Αiw%SSKJr SSKJr SSKrSSKJr SSKJr SSK J r \(aSSK J r SSKJ r SSKrSSKJr SS KJr SS KJr SS KJr \ \\4rS \S '\ \R6\R8\R:\R<4rS \S'\ \\ \\\\R@\\4r!S \S'\ \\ \\\\R@\ \R6\R84\4r"S \S'"SS\ 5r#g)) annotations) TYPE_CHECKINGN)Normal) ExpTransform)TransformedDistribution)Sequence)Union) TypeAlias)Tensor)NestedSequencer _LognormalLocBase_LognormalLocNDArray _LognormalLoc_LognormalScalec^\rSrSr%SrS\S'S\S'S U4Sjjr\SSj5r\SSj5r SS jr SS jr SS jr S r U=r$) LogNormal6a The LogNormal distribution with location `loc` and `scale` parameters. .. math:: X \sim Normal(\mu, \sigma) Y = exp(X) \sim LogNormal(\mu, \sigma) Due to LogNormal distribution is based on the transformation of Normal distribution, we call that :math:`Normal(\mu, \sigma)` is the underlying distribution of :math:`LogNormal(\mu, \sigma)` Mathematical details The probability density function (pdf) is .. math:: pdf(x; \mu, \sigma) = \frac{1}{\sigma x \sqrt{2\pi}}e^{(-\frac{(ln(x) - \mu)^2}{2\sigma^2})} In the above equation: * :math:`loc = \mu`: is the means of the underlying Normal distribution. * :math:`scale = \sigma`: is the stddevs of the underlying Normal distribution. Args: loc(int|float|complex|list|tuple|numpy.ndarray|Tensor): The means of the underlying Normal distribution.The data type is float32, float64, complex64 and complex128. scale(int|float|list|tuple|numpy.ndarray|Tensor): The stddevs of the underlying Normal distribution. Examples: .. code-block:: python >>> import paddle >>> from paddle.distribution import LogNormal >>> # Define a single scalar LogNormal distribution. >>> dist = LogNormal(loc=0., scale=3.) >>> # Define a batch of two scalar valued LogNormals. >>> # The underlying Normal of first has mean 1 and standard deviation 11, the underlying Normal of second 2 and 22. >>> dist = LogNormal(loc=[1., 2.], scale=[11., 22.]) >>> # Get 3 samples, returning a 3 x 2 tensor. >>> dist.sample((3, )) >>> # Define a batch of two scalar valued LogNormals. >>> # Their underlying Normal have mean 1, but different standard deviations. >>> dist = LogNormal(loc=1., scale=[11., 22.]) >>> # Complete example >>> value_tensor = paddle.to_tensor([0.8], dtype="float32") >>> lognormal_a = LogNormal([0.], [1.]) >>> lognormal_b = LogNormal([0.5], [2.]) >>> sample = lognormal_a.sample((2, )) >>> # a random tensor created by lognormal distribution with shape: [2, 1] >>> entropy = lognormal_a.entropy() >>> print(entropy) Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True, [1.41893852]) >>> lp = lognormal_a.log_prob(value_tensor) >>> print(lp) Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True, [-0.72069150]) >>> p = lognormal_a.probs(value_tensor) >>> print(p) Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True, [0.48641577]) >>> kl = lognormal_a.kl_divergence(lognormal_b) >>> print(kl) Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True, [0.34939718]) r locscalec>[XS9UlURRUlURRUl[TU]UR[ 5/5 g)N)rr)r_baserrsuper__init__r)selfrr __class__s ]/var/www/html/banglarbhumi/venv/lib/python3.13/site-packages/paddle/distribution/lognormal.pyrLogNormal.__init__sG1 ::>>ZZ%%  ln%56c[R"URRURRS- -5$)zBMean of lognormal distribution. Returns: Tensor: mean value. )paddleexprmeanvariancers rr#LogNormal.means/zz$**//DJJ,?,?!,CCDDrc[R"URR5[R"SURR -URR-5-$)zJVariance of lognormal distribution. Returns: Tensor: variance value. r )r!expm1rr$r"r#r%s rr$LogNormal.variancesN||DJJ//06::   $**"5"5 54   rcdURR5URR-$)a^Shannon entropy in nats. The entropy is .. math:: entropy(\sigma) = 0.5 \log (2 \pi e \sigma^2) + \mu In the above equation: * :math:`loc = \mu`: is the mean of the underlying Normal distribution. * :math:`scale = \sigma`: is the stddevs of the underlying Normal distribution. Returns: Tensor: Shannon entropy of lognormal distribution. )rentropyr#r%s rr+LogNormal.entropys$$zz!!#djjoo55rcL[R"URU55$)zProbability density/mass function. Args: value (Tensor): The input tensor. Returns: Tensor: probability.The data type is same with :attr:`value` . )r!r"log_prob)rvalues rprobsLogNormal.probsszz$--.//rcLURRUR5$)arThe KL-divergence between two lognormal distributions. The probability density function (pdf) is .. math:: KL\_divergence(\mu_0, \sigma_0; \mu_1, \sigma_1) = 0.5 (ratio^2 + (\frac{diff}{\sigma_1})^2 - 1 - 2 \ln {ratio}) .. math:: ratio = \frac{\sigma_0}{\sigma_1} .. math:: diff = \mu_1 - \mu_0 In the above equation: * :math:`loc = \mu_0`: is the means of current underlying Normal distribution. * :math:`scale = \sigma_0`: is the stddevs of current underlying Normal distribution. * :math:`loc = \mu_1`: is the means of other underlying Normal distribution. * :math:`scale = \sigma_1`: is the stddevs of other underlying Normal distribution. * :math:`ratio`: is the ratio of scales. * :math:`diff`: is the difference between means. Args: other (LogNormal): instance of LogNormal. Returns: Tensor: kl-divergence between two lognormal distributions. )r kl_divergence)rothers rr3LogNormal.kl_divergencesBzz'' 44r)rrr)rrrrreturnNone)r6r )r/r r6r )r4rr6r )__name__ __module__ __qualname____firstlineno____doc____annotations__rpropertyr#r$r+r0r3__static_attributes__ __classcell__)rs@rrr6sYDL K M7 EE  6( 0!5!5rr)$ __future__rtypingrr!paddle.distribution.normalrpaddle.distribution.transformr,paddle.distribution.transformed_distributionrcollections.abcrr numpynp numpy.typingnpttyping_extensionsr r paddle._typingr floatcomplexr r=float32float64 complex64 complex128rNDArrayrrrrrrUs # -6P(+-#(#8y8&+ BJJ bmm;') %"#() ()   M9"' u E"**bjj012  "OYe5'e5r