def logistic(loc=0.0, scale=1.0, size=None, dtype=float):
"""Logistic distribution.
Returns an array of samples drawn from the logistic distribution. Its
probability density function is defined as
.. math::
f(x) = \\frac{e^{-(x-\\mu)/s}}{s(1+e^{-(x-\\mu)/s})^2}.
Args:
loc (float): The location of the mode :math:`\\mu`.
scale (float): The scale parameter :math:`s`.
size (int or tuple of ints): The shape of the array. If ``None``, a
zero-dimensional array is generated.
dtype: Data type specifier. Only :class:`numpy.float32` and
:class:`numpy.float64` types are allowed.
Returns:
cupy.ndarray: Samples drawn from the logistic distribution.
.. seealso::
:func:`numpy.random.logistic`
"""
rs = _generator.get_random_state()
return rs.logistic(loc, scale, size, dtype)
def pareto(a, size=None, dtype=float):
"""Pareto II or Lomax distribution.
Returns an array of samples drawn from the Pareto II distribution. Its
probability density function is defined as
.. math::
f(x) = \\alpha(1+x)^{-(\\alpha+1)}.
Args:
a (float or array_like of floats): Parameter of the Pareto II
distribution :math:`\\alpha`.
size (int or tuple of ints): The shape of the array. If ``None``, this
function generate an array whose shape is `a.shape`.
dtype: Data type specifier. Only :class:`numpy.float32` and
:class:`numpy.float64` types are allowed.
Returns:
cupy.ndarray: Samples drawn from the Pareto II distribution.
.. seealso:: :meth:`numpy.random.pareto
<numpy.random.mtrand.RandomState.pareto>`
"""
rs = _generator.get_random_state()
x = rs.pareto(a, size, dtype)
return x
def zipf(a, size=None, dtype=int):
"""Zipf distribution.
Returns an array of samples drawn from the Zipf distribution. Its
probability mass function is defined as
.. math::
f(x) = \\frac{x^{-a}}{ \\zeta (a)},
where :math:`\\zeta` is the Riemann Zeta function.
Args:
a (float): Parameter of the beta distribution :math:`a`.
size (int or tuple of ints): The shape of the array. If ``None``, a
zero-dimensional array is generated.
dtype: Data type specifier. Only :class:`numpy.int32` and
:class:`numpy.int64` types are allowed.
Returns:
cupy.ndarray: Samples drawn from the Zipf distribution.
.. seealso::
:meth:`numpy.random.zipf
<numpy.random.mtrand.RandomState.zipf>`
"""
rs = _generator.get_random_state()
return rs.zipf(a, size=size, dtype=dtype)
def normal(loc=0.0, scale=1.0, size=None, dtype=float):
"""Returns an array of normally distributed samples.
Args:
loc (float or array_like of floats): Mean of the normal distribution.
scale (float or array_like of floats):
Standard deviation of the normal distribution.
size (int or tuple of ints): The shape of the array. If ``None``, a
zero-dimensional array is generated.
dtype: Data type specifier. Only :class:`numpy.float32` and
:class:`numpy.float64` types are allowed.
Returns:
cupy.ndarray: Normally distributed samples.
.. seealso:: :func:`numpy.random.normal`
"""
rs = _generator.get_random_state()
if size is None and any(isinstance(arg, cupy.ndarray)
for arg in [scale, loc]):
size = cupy.broadcast_arrays(loc, scale)[0].shape
x = rs.normal(0, 1, size, dtype)
cupy.multiply(x, scale, out=x)
cupy.add(x, loc, out=x)
return x
def noncentral_f(dfnum, dfden, nonc, size=None, dtype=float):
"""Noncentral F distribution.
Returns an array of samples drawn from the noncentral F
distribution.
Reference: https://en.wikipedia.org/wiki/Noncentral_F-distribution
Args:
dfnum (float): Parameter of the noncentral F distribution.
dfden (float): Parameter of the noncentral F distribution.
nonc (float): Parameter of the noncentral F distribution.
size (int or tuple of ints): The shape of the array. If ``None``, a
zero-dimensional array is generated.
dtype: Data type specifier. Only :class:`numpy.float32` and
:class:`numpy.float64` types are allowed.
Returns:
cupy.ndarray: Samples drawn from the noncentral F distribution.
.. seealso::
:meth:`numpy.random.noncentral_f
<numpy.random.mtrand.RandomState.noncentral_f>`
"""
rs = _generator.get_random_state()
return rs.noncentral_f(dfnum, dfden, nonc, size=size, dtype=dtype)
def dirichlet(alpha, size=None, dtype=float):
"""Dirichlet distribution.
Returns an array of samples drawn from the dirichlet distribution. Its
probability density function is defined as
.. math::
f(x) = \\frac{\\Gamma(\\sum_{i=1}^K\\alpha_i)} \
{\\prod_{i=1}^{K}\\Gamma(\\alpha_i)} \
\\prod_{i=1}^Kx_i^{\\alpha_i-1}.
Args:
alpha (array): Parameters of the dirichlet distribution
:math:`\\alpha`.
size (int or tuple of ints): The shape of the array. If ``None``, a
zero-dimensional array is generated.
dtype: Data type specifier. Only :class:`numpy.float32` and
:class:`numpy.float64` types are allowed.
Returns:
cupy.ndarray: Samples drawn from the dirichlet distribution.
.. seealso::
:meth:`numpy.random.dirichlet
<numpy.random.mtrand.RandomState.dirichlet>`
"""
rs = _generator.get_random_state()
return rs.dirichlet(alpha, size, dtype)
def weibull(a, size=None, dtype=float):
"""weibull distribution.
Returns an array of samples drawn from the weibull distribution. Its
probability density function is defined as
.. math::
f(x) = ax^{(a-1)}e^{-x^a}.
Args:
a (float): Parameter of the weibull distribution :math:`a`.
size (int or tuple of ints): The shape of the array. If ``None``, a
zero-dimensional array is generated.
dtype: Data type specifier. Only :class:`numpy.float32` and
:class:`numpy.float64` types are allowed.
Returns:
cupy.ndarray: Samples drawn from the weibull distribution.
.. seealso::
:meth:`numpy.random.weibull
<numpy.random.mtrand.RandomState.weibull>`
"""
rs = _generator.get_random_state()
return rs.weibull(a, size=size, dtype=dtype)
def standard_gamma(shape, size=None, dtype=float):
"""Standard gamma distribution.
Returns an array of samples drawn from the standard gamma distribution. Its
probability density function is defined as
.. math::
f(x) = \\frac{1}{\\Gamma(k)}x^{k-1}e^{-x}.
Args:
shape (array): Parameter of the gamma distribution :math:`k`.
size (int or tuple of ints): The shape of the array. If ``None``, a
zero-dimensional array is generated.
dtype: Data type specifier. Only :class:`numpy.float32` and
:class:`numpy.float64` types are allowed.
Returns:
cupy.ndarray: Samples drawn from the standard gamma distribution.
.. seealso::
:meth:`numpy.random.standard_gamma
<numpy.random.mtrand.RandomState.standard_gamma>`
"""
rs = _generator.get_random_state()
return rs.standard_gamma(shape, size, dtype)
def triangular(left, mode, right, size=None, dtype=float):
"""Triangular distribution.
Returns an array of samples drawn from the triangular distribution. Its
probability density function is defined as
.. math::
f(x) = \\begin{cases}
\\frac{2(x-l)}{(r-l)(m-l)} & \\text{for } l \\leq x \\leq m, \\\\
\\frac{2(r-x)}{(r-l)(r-m)} & \\text{for } m \\leq x \\leq r, \\\\
0 & \\text{otherwise}.
\\end{cases}
Args:
left (float): Lower limit :math:`l`.
mode (float): The value where the peak of the distribution occurs.
:math:`m`.
right (float): Higher Limit :math:`r`.
size (int or tuple of ints): The shape of the array. If ``None``, a
zero-dimensional array is generated.
dtype: Data type specifier. Only :class:`numpy.float32` and
:class:`numpy.float64` types are allowed.
Returns:
cupy.ndarray: Samples drawn from the triangular distribution.
.. seealso::
:func:`cupy.random.RandomState.triangular`
:meth:`numpy.random.triangular
<numpy.random.mtrand.RandomState.triangular>`
"""
rs = _generator.get_random_state()
return rs.triangular(left, mode, right, size, dtype)
def hypergeometric(ngood, nbad, nsample, size=None, dtype=int):
"""hypergeometric distribution.
Returns an array of samples drawn from the hypergeometric distribution. Its
probability mass function is defined as
.. math::
f(x) = \\frac{\\binom{m}{n}\\binom{N-m}{n-x}}{\\binom{N}{n}}.
Args:
ngood (int or array_like of ints): Parameter of the hypergeometric
distribution :math:`n`.
nbad (int or array_like of ints): Parameter of the hypergeometric
distribution :math:`m`.
nsample (int or array_like of ints): Parameter of the hypergeometric
distribution :math:`N`.
size (int or tuple of ints): The shape of the array. If ``None``, a
zero-dimensional array is generated.
dtype: Data type specifier. Only :class:`numpy.int32` and
:class:`numpy.int64` types are allowed.
Returns:
cupy.ndarray: Samples drawn from the hypergeometric distribution.
.. seealso::
:meth:`numpy.random.hypergeometric
<numpy.random.mtrand.RandomState.hypergeometric>`
"""
rs = _generator.get_random_state()
return rs.hypergeometric(ngood, nbad, nsample, size, dtype)
def rayleigh(scale=1.0, size=None, dtype=float):
"""Rayleigh distribution.
Returns an array of samples drawn from the rayleigh distribution.
Its probability density function is defined as
.. math::
f(x) = \\frac{x}{\\sigma^2}e^{\\frac{-x^2}{2-\\sigma^2}}, x \\ge 0.
Args:
scale (array): Parameter of the rayleigh distribution :math:`\\sigma`.
size (int or tuple of ints): The shape of the array. If ``None``, a
zero-dimensional array is generated.
dtype: Data type specifier. Only :class:`numpy.float32` and
:class:`numpy.float64` types are allowed.
Returns:
cupy.ndarray: Samples drawn from the rayleigh distribution.
.. seealso:: :meth:`numpy.random.rayleigh
<numpy.random.mtrand.RandomState.rayleigh>`
"""
rs = _generator.get_random_state()
x = rs.rayleigh(scale, size, dtype)
return x
def geometric(p, size=None, dtype=int):
"""Geometric distribution.
Returns an array of samples drawn from the geometric distribution. Its
probability mass function is defined as
.. math::
f(x) = p(1-p)^{k-1}.
Args:
p (float): Success probability of the geometric distribution.
size (int or tuple of ints): The shape of the array. If ``None``, a
zero-dimensional array is generated.
dtype: Data type specifier. Only :class:`numpy.int32` and
:class:`numpy.int64` types are allowed.
Returns:
cupy.ndarray: Samples drawn from the geometric distribution.
.. seealso::
:func:`cupy.random.RandomState.geometric`
:meth:`numpy.random.geometric
<numpy.random.mtrand.RandomState.geometric>`
"""
rs = _generator.get_random_state()
return rs.geometric(p, size, dtype)
def gumbel(loc=0.0, scale=1.0, size=None, dtype=float):
"""Returns an array of samples drawn from a Gumbel distribution.
The samples are drawn from a Gumbel distribution with location ``loc``
and scale ``scale``.
Its probability density function is defined as
.. math::
f(x) = \\frac{1}{\\eta} \
\\exp\\left\\{ - \\frac{x - \\mu}{\\eta} \\right\\} \
\\exp\\left[-\\exp\\left\\{-\\frac{x - \\mu}{\\eta} \
\\right\\}\\right],
where :math:`\\mu` is ``loc`` and :math:`\\eta` is ``scale``.
Args:
loc (float): The location of the mode :math:`\\mu`.
scale (float): The scale parameter :math:`\\eta`.
size (int or tuple of ints): The shape of the array. If ``None``, a
zero-dimensional array is generated.
dtype: Data type specifier. Only :class:`numpy.float32` and
:class:`numpy.float64` types are allowed.
Returns:
cupy.ndarray: Samples drawn from the Gumbel distribution.
.. seealso::
:meth:`numpy.random.gumbel
<numpy.random.mtrand.RandomState.gumbel>`
"""
rs = _generator.get_random_state()
return rs.gumbel(loc, scale, size, dtype)
def f(dfnum, dfden, size=None, dtype=float):
"""F distribution.
