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(testmodels-symbolicuserfunctioncopytest)=
# symbolicUserFunctionCopyTest.py

You can view and download this file on Github: [symbolicUserFunctionCopyTest.py](https://github.com/jgerstmayr/EXUDYN/tree/master/python/TestModels/symbolicUserFunctionCopyTest.py)

```{code-block} python
:linenos:

#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# This is an EXUDYN example
#
# Details:  A model with a symbolic user function, copied through mbs.GetDictionary() and
#           mbs.SetDictionary() into a second system (#1888): the copy keeps the function symbolic
#           and computes the same motion. A mass on a spring, driven by a load whose user function
#           is symbolic; the result is the position of the copy after 1 s, which equals the original.
#
# Author:   Johannes Gerstmayr
# Date:     2026-09-29
#
# Copyright:This file is part of Exudyn. Exudyn is free software. You can redistribute it and/or modify it under the terms of the Exudyn license. See 'LICENSE.txt' for more details.
#
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

import exudyn as exu
from exudyn.utilities import * #includes itemInterface and rigidBodyUtilities

import numpy as np

testIsActive = exu.sys.get('testIsActive', False)
esym = exu.symbolic

SC = exu.SystemContainer()
mbs = SC.AddSystem()

node = mbs.AddNode(NodePoint(referenceCoordinates=[0,0,0]))
mbs.AddObject(ObjectMassPoint(nodeNumber=node, mass=1))
mNode = mbs.AddMarker(MarkerNodePosition(nodeNumber=node))
nFixed = mbs.AddNode(NodePointGround())
mbs.AddObject(ObjectConnectorCartesianSpringDamper(markerNumbers=[mbs.AddMarker(MarkerNodePosition(nodeNumber=nFixed)), mNode],
                                                   stiffness=[100,100,100], damping=[1,1,1]))

def UFload(mbs, t, loadVector):
    return [loadVector[0]*esym.sin(10*t), loadVector[1], 0]

load = mbs.AddLoad(LoadForceVector(markerNumber=mNode, loadVector=[10,5,0]))
symbolicLoad = CreateSymbolicUserFunction(mbs, UFload, 'loadVectorUserFunction', load)
mbs.SetLoadParameter(load, 'loadVectorUserFunction', symbolicLoad)

def Solve(mbs):
    mbs.Assemble()
    simulationSettings = exu.SimulationSettings()
    simulationSettings.timeIntegration.numberOfSteps = 200
    simulationSettings.timeIntegration.endTime = 1
    simulationSettings.solution.file.write = False
    mbs.SolveDynamic(simulationSettings)
    return mbs.GetNodeOutput(node, exu.OutputVariableType.Position)

#the copy is made before solving, from the dictionary of the model
mbsCopy = SC.AddSystem()
mbsCopy.SetDictionary(mbs.GetDictionary())
isSymbolic = mbsCopy.GetLoadParameter(load, 'loadVectorUserFunction')['type'] == 'Symbolic'

pOriginal = Solve(mbs)
pCopy = Solve(mbsCopy)
exu.Print('copy is symbolic:', isSymbolic, ', difference to the original:', np.linalg.norm(pCopy - pOriginal))

testResult = sum(pCopy) + (0 if isSymbolic else 1)
exu.Print('solution of symbolicUserFunctionCopyTest=', testResult)
exu.sys['testResult'] = testResult
```