def test_jacobian(self): """ Unit test for the jacobian function: Solve a reaction system and check if the analytical jacobian matches the finite difference jacobian """ coreSpecies = [self.CH4,self.CH3,self.C2H6,self.C2H5] edgeSpecies = [] rxn1 = Reaction(reactants=[self.C2H6,self.CH3], products=[self.C2H5,self.CH4], kinetics=Arrhenius(A=(686.375*6,'m^3/(mol*s)'), n=4.40721, Ea=(7.82799,'kcal/mol'), T0=(298.15,'K'))) coreReactions = [rxn1] edgeReactions = [] numCoreSpecies = len(coreSpecies) rxnList = [] rxnList.append(Reaction(reactants=[self.C2H6], products=[self.CH3,self.CH3], kinetics=Arrhenius(A=(686.375*6,'1/s'), n=4.40721, Ea=(7.82799,'kcal/mol'), T0=(298.15,'K')))) rxnList.append(Reaction(reactants=[self.CH3,self.CH3], products=[self.C2H6], kinetics=Arrhenius(A=(686.375*6,'m^3/(mol*s)'), n=4.40721, Ea=(7.82799,'kcal/mol'), T0=(298.15,'K')))) rxnList.append(Reaction(reactants=[self.C2H6,self.CH3], products=[self.C2H5,self.CH4], kinetics=Arrhenius(A=(46.375*6,'m^3/(mol*s)'), n=3.40721, Ea=(6.82799,'kcal/mol'), T0=(298.15,'K')))) rxnList.append(Reaction(reactants=[self.C2H5,self.CH4], products=[self.C2H6,self.CH3], kinetics=Arrhenius(A=(46.375*6,'m^3/(mol*s)'), n=3.40721, Ea=(6.82799,'kcal/mol'), T0=(298.15,'K')))) rxnList.append(Reaction(reactants=[self.C2H5,self.CH4], products=[self.CH3,self.CH3,self.CH3], kinetics=Arrhenius(A=(246.375*6,'m^3/(mol*s)'), n=1.40721, Ea=(3.82799,'kcal/mol'), T0=(298.15,'K')))) rxnList.append(Reaction(reactants=[self.CH3,self.CH3,self.CH3], products=[self.C2H5,self.CH4], kinetics=Arrhenius(A=(246.375*6,'m^6/(mol^2*s)'), n=1.40721, Ea=(3.82799,'kcal/mol'), T0=(298.15,'K'))))# rxnList.append(Reaction(reactants=[self.C2H6,self.CH3,self.CH3], products=[self.C2H5,self.C2H5,self.H2], kinetics=Arrhenius(A=(146.375*6,'m^6/(mol^2*s)'), n=2.40721, Ea=(8.82799,'kcal/mol'), T0=(298.15,'K')))) rxnList.append(Reaction(reactants=[self.C2H5,self.C2H5,self.H2], products=[self.C2H6,self.CH3,self.CH3], kinetics=Arrhenius(A=(146.375*6,'m^6/(mol^2*s)'), n=2.40721, Ea=(8.82799,'kcal/mol'), T0=(298.15,'K')))) rxnList.append(Reaction(reactants=[self.C2H6,self.C2H6], products=[self.CH3,self.CH4,self.C2H5], kinetics=Arrhenius(A=(1246.375*6,'m^3/(mol*s)'), n=0.40721, Ea=(8.82799,'kcal/mol'), T0=(298.15,'K')))) rxnList.append(Reaction(reactants=[self.CH3,self.CH4,self.C2H5], products=[self.C2H6,self.C2H6], kinetics=Arrhenius(A=(46.375*6,'m^6/(mol^2*s)'), n=0.10721, Ea=(8.82799,'kcal/mol'), T0=(298.15,'K')))) for rxn in rxnList: coreSpecies = [self.CH4,self.CH3,self.C2H6,self.C2H5,self.H2] edgeSpecies = [] coreReactions = [rxn] c0={self.CH4:0.2,self.CH3:0.1,self.C2H6:0.35,self.C2H5:0.15, self.H2:0.2} rxnSystem0 = LiquidReactor(self.T, c0,termination=[]) rxnSystem0.initializeModel(coreSpecies, coreReactions, edgeSpecies, edgeReactions) dydt0 = rxnSystem0.residual(0.0, rxnSystem0.y, numpy.zeros(rxnSystem0.y.shape))[0] dN = .000001*sum(rxnSystem0.y) dN_array = dN*numpy.eye(numCoreSpecies) dydt = [] for i in xrange(numCoreSpecies): rxnSystem0.y[i] += dN dydt.append(rxnSystem0.residual(0.0, rxnSystem0.y, numpy.zeros(rxnSystem0.y.shape))[0]) rxnSystem0.y[i] -= dN # reset y to original y0 # Let the solver compute the jacobian solverJacobian = rxnSystem0.jacobian(0.0, rxnSystem0.y, dydt0, 0.0) # Compute the jacobian using finite differences jacobian = numpy.zeros((numCoreSpecies, numCoreSpecies)) for i in xrange(numCoreSpecies): for j in xrange(numCoreSpecies): jacobian[i,j] = (dydt[j][i]-dydt0[i])/dN self.assertAlmostEqual(jacobian[i,j], solverJacobian[i,j], delta=abs(1e-4*jacobian[i,j]))
def test_compute_derivative(self): rxnList = [] rxnList.append(Reaction(reactants=[self.C2H6], products=[self.CH3,self.CH3], kinetics=Arrhenius(A=(686.375e6,'1/s'), n=4.40721, Ea=(7.82799,'kcal/mol'), T0=(298.15,'K')))) rxnList.append(Reaction(reactants=[self.C2H6,self.CH3], products=[self.C2H5,self.CH4], kinetics=Arrhenius(A=(46.375*6,'m^3/(mol*s)'), n=3.40721, Ea=(6.82799,'kcal/mol'), T0=(298.15,'K')))) rxnList.append(Reaction(reactants=[self.C2H6,self.CH3,self.CH3], products=[self.C2H5,self.C2H5,self.H2], kinetics=Arrhenius(A=(146.375*6,'m^6/(mol^2*s)'), n=2.40721, Ea=(8.82799,'kcal/mol'), T0=(298.15,'K')))) coreSpecies = [self.CH4,self.CH3,self.C2H6,self.C2H5, self.H2] edgeSpecies = [] coreReactions = rxnList edgeReactions = [] numCoreSpecies = len(coreSpecies) c0={self.CH4:0.2,self.CH3:0.1,self.C2H6:0.35,self.C2H5:0.15, self.H2:0.2} rxnSystem0 = LiquidReactor(self.T, c0,termination=[]) rxnSystem0.initializeModel(coreSpecies, coreReactions, edgeSpecies, edgeReactions) dfdt0 = rxnSystem0.residual(0.0, rxnSystem0.y, numpy.zeros(rxnSystem0.y.shape))[0] solver_dfdk = rxnSystem0.computeRateDerivative() #print 'Solver d(dy/dt)/dk' #print solver_dfdk integrationTime = 1e-8 rxnSystem0.termination.append(TerminationTime((integrationTime,'s'))) rxnSystem0.simulate(coreSpecies, coreReactions, [], [], 0, 1, 0) y0 = rxnSystem0.y dfdk = numpy.zeros((numCoreSpecies,len(rxnList))) # d(dy/dt)/dk c0={self.CH4:0.2,self.CH3:0.1,self.C2H6:0.35,self.C2H5:0.15, self.H2:0.2} for i in xrange(len(rxnList)): k0 = rxnList[i].getRateCoefficient(self.T) rxnList[i].kinetics.A.value_si = rxnList[i].kinetics.A.value_si*(1+1e-3) dk = rxnList[i].getRateCoefficient(self.T) - k0 rxnSystem = LiquidReactor(self.T, c0,termination=[]) rxnSystem.initializeModel(coreSpecies, coreReactions, edgeSpecies, edgeReactions) dfdt = rxnSystem.residual(0.0, rxnSystem.y, numpy.zeros(rxnSystem.y.shape))[0] dfdk[:,i]=(dfdt-dfdt0)/dk rxnSystem.termination.append(TerminationTime((integrationTime,'s'))) rxnSystem.simulate(coreSpecies, coreReactions, [], [], 0, 1, 0) rxnList[i].kinetics.A.value_si = rxnList[i].kinetics.A.value_si/(1+1e-3) # reset A factor for i in xrange(numCoreSpecies): for j in xrange(len(rxnList)): self.assertAlmostEqual(dfdk[i,j], solver_dfdk[i,j], delta=abs(1e-3*dfdk[i,j]))
