def simulate(self, Tend, nIntervals, gridWidth):
problem = Explicit_Problem(self.rhs, self.y0)
problem.name = 'CVode'
# solver.rhs = self.right_hand_side
problem.handle_result = self.handle_result
problem.state_events = self.state_events
problem.handle_event = self.handle_event
problem.time_events = self.time_events
problem.finalize = self.finalize
simulation = CVode(problem)
# Change multistep method: 'adams' or 'VDF'
if self.discr == 'Adams':
simulation.discr = 'Adams'
simulation.maxord = 12
else:
simulation.discr = 'BDF'
simulation.maxord = 5
# Change iteration algorithm: functional(FixedPoint) or newton
if self.iter == 'FixedPoint':
simulation.iter = 'FixedPoint'
else:
simulation.iter = 'Newton'
# Sets additional parameters
simulation.atol = self.atol
simulation.rtol = self.rtol
simulation.verbosity = self.verbosity
if hasattr(simulation, 'continuous_output'):
simulation.continuous_output = False # default 0, if one step approach should be used
elif hasattr(simulation, 'report_continuously'):
simulation.report_continuously = False # default 0, if one step approach should be used
# '''Initialize problem '''
# self.t_cur = self.t0
# self.y_cur = self.y0
# Calculate nOutputIntervals:
if gridWidth <> None:
nOutputIntervals = int((Tend - self.t0) / gridWidth)
else:
nOutputIntervals = nIntervals
# Check for feasible input parameters
if nOutputIntervals == 0:
print 'Error: gridWidth too high or nIntervals set to 0! Continue with nIntervals=1'
nOutputIntervals = 1
# Perform simulation
simulation.simulate(
Tend, nOutputIntervals
) # to get the values: t_new, y_new = simulation.simulate
def simulate(self, Tend, nIntervals, gridWidth):
problem = Explicit_Problem(self.rhs, self.y0)
problem.name = 'CVode'
# solver.rhs = self.right_hand_side
problem.handle_result = self.handle_result
problem.state_events = self.state_events
problem.handle_event = self.handle_event
problem.time_events = self.time_events
problem.finalize = self.finalize
simulation = CVode(problem)
# Change multistep method: 'adams' or 'VDF'
if self.discr == 'Adams':
simulation.discr = 'Adams'
simulation.maxord = 12
else:
simulation.discr = 'BDF'
simulation.maxord = 5
# Change iteration algorithm: functional(FixedPoint) or newton
if self.iter == 'FixedPoint':
simulation.iter = 'FixedPoint'
else:
simulation.iter = 'Newton'
# Sets additional parameters
simulation.atol = self.atol
simulation.rtol = self.rtol
simulation.verbosity = self.verbosity
if hasattr(simulation, 'continuous_output'):
simulation.continuous_output = False # default 0, if one step approach should be used
elif hasattr(simulation, 'report_continuously'):
simulation.report_continuously = False # default 0, if one step approach should be used
# '''Initialize problem '''
# self.t_cur = self.t0
# self.y_cur = self.y0
# Calculate nOutputIntervals:
if gridWidth <> None:
nOutputIntervals = int((Tend - self.t0) / gridWidth)
else:
nOutputIntervals = nIntervals
# Check for feasible input parameters
if nOutputIntervals == 0:
print 'Error: gridWidth too high or nIntervals set to 0! Continue with nIntervals=1'
nOutputIntervals = 1
# Perform simulation
simulation.simulate(Tend, nOutputIntervals) # to get the values: t_new, y_new = simulation.simulate
def doSimulate():
theta0 = 1.0 # radianer, startvinkel från lodrätt
tfinal = 3
title = 'k = {0}, stretch = {1}, {2}'.format(k, stretch, solver)
r0 = 1.0 + stretch
x0 = r0 * np.sin(theta0)
y0 = -r0 * np.cos(theta0)
t0 = 0.0
y_init = np.array([x0, y0, 0, 0])
ElasticSpring = Explicit_Problem(rhs, y_init, t0)
if solver.lower() == "cvode":
sim = CVode(ElasticSpring)
elif solver.lower() == "bdf_2":
sim = BDF_2(ElasticSpring)
elif solver.lower() == "ee":
sim = EE(ElasticSpring)
else:
sim == None
raise ValueError('Expected "CVode", "EE" or "BDF_2"')
sim.report_continuously = False
npoints = 100 * tfinal
#t,y = sim.simulate(tfinal,npoints)
try:
#for i in [1]:
t, y = sim.simulate(tfinal)
xpos, ypos = y[:, 0], y[:, 1]
#plt.plot(t,y[:,0:2])
plt.plot(xpos, ypos)
plt.plot(xpos[0], ypos[0], 'or')
plt.xlabel('y_1')
plt.ylabel('y_2')
plt.title(title)
plt.axis('equal')
plt.show()
except Explicit_ODE_Exception as e:
print(e.message)
print("for the case {0}.".format(title))
def make_explicit_sim(self):
explicit_sim = CVode(self.explicit_problem)
explicit_sim.iter = 'Newton'
explicit_sim.discr = 'BDF'
explicit_sim.rtol = 1e-7
explicit_sim.atol = 1e-7
explicit_sim.sensmethod = 'SIMULTANEOUS'
explicit_sim.suppress_sens = True
explicit_sim.report_continuously = False
explicit_sim.usesens = False
explicit_sim.verbosity = 50
if self.use_jac and self.model_jac is not None:
explicit_sim.usejac = True
else:
explicit_sim.usejac = False
return explicit_sim
def s_cvode_natural(self,params):
from assimulo.problem import Explicit_Problem
from assimulo.solvers import CVode
problem = Explicit_Problem(lambda t,x,p:self.create_dx(p)(t,x)['f'](),
[1.0,1.0,1.0],0,
[params[p] for p in self.params])
sim = CVode(problem)
sim.report_continuously = True
t,x = sim.simulate(250,self.time.shape[0]-1)
dataframe = pandas.DataFrame(x,
columns=['population','burden','economy'])
d = {}
sens = np.array(sim.p_sol)
for i,col in enumerate(self.cols):
for j,param in enumerate(
('birthrate','deathrate','regenerationrate',
'burdenrate','economyaim','growthrate')):
d['{0},{1}'.format(col,param)] = sens[j,:,i]
dataframe_sens = pandas.DataFrame(d,index=self.time)
return dataframe_sens
def prepareSimulation(self, params = None):
if params == None:
params = AttributeDict({
'absTol' : 1e-6,
'relTol' : 1e-6,
})
#Define an explicit solver
simSolver = CVode(self)
#Create a CVode solver
#Sets the parameters
#simSolver.verbosity = LOUD
simSolver.report_continuously = True
simSolver.iter = 'Newton' #Default 'FixedPoint'
simSolver.discr = 'BDF' #Default 'Adams'
#simSolver.discr = 'Adams'
simSolver.atol = [params.absTol] #Default 1e-6
simSolver.rtol = params.relTol #Default 1e-6
simSolver.problem_info['step_events'] = True # activates step events
#simSolver.maxh = 1.0
simSolver.store_event_points = True
self.simSolver = simSolver
def prepareSimulation(self, params=None):
if params == None:
params = AttributeDict({
'absTol': 1e-6,
'relTol': 1e-6,
})
#Define an explicit solver
simSolver = CVode(self)
#Create a CVode solver
#Sets the parameters
#simSolver.verbosity = LOUD
simSolver.report_continuously = True
simSolver.iter = 'Newton' #Default 'FixedPoint'
simSolver.discr = 'BDF' #Default 'Adams'
#simSolver.discr = 'Adams'
simSolver.atol = [params.absTol] #Default 1e-6
simSolver.rtol = params.relTol #Default 1e-6
simSolver.problem_info['step_events'] = True # activates step events
#simSolver.maxh = 1.0
simSolver.store_event_points = True
self.simSolver = simSolver
def run_example(with_plots=True):
"""
Example of the use of CVode for a differential equation
with a iscontinuity (state event) and the need for an event iteration.
on return:
- :dfn:`exp_mod` problem instance
- :dfn:`exp_sim` solver instance
"""
#Create an instance of the problem
exp_mod = Extended_Problem() #Create the problem
exp_sim = CVode(exp_mod) #Create the solver
exp_sim.verbosity = 0
exp_sim.report_continuously = True
#Simulate
t, y = exp_sim.simulate(
10.0, 1000) #Simulate 10 seconds with 1000 communications points
exp_sim.print_event_data()
#Plot
if with_plots:
import pylab as P
P.plot(t, y)
P.title(exp_mod.name)
P.ylabel('States')
P.xlabel('Time')
P.show()
#Basic test
nose.tools.assert_almost_equal(y[-1][0], 8.0)
nose.tools.assert_almost_equal(y[-1][1], 3.0)
nose.tools.assert_almost_equal(y[-1][2], 2.0)
return exp_mod, exp_sim
def simulate(self, Tend, nIntervals, gridWidth):
# define assimulo problem:(has to be done here because of the starting value in Explicit_Problem
solver = Explicit_Problem(self.rhs, self.y0)
''' *******DELETE LATER '''''''''
# problem.handle_event = handle_event
# problem.state_events = state_events
# problem.init_mode = init_mode
solver.handle_result = self.handle_result
solver.name = 'Simple Explicit Example'
simulation = CVode(solver) # Create a RungeKutta34 solver
# simulation.inith = 0.1 #Sets the initial step, default = 0.01
# Change multistep method: 'adams' or 'VDF'
if self.discr == 'Adams':
simulation.discr = 'Adams'
simulation.maxord = 12
else:
simulation.discr = 'BDF'
simulation.maxord = 5
# Change iteration algorithm: functional(FixedPoint) or newton
if self.iter == 'FixedPoint':
simulation.iter = 'FixedPoint'
else:
simulation.iter = 'Newton'
# Sets additional parameters
simulation.atol = self.atol
simulation.rtol = self.rtol
simulation.verbosity = 0
if hasattr(simulation, 'continuous_output'):
simulation.continuous_output = False # default 0, if one step approach should be used
elif hasattr(simulation, 'report_continuously'):
simulation.report_continuously = False # default 0, if one step approach should be used
# Create Solver and set settings
# noRootFunctions = np.size(self.state_events(self.t0, np.array(self.y0)))
# solver = sundials.CVodeSolver(RHS = self.f, ROOT = self.rootf, SW = [False]*noRootFunctions,
# abstol = self.atol, reltol = self.rtol)
# solver.settings.JAC = None #Add user-dependent jacobian here
'''Initialize problem '''
# solver.init(self.t0, self.y0)
self.handle_result(self.t0, self.y0)
nextTimeEvent = self.time_events(self.t0, self.y0)
self.t_cur = self.t0
self.y_cur = self.y0
state_event = False
#
#
if gridWidth <> None:
nOutputIntervals = int((Tend - self.t0) / gridWidth)
else:
nOutputIntervals = nIntervals
# Define step length depending on if gridWidth or nIntervals has been chosen
if nOutputIntervals > 0:
# Last point on grid (does not have to be Tend:)
if(gridWidth <> None):
dOutput = gridWidth
else:
dOutput = (Tend - self.t0) / nIntervals
else:
dOutput = Tend
outputStepCounter = long(1)
nextOutputPoint = min(self.t0 + dOutput, Tend)
while self.t_cur < Tend:
# Time-Event detection and step time adjustment
if nextTimeEvent is None or nextOutputPoint < nextTimeEvent:
time_event = False
self.t_cur = nextOutputPoint
else:
time_event = True
self.t_cur = nextTimeEvent
try:
# #Integrator step
# self.y_cur = solver.step(self.t_cur)
# self.y_cur = np.array(self.y_cur)
# state_event = False
# Simulate
# take a step to next output point:
t_new, y_new = simulation.simulate(self.t_cur) # 5, 10) #5, 10 self.t_cur self.t_cur 2. argument nsteps Simulate 5 seconds
# t_new, y_new are both vectors of the time and states at t_cur and all intermediate
# points before it! So take last values:
self.t_cur = t_new[-1]
self.y_cur = y_new[-1]
state_event = False
except:
import sys
print "Unexpected error:", sys.exc_info()[0]
# except CVodeRootException, info:
# self.t_cur = info.t
# self.y_cur = info.y
# self.y_cur = np.array(self.y_cur)
# time_event = False
# state_event = True
#
#
# Depending on events have been detected do different tasks
if time_event or state_event:
event_info = [state_event, time_event]
if not self.handle_event(self, event_info):
break
solver.init(self.t_cur, self.y_cur)
nextTimeEvent = self.time_events(self.t_cur, self.y_cur)
# If no timeEvent happens:
if nextTimeEvent <= self.t_cur:
nextTimeEvent = None
if self.t_cur == nextOutputPoint:
# Write output if not happened before:
if not time_event and not state_event:
self.handle_result(nextOutputPoint, self.y_cur)
outputStepCounter += 1
nextOutputPoint = min(self.t0 + outputStepCounter * dOutput, Tend)
self.finalize()
def run_example(with_plots=True):
r"""
Example for the use of the stability limit detection algorithm
in CVode.
.. math::
\dot y_1 &= y_2 \\
\dot y_2 &= \mu ((1.-y_1^2) y_2-y_1) \\
\dot y_3 &= sin(ty_2)
with :math:`\mu=\frac{1}{5} 10^3`.
on return:
- :dfn:`exp_mod` problem instance
- :dfn:`exp_sim` solver instance
"""
class Extended_Problem(Explicit_Problem):
order = []
def handle_result(self, solver, t, y):
Explicit_Problem.handle_result(self, solver, t, y)
self.order.append(solver.get_last_order())
eps = 5.e-3
my = 1./eps
#Define the rhs
def f(t,y):
yd_0 = y[1]
yd_1 = my*((1.-y[0]**2)*y[1]-y[0])
yd_2 = N.sin(t*y[1])
return N.array([yd_0,yd_1, yd_2])
y0 = [2.0,-0.6, 0.1] #Initial conditions
#Define an Assimulo problem
exp_mod = Extended_Problem(f,y0,
name = "CVode: Stability problem")
#Define an explicit solver
exp_sim = CVode(exp_mod) #Create a CVode solver
#Sets the parameters
exp_sim.stablimdet = True
exp_sim.report_continuously = True
#Simulate
t, y = exp_sim.simulate(2.0) #Simulate 2 seconds
#Plot
if with_plots:
P.subplot(211)
P.plot(t,y[:,2])
P.ylabel("State: $y_1$")
P.subplot(212)
P.plot(t,exp_mod.order)
P.ylabel("Order")
P.suptitle(exp_mod.name)
P.xlabel("Time")
P.show()
#Basic test
x1 = y[:,0]
assert N.abs(x1[-1]-1.8601438) < 1e-1 #For test purpose
return exp_mod, exp_sim
def run_simulation(filename, save_output, start_time, temp, RH, RO2_indices,
H2O, PInit, y_cond, input_dict, simulation_time, batch_step,
plot_mass):
from assimulo.solvers import RodasODE, CVode, RungeKutta4, LSODAR #Choose solver accoring to your need.
from assimulo.problem import Explicit_Problem
# In this function, we import functions that have been pre-compiled for use in the ODE solver
# The function that calculates the RHS of the ODE is also defined within this function, such
# that it can be used by the Assimulo solvers
# The variables passed to this function are defined as follows:
#-------------------------------------------------------------------------------------
#-------------------------------------------------------------------------------------
# define the ODE function to be called
def dydt_func(t, y):
"""
This function defines the right-hand side [RHS] of the ordinary differential equations [ODEs] to be solved
input:
• t - time variable [internal to solver]
• y - array holding concentrations of all compounds in both gas and particulate [molecules/cc]
output:
dydt - the dy_dt of each compound in both gas and particulate phase [molecules/cc.sec]
"""
dy_dt = numpy.zeros((total_length_y, 1), )
#pdb.set_trace()
# Calculate time of day
time_of_day_seconds = start_time + t
#pdb.set_trace()
# make sure the y array is not a list. Assimulo uses lists
y_asnumpy = numpy.array(y)
Model_temp = temp
#pdb.set_trace()
#Calculate the concentration of RO2 species, using an index file created during parsing
RO2 = numpy.sum(y[RO2_indices])
#Calculate reaction rate for each equation.
# Note that H2O will change in parcel mode
# The time_of_day_seconds is used for photolysis rates - need to change this if want constant values
rates = evaluate_rates_fortran(RO2, H2O, Model_temp,
time_of_day_seconds)
#pdb.set_trace()
# Calculate product of all reactants and stochiometry for each reaction [A^a*B^b etc]
reactants = reactants_fortran(y_asnumpy[0:num_species - 1])
#pdb.set_trace()
#Multiply product of reactants with rate coefficient to get reaction rate
reactants = numpy.multiply(reactants, rates)
#pdb.set_trace()
# Now use reaction rates with the loss_gain matri to calculate the final dydt for each compound
# With the assimulo solvers we need to output numpy arrays
dydt_gas = loss_gain_fortran(reactants)
#pdb.set_trace()
dy_dt[0:num_species - 1, 0] = dydt_gas
# Change the saturation vapour pressure of water
# Need to re-think the change of organic vapour pressures with temperature.
# At the moment this is kept constant as re-calulation using UManSysProp very slow
sat_vap_water = numpy.exp((-0.58002206E4 / Model_temp) + 0.13914993E1 - \
(0.48640239E-1 * Model_temp) + (0.41764768E-4 * (Model_temp**2.0E0))- \
(0.14452093E-7 * (Model_temp**3.0E0)) + (0.65459673E1 * numpy.log(Model_temp)))
sat_vp[-1] = (numpy.log10(sat_vap_water * 9.86923E-6))
Psat = numpy.power(10.0, sat_vp)
# Convert the concentration of each component in the gas phase into a partial pressure using the ideal gas law
# Units are Pascals
Pressure_gas = (y_asnumpy[0:num_species, ] /
NA) * 8.314E+6 * Model_temp #[using R]
core_mass_array = numpy.multiply(ycore_asnumpy / NA, core_molw_asnumpy)
####### Calculate the thermal conductivity of gases according to the new temperature ########
K_water_vapour = (
5.69 + 0.017 *
(Model_temp - 273.15)) * 1e-3 * 4.187 #[W/mK []has to be in W/m.K]
# Use this value for all organics, for now. If you start using a non-zero enthalpy of
# vapourisation, this needs to change.
therm_cond_air = K_water_vapour
#----------------------------------------------------------------------------
#F2c) Extract the current gas phase concentrations to be used in pressure difference calculations
C_g_i_t = y_asnumpy[0:num_species, ]
#Set the values for oxidants etc to 0 as will force no mass transfer
#C_g_i_t[ignore_index]=0.0
C_g_i_t = C_g_i_t[include_index]
#pdb.set_trace()
total_SOA_mass,aw_array,size_array,dy_dt_calc = dydt_partition_fortran(y_asnumpy,ycore_asnumpy,core_dissociation, \
core_mass_array,y_density_array_asnumpy,core_density_array_asnumpy,ignore_index_fortran,y_mw,Psat, \
DStar_org_asnumpy,alpha_d_org_asnumpy,C_g_i_t,N_perbin,gamma_gas_asnumpy,Latent_heat_asnumpy,GRAV, \
Updraft,sigma,NA,kb,Rv,R_gas,Model_temp,cp,Ra,Lv_water_vapour)
#pdb.set_trace()
# Add the calculated gains/losses to the complete dy_dt array
dy_dt[0:num_species + (num_species_condensed * num_bins),
0] += dy_dt_calc[:]
#pdb.set_trace()
#----------------------------------------------------------------------------
#F4) Now calculate the change in water vapour mixing ratio.
#To do this we need to know what the index key for the very last element is
#pdb.set_trace()
#pdb.set_trace()
#print "elapsed time=", elapsedTime
dydt_func.total_SOA_mass = total_SOA_mass
dydt_func.size_array = size_array
dydt_func.temp = Model_temp
dydt_func.RH = Pressure_gas[-1] / (Psat[-1] * 101325.0)
dydt_func.water_activity = aw_array
#----------------------------------------------------------------------------
return dy_dt
#-------------------------------------------------------------------------------------
#-------------------------------------------------------------------------------------
#import static compilation of Fortran functions for use in ODE solver
print("Importing pre-compiled Fortran modules")
from rate_coeff_f2py import evaluate_rates as evaluate_rates_fortran
from reactants_conc_f2py import reactants as reactants_fortran
from loss_gain_f2py import loss_gain as loss_gain_fortran
from partition_f2py import dydt_partition as dydt_partition_fortran
# 'Unpack' variables from input_dict
species_dict = input_dict['species_dict']
species_dict2array = input_dict['species_dict2array']
species_initial_conc = input_dict['species_initial_conc']
equations = input_dict['equations']
num_species = input_dict['num_species']
num_species_condensed = input_dict['num_species_condensed']
y_density_array_asnumpy = input_dict['y_density_array_asnumpy']
y_mw = input_dict['y_mw']
sat_vp = input_dict['sat_vp']
Delta_H = input_dict['Delta_H']
Latent_heat_asnumpy = input_dict['Latent_heat_asnumpy']
DStar_org_asnumpy = input_dict['DStar_org_asnumpy']
alpha_d_org_asnumpy = input_dict['alpha_d_org_asnumpy']
gamma_gas_asnumpy = input_dict['gamma_gas_asnumpy']
Updraft = input_dict['Updraft']
GRAV = input_dict['GRAV']
Rv = input_dict['Rv']
Ra = input_dict['Ra']
R_gas = input_dict['R_gas']
R_gas_other = input_dict['R_gas_other']
cp = input_dict['cp']
sigma = input_dict['sigma']
NA = input_dict['NA']
kb = input_dict['kb']
Lv_water_vapour = input_dict['Lv_water_vapour']
ignore_index = input_dict['ignore_index']
ignore_index_fortran = input_dict['ignore_index_fortran']
ycore_asnumpy = input_dict['ycore_asnumpy']
core_density_array_asnumpy = input_dict['core_density_array_asnumpy']
y_cond = input_dict['y_cond_initial']
num_bins = input_dict['num_bins']
core_molw_asnumpy = input_dict['core_molw_asnumpy']
core_dissociation = input_dict['core_dissociation']
N_perbin = input_dict['N_perbin']
include_index = input_dict['include_index']
# pdb.set_trace()
#Specify some starting concentrations [ppt]
Cfactor = 2.55e+10 #ppb-to-molecules/cc
# Create variables required to initialise ODE
y0 = [0] * (num_species + num_species_condensed * num_bins
) #Initial concentrations, set to 0
t0 = 0.0 #T0
# Define species concentrations in ppb fr the gas phase
# You have already set this in the front end script, and now we populate the y array with those concentrations
for specie in species_initial_conc.keys():
if specie is not 'H2O':
y0[species_dict2array[specie]] = species_initial_conc[
specie] * Cfactor #convert from pbb to molcules/cc
elif specie is 'H2O':
y0[species_dict2array[specie]] = species_initial_conc[specie]
# Now add the initial condensed phase [including water]
#pdb.set_trace()
y0[num_species:num_species +
((num_bins) * num_species_condensed)] = y_cond[:]
#pdb.set_trace()
#Set the total_time of the simulation to 0 [havent done anything yet]
total_time = 0.0
# Define a 'key' that represents the end of the composition variables to track
total_length_y = len(y0)
key = num_species + ((num_bins) * num_species) - 1
#pdb.set_trace()
# Now run through the simulation in batches.
# I do this to enable testing of coupling processes. Some initial investigations with non-ideality in
# the condensed phase indicated that even defining a maximum step was not enough for ODE solvers to
# overshoot a stable region. It also helps with in-simulation debugging. Its up to you if you want to keep this.
# To not run in batches, just define one batch as your total simulation time. This will reduce any overhead with
# initialising the solvers
# Set total simulation time and batch steps in seconds
# Note also that the current module outputs solver information after each batch step. This can be turned off and the
# the batch step change for increased speed
# simulation_time= 3600.0
# batch_step=300.0
t_array = []
time_step = 0
number_steps = int(
simulation_time /
batch_step) # Just cycling through 3 steps to get to a solution
# Define a matrix that stores values as outputs from the end of each batch step. Again, you can remove
# the need to run in batches. You can tell the Assimulo solvers the frequency of outputs.
y_matrix = numpy.zeros((int(number_steps), len(y0)))
# Also define arrays and matrices that hold information such as total SOA mass
SOA_matrix = numpy.zeros((int(number_steps), 1))
size_matrix = numpy.zeros((int(number_steps), num_bins))
print("Starting simulation")
# In the following, we can
while total_time < simulation_time:
if total_time == 0.0:
#Define an Assimulo problem
#Define an explicit solver
exp_mod = Explicit_Problem(dydt_func, y0, t0, name=filename)
else:
y0 = y_output[
-1, :] # Take the output from the last batch as the start of this
exp_mod = Explicit_Problem(dydt_func, y0, t0, name=filename)
# Define ODE parameters.
# Initial steps might be slower than mid-simulation. It varies.
#exp_mod.jac = dydt_jac
# Define which ODE solver you want to use
exp_sim = CVode(exp_mod)
tol_list = [1.0e-2] * len(y0)
exp_sim.atol = tol_list #Default 1e-6
exp_sim.rtol = 1.0e-4 #Default 1e-6
exp_sim.inith = 1.0e-6 #Initial step-size
#exp_sim.discr = 'Adams'
exp_sim.maxh = 100.0
# Use of a jacobian makes a big differece in simulation time. This is relatively
# easy to define for a gas phase - not sure for an aerosol phase with composition
# dependent processes.
exp_sim.usejac = False # To be provided as an option in future update.
#exp_sim.fac1 = 0.05
#exp_sim.fac2 = 50.0
exp_sim.report_continuously = True
exp_sim.maxncf = 1000
#Sets the parameters
t_output, y_output = exp_sim.simulate(
batch_step) #Simulate 'batch' seconds
total_time += batch_step
t_array.append(
total_time
) # Save the output from the end step, of the current batch, to a matrix
y_matrix[time_step, :] = y_output[-1, :]
SOA_matrix[time_step, 0] = dydt_func.total_SOA_mass
size_matrix[time_step, :] = dydt_func.size_array
print("SOA [micrograms/m3] = ", dydt_func.total_SOA_mass)
#now save this information into a matrix for later plotting.
time_step += 1
if save_output is True:
print(
"Saving the model output as a pickled object for later retrieval")
# save the dictionary to a file for later retrieval - have to do each seperately.
with open(filename + '_y_output.pickle', 'wb') as handle:
pickle.dump(y_matrix, handle, protocol=pickle.HIGHEST_PROTOCOL)
with open(filename + '_t_output.pickle', 'wb') as handle:
pickle.dump(t_array, handle, protocol=pickle.HIGHEST_PROTOCOL)
with open(filename + '_SOA_output.pickle', 'wb') as handle:
pickle.dump(SOA_matrix, handle, protocol=pickle.HIGHEST_PROTOCOL)
with open(filename + '_size_output.pickle', 'wb') as handle:
pickle.dump(size_matrix, handle, protocol=pickle.HIGHEST_PROTOCOL)
with open(filename + 'include_index.pickle', 'wb') as handle:
pickle.dump(include_index,
handle,
protocol=pickle.HIGHEST_PROTOCOL)
#pdb.set_trace()
#Plot the change in concentration over time for a given specie. For the user to change / remove
#In a future release I will add this as a seperate module
if plot_mass is True:
try:
P.plot(t_array, SOA_matrix[:, 0], marker='o')
P.title(exp_mod.name)
P.ylabel("SOA mass [micrograms/m3]")
P.xlabel("Time [seconds] since start of simulation")
P.show()
except:
print(
"There is a problem using Matplotlib in your environment. If using this within a docker container, you will need to transfer the data to the host or configure your container to enable graphical displays. More information can be found at http://wiki.ros.org/docker/Tutorials/GUI "
)
def run_example(with_plots=True):
r"""
This example shows how to use Assimulo and CVode for simulating sensitivities
for initial conditions.
.. math::
\dot y_1 &= -(k_{01}+k_{21}+k_{31}) y_1 + k_{12} y_2 + k_{13} y_3 + b_1\\
\dot y_2 &= k_{21} y_1 - (k_{02}+k_{12}) y_2 \\
\dot y_3 &= k_{31} y_1 - k_{13} y_3
with the parameter dependent inital conditions
:math:`y_1(0) = 0, y_2(0) = 0, y_3(0) = 0` . The initial values are taken as parameters :math:`p_1,p_2,p_3`
for the computation of the sensitivity matrix,
see http://sundials.2283335.n4.nabble.com/Forward-sensitivities-for-initial-conditions-td3239724.html
on return:
- :dfn:`exp_mod` problem instance
- :dfn:`exp_sim` solver instance
"""
def f(t, y, p):
y1, y2, y3 = y
k01 = 0.0211
k02 = 0.0162
k21 = 0.0111
k12 = 0.0124
k31 = 0.0039
k13 = 0.000035
b1 = 49.3
yd_0 = -(k01 + k21 + k31) * y1 + k12 * y2 + k13 * y3 + b1
yd_1 = k21 * y1 - (k02 + k12) * y2
yd_2 = k31 * y1 - k13 * y3
return N.array([yd_0, yd_1, yd_2])
#The initial conditions
y0 = [0.0, 0.0, 0.0] #Initial conditions for y
p0 = [0.0, 0.0, 0.0] #Initial conditions for parameters
yS0 = N.array([[1, 0, 0], [0, 1, 0], [0, 0, 1.]])
#Create an Assimulo explicit problem
exp_mod = Explicit_Problem(f,
y0,
p0=p0,
name='Example: Computing Sensitivities')
#Sets the options to the problem
exp_mod.yS0 = yS0
#Create an Assimulo explicit solver (CVode)
exp_sim = CVode(exp_mod)
#Sets the paramters
exp_sim.iter = 'Newton'
exp_sim.discr = 'BDF'
exp_sim.rtol = 1e-7
exp_sim.atol = 1e-6
exp_sim.pbar = [
1, 1, 1
] #pbar is used to estimate the tolerances for the parameters
exp_sim.report_continuously = True #Need to be able to store the result using the interpolate methods
exp_sim.sensmethod = 'SIMULTANEOUS' #Defines the sensitvity method used
exp_sim.suppress_sens = False #Dont suppress the sensitivity variables in the error test.
