Add MultivariateNormal distribution API

python/paddle/distribution/kl.py

@@ -22,6 +22,7 @@
 from paddle.distribution.exponential_family import ExponentialFamily
 from paddle.distribution.laplace import Laplace
 from paddle.distribution.lognormal import LogNormal
+from paddle.distribution.multivariate_normal import MultivariateNormal
 from paddle.distribution.normal import Normal
 from paddle.distribution.uniform import Uniform
 from paddle.fluid.framework import _non_static_mode
@@ -34,53 +35,38 @@
 def kl_divergence(p, q):
     r"""
     Kullback-Leibler divergence between distribution p and q.
-
     .. math::
-
         KL(p||q) = \int p(x)log\frac{p(x)}{q(x)} \mathrm{d}x
-
     Args:
         p (Distribution): ``Distribution`` object. Inherits from the Distribution Base class.
         q (Distribution): ``Distribution`` object. Inherits from the Distribution Base class.
-
     Returns:
         Tensor, Batchwise KL-divergence between distribution p and q.
-
     Examples:
-
         .. code-block:: python
-
             import paddle
-
             p = paddle.distribution.Beta(alpha=0.5, beta=0.5)
             q = paddle.distribution.Beta(alpha=0.3, beta=0.7)
-
             print(paddle.distribution.kl_divergence(p, q))
             # Tensor(shape=[1], dtype=float32, place=CUDAPlace(0), stop_gradient=True,
             #        [0.21193528])
-
     """
     return _dispatch(type(p), type(q))(p, q)
 
 
 def register_kl(cls_p, cls_q):
     """Decorator for register a KL divergence implemention function.
-
     The ``kl_divergence(p, q)`` function will search concrete implemention
     functions registered by ``register_kl``, according to multi-dispatch pattern.
     If an implemention function is found, it will return the result, otherwise,
     it will raise ``NotImplementError`` exception. Users can register
     implemention funciton by the decorator.
-
     Args:
         cls_p (Distribution): The Distribution type of Instance p. Subclass derived from ``Distribution``.
         cls_q (Distribution): The Distribution type of Instance q. Subclass derived from ``Distribution``.
-
     Examples:
         .. code-block:: python
-
             import paddle
-
             @paddle.distribution.register_kl(paddle.distribution.Beta, paddle.distribution.Beta)
             def kl_beta_beta():
                 pass # insert implementation here
@@ -194,6 +180,11 @@ def _kl_laplace_laplace(p, q):
     return p.kl_divergence(q)
 
 
+@register_kl(MultivariateNormal, MultivariateNormal)
+def _kl_multnormal_multnormal(p, q):
+    return p.kl_divergence(q)
+
+
 @register_kl(ExponentialFamily, ExponentialFamily)
 def _kl_expfamily_expfamily(p, q):
     """Compute kl-divergence using `Bregman divergences <https://www.lix.polytechnique.fr/~nielsen/EntropyEF-ICIP2010.pdf>`_"""