#!/usr/bin/env python
# coding: utf-8

# # MuMoT test notebook for using letters from the Greek alphabet

# This notebook tests some basic functionality of MuMoT when reactants and rates are Greek letters (with Greek indices). The analysis is based on the honeybee stop-signal model (Seeley et al. (2012) & Pais et al. (2013)) studied in more detail in the user manual. 

# In[ ]:


import mumot

mumot.__version__


# In[ ]:


model1 = mumot.parseModel(r"""
U -> \alpha : g_1
U -> \Gamma_\beta : g_2
\alpha -> U : a_1
\Gamma_\beta -> U : a_2
\alpha + U -> \alpha + \alpha : r_1
\Gamma_\beta + U -> \Gamma_\beta + \Gamma_\beta : r_2
\alpha + \Gamma_\beta -> \alpha + U : \sigma
\alpha + \Gamma_\beta -> \Gamma_\beta + U : \sigma
""")


# In[ ]:


int1 = model1.integrate(showStateVars=['\\alpha', '\\Gamma_\\beta', 'U'],
                        initWidgets={'maxTime':[10,5,50,1], 
                                     'initialState':{'U': [0.5,0,1,0.01],'\\Gamma_\\beta': [0.5,0,1,0.1],'\\alpha': [0,0,1,0.1]},
                                    'g_{1}':[0.5,0,1,0.01]},
        
                       conserved=True)


# In[ ]:


int1.showLogs()


# In[ ]:


model2 = model1.substitute('a_1 = 1/v_1, a_2 = 1/v_2, g_1 = v_1, g_2 = v_2, r_1 = v_1, r_2 = v_2')


# In[ ]:


model3 = model2.substitute('v_1 = \\mu + \\Delta/2, v_2 = \\mu - \\Delta/2')


# In[ ]:


model3.showODEs()


# In[ ]:


model3.show()


# In[ ]:


model4 = model3.substitute('U = N - \\alpha - \\Gamma_\\beta')


# In[ ]:


modelBifCont1 = model4.bifurcation('\\sigma','\\alpha-\\Gamma_\\beta', 
                                   initWidgets={'mu':[3, 1, 5, 0.5], 'Delta':[0, 0, 2, 0.1], 
                                                'initBifParam':[4.8, 3, 5, 0.1]},
                                   choose_xrange=[0, 5])


# In[ ]:


modelStreamCont1 = model4.stream('\\alpha', '\\Gamma_\\beta',fontsize=25, xlab=r'this is the x-label', 
                                 showFixedPoints=False, showNoise=False)


# In[ ]:


model4.SSA()


# In[ ]:


model4.showODEs(method='vanKampen')


# In[ ]:


model4.showMasterEquation()


# In[ ]:


model4.showFokkerPlanckEquation()


# In[ ]:


model4.showVanKampenExpansion()