#!/usr/bin/env python
# -*- coding: utf-8 -*-
# This file is part of the Cortix toolkit environment.
# https://cortix.org
import numpy as np
import scipy.constants as const
from scipy.integrate import odeint
from cortix import Module
from cortix import Phase
from cortix import Quantity
[docs]class Prison(Module):
'''
Prison Cortix module used to model criminal group population in a prison.
Notes
-----
These are the `port` names available in this module to connect to respective
modules: `parole`, `adjudication`, `jail`, and `community`.
See instance attribute `port_names_expected`.
'''
[docs] def __init__(self, n_groups=1, pool_size=0.0):
'''
Parameters
----------
n_groups: int
Number of groups in the population.
pool_size: float
Upperbound on the range of the existing population groups. A random value
from 0 to the upperbound value will be assigned to each group.
'''
super().__init__()
self.port_names_expected = ['parole','adjudication','jail','community']
quantities = list()
self.ode_params = dict()
self.initial_time = 0.0 * const.day
self.end_time = 100 * const.day
self.time_step = 0.5 * const.day
# Population groups
self.n_groups = n_groups
# Prison population groups
fpg_0 = np.random.random(self.n_groups) * pool_size
fpg = Quantity(name='fpg', formalName='prison-pop-grps',
unit='individual', value=fpg_0)
quantities.append(fpg)
# Model parameters: commitment coefficients and their modifiers
# Prison to community
cp0g_0 = np.random.random(self.n_groups) / const.day
cp0g = Quantity(name='cp0g', formalName='commit-community-coeff-grps',
unit='individual', value=cp0g_0)
self.ode_params['commit-to-community-coeff-grps'] = cp0g_0
quantities.append(cp0g)
mp0g_0 = np.random.random(self.n_groups)
mp0g = Quantity(name='mp0g', formalName='commit-community-coeff-mod-grps',
unit='individual', value=mp0g_0)
self.ode_params['commit-to-community-coeff-mod-grps'] = mp0g_0
quantities.append(mp0g)
# Prison to parole
cpeg_0 = np.random.random(self.n_groups) / const.day
cpeg = Quantity(name='cpeg', formalName='commit-parole-coeff-grps',
unit='individual', value=cpeg_0)
self.ode_params['commit-to-parole-coeff-grps'] = cpeg_0
quantities.append(cpeg)
mpeg_0 = np.random.random(self.n_groups)
mpeg = Quantity(name='mpeg', formalName='commit-parole-coeff-mod-grps',
unit='individual', value=mpeg_0)
self.ode_params['commit-to-parole-coeff-mod-grps'] = mpeg_0
quantities.append(mpeg)
# Death term
self.ode_params['death-rates'] = np.zeros(self.n_groups)
# Phase state
self.population_phase = Phase(self.initial_time, time_unit='s',
quantities=quantities)
self.population_phase.SetValue('fpg', fpg_0, self.initial_time)
# Initialize inflows to zero
self.ode_params['parole-inflow-rates'] = np.zeros(self.n_groups)
self.ode_params['adjudication-inflow-rates'] = np.zeros(self.n_groups)
self.ode_params['jail-inflow-rates'] = np.zeros(self.n_groups)
return
[docs] def run(self, *args):
self.__zero_ode_parameters()
time = self.initial_time
while time < self.end_time:
# Interactions in the parole port
#--------------------------------
# two way "from" and "to" parole
# from
self.send( time, 'parole' )
(check_time, inflow_rates) = self.recv('parole')
assert abs(check_time-time) <= 1e-6
self.ode_params['parole-inflow-rates'] = inflow_rates
# to
message_time = self.recv('parole')
outflow_rates = self.__compute_outflow_rates( message_time, 'parole' )
self.send( (message_time, outflow_rates), 'parole' )
# Interactions in the adjudication port
#------------------------------------
