This is a simple model that simulates the tendency of state of grace for people with Judger and Perceiver personality types. Written by David Mascarenas, 2013-01-06 Keywords: computational theology, judger, perceiver, temperament, personality, every voluntary act, fundamental option, Jung, salvation Fundamental option vs Every Voluntary act http…

JP_montecarlo.py

#!/usr/bin/python

'''
This is a simple model that simulates the tendency of state of grace for 
people with Judger and Perceiver personality types.  

Written by David Mascarenas, 2013-01-06

Keywords:
computational theology, judger, perceiver, temperment, personality, every voluntary act, fundamental option, Jung,

Fundamental option vs Every Voluntary act
http://www.ewtn.com/library/DOCTRINE/VSDEFEAT.TXT
http://www.pathsoflove.com/blog/2010/05/fundamental-option-and-salvation/
'''


import numpy
import pylab


if __name__ == '__main__':
   
    print 'Lets look at J-P characteristics '
    N = 1024
    age_yr = 100

    step_yr = float(age_yr)/N
    filter_len = 100
    t_yr = numpy.arange(0, age_yr, step_yr )
   
    #J_lpfilter = numpy.fliplr( numpy.exp( numpy.arange( filter_len ) ) )
    J_lpfilter = numpy.exp( -.001 * numpy.arange( filter_len*2 ) )
   
    P_hlpfilter = numpy.exp( -.01 * numpy.arange( filter_len ) ) * numpy.cos( 2*numpy.pi*numpy.arange( float(filter_len) )/50  )
    #P_hlpfilter = numpy.exp( -.1 * numpy.arange( filter_len ) )
   
   
    pylab.figure()
    pylab.subplot('211')
    pylab.plot(numpy.arange(len( J_lpfilter))*step_yr, J_lpfilter)
    pylab.title('Proposed Judger Finite Impulse Response Filter\n(NOTE: No Complex exponential components to induce oscillation)')
   
    pylab.subplot('212')
    pylab.plot( numpy.arange(len(P_hlpfilter))*step_yr, P_hlpfilter)
    pylab.xlabel('time (yrs)')
    pylab.title('Proposed Perceiver Finite Impulse Response Filter\n(NOTE: Complex exponential components present that allow oscillation)')
   
   
   
   
    ##############################################
    # Begin - check for grace by monte carlo
    ##############################################
    NN = 10000          #Number of monte carlo runs
   
    J_heaven_array = []
    J_hell_array = []
    J_grace_net_array = []
   
    P_heaven_array = []
    P_hell_array = []
    P_grace_net_array = []
   
    for nn in range( NN ):
   
        J_heaven = 0
        J_hell = 0
       
        P_heaven = 0
        P_hell = 0
       
        stimulus_time_series = numpy.random.randn( N )
       
        #This is just here to check my impulse response functions work correctly
        #stimulus_time_series = numpy.zeros( N )
        #stimulus_time_series[0] = 1
   
        P_time_series_filtered = numpy.convolve(stimulus_time_series, P_hlpfilter, mode='same')
        J_time_series_filtered = numpy.convolve(stimulus_time_series, J_lpfilter, mode='same')
       
        for ii in range(N):
           
            if P_time_series_filtered[ii] > 0:
                P_heaven = P_heaven + 1
            else:
                P_hell = P_hell + 1
       
            if J_time_series_filtered[ii] > 0:
                J_heaven = J_heaven + 1
            else:
                J_hell = J_hell + 1
       
        J_grace_net_array.append( (J_heaven - J_hell) * step_yr )
        P_grace_net_array.append( (P_heaven - P_hell) * step_yr  )
       
        J_heaven_array.append( J_heaven * step_yr )
        J_hell_array.append( J_hell * step_yr )
       
        P_heaven_array.append( P_heaven * step_yr )
        P_hell_array.append( P_hell * step_yr )
   
    '''     
    print "Time J_heaven = " + str( J_heaven * step_yr )
    print "Time J_hell = " + str( J_hell * step_yr )
    print "Time P_heaven = " + str( P_heaven * step_yr )
    print "Time P_hell = " + str( P_hell * step_yr )
    '''
    ##############################################
    # End - check for grace by monte carlo
    ##############################################
    print 'mean years J heaven = ' + str( numpy.mean(J_heaven_array) )
    print 'mean years J hell = ' + str( numpy.mean(J_hell_array) )
    print 'mean years P heaven = ' + str( numpy.mean(P_heaven_array) )
    print 'mean years P hell = ' + str( numpy.mean(P_hell_array) )

    pylab.figure()
    #pylab.plot( t_yr, stimulus_time_series )
    
    
    pylab.subplot('211')
    pylab.plot( t_yr, J_time_series_filtered )
    #pylab.plot( J_lpfilter )
    #pylab.plot( P_hlpfilter )
    pylab.title( 'Judger personality state of grace over lifespan' )
    pylab.ylabel('State of Grace ')
    pylab.xlim([0,age_yr - 10])
    #pylab.axes( (0, (age_yr-10), numpy.min( J_time_series_filtered ), numpy.max( J_time_series_filtered ) ) )
    pylab.grid(True)

    pylab.subplot('212')
    pylab.plot( t_yr, P_time_series_filtered )
    pylab.title( 'Perceiver personality state of grace over lifespan' )
    pylab.ylabel('State of Grace')
    pylab.xlim([0,age_yr - 10])
    pylab.xlabel('time (yrs)')
    #pylab.axes( (0, (age_yr-10), numpy.min( P_time_series_filtered ), numpy.max( P_time_series_filtered ) ) )
    #pylab.xlabel('time (yrs)')
    pylab.grid(True)


    num_bins = 100
    pylab.figure()
    pylab.subplot('221')
    pylab.hist( numpy.array(J_heaven_array), num_bins )
    pylab.title( 'J heaven' )
   
    pylab.subplot('222')
    pylab.hist( numpy.array(J_hell_array), num_bins )
    pylab.title( 'J hell' )
   
    pylab.subplot('223')
    pylab.hist( numpy.array(P_heaven_array), num_bins )
    pylab.title( 'P heaven' )
   
    pylab.subplot('224')
    pylab.hist( numpy.array(P_hell_array), num_bins )
    pylab.title( 'P hell' )
   
   
   
    bins = numpy.arange( -100, 100 )
    pylab.figure()
    pylab.subplot('211')
    pylab.hist( numpy.array( J_grace_net_array ), bins )
    pylab.title( 'J grace, Expected Value = ' + str(numpy.mean(J_grace_net_array)) + ', Number Simulations = ' + str(NN) )
   
    pylab.subplot('212')
    pylab.hist( numpy.array( P_grace_net_array ), bins )
    pylab.title( 'P grace, Expected Value = ' + str(numpy.mean(P_grace_net_array)) + ', Number Simulations = ' + str(NN) )
   
    print J_heaven_array
    pylab.show()
   
    '''
    Fundamental option vs Every Voluntary act
    http://www.ewtn.com/library/DOCTRINE/VSDEFEAT.TXT
    http://www.pathsoflove.com/blog/2010/05/fundamental-option-and-salvation/
    '''