#Simulate
t, y = exp_sim.simulate(400) #Simulate 400 seconds
#Basic test
nose.tools.assert_almost_equal(y[-1][0], 1577.6552477, 5)
nose.tools.assert_almost_equal(y[-1][1], 611.9574565, 5)
nose.tools.assert_almost_equal(y[-1][2], 2215.88563217, 5)
nose.tools.assert_almost_equal(exp_sim.p_sol[0][1][0], 1.0)
#Plot
if with_plots:
title_text = r"Sensitivity w.r.t. ${}$"
legend_text = r"$\mathrm{{d}}{}/\mathrm{{d}}{}$"
P.figure(1)
P.subplot(221)
P.plot(t,
N.array(exp_sim.p_sol[0])[:, 0], t,
N.array(exp_sim.p_sol[0])[:, 1], t,
N.array(exp_sim.p_sol[0])[:, 2])
P.title(title_text.format('p_1'))
P.legend((legend_text.format('y_1',
'p_1'), legend_text.format('y_1', 'p_2'),
legend_text.format('y_1', 'p_3')))
P.subplot(222)
P.plot(t,
N.array(exp_sim.p_sol[1])[:, 0], t,
N.array(exp_sim.p_sol[1])[:, 1], t,
N.array(exp_sim.p_sol[1])[:, 2])
P.title(title_text.format('p_2'))
P.legend((legend_text.format('y_2',
'p_1'), legend_text.format('y_2', 'p_2'),
legend_text.format('y_2', 'p_3')))
P.subplot(223)
P.plot(t,
N.array(exp_sim.p_sol[2])[:, 0], t,
N.array(exp_sim.p_sol[2])[:, 1], t,
N.array(exp_sim.p_sol[2])[:, 2])
P.title(title_text.format('p_3'))
P.legend((legend_text.format('y_3',
'p_1'), legend_text.format('y_3', 'p_2'),
legend_text.format('y_3', 'p_3')))
P.subplot(224)
P.title('ODE Solution')
P.plot(t, y)
P.suptitle(exp_mod.name)
P.show()
return exp_mod, exp_sim
def run_example(with_plots=True):
"""
This is the same example from the Sundials package (cvsRoberts_FSA_dns.c)
This simple example problem for CVode, due to Robertson,
is from chemical kinetics, and consists of the following three
equations:
.. math::
\dot y_1 &= -p_1 y_1 + p_2 y_2 y_3 \\
\dot y_2 &= p_1 y_1 - p_2 y_2 y_3 - p_3 y_2^2 \\
\dot y_3 &= p_3 y_2^2
on return:
- :dfn:`exp_mod` problem instance
- :dfn:`exp_sim` solver instance
"""
def f(t, y, p):
p3 = 3.0e7
yd_0 = -p[0] * y[0] + p[1] * y[1] * y[2]
yd_1 = p[0] * y[0] - p[1] * y[1] * y[2] - p3 * y[1]**2
yd_2 = p3 * y[1]**2
return N.array([yd_0, yd_1, yd_2])
#The initial conditions
y0 = [1.0, 0.0, 0.0] #Initial conditions for y
#Create an Assimulo explicit problem
exp_mod = Explicit_Problem(f,
y0,
name='Sundials test example: Chemical kinetics')
#Sets the options to the problem
exp_mod.p0 = [0.040, 1.0e4] #Initial conditions for parameters
exp_mod.pbar = [0.040, 1.0e4]
#Create an Assimulo explicit solver (CVode)
exp_sim = CVode(exp_mod)
#Sets the paramters
exp_sim.iter = 'Newton'
exp_sim.discr = 'BDF'
exp_sim.rtol = 1.e-4
exp_sim.atol = N.array([1.0e-8, 1.0e-14, 1.0e-6])
exp_sim.sensmethod = 'SIMULTANEOUS' #Defines the sensitvity method used
exp_sim.suppress_sens = False #Dont suppress the sensitivity variables in the error test.
exp_sim.report_continuously = True
#Simulate
t, y = exp_sim.simulate(
4, 400) #Simulate 4 seconds with 400 communication points
#Plot
if with_plots:
import pylab as P
P.plot(t, y)
P.xlabel('Time')
P.ylabel('State')
P.title(exp_mod.name)
P.show()
#Basic test
nose.tools.assert_almost_equal(y[-1][0], 9.05518032e-01, 4)
nose.tools.assert_almost_equal(y[-1][1], 2.24046805e-05, 4)
nose.tools.assert_almost_equal(y[-1][2], 9.44595637e-02, 4)
nose.tools.assert_almost_equal(
exp_sim.p_sol[0][-1][0], -1.8761,
2) #Values taken from the example in Sundials
nose.tools.assert_almost_equal(exp_sim.p_sol[1][-1][0], 2.9614e-06, 8)
return exp_mod, exp_sim
def run_simulation(filename, start_time, save_output, temp, RH, RO2_indices,
H2O, input_dict, simulation_time, batch_step):
from assimulo.solvers import RodasODE, CVode #Choose solver accoring to your need.
from assimulo.problem import Explicit_Problem
# In this function, we import functions that have been pre-compiled for use in the ODE solver
# The function that calculates the RHS of the ODE is also defined within this function, such
# that it can be used by the Assimulo solvers
# The variables passed to this function are defined as follows:
#-------------------------------------------------------------------------------------
# define the ODE function to be called
def dydt_func(t, y):
"""
This function defines the right-hand side [RHS] of the ordinary differential equations [ODEs] to be solved
input:
• t - time variable [internal to solver]
• y - array holding concentrations of all compounds in both gas and particulate [molecules/cc]
output:
dydt - the dy_dt of each compound in both gas and particulate phase [molecules/cc.sec]
"""
#pdb.set_trace()
# Calculate time of day
time_of_day_seconds = start_time + t
# make sure the y array is not a list. Assimulo uses lists
y_asnumpy = numpy.array(y)
#Calculate the concentration of RO2 species, using an index file created during parsing
RO2 = numpy.sum(y[RO2_indices])
#Calculate reaction rate for each equation.
# Note that H2O will change in parcel mode
# The time_of_day_seconds is used for photolysis rates - need to change this if want constant values
rates = evaluate_rates_fortran(RO2, H2O, temp, time_of_day_seconds)
#pdb.set_trace()
# Calculate product of all reactants and stochiometry for each reaction [A^a*B^b etc]
reactants = reactants_fortran(y_asnumpy)
#pdb.set_trace()
#Multiply product of reactants with rate coefficient to get reaction rate
reactants = numpy.multiply(reactants, rates)
#pdb.set_trace()
# Now use reaction rates with the loss_gain matri to calculate the final dydt for each compound
# With the assimulo solvers we need to output numpy arrays
dydt = loss_gain_fortran(reactants)
#pdb.set_trace()
return dydt
#-------------------------------------------------------------------------------------
#-------------------------------------------------------------------------------------
# define jacobian function to be called
def jacobian(t, y):
"""
This function defines Jacobian of the ordinary differential equations [ODEs] to be solved
input:
• t - time variable [internal to solver]
• y - array holding concentrations of all compounds in both gas and particulate [molecules/cc]
output:
dydt_dydt - the N_compounds x N_compounds matrix of Jacobian values
"""
# Different solvers might call jacobian at different stages, so we have to redo some calculations here
# Calculate time of day
time_of_day_seconds = start_time + t
# make sure the y array is not a list. Assimulo uses lists
y_asnumpy = numpy.array(y)
#Calculate the concentration of RO2 species, using an index file created during parsing
RO2 = numpy.sum(y[RO2_indices])
#Calculate reaction rate for each equation.
