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"""LogNormal Distribution"""
import numpy as np
from mindspore.ops import operations as P
from mindspore.common import dtype as mstype
import mindspore.nn.probability.bijector as msb
import mindspore.nn.probability.distribution as msd
from ._utils.utils import check_distribution_name
from ._utils.custom_ops import exp_generic, log_generic
[docs]class LogNormal(msd.TransformedDistribution):
r"""
LogNormal distribution.
A log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose
logarithm is normally distributed.
The log-normal distribution has the range :math:`(0, \inf)` with the pdf as
.. math::
f(x, \mu, \sigma) = 1 / x\sigma\sqrt{2\pi} \exp(-(\ln(x) - \mu)^2 / 2\sigma^2).
where :math:`\mu, \sigma` are the mean and
the standard deviation of the underlying normal distribution respectively.
It is constructed as the exponential transformation of a Normal distribution.
Args:
loc (int, float, list, numpy.ndarray, Tensor): The mean of the underlying Normal distribution. Default: None.
scale (int, float, list, numpy.ndarray, Tensor): The standard deviation of the underlying
Normal distribution. Default: None.
seed (int): the seed used in sampling. The global seed is used if it is None. Default: 0.
dtype (mindspore.dtype): type of the distribution. Default: mstype.float32.
name (str): the name of the distribution. Default: 'LogNormal'.
Inputs and Outputs of APIs:
The accessible APIs of the Log-Normal distribution are defined in the base class, including:
- `prob`, `log_prob`, `cdf`, `log_cdf`, `survival_function`, and `log_survival`
- `mean`, `sd`, `mode`, `var`, and `entropy`
- `kl_loss` and `cross_entropy`
- `sample`
For more details of all APIs, including the inputs and outputs of APIs of the Log-Normal distribution,
please refer to :class:`mindspore.nn.probability.distribution.Distribution`, and examples below.
Supported Platforms:
``Ascend`` ``GPU``
Note:
`scale` must be greater than zero.
`dist_spec_args` are `loc` and `scale`.
`dtype` must be a float type because LogNormal distributions are continuous.
Raises:
ValueError: When scale <= 0.
TypeError: When the input `dtype` is not a subclass of float.
Examples:
>>> import numpy as np
>>> import mindspore
>>> import mindspore.nn as nn
>>> import mindspore.nn.probability.distribution as msd
>>> from mindspore import Tensor
>>> class Prob(nn.Cell):
... def __init__(self):
... super(Prob, self).__init__()
... self.ln = msd.LogNormal(np.array([0.3]), np.array([[0.2], [0.4]]), dtype=mindspore.float32)
... def construct(self, x_):
... return self.ln.prob(x_)
>>> pdf = Prob()
>>> output = pdf(Tensor([1.0, 2.0], dtype=mindspore.float32))
>>> print(output.shape)
(2, 2)
"""
def __init__(self,
loc=None,
scale=None,
seed=0,
dtype=mstype.float32,
name="LogNormal"):
"""
Constructor of LogNormal distribution.
"""
super(LogNormal, self).__init__(distribution=msd.Normal(loc, scale, dtype=dtype),
bijector=msb.Exp(),
seed=seed, name=name)
# overwrite default_parameters and parameter_names
self._reset_parameters()
self._loc = self._add_parameter(loc, 'loc')
self._scale = self._add_parameter(scale, 'scale')
self.log_2pi = np.log(2 * np.pi)
# ops needed for the class
self.dtypeop = P.DType()
self.exp = exp_generic
self.expm1 = P.Expm1()
self.log = log_generic
self.const = P.ScalarToArray()
self.erf = P.Erf()
self.fill = P.Fill()
self.greater = P.Greater()
self.select = P.Select()
self.shape = P.Shape()
self.sq = P.Square()
self.sqrt = P.Sqrt()
self.cast = P.Cast()
self.squeeze = P.Squeeze(0)
@property
def loc(self):
"""
Distribution parameter for the pre-transformed mean
after casting to dtype.
Output:
Tensor, the loc parameter of the distribution.
"""
return self._loc
@property
def scale(self):
"""
Distribution parameter for the pre-transformed standard deviation
after casting to dtype.
Output:
Tensor, the scale parameter of the distribution.
"""
return self._scale
def _get_dist_type(self):
return "LogNormal"
def _get_dist_args(self, loc=None, scale=None):
if loc is not None:
self.checktensor(loc, 'loc')
else:
loc = self.loc
if scale is not None:
self.checktensor(scale, 'scale')
else:
scale = self.scale
return loc, scale
[docs] def extend_repr(self):
"""Display instance object as string."""
if self.is_scalar_batch:
s = 'loc = {}, scale = {}'.format(self.loc, self.scale)
else:
s = 'batch_shape = {}'.format(self.broadcast_shape)
return s
def _mean(self, loc=None, scale=None):
"""
The mean of the distribution.