Returns an array of samples drawn from the f distribution. Its probability
density function is defined as
.. math::
f(x) = \\frac{1}{B(\\frac{d_1}{2},\\frac{d_2}{2})} \
\\left(\\frac{d_1}{d_2}\\right)^{\\frac{d_1}{2}} \
x^{\\frac{d_1}{2}-1} \
\\left(1+\\frac{d_1}{d_2}x\\right) \
^{-\\frac{d_1+d_2}{2}}.
Args:
dfnum (float or array_like of floats): Parameter of the f distribution
:math:`d_1`.
dfden (float or array_like of floats): Parameter of the f distribution
:math:`d_2`.
size (int or tuple of ints): The shape of the array. If ``None``, a
zero-dimensional array is generated.
dtype: Data type specifier. Only :class:`numpy.float32` and
:class:`numpy.float64` types are allowed.
Returns:
cupy.ndarray: Samples drawn from the f distribution.
.. seealso::
:meth:`numpy.random.f
<numpy.random.mtrand.RandomState.f>`
"""
rs = _generator.get_random_state()
return rs.f(dfnum, dfden, size, dtype)
def exponential(scale, size=None, dtype=float):
"""Exponential distribution.
Returns an array of samples drawn from the exponential distribution. Its
probability density function is defined as
.. math::
f(x) = \\frac{1}{\\beta}\\exp (-\\frac{x}{\\beta}).
Args:
scale (float or array_like of floats): The scale parameter
:math:`\\beta`.
size (int or tuple of ints): The shape of the array. If ``None``, a
zero-dimensional array is generated.
dtype: Data type specifier. Only :class:`numpy.float32` and
:class:`numpy.float64` types are allowed.
Returns:
cupy.ndarray: Samples drawn from the exponential distribution.
.. seealso::
:meth:`numpy.random.exponential
<numpy.random.mtrand.RandomState.exponential>`
"""
rs = _generator.get_random_state()
return rs.exponential(scale, size, dtype)
def choice(a, size=None, replace=True, p=None):
"""Returns an array of random values from a given 1-D array.
Each element of the returned array is independently sampled
from ``a`` according to ``p`` or uniformly.
.. note::
Currently ``p`` is not supported when ``replace=False``.
Args:
a (1-D array-like or int):
If an array-like,
a random sample is generated from its elements.
If an int, the random sample is generated as if ``a`` was
``cupy.arange(n)``
size (int or tuple of ints): The shape of the array.
replace (boolean): Whether the sample is with or without replacement.
p (1-D array-like):
The probabilities associated with each entry in ``a``.
If not given the sample assumes a uniform distribution over all
entries in ``a``.
Returns:
cupy.ndarray: An array of ``a`` values distributed according to
``p`` or uniformly.
.. seealso:: :meth:`numpy.random.choice
<numpy.random.mtrand.RandomState.choice>`
"""
rs = _generator.get_random_state()
return rs.choice(a, size, replace, p)
def poisson(lam=1.0, size=None, dtype=int):
"""Poisson distribution.
Returns an array of samples drawn from the poisson distribution. Its
probability mass function is defined as
.. math::
f(x) = \\frac{\\lambda^xe^{-\\lambda}}{k!}.
Args:
lam (array_like of floats): Parameter of the poisson distribution
:math:`\\lambda`.
size (int or tuple of ints): The shape of the array. If ``None``, this
function generate an array whose shape is `lam.shape`.
dtype: Data type specifier. Only :class:`numpy.int32` and
:class:`numpy.int64` types are allowed.
Returns:
cupy.ndarray: Samples drawn from the poisson distribution.
.. seealso:: :meth:`numpy.random.poisson
<numpy.random.mtrand.RandomState.poisson>`
"""
rs = _generator.get_random_state()
x = rs.poisson(lam, size, dtype)
return x
def laplace(loc=0.0, scale=1.0, size=None, dtype=float):
"""Laplace distribution.
Returns an array of samples drawn from the laplace distribution. Its
probability density function is defined as
.. math::
f(x) = \\frac{1}{2b}\\exp\\left(-\\frac{|x-\\mu|}{b}\\right).
