DSGRN Python Interface Tutorial

This notebook shows the basics of manipulating DSGRN with the python interface.



In [1]:

    
import DSGRN

Network

The starting point of the DSGRN analysis is a network specification. We write each node name, a colon, and then a formula specifying how it reacts to its inputs.



In [2]:

    
network = DSGRN.Network("""
X1 : (X1+X2)(~X3)
X2 : (X1)
X3 : (X1)(~X2)""")



In [3]:

    
DSGRN.DrawGraph(network)









    Out[3]:

ParameterGraph

Given a network, there is an associated "Parameter Graph", which is a combinatorial representation of parameter space.



In [4]:

    
parametergraph = DSGRN.ParameterGraph(network)



In [5]:

    
print("There are " + str(parametergraph.size()) + " nodes in the parameter graph.")









    



There are 326592 nodes in the parameter graph.

Parameter

The ParameterGraph class may be regarded as a factory which produces parameter nodes. In the DSGRN code, parameter nodes are referred to simply as "parameters" and are represented as "Parameter" objects.



In [6]:

    
parameterindex = 34892  # An arbitrarily selected integer in [0,326592)



In [7]:

    
parameter = parametergraph.parameter(parameterindex)



In [8]:

    
print(parameter)









    



[["X1",[3,3,"6D9000"],[0,2,1]],["X2",[1,2,"D"],[0,1]],["X3",[2,1,"8"],[0]]]

DomainGraph

Let's compute the dynamics corresponding to this parameter node. In particular, we can instruct DSGRN to create a "domaingraph" object.



In [9]:

    
domaingraph = DSGRN.DomainGraph(parameter)



In [10]:

    
DSGRN.DrawGraph(domaingraph)









    Out[10]:



In [11]:

    
print(domaingraph.coordinates(5)) # ... I wonder what region in phase space domain 5 corresponds to.









    



[1, 1, 0]

MorseDecomposition

Let's compute the partially ordered set of recurrent components (strongly connected components with an edge) of the domain graph.



In [12]:

    
morsedecomposition = DSGRN.MorseDecomposition(domaingraph.digraph())



In [13]:

    
DSGRN.DrawGraph(morsedecomposition)









    Out[13]:

MorseGraph

The final step in our analysis is the production of an annotated Morse graph.



In [14]:

    
morsegraph = DSGRN.MorseGraph(domaingraph, morsedecomposition)



In [15]:

    
DSGRN.DrawGraph(morsegraph)









    Out[15]:

Drawing Tables



In [16]:

    
from DSGRN import *
pg = ParameterGraph(Network("X : ~Y\nY : ~X\n"))



In [17]:

    
Table(["Parameter Index", "Morse Graph"], 
      [ [ i, DrawGraph(MorseGraph(DomainGraph(pg.parameter(i))))] for i in range(0,pg.size())])









    Out[17]:




Parameter Index Morse Graph
0 





1 





2 





3 





4 





5 





6 





7 





8

ParameterSampler

We can sample real-valued parameter values from combinatorial parameter regions using the ParameterSampler class. This class provides a method sample which takes an integer parameter index and returns a string describing a randomly sampled instance within the associated parameter region.



In [18]:

    
sampler = DSGRN.ParameterSampler(parametergraph)
sampler.sample(parameterindex)









    Out[18]:





'{"ParameterIndex":34892,"Parameter":{"L[X1, X1]" : 0.26189317114915911, "L[X1, X2]" : 0.047527672343930391, "L[X1, X3]" : 0.21385722418770212, "L[X2, X1]" : 0.0083569702162772409, "L[X2, X3]" : 0.13477572472965574, "L[X3, X1]" : 0.81414161582444289, "T[X1, X1]" : 0.42280525715172884, "T[X1, X2]" : 1.6293141045393824, "T[X1, X3]" : 1.0824055111883504, "T[X2, X1]" : 0.018249770181381512, "T[X2, X3]" : 0.16314316602148091, "T[X3, X1]" : 1.5770292044658094, "U[X1, X1]" : 0.36915443410830018, "U[X1, X2]" : 1.6814679188873936, "U[X1, X3]" : 1.6853427566781969, "U[X2, X1]" : 0.97980155236308419, "U[X2, X3]" : 1.6038764331358468, "U[X3, X1]" : 0.90367375128805294}}'



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