# one way "from" adjudication
self.send( time, 'adjudication' )
(check_time, inflow_rates) = self.recv('adjudication')
assert abs(check_time-time) <= 1e-6
self.ode_params['adjudication-inflow-rates'] = inflow_rates
# Interactions in the jail port
#------------------------------
# one way "from" jail
self.send( time, 'jail' )
(check_time, inflow_rates) = self.recv('jail')
assert abs(check_time-time) <= 1e-6
self.ode_params['jail-inflow-rates'] = inflow_rates
# Interactions in the community port
#------------------------------
# one way "to" community
message_time = self.recv('community')
outflow_rates = self.__compute_outflow_rates( message_time, 'community' )
self.send( (message_time, outflow_rates), 'community' )
# Evolve prison group population to the next time stamp
#------------------------------------------------------
time = self.__step( time )
def __rhs_fn(self, u_vec, t, params):
fpg = u_vec # prison population groups
parole_inflow_rates = params['parole-inflow-rates']
adjudication_inflow_rates = params['adjudication-inflow-rates']
jail_inflow_rates = params['jail-inflow-rates']
inflow_rates = parole_inflow_rates + adjudication_inflow_rates + jail_inflow_rates
cp0g = self.ode_params['commit-to-community-coeff-grps']
mp0g = self.ode_params['commit-to-community-coeff-mod-grps']
cpeg = self.ode_params['commit-to-parole-coeff-grps']
mpeg = self.ode_params['commit-to-parole-coeff-mod-grps']
outflow_rates = ( cp0g * mp0g + cpeg * mpeg ) * fpg
death_rates = params['death-rates']
dt_fpg = inflow_rates - outflow_rates - death_rates
return dt_fpg
def __step(self, time=0.0):
r'''
ODE IVP problem:
Given the initial data at :math:`t=0`,
:math:`u = (u_1(0),u_2(0),\ldots)`
solve :math:`\frac{\text{d}u}{\text{d}t} = f(u)` in the interval
:math:`0\le t \le t_f`.
Parameters
----------
time: float
Time in SI unit.
Returns
-------
None
'''
u_vec_0 = self.population_phase.GetValue('fpg', time)
t_interval_sec = np.linspace(0.0, self.time_step, num=2)
(u_vec_hist, info_dict) = odeint(self.__rhs_fn,
u_vec_0, t_interval_sec,
args=( self.ode_params, ),
rtol=1e-4, atol=1e-8, mxstep=200,
full_output=True)
assert info_dict['message'] =='Integration successful.', info_dict['message']
u_vec = u_vec_hist[1,:] # solution vector at final time step
values = self.population_phase.GetRow(time) # values at previous time
time += self.time_step
self.population_phase.AddRow(time, values)
# Update current values
self.population_phase.SetValue('fpg', u_vec, time)
return time
def __compute_outflow_rates(self, time, name):
fpg = self.population_phase.GetValue('fpg',time)
assert np.all(fpg>=0.0), 'values: %r'%fpg
if name == 'parole':
cpeg = self.ode_params['commit-to-parole-coeff-grps']
mpeg = self.ode_params['commit-to-parole-coeff-mod-grps']
outflow_rates = cpeg * mpeg * fpg
if name == 'community':
cp0g = self.ode_params['commit-to-community-coeff-grps']
mp0g = self.ode_params['commit-to-community-coeff-mod-grps']
outflow_rates = cp0g * mp0g * fpg
return outflow_rates
def __zero_ode_parameters(self):
'''
If ports are not connected the corresponding outflows must be zero.
'''
zeros = np.zeros(self.n_groups)
p_names = [p.name for p in self.ports]
if 'community' not in p_names:
self.ode_params['commit-to-community-coeff-grps'] = zeros
self.ode_params['commit-to-community-coeff-mod-grps'] = zeros
if 'parole' not in p_names:
self.ode_params['commit-to-parole-coeff-grps'] = zeros
self.ode_params['commit-to-parole-coeff-mod-grps'] = zeros
return