Args:
loc (float): The location of the mode :math:`\\mu`.
scale (float): The scale parameter :math:`b`.
size (int or tuple of ints): The shape of the array. If ``None``, a
zero-dimensional array is generated.
dtype: Data type specifier. Only :class:`numpy.float32` and
:class:`numpy.float64` types are allowed.
Returns:
cupy.ndarray: Samples drawn from the laplace distribution.
.. seealso::
:meth:`numpy.random.laplace
<numpy.random.mtrand.RandomState.laplace>`
"""
rs = _generator.get_random_state()
return rs.laplace(loc, scale, size, dtype)
def chisquare(df, size=None, dtype=float):
"""Chi-square distribution.
Returns an array of samples drawn from the chi-square distribution. Its
probability density function is defined as
.. math::
f(x) = \\frac{(1/2)^{k/2}}{\\Gamma(k/2)}x^{k/2-1}e^{-x/2}.
Args:
df (int or array_like of ints): Degree of freedom :math:`k`.
size (int or tuple of ints): The shape of the array. If ``None``, a
zero-dimensional array is generated.
dtype: Data type specifier. Only :class:`numpy.float32` and
:class:`numpy.float64` types are allowed.
Returns:
cupy.ndarray: Samples drawn from the chi-square distribution.
.. seealso::
:meth:`numpy.random.chisquare
<numpy.random.mtrand.RandomState.chisquare>`
"""
rs = _generator.get_random_state()
return rs.chisquare(df, size, dtype)
def binomial(n, p, size=None, dtype=int):
"""Binomial distribution.
Returns an array of samples drawn from the binomial distribution. Its
probability mass function is defined as
.. math::
f(x) = \\binom{n}{x}p^x(1-p)^{n-x}.
Args:
n (int): Trial number of the binomial distribution.
p (float): Success probability of the binomial distribution.
size (int or tuple of ints): The shape of the array. If ``None``, a
zero-dimensional array is generated.
dtype: Data type specifier. Only :class:`numpy.int32` and
:class:`numpy.int64` types are allowed.
Returns:
cupy.ndarray: Samples drawn from the binomial distribution.
.. seealso::
:meth:`numpy.random.binomial
<numpy.random.mtrand.RandomState.binomial>`
"""
rs = _generator.get_random_state()
return rs.binomial(n, p, size, dtype)
def beta(a, b, size=None, dtype=float):
"""Beta distribution.
Returns an array of samples drawn from the beta distribution. Its
probability density function is defined as
.. math::
f(x) = \\frac{x^{\\alpha-1}(1-x)^{\\beta-1}}{B(\\alpha,\\beta)}.
Args:
a (float): Parameter of the beta distribution :math:`\\alpha`.
b (float): Parameter of the beta distribution :math:`\\beta`.
size (int or tuple of ints): The shape of the array. If ``None``, a
zero-dimensional array is generated.
dtype: Data type specifier. Only :class:`numpy.float32` and
:class:`numpy.float64` types are allowed.
Returns:
cupy.ndarray: Samples drawn from the beta distribution.
.. seealso::
:meth:`numpy.random.beta
<numpy.random.mtrand.RandomState.beta>`
"""
rs = _generator.get_random_state()
return rs.beta(a, b, size, dtype)
def logseries(p, size=None, dtype=int):
"""Log series distribution.
Returns an array of samples drawn from the log series distribution. Its
probability mass function is defined as
.. math::
f(x) = \\frac{-p^x}{x\\ln(1-p)}.
Args:
p (float): Parameter of the log series distribution :math:`p`.
size (int or tuple of ints): The shape of the array. If ``None``, a
zero-dimensional array is generated.
dtype: Data type specifier. Only :class:`numpy.int32` and
:class:`numpy.int64` types are allowed.
Returns:
cupy.ndarray: Samples drawn from the log series distribution.
.. seealso:: :meth:`numpy.random.logseries
<numpy.random.mtrand.RandomState.logseries>`
"""
rs = _generator.get_random_state()
return rs.logseries(p, size=size, dtype=dtype)
def standard_t(df, size=None, dtype=float):
"""Standard Student's t distribution.
Returns an array of samples drawn from the standard Student's t
distribution. Its probability density function is defined as
.. math::
f(x) = \\frac{\\Gamma(\\frac{\\nu+1}{2})} \
{\\sqrt{\\nu\\pi}\\Gamma(\\frac{\\nu}{2})} \
\\left(1 + \\frac{x^2}{\\nu} \\right)^{-(\\frac{\\nu+1}{2})}.
Args:
df (float or array_like of floats): Degree of freedom :math:`\\nu`.
size (int or tuple of ints): The shape of the array. If ``None``, a
zero-dimensional array is generated.
dtype: Data type specifier. Only :class:`numpy.float32` and
:class:`numpy.float64` types are allowed.
Returns:
cupy.ndarray: Samples drawn from the standard Student's t distribution.
.. seealso::
:meth:`numpy.random.standard_t
<numpy.random.mtrand.RandomState.standard_t>`
"""
rs = _generator.get_random_state()
return rs.standard_t(df, size, dtype)
def negative_binomial(n, p, size=None, dtype=int):
"""Negative binomial distribution.
Returns an array of samples drawn from the negative binomial distribution.
Its probability mass function is defined as
.. math::
f(x) = \\binom{x + n - 1}{n - 1}p^n(1-p)^{x}.
Args:
n (int): Parameter of the negative binomial distribution :math:`n`.
p (float): Parameter of the negative binomial distribution :math:`p`.
size (int or tuple of ints): The shape of the array. If ``None``, a
zero-dimensional array is generated.
dtype: Data type specifier. Only :class:`numpy.int32` and
:class:`numpy.int64` types are allowed.
Returns:
cupy.ndarray: Samples drawn from the negative binomial distribution.
.. seealso::
:meth:`numpy.random.negative_binomial
<numpy.random.mtrand.RandomState.negative_binomial>`
"""
rs = _generator.get_random_state()
return rs.negative_binomial(n, p, size=size, dtype=dtype)
def vonmises(mu, kappa, size=None, dtype=float):
"""von Mises distribution.
Returns an array of samples drawn from the von Mises distribution. Its
probability density function is defined as
.. math::
f(x) = \\frac{e^{\\kappa \\cos(x-\\mu)}}{2\\pi I_0(\\kappa)}.
Args:
mu (float): Parameter of the von Mises distribution :math:`\\mu`.
kappa (float): Parameter of the von Mises distribution :math:`\\kappa`.
size (int or tuple of ints): The shape of the array. If ``None``, a
zero-dimensional array is generated.
dtype: Data type specifier. Only :class:`numpy.float32` and
:class:`numpy.float64` types are allowed.
Returns:
cupy.ndarray: Samples drawn from the von Mises distribution.
.. seealso::
:meth:`numpy.random.vonmises
<numpy.random.mtrand.RandomState.vonmises>`
"""
rs = _generator.get_random_state()
return rs.vonmises(mu, kappa, size=size, dtype=dtype)
def test_get_random_state_memoized(self):
_generator._random_states = {self.device_id: 'expected',
self.device_id + 1: 'dummy'}
rs = _generator.get_random_state()
assert 'expected' == _generator._random_states[self.device_id]
assert 'dummy' == _generator._random_states[self.device_id + 1]
assert 'expected' == rs
def wald(mean, scale, size=None, dtype=float):
"""Wald distribution.
Returns an array of samples drawn from the Wald distribution. Its
probability density function is defined as
.. math::
f(x) = \\sqrt{\\frac{\\lambda}{2\\pi x^3}}\\
e^{\\frac{-\\lambda(x-\\mu)^2}{2\\mu^2x}}.
Args:
mean (float): Parameter of the wald distribution :math:`\\mu`.
scale (float): Parameter of the wald distribution :math:`\\lambda`.
size (int or tuple of ints): The shape of the array. If ``None``, a
zero-dimensional array is generated.
dtype: Data type specifier. Only :class:`numpy.float32` and
:class:`numpy.float64` types are allowed.
Returns:
cupy.ndarray: Samples drawn from the wald distribution.
.. seealso::
:func:`cupy.random.RandomState.wald`
:meth:`numpy.random.wald
<numpy.random.mtrand.RandomState.wald>`
"""
rs = _generator.get_random_state()
return rs.wald(mean, scale, size, dtype)
def noncentral_chisquare(df, nonc, size=None, dtype=float):
"""Noncentral chisquare distribution.