# Note that H2O will change in parcel mode
rates = evaluate_rates_fortran(RO2, H2O, temp, time_of_day_seconds)
#pdb.set_trace()
# Now use reaction rates with the loss_gain matrix to calculate the final dydt for each compound
# With the assimulo solvers we need to output numpy arrays
dydt_dydt = jacobian_fortran(rates, y_asnumpy)
#pdb.set_trace()
return dydt_dydt
#-------------------------------------------------------------------------------------
#import static compilation of Fortran functions for use in ODE solver
print("Importing pre-compiled Fortran modules")
from rate_coeff_f2py import evaluate_rates as evaluate_rates_fortran
from reactants_conc_f2py import reactants as reactants_fortran
from loss_gain_f2py import loss_gain as loss_gain_fortran
from jacobian_f2py import jacobian as jacobian_fortran
# 'Unpack' variables from input_dict
species_dict = input_dict['species_dict']
species_dict2array = input_dict['species_dict2array']
species_initial_conc = input_dict['species_initial_conc']
equations = input_dict['equations']
#Specify some starting concentrations [ppt]
Cfactor = 2.55e+10 #ppb-to-molecules/cc
# Create variables required to initialise ODE
num_species = len(species_dict.keys())
y0 = [0] * num_species #Initial concentrations, set to 0
t0 = 0.0 #T0
# Define species concentrations in ppb
# You have already set this in the front end script, and now we populate the y array with those concentrations
for specie in species_initial_conc.keys():
y0[species_dict2array[specie]] = species_initial_conc[
specie] * Cfactor #convert from pbb to molcules/cc
#Set the total_time of the simulation to 0 [havent done anything yet]
total_time = 0.0
# Now run through the simulation in batches.
# I do this to enable testing of coupling processes. Some initial investigations with non-ideality in
# the condensed phase indicated that even defining a maximum step was not enough for ODE solvers to
# overshoot a stable region. It also helps with in-simulation debugging. Its up to you if you want to keep this.
# To not run in batches, just define one batch as your total simulation time. This will reduce any overhead with
# initialising the solvers
# Set total simulation time and batch steps in seconds
# Note also that the current module outputs solver information after each batch step. This can be turned off and the
# the batch step change for increased speed
#simulation_time= 3600.0
#batch_step=100.0
t_array = []
time_step = 0
number_steps = int(
simulation_time /
batch_step) # Just cycling through 3 steps to get to a solution
# Define a matrix that stores values as outputs from the end of each batch step. Again, you can remove
# the need to run in batches. You can tell the Assimulo solvers the frequency of outputs.
y_matrix = numpy.zeros((int(number_steps), len(y0)))
print("Starting simulation")
# In the following, we can
while total_time < simulation_time:
if total_time == 0.0:
#Define an Assimulo problem
#Define an explicit solver
exp_mod = Explicit_Problem(dydt_func, y0, t0, name=filename)
else:
y0 = y_output[
-1, :] # Take the output from the last batch as the start of this
exp_mod = Explicit_Problem(dydt_func, y0, t0, name=filename)
# Define ODE parameters.
# Initial steps might be slower than mid-simulation. It varies.
#exp_mod.jac = dydt_jac
# Define which ODE solver you want to use
exp_sim = CVode(exp_mod)
tol_list = [1.0e-3] * num_species
exp_sim.atol = tol_list #Default 1e-6
exp_sim.rtol = 0.03 #Default 1e-6
exp_sim.inith = 1.0e-6 #Initial step-size
#exp_sim.discr = 'Adams'
exp_sim.maxh = 100.0
# Use of a jacobian makes a big differece in simulation time. This is relatively
# easy to define for a gas phase - not sure for an aerosol phase with composition
# dependent processes.
exp_sim.usejac = True # To be provided as an option in future update.
#exp_sim.fac1 = 0.05
#exp_sim.fac2 = 50.0
exp_sim.report_continuously = True
exp_sim.maxncf = 1000
#Sets the parameters
t_output, y_output = exp_sim.simulate(
batch_step) #Simulate 'batch' seconds
total_time += batch_step
t_array.append(
total_time
) # Save the output from the end step, of the current batch, to a matrix
y_matrix[time_step, :] = y_output[-1, :]
#now save this information into a matrix for later plotting.
time_step += 1
# Do you want to save the generated matrix of outputs?
if save_output:
numpy.save(filename + '_output', y_matrix)
df = pd.DataFrame(y_matrix)
df.to_csv(filename + "_output_matrix.csv")
w = csv.writer(open(filename + "_output_names.csv", "w"))
for specie, number in species_dict2array.items():
w.writerow([specie, number])
with_plots = True
#pdb.set_trace()
#Plot the change in concentration over time for a given specie. For the user to change / remove
#In a future release I will add this as a seperate module
if with_plots:
try:
P.plot(t_array,
numpy.log10(y_matrix[:, species_dict2array['APINENE']]),
marker='o',
label="APINENE")
P.plot(t_array,
numpy.log10(y_matrix[:, species_dict2array['PINONIC']]),
marker='o',
label="PINONIC")
P.title(exp_mod.name)
P.legend(loc='upper left')
P.ylabel("Concetration log10[molecules/cc]")
P.xlabel("Time [seconds] since start of simulation")
P.show()
except:
print(
"There is a problem using Matplotlib in your environment. If using this within a docker container, you will need to transfer the data to the host or configure your container to enable graphical displays. More information can be found at http://wiki.ros.org/docker/Tutorials/GUI "
)
def simulate(self, Tend, nIntervals, gridWidth):
# define assimulo problem:(has to be done here because of the starting value in Explicit_Problem
solver = Explicit_Problem(self.rhs, self.y0)
''' *******DELETE LATER '''''''''
# problem.handle_event = handle_event
# problem.state_events = state_events
# problem.init_mode = init_mode
solver.handle_result = self.handle_result
solver.name = 'Simple Explicit Example'
simulation = CVode(solver) # Create a RungeKutta34 solver
# simulation.inith = 0.1 #Sets the initial step, default = 0.01
# Change multistep method: 'adams' or 'VDF'
if self.discr == 'Adams':
simulation.discr = 'Adams'
simulation.maxord = 12
else:
simulation.discr = 'BDF'
simulation.maxord = 5
# Change iteration algorithm: functional(FixedPoint) or newton
if self.iter == 'FixedPoint':
simulation.iter = 'FixedPoint'
else:
simulation.iter = 'Newton'
# Sets additional parameters
simulation.atol = self.atol
simulation.rtol = self.rtol
simulation.verbosity = 0
if hasattr(simulation, 'continuous_output'):
simulation.continuous_output = False # default 0, if one step approach should be used
elif hasattr(simulation, 'report_continuously'):
simulation.report_continuously = False # default 0, if one step approach should be used
# Create Solver and set settings
# noRootFunctions = np.size(self.state_events(self.t0, np.array(self.y0)))
# solver = sundials.CVodeSolver(RHS = self.f, ROOT = self.rootf, SW = [False]*noRootFunctions,
# abstol = self.atol, reltol = self.rtol)
# solver.settings.JAC = None #Add user-dependent jacobian here
'''Initialize problem '''
# solver.init(self.t0, self.y0)
self.handle_result(self.t0, self.y0)
nextTimeEvent = self.time_events(self.t0, self.y0)
self.t_cur = self.t0
self.y_cur = self.y0
state_event = False
#
#
if gridWidth <> None:
nOutputIntervals = int((Tend - self.t0) / gridWidth)
else:
nOutputIntervals = nIntervals
# Define step length depending on if gridWidth or nIntervals has been chosen
if nOutputIntervals > 0:
# Last point on grid (does not have to be Tend:)
if(gridWidth <> None):
dOutput = gridWidth
else:
dOutput = (Tend - self.t0) / nIntervals
else:
dOutput = Tend
outputStepCounter = long(1)
nextOutputPoint = min(self.t0 + dOutput, Tend)
while self.t_cur < Tend:
# Time-Event detection and step time adjustment
if nextTimeEvent is None or nextOutputPoint < nextTimeEvent:
time_event = False
self.t_cur = nextOutputPoint
else:
time_event = True
self.t_cur = nextTimeEvent
try:
# #Integrator step
# self.y_cur = solver.step(self.t_cur)
# self.y_cur = np.array(self.y_cur)
# state_event = False
# Simulate
# take a step to next output point:
t_new, y_new = simulation.simulate(self.t_cur) # 5, 10) #5, 10 self.t_cur self.t_cur 2. argument nsteps Simulate 5 seconds
# t_new, y_new are both vectors of the time and states at t_cur and all intermediate
# points before it! So take last values:
self.t_cur = t_new[-1]
self.y_cur = y_new[-1]
state_event = False
except:
import sys
print "Unexpected error:", sys.exc_info()[0]
# except CVodeRootException, info:
# self.t_cur = info.t
# self.y_cur = info.y
# self.y_cur = np.array(self.y_cur)
# time_event = False
# state_event = True
#
#
# Depending on events have been detected do different tasks
if time_event or state_event:
event_info = [state_event, time_event]
if not self.handle_event(self, event_info):
break
solver.init(self.t_cur, self.y_cur)
nextTimeEvent = self.time_events(self.t_cur, self.y_cur)
# If no timeEvent happens:
if nextTimeEvent <= self.t_cur:
nextTimeEvent = None
if self.t_cur == nextOutputPoint:
# Write output if not happened before:
if not time_event and not state_event:
self.handle_result(nextOutputPoint, self.y_cur)
outputStepCounter += 1
nextOutputPoint = min(self.t0 + outputStepCounter * dOutput, Tend)
self.finalize()
def run_simulation(filename, save_output, start_time, temp, RH, RO2_indices,
H2O, input_dict, simulation_time, batch_step):
from assimulo.solvers import RodasODE, CVode #Choose solver accoring to your need.
from assimulo.problem import Explicit_Problem
# In this function, we import functions that have been pre-compiled for use in the ODE solver
# The function that calculates the RHS of the ODE is also defined within this function, such
# that it can be used by the Assimulo solvers
# In the standard Python version [not using Numba] I use Sparse matrix operations in calculating loss/gain of each compound.
# This function loads the matrix created at the beginning of the module.
def load_sparse_csr(filename):
loader = numpy.load('loss_gain_' + filename + '.npz')
return csr_matrix(
(loader['data'], loader['indices'], loader['indptr']),
shape=loader['shape'])
def load_sparse_csr_reactants(filename):
loader = numpy.load('reactants_indices_sparse_' + filename + '.npz')
return csr_matrix(
(loader['data'], loader['indices'], loader['indptr']),
shape=loader['shape'])
#-------------------------------------------------------------------------------------
# define the ODE function to be called
def dydt_func(t, y):
"""
This function defines the right-hand side [RHS] of the ordinary differential equations [ODEs] to be solved
input:
• t - time variable [internal to solver]
• y - array holding concentrations of all compounds in both gas and particulate [molecules/cc]
output:
dydt - the dy_dt of each compound in both gas and particulate phase [molecules/cc.sec]
"""
#pdb.set_trace()
#Here we use the pre-created Numba based functions to arrive at our value for dydt
# Calculate time of day
time_of_day_seconds = start_time + t
# make sure the y array is not a list. Assimulo uses lists
y_asnumpy = numpy.array(y)
#pdb.set_trace()
# reactants=numpy.zeros((equations),)
#pdb.set_trace()
#Calculate the concentration of RO2 species, using an index file created during parsing
RO2 = numpy.sum(y[RO2_indices])
#Calculate reaction rate for each equation.
# Note that H2O will change in parcel mode [to be changed in the full aerosol mode]
# The time_of_day_seconds is used for photolysis rates - need to change this if want constant values
#pdb.set_trace()
rates = evaluate_rates(time_of_day_seconds, RO2, H2O, temp,
numpy.zeros((equations)), numpy.zeros((63)))
# Calculate product of all reactants and stochiometry for each reaction [A^a*B^b etc]
reactants = reactant_product(y_asnumpy, equations,
numpy.zeros((equations)))
#Multiply product of reactants with rate coefficient to get reaction rate
#pdb.set_trace()
reactants = numpy.multiply(reactants, rates)
# Now use reaction rates with the loss_gain information in a pre-created Numba file to calculate the final dydt for each compound
dydt = dydt_eval(numpy.zeros((len(y_asnumpy))), reactants)
#pdb.set_trace()
############ Development place-holder ##############
# ----------------------------------------------------------------------------------
# The following demonstrates the same procedure but using only Numpy and pure python
# For the full MCM this is too slow, but is useful for demonstrations and testing
#Calculate reaction rate for each equation.
## rates=test(time_of_day_seconds,RO2,H2O,temp)
# Calculate product of all reactants and stochiometry for each reaction [A^a*B^b etc]
# Take the approach of using sparse matrix operations from a python perspective
# This approach uses the rule of logarithms and sparse matrix multiplication
##temp_array=reactants_indices_sparse @ numpy.log(y_asnumpy)
##indices=numpy.where(temp_array > 0.0)
##reactants[indices]=numpy.exp(temp_array[indices])
#Multiply product of reactants with rate coefficient to get reaction rate
## reactants = numpy.multiply(reactants,rates)
# Now use reaction rates with the loss_gain matri to calculate the final dydt for each compound
# With the assimulo solvers we need to output numpy arrays
##dydt=numpy.array(loss_gain @ reactants)
# ----------------------------------------------------------------------------------
return dydt
#-------------------------------------------------------------------------------------
print(
"Importing Numba modules [compiling if first import or clean build...please be patient]"
)
#import Numba functions for use in ODE solver
from Rate_coefficients_numba import evaluate_rates
from Reactants_conc_numba import reactants as reactant_product
from Loss_Gain_numba import dydt as dydt_eval
# 'Unpack' variables from input_dict
species_dict = input_dict['species_dict']
species_dict2array = input_dict['species_dict2array']
species_initial_conc = input_dict['species_initial_conc']
equations = input_dict['equations']
# Set dive by zero to ignore for use of any sparse matrix multiplication
numpy.errstate(divide='ignore')
# --- For Numpy and pure Python runs ----
# Load the sparse matrix used in calculating the reactant products and dydt function
## reactants_indices_sparse = load_sparse_csr_reactants(filename)
## loss_gain = load_sparse_csr(filename)
#Specify some starting concentrations [ppt]
Cfactor = 2.55e+10 #ppb-to-molecules/cc
# Create variables required to initialise ODE
num_species = len(species_dict.keys())
y0 = [0] * num_species #Initial concentrations, set to 0
t0 = 0.0 #T0
# Define species concentrations in ppb
# You have already set this in the front end script, and now we populate the y array with those concentrations
for specie in species_initial_conc.keys():
y0[species_dict2array[specie]] = species_initial_conc[
specie] * Cfactor #convert from pbb to molcules/cc
#Set the total_time of the simulation to 0 [havent done anything yet]
