SumFunction

class probnum.functions.SumFunction(*summands)

Bases: Function

Pointwise sum of Functions.

Given functions \(f_1, \dotsc, f_n \colon \mathbb{R}^n \to \mathbb{R}^m\), this defines a new function

\[\sum_{i = 1}^n f_i \colon \mathbb{R}^n \to \mathbb{R}^m, x \mapsto \sum_{i = 1}^n f_i(x).\]

Parameters

• *summands – The functions \(f_1, \dotsc, f_n\).

• summands (Function) –

Return type

None

Attributes Summary

input_ndim	Syntactic sugar for len(input_shape).
input_shape	Shape of the function's input.
output_ndim	Syntactic sugar for len(output_shape).
output_shape	Shape of the function's output.
summands	The functions \(f_1, \dotsc, f_n\) to be added.

Methods Summary

__call__(x)

Evaluate the function at a given input.

Attributes Documentation

input_ndim

Syntactic sugar for len(input_shape).

input_shape

Shape of the function’s input.

For a scalar-input function, this is an empty tuple.

output_ndim

Syntactic sugar for len(output_shape).

output_shape

Shape of the function’s output.

For scalar-valued function, this is an empty tuple.

summands

The functions \(f_1, \dotsc, f_n\) to be added.

Methods Documentation

__call__(x)

Evaluate the function at a given input.

The function is vectorized over the batch shape of the input.

Parameters

x (ArrayLike) – shape= batch_shape + input_shape – (Batch of) input(s) at which to evaluate the function.

Returns

shape= batch_shape + output_shape – Function evaluated at the given (batch of) input(s).

Return type

fx

Raises

ValueError – If the shape of x does not match input_shape along its last dimensions.