# Field functions¶

A field function where and is defined by:

(1)

with and . A field function transforms a multivariate stochastic process:

where is discretized according to the into the multivariate stochastic process:

such that:

where the mesh is discretized according to the .

A field function also acts on fields and produces fields of possibly different dimension () and mesh ( or ).

Value function

A value function is a particular field function that lets invariant the mesh of a field and defined by a function such that:

(2)

Let’s note that the input dimension of still designs the dimension of : . Its output dimension is equal to .
The creation of a value function requires the function and the integer : the dimension of the vertices of the mesh . This data is required for tests on the compatibility of dimension when a composite process is created using the value function.

Vertex value function

A vertex-value function is a particular field function that lets invariant the mesh of a field and defined by a function such that:

(3)

Let’s note that the input dimension of still design the dimension of : . Its output dimension is equal to .

API:

Examples: