o Me)@sddlZddlZddlZddlmZmZddlmZddl m Z ddl m Z m Z mZmZddlmZmZddlmZmZmZmZmZmZmZmZGdd d ejZdS) N)_C_ops _legacy_C_ops) distribution)core) check_dtype check_typecheck_variable_and_dtype convert_dtype)_non_static_modein_dygraph_mode) control_flowelementwise_addelementwise_divelementwise_mulelementwise_subnnopstensorcsLeZdZdZdfdd ZdddZdd Zd d Zd d ZddZ Z S)NormalaThe Normal distribution with location `loc` and `scale` parameters. Mathematical details The probability density function (pdf) is .. math:: pdf(x; \mu, \sigma) = \frac{1}{Z}e^{\frac {-0.5 (x - \mu)^2} {\sigma^2} } .. math:: Z = (2 \pi \sigma^2)^{0.5} In the above equation: * :math:`loc = \mu`: is the mean. * :math:`scale = \sigma`: is the std. * :math:`Z`: is the normalization constant. Args: loc(int|float|list|tuple|numpy.ndarray|Tensor): The mean of normal distribution.The data type is float32 and float64. scale(int|float|list|tuple|numpy.ndarray|Tensor): The std of normal distribution.The data type is float32 and float64. name(str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Examples: .. code-block:: python import paddle from paddle.distribution import Normal # Define a single scalar Normal distribution. dist = Normal(loc=0., scale=3.) # Define a batch of two scalar valued Normals. # The first has mean 1 and standard deviation 11, the second 2 and 22. dist = Normal(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 Normals. # Both have mean 1, but different standard deviations. dist = Normal(loc=1., scale=[11., 22.]) # Complete example value_tensor = paddle.to_tensor([0.8], dtype="float32") normal_a = Normal([0.], [1.]) normal_b = Normal([0.5], [2.]) sample = normal_a.sample([2]) # a random tensor created by normal distribution with shape: [2, 1] entropy = normal_a.entropy() # [1.4189385] with shape: [1] lp = normal_a.log_prob(value_tensor) # [-1.2389386] with shape: [1] p = normal_a.probs(value_tensor) # [0.28969154] with shape: [1] kl = normal_a.kl_divergence(normal_b) # [0.34939718] with shape: [1] Nc s|ts!t|dtttjtjtt fdt|dtttjtjtt fdd|_ d|_ |dur-|nd|_ d|_ t|trShannon entropy in nats. The entropy is .. math:: entropy(\sigma) = 0.5 \log (2 \pi e \sigma^2) In the above equation: * :math:`scale = \sigma`: is the std. Returns: Tensor, Shannon entropy of normal distribution.The data type is float32. Z_entropyr0?r3) r"rrrr(rr4rr mathlogpir)r)r"r5r6r,r,r-entropys "zNormal.entropyc Csp|jd}||j|}|j|j}t|j}td||j||jd||ttdtj |dS)zLog probability density/mass function. Args: value (Tensor): The input tensor. Returns: Tensor: log probability.The data type is same with value. Z _log_prob@r3) r"_check_values_dtype_in_probsrrrr;rr:sqrtr<)r)valuer"varZ log_scaler,r,r-log_probs   zNormal.log_probcCsf|jd}||j|}|j|j}ttd||j||jd|tdtj |j|dS)zProbability density/mass function. Args: value (Tensor): The input tensor. Returns: Tensor, probability. The data type is same with value. Z_probsr>r?r9r3) r"r@rrrrexpr:rAr<)r)rBr"rCr,r,r-probss  z Normal.probscCspts t|dtd|jd}|j|j}||}|j|j|j}||}td|d|dt||dS)aThe KL-divergence between two normal 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 mean of current Normal distribution. * :math:`scale = \sigma_0`: is the std of current Normal distribution. * :math:`loc = \mu_1`: is the mean of other Normal distribution. * :math:`scale = \sigma_1`: is the std of other Normal distribution. * :math:`ratio`: is the ratio of scales. * :math:`diff`: is the difference between means. Args: other (Normal): instance of Normal. Returns: Tensor, kl-divergence between two normal distributions.The data type is float32. other kl_divergenceZ_kl_divergencer8r1r3) r rrr"rrr rr;)r)rGr"Z var_ratiot1r,r,r-rH s!  zNormal.kl_divergence)N)r) __name__ __module__ __qualname____doc__r'r.r=rDrFrH __classcell__r,r,r*r-r)s< 2*r)r:warningsnumpyrZpaddlerrZpaddle.distributionrZ paddle.fluidrZpaddle.fluid.data_feederrrrr Zpaddle.fluid.frameworkr r Zpaddle.fluid.layersr r rrrrrr Distributionrr,r,r,r-s  (