General Functions

Note: this documentation has not yet been updated for v3 of Dedalus.

The GeneralFunction class enables users to simply define new explicit operators for the right-hand side and analysis tasks of their simulations. Such operators can be used to apply arbitrary user-defined functions to the grid values or coefficients of some set of input fields, or even do things like introduce random data or read data from an external source.

A GeneralFunction object is instantiated with a Dedalus domain, a layout object or descriptor (e.g. 'g' or 'c' for grid or coefficient space), a function, a list of arguments, and a dictionary of keywords. The resulting object is a Dedalus operator that can be evaluated and composed like other Dedalus operators. It operates by first ensuring that any arguments that are Dedalus field objects are in the specified layout, then calling the function with the specified arguments and keywords, and finally setting the result as the output data in the specified layout.

Here’s an example how you can use this class to apply a nonlinear function to the grid data of a single Dedalus field. First, we define the underlying function we want to apply to the field data – say the error function from scipy:

from scipy import special

def erf_func(field):
    # Call scipy erf function on the field's data
    return special.erf(field.data)

Second, we make a wrapper that returns a GeneralFunction instance that applies erf_func to a provided field in grid space. This function produces a Dedalus operator, so it’s what we want to use on the RHS or in analysis tasks:

import dedalus.public as de

def erf_operator(field):
    # Return GeneralFunction instance that applies erf_func in grid space
    return de.operators.GeneralFunction(
        field.domain,
        layout = 'g',
        func = erf_func,
        args = (field,)
    )

Finally, we add this wrapper to the parsing namespace to make it available in string-specified equations and analysis tasks:

de.operators.parseables['erf'] = erf_operator