"""
mean, sd = self._check_param_type(loc, scale)
var = self.distribution("var", mean=mean, sd=sd)
return self.exp(mean + 0.5 * var)
def _mode(self, loc=None, scale=None):
"""
The mode of the distribution.
"""
mean, sd = self._check_param_type(loc, scale)
var = self.distribution("var", mean=mean, sd=sd)
return self.exp(mean - var)
def _var(self, loc=None, scale=None):
"""
The variance of the distribution.
"""
mean, sd = self._check_param_type(loc, scale)
var = self.distribution("var", mean=mean, sd=sd)
return self.expm1(var) * self.exp(2. * mean + var)
def _entropy(self, loc=None, scale=None):
r"""
Evaluate entropy.
.. math::
H(X) = μ + 0.5 + \log(σ) + 0.5 * \log(2pi)
"""
mean, sd = self._check_param_type(loc, scale)
return mean + 0.5 + self.log(sd) + 0.5 * self.log_2pi
def _cdf(self, value, loc=None, scale=None):
r"""
Compute the cdf via the below formula,
where g is the exp bijector,
and P is the cdf of the underlying normal dist
.. math::
Y = g(X)
P(Y <= a) = P(X <= g^{-1}(a))
"""
mean, sd = self._check_param_type(loc, scale)
inverse_value = self.bijector("inverse", value)
cdf = self.distribution("cdf", inverse_value, mean, sd)
# to increase numerical stability, set cdf = 0 when value <= 0
zeros = self.fill(self.dtypeop(cdf), self.shape(cdf), 0.0)
return self.select(self.greater(value, 0.), cdf, zeros)
def _log_prob(self, value, loc=None, scale=None):
r"""
Compute the log prob via the below formula,
where g is the exp bijector,
and P is the pdf of the underlying normal dist
.. math::
Y = g(X)
Py(a) = Px(g^{-1}(a)) * (g^{-1})'(a)
\log(Py(a)) = \log(Px(g^{-1}(a))) + \log((g^{-1})'(a))
"""
mean, sd = self._check_param_type(loc, scale)
inverse_value = self.bijector("inverse", value)
unadjust_prob = self.distribution("log_prob", inverse_value, mean, sd)
log_jacobian = self.bijector("inverse_log_jacobian", value)
return unadjust_prob + log_jacobian
def _cross_entropy(self, dist, loc_b, scale_b, loc_a=None, scale_a=None):
r"""
Evaluate cross entropy between lognormal distributions.
Args:
dist (str): The type of the distributions. Should be "LogNormal" in this case.
loc_b (Tensor): The loc of distribution b.
scale_b (Tensor): The scale of distribution b.
loc_a (Tensor): The loc of distribution a. Default: None.
scale_a (Tensor): The scale of distribution a. Default: None.
"""
check_distribution_name(dist, 'LogNormal')
return self._entropy(loc_a, scale_a) + self._kl_loss(dist, loc_b, scale_b, loc_a, scale_a)
def _kl_loss(self, dist, loc_b, scale_b, loc_a=None, scale_a=None):
r"""
Evaluate LogNormal-LogNormal kl divergence, i.e. KL(a||b).
Args:
dist (str): The type of the distributions. Should be "LogNormal" in this case.
loc_b (Tensor): The loc of distribution b.
scale_b (Tensor): The scale of distribution b.
loc_a (Tensor): The loc of distribution a. Default: None.
scale_a (Tensor): The scale of distribution a. Default: None.
.. math::
KL(a||b) = 0.5 * (\fract{MEAN(a)}{STD(b)} - \fract{MEAN(b)}{STD(b)}) ^ 2 +
0.5 * EXPM1(2 * (\log(STD(a)) - \log(STD(b))) - (\log(STD(a)) - \log(STD(b)))
"""
check_distribution_name(dist, 'LogNormal')
return self.distribution("kl_loss", 'Normal', loc_b, scale_b, loc_a, scale_a)
def _sample(self, shape=(), loc=None, scale=None):
r"""
Generate samples via mapping the samples from the underlying normal dist.
"""
shape = self.checktuple(shape, 'shape')
mean, sd = self._check_param_type(loc, scale)
if shape == ():
sample_shape = (1,)
else:
sample_shape = shape
org_sample = self.distribution("sample", sample_shape, mean, sd)
org_sample = self.cast(org_sample, self.dtype)
value = self.bijector("forward", org_sample)
if shape == ():
value = self.squeeze(value)
return value