\;jFddlZddlmZddlmZddlmZGddeZy)N)Normal) ExpTransform)TransformedDistributioncTeZdZdZfdZedZedZdZdZ dZ xZ S) LogNormalan 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|list|tuple|numpy.ndarray|Tensor): The means of the underlying Normal distribution. 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]) ct|||_|jj|_|jj|_t||jt gy)N)locscale)r_baser r super__init__r)selfr r __class__s fG:\00. PROJECTS\API\Inventory\templateJSON\kerjaOCR\Lib\site-packages\paddle/distribution/lognormal.pyr zLogNormal.__init__\sI51 ::>>ZZ%%  ln%56ctj|jj|jjdz zS)zYMean of lognormal distribuion. Returns: Tensor: mean value. )paddleexpr meanvariancers rrzLogNormal.meanbs/zz$**//DJJ,?,?!,CCDDrctj|jjtjd|jj z|jjzzS)zbVariance of lognormal distribution. Returns: Tensor: variance value. r)rexpm1r rrrrs rrzLogNormal.varianceksN||DJJ//06::   $**"5"5 54   rcd|jj|jjzS)aShannon 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. )r entropyrrs rrzLogNormal.entropyvs$$zz!!#djjoo55rcJtj|j|S)zProbability density/mass function. Args: value (Tensor): The input tensor. Returns: Tensor: probability.The data type is same with :attr:`value` . )rrlog_prob)rvalues rprobszLogNormal.probsszz$--.//rcL|jj|jS)a The 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 rr"zLogNormal.kl_divergencesBzz'' 44r) __name__ __module__ __qualname____doc__r propertyrrrr r" __classcell__)rs@rrrsHDL7 EE  6( 0!5rr)rpaddle.distribution.normalrpaddle.distribution.transformr,paddle.distribution.transformed_distributionrrrrr.s"-6Pb5'b5r