def test_compute_derivative(self): rxnList = [] rxnList.append(Reaction(reactants=[self.C2H6], products=[self.CH3,self.CH3], kinetics=Arrhenius(A=(686.375e6,'1/s'), n=4.40721, Ea=(7.82799,'kcal/mol'), T0=(298.15,'K')))) rxnList.append(Reaction(reactants=[self.C2H6,self.CH3], products=[self.C2H5,self.CH4], kinetics=Arrhenius(A=(46.375*6,'m^3/(mol*s)'), n=3.40721, Ea=(6.82799,'kcal/mol'), T0=(298.15,'K')))) rxnList.append(Reaction(reactants=[self.C2H6,self.CH3,self.CH3], products=[self.C2H5,self.C2H5,self.H2], kinetics=Arrhenius(A=(146.375*6,'m^6/(mol^2*s)'), n=2.40721, Ea=(8.82799,'kcal/mol'), T0=(298.15,'K')))) coreSpecies = [self.CH4,self.CH3,self.C2H6,self.C2H5, self.H2] edgeSpecies = [] coreReactions = rxnList edgeReactions = [] numCoreSpecies = len(coreSpecies) c0={self.CH4:0.2,self.CH3:0.1,self.C2H6:0.35,self.C2H5:0.15, self.H2:0.2} rxnSystem0 = LiquidReactor(self.T, c0,termination=[]) rxnSystem0.initializeModel(coreSpecies, coreReactions, edgeSpecies, edgeReactions) dfdt0 = rxnSystem0.residual(0.0, rxnSystem0.y, numpy.zeros(rxnSystem0.y.shape))[0] solver_dfdk = rxnSystem0.computeRateDerivative() #print 'Solver d(dy/dt)/dk' #print solver_dfdk integrationTime = 1e-8 rxnSystem0.termination.append(TerminationTime((integrationTime,'s'))) rxnSystem0.simulate(coreSpecies, coreReactions, [], [], [],[], 0, 1, 0) y0 = rxnSystem0.y dfdk = numpy.zeros((numCoreSpecies,len(rxnList))) # d(dy/dt)/dk c0={self.CH4:0.2,self.CH3:0.1,self.C2H6:0.35,self.C2H5:0.15, self.H2:0.2} for i in xrange(len(rxnList)): k0 = rxnList[i].getRateCoefficient(self.T) rxnList[i].kinetics.A.value_si = rxnList[i].kinetics.A.value_si*(1+1e-3) dk = rxnList[i].getRateCoefficient(self.T) - k0 rxnSystem = LiquidReactor(self.T, c0,termination=[]) rxnSystem.initializeModel(coreSpecies, coreReactions, edgeSpecies, edgeReactions) dfdt = rxnSystem.residual(0.0, rxnSystem.y, numpy.zeros(rxnSystem.y.shape))[0] dfdk[:,i]=(dfdt-dfdt0)/dk rxnSystem.termination.append(TerminationTime((integrationTime,'s'))) rxnSystem.simulate(coreSpecies, coreReactions, [], [],[],[], 0, 1, 0) rxnList[i].kinetics.A.value_si = rxnList[i].kinetics.A.value_si/(1+1e-3) # reset A factor for i in xrange(numCoreSpecies): for j in xrange(len(rxnList)): self.assertAlmostEqual(dfdk[i,j], solver_dfdk[i,j], delta=abs(1e-3*dfdk[i,j]))
def test_compute_derivative(self): rxn_list = [ Reaction(reactants=[self.C2H6], products=[self.CH3, self.CH3], kinetics=Arrhenius(A=(686.375e6, '1/s'), n=4.40721, Ea=(7.82799, 'kcal/mol'), T0=(298.15, 'K'))), Reaction(reactants=[self.C2H6, self.CH3], products=[self.C2H5, self.CH4], kinetics=Arrhenius(A=(46.375 * 6, 'm^3/(mol*s)'), n=3.40721, Ea=(6.82799, 'kcal/mol'), T0=(298.15, 'K'))), Reaction(reactants=[self.C2H6, self.CH3, self.CH3], products=[self.C2H5, self.C2H5, self.H2], kinetics=Arrhenius(A=(146.375 * 6, 'm^6/(mol^2*s)'), n=2.40721, Ea=(8.82799, 'kcal/mol'), T0=(298.15, 'K'))), ] core_species = [self.CH4, self.CH3, self.C2H6, self.C2H5, self.H2] edge_species = [] core_reactions = rxn_list edge_reactions = [] num_core_species = len(core_species) c0 = { self.CH4: 0.2, self.CH3: 0.1, self.C2H6: 0.35, self.C2H5: 0.15, self.H2: 0.2 } rxn_system0 = LiquidReactor(self.T, c0, 1, termination=[]) rxn_system0.initialize_model(core_species, core_reactions, edge_species, edge_reactions) dfdt0 = rxn_system0.residual(0.0, rxn_system0.y, np.zeros(rxn_system0.y.shape))[0] solver_dfdk = rxn_system0.compute_rate_derivative() # print 'Solver d(dy/dt)/dk' # print solver_dfdk integration_time = 1e-8 model_settings = ModelSettings(tol_keep_in_edge=0, tol_move_to_core=1, tol_interrupt_simulation=0) simulator_settings = SimulatorSettings() rxn_system0.termination.append(TerminationTime( (integration_time, 's'))) rxn_system0.simulate(core_species, core_reactions, [], [], [], [], model_settings=model_settings, simulator_settings=simulator_settings) y0 = rxn_system0.y dfdk = np.zeros((num_core_species, len(rxn_list))) # d(dy/dt)/dk c0 = { self.CH4: 0.2, self.CH3: 0.1, self.C2H6: 0.35, self.C2H5: 0.15, self.H2: 0.2 } for i in range(len(rxn_list)): k0 = rxn_list[i].get_rate_coefficient(self.T) rxn_list[i].kinetics.A.value_si = rxn_list[ i].kinetics.A.value_si * (1 + 1e-3) dk = rxn_list[i].get_rate_coefficient(self.T) - k0 rxn_system = LiquidReactor(self.T, c0, 1, termination=[]) rxn_system.initialize_model(core_species, core_reactions, edge_species, edge_reactions) dfdt = rxn_system.residual(0.0, rxn_system.y, np.zeros(rxn_system.y.shape))[0] dfdk[:, i] = (dfdt - dfdt0) / dk rxn_system.termination.append( TerminationTime((integration_time, 's'))) model_settings = ModelSettings(tol_keep_in_edge=0, tol_move_to_core=1, tol_interrupt_simulation=0) simulator_settings = SimulatorSettings() rxn_system.simulate(core_species, core_reactions, [], [], [], [], model_settings=model_settings, simulator_settings=simulator_settings) rxn_list[i].kinetics.A.value_si = rxn_list[ i].kinetics.A.value_si / (1 + 1e-3) # reset A factor for i in range(num_core_species): for j in range(len(rxn_list)): self.assertAlmostEqual(dfdk[i, j], solver_dfdk[i, j], delta=abs(1e-3 * dfdk[i, j]))
def test_jacobian(self): """ Unit test for the jacobian function: Solve a reaction system and check if the analytical jacobian matches the finite difference jacobian. """ core_species = [self.CH4, self.CH3, self.C2H6, self.C2H5, self.H2] edge_species = [] num_core_species = len(core_species) c0 = { self.CH4: 0.2, self.CH3: 0.1, self.C2H6: 0.35, self.C2H5: 0.15, self.H2: 0.2 } edge_reactions = [] rxn_list = [ Reaction(reactants=[self.C2H6], products=[self.CH3, self.CH3], kinetics=Arrhenius(A=(686.375 * 6, '1/s'), n=4.40721, Ea=(7.82799, 'kcal/mol'), T0=(298.15, 'K'))), Reaction(reactants=[self.CH3, self.CH3], products=[self.C2H6], kinetics=Arrhenius(A=(686.375 * 6, 'm^3/(mol*s)'), n=4.40721, Ea=(7.82799, 'kcal/mol'), T0=(298.15, 'K'))), Reaction(reactants=[self.C2H6, self.CH3], products=[self.C2H5, self.CH4], kinetics=Arrhenius(A=(46.375 * 6, 'm^3/(mol*s)'), n=3.40721, Ea=(6.82799, 'kcal/mol'), T0=(298.15, 'K'))), Reaction(reactants=[self.C2H5, self.CH4], products=[self.C2H6, self.CH3], kinetics=Arrhenius(A=(46.375 * 6, 'm^3/(mol*s)'), n=3.40721, Ea=(6.82799, 'kcal/mol'), T0=(298.15, 'K'))), Reaction(reactants=[self.C2H5, self.CH4], products=[self.CH3, self.CH3, self.CH3], kinetics=Arrhenius(A=(246.375 * 6, 'm^3/(mol*s)'), n=1.40721, Ea=(3.82799, 'kcal/mol'), T0=(298.15, 'K'))), Reaction(reactants=[self.CH3, self.CH3, self.CH3], products=[self.C2H5, self.CH4], kinetics=Arrhenius(A=(246.375 * 6, 'm^6/(mol^2*s)'), n=1.40721, Ea=(3.82799, 'kcal/mol'), T0=(298.15, 'K'))), Reaction(reactants=[self.C2H6, self.CH3, self.CH3], products=[self.C2H5, self.C2H5, self.H2], kinetics=Arrhenius(A=(146.375 * 6, 'm^6/(mol^2*s)'), n=2.40721, Ea=(8.82799, 'kcal/mol'), T0=(298.15, 