# Normal¶

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

The Normal distribution with location loc and scale parameters.

Mathematical details

The probability density function (pdf) is,

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

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