def rule_odes(m, t):
exprs = dict()
exprs['A'] = -m.P['k1'] * m.Z[t, 'A']
exprs['B'] = m.P['k1'] * m.Z[t, 'A'] - m.P['k2'] * m.Z[t, 'B']
exprs['C'] = m.P['k2'] * m.Z[t, 'B']
exprs['D'] = -m.P['k3'] * m.Z[t, 'D']
exprs['E'] = m.P['k3'] * m.Z[t, 'D']
return exprs
# As with other multiple experiments KIPET examples, we have different TemplateBuilders for
# each of the experiments.
builder1.set_odes_rule(rule_odes)
# In this example, it is useful to bound the profiles to stop the components with 0 concentration,
# i.e. D and E, from having very large absorbances.
builder1.bound_profile(var='S', bounds=(0, 10))
#=========================================================================
# EXPERIMENT 2 and 3
#=========================================================================
builder2 = TemplateBuilder()
components2 = {'A': 3e-3, 'B': 0, 'C': 0, 'D': 1e-3, 'E': 0}
builder2.add_mixture_component(components2)
builder2.add_parameter('k1', init=1.5, bounds=(0.001, 10))
#There is also the option of providing initial values: Just add init=... as additional argument as above.
builder2.add_parameter('k2', init=0.2, bounds=(0.0001, 1))
builder2.add_parameter('k3', init=0.6, bounds=(0.3, 2))
# Additionally, we do not add the spectral data to the TemplateBuilder, rather supplying the
# TemplateBuilder before data is added as an argument into the function
builder.add_parameter('k1', init=2.0, bounds=(1.0,5.0))
#There is also the option of providing initial values: Just add init=... as additional argument as above.
builder.add_parameter('k2',init = 0.2, bounds=(0.0,1))
builder.add_spectral_data(D_frame)
# define explicit system of ODEs
def rule_odes(m,t):
exprs = dict()
exprs['A'] = -m.P['k1']*m.Z[t,'A']
exprs['B'] = m.P['k1']*m.Z[t,'A']-m.P['k2']*m.Z[t,'B']
exprs['C'] = m.P['k2']*m.Z[t,'B']
return exprs
builder.set_odes_rule(rule_odes)
builder.bound_profile(var = 'S', bounds = (0,200))
opt_model = builder.create_pyomo_model(0.0,10.0)
#=========================================================================
#USER INPUT SECTION - VARIANCE ESTIMATION
#=========================================================================
# For this problem we have an input D matrix that has some noise in it
# We can therefore use the variance estimator described in the Overview section
# of the documentation and Section 4.3.3
v_estimator = VarianceEstimator(opt_model)
v_estimator.apply_discretization('dae.collocation',nfe=100,ncp=3,scheme='LAGRANGE-RADAU')
# It is often requried for larger problems to give the solver some direct instructions
# These must be given in the form of a dictionary
options = {}
# While this problem should solve without changing the deault options, example code is
# define explicit system of ODEs
def rule_odes(m, t):
exprs = dict()
exprs['A'] = -m.P['k1'] * m.Z[t, 'A']
exprs['B'] = m.P['k1'] * m.Z[t, 'A'] - m.P['k2'] * m.Z[t, 'B']
exprs['C'] = m.P['k2'] * m.Z[t, 'B']
return exprs
builder.set_odes_rule(rule_odes)
# if we know that a certain concentration or absorbance cannot be higher than a certain value
# and we wish to constrain the variable with some bound then we can use the following approach:
#Please note that by adding in additional bounds and constraints
builder.bound_profile(var='S', comp='B', bounds=(0, 200))
builder.bound_profile(var='S',
comp='A',
bounds=(50, 65),
profile_range=(1650, 1800))
builder.bound_profile(var='C',
comp='B',
bounds=(0.00, 0.00022),
profile_range=(0, 2))
# here the function arguments are for which profile, which component, the bounds that you wish to set
# and finally the profile_range over which to set the bound (i.e. wavelength or time). Also not that the
# function is called before the create_pyomo_model and also that if all component profiles should be bounded
# we can use:
# builder.bound_profile(var = 'S', bounds = (0,200))
