None, out=None, **kwargs):
"""Draw random samples from a discrete uniform distribution.
Samples are uniformly distributed over the half-open interval *[low, high)*
(includes *low*, but excludes *high*).
Parameters
----------
low : int, required
Lower boundary of the output interval. All values generated will be
greater than or equal to low.
high : int, required
Upper boundary of the output interval. All values generated will be
less than high.
shape : int or tuple of ints, optional
The number of samples to draw. If shape is, e.g., `(m, n)` and `low` and
`high` are scalars, output shape will be `(m, n)`.
dtype : {'int32', 'int64'}, optional
Data type of output samples. Default is 'int32'
ctx : Context, optional
Device context of output. Default is current context. Overridden by
`low.context` when `low` is an NDArray.
out : NDArray, optional
Store output to an existing NDArray.
Returns
-------
NDArray
An NDArray of type `dtype`. If input `shape` has shape, e.g.,
`(m, n)`, the returned NDArray will shape will be `(m, n)`. Contents
of the returned NDArray will be samples from the interval `[low, high)`.
Examples
--------
>>> mx.nd.random.randint(5, 100)
[ 90]
>>> mx.nd.random.randint(-10, 2, ctx=mx.gpu(0))
[ -8]
>>> mx.nd.random.randint(-10, 10, shape=(2,))
[ -5 4]
"""
return _random_helper(_internal._random_randint, None,
[low, high], shape, dtype, ctx, out, kwargs)