total_time = 0.0
# Now run through the simulation in batches.
# I do this to enable testing of coupling processes. Some initial investigations with non-ideality in
# the condensed phase indicated that even defining a maximum step was not enough for ODE solvers to
# overshoot a stable region. It also helps with in-simulation debugging. Its up to you if you want to keep this.
# To not run in batches, just define one batch as your total simulation time. This will reduce any overhead with
# initialising the solvers
# Set total simulation time and batch steps in seconds
# Note also that the current module outputs solver information after each batch step. This can be turned off and the
# the batch step change for increased speed
# simulation_time= 3600.0 # seconds
# batch_step=100.0 # seconds
t_array = []
time_step = 0
number_steps = int(
simulation_time /
batch_step) # Just cycling through 3 steps to get to a solution
# Define a matrix that stores values as outputs from the end of each batch step. Again, you can remove
# the need to run in batches. You can tell the Assimulo solvers the frequency of outputs.
y_matrix = numpy.zeros((int(number_steps), len(y0)))
print("Starting simulation")
#pdb.set_trace()
while total_time < simulation_time:
if total_time == 0.0:
#Define an Assimulo problem
#Define an explicit solver
#pdb.set_trace()
exp_mod = Explicit_Problem(dydt_func, y0, t0, name=filename)
else:
y0 = y_output[
-1, :] # Take the output from the last batch as the start of this
exp_mod = Explicit_Problem(dydt_func, y0, t0, name=filename)
# Define ODE parameters.
# Initial steps might be slower than mid-simulation. It varies.
#exp_mod.jac = dydt_jac
# Define which ODE solver you want to use
exp_sim = CVode(exp_mod)
tol_list = [1.0e-3] * num_species
exp_sim.atol = tol_list #Default 1e-6
exp_sim.rtol = 1e-6 #Default 1e-6
exp_sim.inith = 1.0e-6 #Initial step-size
#exp_sim.discr = 'Adams'
exp_sim.maxh = 100.0
# Use of a jacobian makes a big differece in simulation time. This is relatively
# easy to define for a gas phase - not sure for an aerosol phase with composition
# dependent processes.
exp_sim.usejac = False # To be provided as an option in future update. See Fortran variant for use of Jacobian
#exp_sim.fac1 = 0.05
#exp_sim.fac2 = 50.0
exp_sim.report_continuously = True
exp_sim.maxncf = 1000
#Sets the parameters
t_output, y_output = exp_sim.simulate(
batch_step) #Simulate 'batch' seconds
total_time += batch_step
t_array.append(
total_time
) # Save the output from the end step, of the current batch, to a matrix
y_matrix[time_step, :] = y_output[-1, :]
#pdb.set_trace()
#now save this information into a matrix for later plotting.
time_step += 1
# Do you want to save the generated matrix of outputs?
if save_output:
numpy.save(filename + '_output', y_matrix)
df = pd.DataFrame(y_matrix)
df.to_csv(filename + "_output_matrix.csv")
w = csv.writer(open(filename + "_output_names.csv", "w"))
for specie, number in species_dict2array.items():
w.writerow([specie, number])
with_plots = True
#pdb.set_trace()
#Plot the change in concentration over time for a given specie. For the user to change / remove
#In a future release I will add this as a seperate module
if with_plots:
try:
P.plot(t_array,
numpy.log10(y_matrix[:, species_dict2array['APINENE']]),
marker='o',
label="APINENE")
P.plot(t_array,
numpy.log10(y_matrix[:, species_dict2array['PINONIC']]),
marker='o',
label="PINONIC")
P.title(exp_mod.name)
P.legend(loc='upper left')
P.ylabel("Concetration log10[molecules/cc]")
P.xlabel("Time [seconds] since start of simulation")
P.show()
except:
print(
"There is a problem using Matplotlib in your environment. If using this within a docker container, you will need to transfer the data to the host or configure your container to enable graphical displays. More information can be found at http://wiki.ros.org/docker/Tutorials/GUI "
)
def run_example(with_plots=True):
r"""
This is the same example from the Sundials package (cvsRoberts_FSA_dns.c)
Its purpose is to demonstrate the use of parameters in the differential equation.
This simple example problem for CVode, due to Robertson
see http://www.dm.uniba.it/~testset/problems/rober.php,
is from chemical kinetics, and consists of the system:
.. math::
\dot y_1 &= -p_1 y_1 + p_2 y_2 y_3 \\
\dot y_2 &= p_1 y_1 - p_2 y_2 y_3 - p_3 y_2^2 \\
\dot y_3 &= p_3 y_ 2^2
on return:
- :dfn:`exp_mod` problem instance
- :dfn:`exp_sim` solver instance
"""
def f(t, y, p):
yd_0 = -p[0]*y[0]+p[1]*y[1]*y[2]
yd_1 = p[0]*y[0]-p[1]*y[1]*y[2]-p[2]*y[1]**2
yd_2 = p[2]*y[1]**2
return N.array([yd_0,yd_1,yd_2])
def jac(t,y, p):
J = N.array([[-p[0], p[1]*y[2], p[1]*y[1]],
[p[0], -p[1]*y[2]-2*p[2]*y[1], -p[1]*y[1]],
[0.0, 2*p[2]*y[1],0.0]])
return J
def fsens(t, y, s, p):
J = N.array([[-p[0], p[1]*y[2], p[1]*y[1]],
[p[0], -p[1]*y[2]-2*p[2]*y[1], -p[1]*y[1]],
[0.0, 2*p[2]*y[1],0.0]])
P = N.array([[-y[0],y[1]*y[2],0],
[y[0], -y[1]*y[2], -y[1]**2],
[0,0,y[1]**2]])
return J.dot(s)+P
#The initial conditions
y0 = [1.0,0.0,0.0] #Initial conditions for y
#Create an Assimulo explicit problem
exp_mod = Explicit_Problem(f,y0, name='Robertson Chemical Kinetics Example')
exp_mod.rhs_sens = fsens
exp_mod.jac = jac
#Sets the options to the problem
exp_mod.p0 = [0.040, 1.0e4, 3.0e7] #Initial conditions for parameters
exp_mod.pbar = [0.040, 1.0e4, 3.0e7]
#Create an Assimulo explicit solver (CVode)
exp_sim = CVode(exp_mod)
#Sets the solver paramters
exp_sim.iter = 'Newton'
exp_sim.discr = 'BDF'
exp_sim.rtol = 1.e-4
exp_sim.atol = N.array([1.0e-8, 1.0e-14, 1.0e-6])
exp_sim.sensmethod = 'SIMULTANEOUS' #Defines the sensitvity method used
exp_sim.suppress_sens = False #Dont suppress the sensitivity variables in the error test.
exp_sim.report_continuously = True
#Simulate
t, y = exp_sim.simulate(4,400) #Simulate 4 seconds with 400 communication points
#Basic test
nose.tools.assert_almost_equal(y[-1][0], 9.05518032e-01, 4)
nose.tools.assert_almost_equal(y[-1][1], 2.24046805e-05, 4)
nose.tools.assert_almost_equal(y[-1][2], 9.44595637e-02, 4)
nose.tools.assert_almost_equal(exp_sim.p_sol[0][-1][0], -1.8761, 2) #Values taken from the example in Sundials
nose.tools.assert_almost_equal(exp_sim.p_sol[1][-1][0], 2.9614e-06, 8)
nose.tools.assert_almost_equal(exp_sim.p_sol[2][-1][0], -4.9334e-10, 12)
#Plot
if with_plots:
P.plot(t, y)
P.title(exp_mod.name)
P.xlabel('Time')
P.ylabel('State')
P.show()
return exp_mod, exp_sim
