# Normal¶

class paddle.fluid.layers.distributions. Normal ( loc, scale ) [source]

The Normal distribution with location loc and scale parameters.

Mathematical details

The probability density function (pdf) is,

$\begin{split}pdf(x; \mu, \sigma) = \\frac{1}{Z}e^{\\frac {-0.5 (x - \mu)^2} {\sigma^2} }\end{split}$
$Z = (2 \pi \sigma^2)^{0.5}$

In the above equation:

• $$loc = \mu$$: is the mean.

• $$scale = \sigma$$: is the std.

• $$Z$$: is the normalization constant.

Parameters
• loc (float|list|numpy.ndarray|Variable) – The mean of normal distribution.The data type is float32.

• scale (float|list|numpy.ndarray|Variable) – The std of normal distribution.The data type is float32.

Examples

import numpy as np

# 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()

# 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_npdata = np.array([0.8], dtype="float32")
value_tensor = layers.create_tensor(dtype="float32")
layers.assign(value_npdata, value_tensor)

normal_a = Normal([0.], [1.])
normal_b = Normal([0.5], [2.])

sample = normal_a.sample()
# a random tensor created by normal distribution with shape: [2, 1]
entropy = normal_a.entropy()
# [1.4189385] with shape: 
lp = normal_a.log_prob(value_tensor)
# [-1.2389386] with shape: 
kl = normal_a.kl_divergence(normal_b)
# [0.34939718] with shape: 

sample ( shape, seed=0 )

Generate samples of the specified shape.

Parameters
• shape (list) – 1D int32. Shape of the generated samples.

• seed (int) – Python integer number.

Returns

A tensor with prepended dimensions shape.The data type is float32.

Return type

Variable

entropy ( )

Shannon entropy in nats.

Returns

Shannon entropy of normal distribution.The data type is float32.

Return type

Variable

log_prob ( value )

Log probability density/mass function.

Parameters

value (Variable) – The input tensor.

Returns

log probability.The data type is same with value.

Return type

Variable

kl_divergence ( other )

The KL-divergence between two normal distributions.

Parameters

other (Normal) – instance of Normal.

Returns

kl-divergence between two normal distributions.The data type is float32.

Return type

Variable