# ScaledFunction¶

class probnum.functions.ScaledFunction(function, scalar)[source]

Bases: Function

Function multiplied pointwise with a scalar.

Given a function $$f \colon \mathbb{R}^n \to \mathbb{R}^m$$ and a scalar $$\alpha \in \mathbb{R}$$, this defines a new function

$\alpha f \colon \mathbb{R}^n \to \mathbb{R}^m, x \mapsto (\alpha f)(x) = \alpha f(x).$
Parameters
• function (Function) – The function $$f$$.

• scalar (ScalarLike) – The scalar $$\alpha$$.

Attributes Summary

 function The function $$f$$. 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. scalar The scalar $$\alpha$$.

Methods Summary

 Evaluate the function at a given input.

Attributes Documentation

function

The function $$f$$.

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.

scalar

The scalar $$\alpha$$.

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.