InverseProblem/simulation_plots.py at master · MathBioCU/InverseProblem · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
# -*- coding: utf-8 -*-
"""
Created on May 10, 2016

@author: Inom Mirzaev

Simulates the forward problem and plots the results.
Uses the rates specified in model_rates.py file.
"""

from __future__ import division

import numpy as np
import matplotlib.pyplot as plt
import os
import model_rates as mr

from scipy.integrate import odeint
from functools import partial


#Extension to be attached to the output file
ext = '_alpha_'+str( mr.a )


plt.close('all')


#==============================================================================
# Simulations of the forwards problem
#==============================================================================

fig = plt.figure( 1 )

ax = fig.add_subplot(111)


num_plots = 5
a = int( len( mr.mytime) / num_plots )
x = mr.nu[:-1]

linestyles = ['-', '--', '-.', ':']
lnst = 0

for nn in range(0, len(mr.mytime) , a)+[-1]:

    y = mr.mydata[nn]

    mytxt = '$t=' + str( round(mr.mytime[nn] , 0) ) +'$'
    ax.plot( x ,  y , label=mytxt , linewidth=2  , linestyle = linestyles[ np.mod( lnst , 4) ] )
    lnst+=1

plt.legend(loc='best', fontsize=20)
plt.ylabel('$b(t,x) $', fontsize=25)
plt.xlabel('$x$', fontsize=25)

fig_name = 'simulation'+ext+'.png'
plt.savefig( os.path.join( 'images' , fig_name ) , dpi=400 , bbox_inches='tight' )


#==============================================================================
# Plot of the Gamma (pdf) and F (cdf) for fixed values of y
#==============================================================================
f, ax = plt.subplots(2, sharex=True)

x = mr.nu[:-1]
yy = [0.2, 0.5, 1.0]


for mm in range( len(yy) ):

    y = mr.gam( x , yy[mm] )
    mytxt = '$\Gamma(x,\ ' + str( yy[mm] ) +')$'
    ax[0].plot( x ,  y , label=mytxt , linewidth=2 , linestyle = linestyles[ mm ] )

    F_y  = np.cumsum( y )
    F_y = F_y / np.max( F_y )
    mytxt = '$F(x,\ ' + str( yy[mm] ) +')$'
    ax[1].plot( x ,  F_y , label=mytxt , linewidth = 2 , linestyle = linestyles[ mm ] )


ax[0].legend( loc='best' , fontsize=15 )
ax[0].set_ylabel( r'$\Gamma(x,\ y) $' , fontsize=20 )
myaxis = list( ax[0].axis() )
myaxis[-1]+=0.2
ax[0].axis( myaxis )

ax[1].legend( loc='lower right' , fontsize=15 )
ax[1].set_ylabel( r'$F(x,\ y) $' , fontsize=20 )
ax[1].set_xlabel( '$x$' , fontsize=20 )
myaxis = list( ax[1].axis() )
myaxis[-1]+=0.1
ax[1].axis( myaxis )


fig_name = 'gamma'+ext+'.png'
plt.savefig( os.path.join( 'images' , fig_name ) , dpi=400 , bbox_inches='tight' )


dimens  = np.linspace(10, 100, 20)
conv_error = np.array([])

for ndim in range(len(dimens)):

    Ain, Aout, Fin, Fout, nu, N, dx = mr.initialization( int( dimens[ndim]) )
    mytime = np.linspace( 0 , 1 , 1000 )

    y0 = mr.ICproj(N)

    data_generator = partial( mr.dataRHS , N=N , Ain=Ain , Aout=Aout , Fin=Fin , Fout=Fout )
    mydata = odeint( data_generator , y0 , mytime ,  rtol=1e-6, atol=1e-6 )
    #Approximate steady state calculated as a root of G_n
    appr_sol = mydata

    grid_x = np.linspace( mr.x0 , mr.x1 , N )
    actual_sol =  mr.interp_func( grid_x , mytime )

    #L1 error between exact and approximate solutions
    L1_error =  np.trapz( np.trapz( np.abs( actual_sol - appr_sol )  , dx=dx, axis=1 ) , dx=mytime[1] )
    conv_error = np.append( conv_error, L1_error )


#==============================================================================
# Generates error plot for the forward simulation.
#==============================================================================

fig = plt.figure(3)
ax = fig.add_subplot(111)

logx = np.log(  1/dimens )
logy = np.log( conv_error )

coeffs = np.polyfit( logx , logy ,deg=1 )

ax.loglog( 1/dimens ,  conv_error , linewidth=1, color='blue', marker='o', markersize=10 )

x1, x2, y1, y2 = plt.axis()
ax.axis([x1 - 0.1*x1, x2+0.01*x2, y1, y2])
ax.set_ylabel( '$\Vert u_{1000} - u_N  \Vert_{1}$', fontsize=25)
ax.set_xlabel( r'$\Delta x=\frac{ \overline{x} } {N}$', fontsize=25 )
mytext = 'Slope =$'+str( round(coeffs[0] , 1) ) + '$'

ax.text(0.7, 0.9,  mytext , style='italic',
        bbox={'facecolor':'#87CEFA', 'alpha':0.5, 'pad':10} ,
        transform=ax.transAxes, fontsize = 20)


fig_name = 'frwd_converg'+ext+'.png'
plt.savefig( os.path.join( 'images' , fig_name ) , dpi=400 , bbox_inches='tight' )