megengine.functional.nn.logsumexp

logsumexp(inp, axis, keepdims=False)

Calculates the logarithm of the inputs’ exponential sum along the given axis.

\[\text{logsumexp}(x)= \log \sum_{j=1}^{n} \exp \left(x_{j}\right)\]

For numerical stability, the implementation follows this transformation:

\[\text{logsumexp}(x)= \log \sum_{j=1}^{n} \exp \left(x_{j}\right) = \text{logsumexp}(x)=b+\log \sum_{j=1}^{n} \exp \left(x_{j}-b\right)\]

where

\[b = \max(x_j)\]

Examples

>>> import numpy as np
>>> x = Tensor(np.arange(-5, 5, dtype=np.float32)).reshape(2,5)
>>> y = F.logsumexp(x, axis=1, keepdims=False)
>>> y.numpy().round(decimals=4)
array([-0.5481,  4.4519], dtype=float32)

Return type:

Tensor