Returns an array of samples drawn from the noncentral chisquare
distribution. Its probability density function is defined as
.. math::
f(x) = \\frac{1}{2}e^{-(x+\\lambda)/2} \\
\\left(\\frac{x}{\\lambda}\\right)^{k/4 - 1/2} \\
I_{k/2 - 1}(\\sqrt{\\lambda x}),
where :math:`I` is the modified Bessel function of the first kind.
Args:
df (float): Parameter of the noncentral chisquare distribution
:math:`k`.
nonc (float): Parameter of the noncentral chisquare distribution
:math:`\\lambda`.
size (int or tuple of ints): The shape of the array. If ``None``, a
zero-dimensional array is generated.
dtype: Data type specifier. Only :class:`numpy.float32` and
:class:`numpy.float64` types are allowed.
Returns:
cupy.ndarray: Samples drawn from the noncentral chisquare distribution.
.. seealso::
:meth:`numpy.random.noncentral_chisquare
<numpy.random.mtrand.RandomState.noncentral_chisquare>`
"""
rs = _generator.get_random_state()
return rs.noncentral_chisquare(df, nonc, size=size, dtype=dtype)
def test_get_random_state_memoized(self):
_generator._random_states = {self.device_id: 'expected',
self.device_id + 1: 'dummy'}
rs = _generator.get_random_state()
self.assertEqual('expected', _generator._random_states[self.device_id])
self.assertEqual(
'dummy', _generator._random_states[self.device_id + 1])
self.assertEqual('expected', rs)
def multivariate_normal(mean, cov, size=None, check_valid='ignore',
tol=1e-08, method='cholesky', dtype=float):
"""Multivariate normal distribution.
Returns an array of samples drawn from the multivariate normal
distribution. Its probability density function is defined as
.. math::
f(x) = \\frac{1}{(2\\pi|\\Sigma|)^(n/2)} \
\\exp\\left(-\\frac{1}{2} \
(x-\\mu)^{\\top}\\Sigma^{-1}(x-\\mu)\\right).
Args:
mean (1-D array_like, of length N): Mean of the multivariate normal
distribution :math:`\\mu`.
cov (2-D array_like, of shape (N, N)): Covariance matrix
:math:`\\Sigma` of the multivariate normal distribution. It must be
symmetric and positive-semidefinite for proper sampling.
size (int or tuple of ints): The shape of the array. If ``None``, a
zero-dimensional array is generated.
check_valid ('warn', 'raise', 'ignore'): Behavior when the covariance
matrix is not positive semidefinite.
tol (float): Tolerance when checking the singular values in
covariance matrix.
method : { 'cholesky', 'eigh', 'svd'}, optional
The cov input is used to compute a factor matrix A such that
``A @ A.T = cov``. This argument is used to select the method
used to compute the factor matrix A. The default method 'cholesky'
is the fastest, while 'svd' is the slowest but more robust than
the fastest method. The method `eigh` uses eigen decomposition to
compute A and is faster than svd but slower than cholesky.
dtype: Data type specifier. Only :class:`numpy.float32` and
:class:`numpy.float64` types are allowed.
Returns:
cupy.ndarray: Samples drawn from the multivariate normal distribution.
.. note:: Default `method` is set to fastest, 'cholesky', unlike numpy
which defaults to 'svd'. Cholesky decomposition in CuPy will fail
silently if the input covariance matrix is not positive definite and
give invalid results, unlike in numpy, where an invalid covariance
matrix will raise an exception. Setting `check_valid` to 'raise' will
replicate numpy behavior by checking the input, but will also force
device synchronization. If validity of input is unknown, setting
`method` to 'einh' or 'svd' and `check_valid` to 'warn' will use
cholesky decomposition for positive definite matrices, and fallback to
the specified `method` for other matrices (i.e., not positive
semi-definite), and will warn if decomposition is suspect.
.. seealso:: :func:`numpy.random.multivariate_normal`
"""
_util.experimental('cupy.random.multivariate_normal')
rs = _generator.get_random_state()
x = rs.multivariate_normal(mean, cov, size, check_valid, tol, method,
dtype)
return x