'K'))), Reaction(reactants=[self.C2H5, self.C2H5, self.H2], products=[self.C2H6, self.CH3, self.CH3], kinetics=Arrhenius(A=(146.375 * 6, 'm^6/(mol^2*s)'), n=2.40721, Ea=(8.82799, 'kcal/mol'), T0=(298.15, 'K'))), Reaction(reactants=[self.C2H6, self.C2H6], products=[self.CH3, self.CH4, self.C2H5], kinetics=Arrhenius(A=(1246.375 * 6, 'm^3/(mol*s)'), n=0.40721, Ea=(8.82799, 'kcal/mol'), T0=(298.15, 'K'))), Reaction(reactants=[self.CH3, self.CH4, self.C2H5], products=[self.C2H6, self.C2H6], kinetics=Arrhenius(A=(46.375 * 6, 'm^6/(mol^2*s)'), n=0.10721, Ea=(8.82799, 'kcal/mol'), T0=(298.15, 'K'))), ] # Analytical Jacobian for reaction 6 def jacobian_rxn6(c, kf, kr, s): c1, c2, c3, c4 = c[s[1]], c[s[2]], c[s[3]], c[s[4]] jaco = np.zeros((5, 5)) jaco[1, 1] = -4 * kf * c1 * c2 jaco[1, 2] = -2 * kf * c1 * c1 jaco[1, 3] = 4 * kr * c3 * c4 jaco[1, 4] = 2 * kr * c3 * c3 jaco[2, 1:] = 0.5 * jaco[1, 1:] jaco[3, 1:] = -jaco[1, 1:] jaco[4, 1:] = -0.5 * jaco[1, 1:] return jaco # Analytical Jacobian for reaction 7 def jacobian_rxn7(c, kf, kr, s): c1, c2, c3, c4 = c[s[1]], c[s[2]], c[s[3]], c[s[4]] jaco = np.zeros((5, 5)) jaco[1, 1] = -4 * kr * c1 * c2 jaco[1, 2] = -2 * kr * c1 * c1 jaco[1, 3] = 4 * kf * c3 * c4 jaco[1, 4] = 2 * kf * c3 * c3 jaco[2, 1:] = 0.5 * jaco[1, 1:] jaco[3, 1:] = -jaco[1, 1:] jaco[4, 1:] = -0.5 * jaco[1, 1:] return jaco for rxn_num, rxn in enumerate(rxn_list): core_reactions = [rxn] rxn_system0 = LiquidReactor(self.T, c0, 1, termination=[]) rxn_system0.initialize_model(core_species, core_reactions, edge_species, edge_reactions) dydt0 = rxn_system0.residual(0.0, rxn_system0.y, np.zeros(rxn_system0.y.shape))[0] dN = .000001 * sum(rxn_system0.y) # Let the solver compute the jacobian solver_jacobian = rxn_system0.jacobian(0.0, rxn_system0.y, dydt0, 0.0) if rxn_num not in (6, 7): dydt = [] for i in range(num_core_species): rxn_system0.y[i] += dN dydt.append( rxn_system0.residual(0.0, rxn_system0.y, np.zeros(rxn_system0.y.shape))[0]) rxn_system0.y[i] -= dN # reset y # Compute the jacobian using finite differences jacobian = np.zeros((num_core_species, num_core_species)) for i in range(num_core_species): for j in range(num_core_species): jacobian[i, j] = (dydt[j][i] - dydt0[i]) / dN self.assertAlmostEqual(jacobian[i, j], solver_jacobian[i, j], delta=abs(1e-4 * jacobian[i, j])) # The forward finite difference is very unstable for reactions # 6 and 7. Use Jacobians calculated by hand instead. elif rxn_num == 6: kforward = rxn.get_rate_coefficient(self.T) kreverse = kforward / rxn.get_equilibrium_constant(self.T) jacobian = jacobian_rxn6(c0, kforward, kreverse, core_species) for i in range(num_core_species): for j in range(num_core_species): self.assertAlmostEqual(jacobian[i, j], solver_jacobian[i, j], delta=abs(1e-4 * jacobian[i, j])) elif rxn_num == 7: kforward = rxn.get_rate_coefficient(self.T) kreverse = kforward / rxn.get_equilibrium_constant(self.T) jacobian = jacobian_rxn7(c0, kforward, kreverse, core_species) for i in range(num_core_species): for j in range(num_core_species): self.assertAlmostEqual(jacobian[i, j], solver_jacobian[i, j], delta=abs(1e-4 * jacobian[i, j]))
def test_jacobian(self): """ Unit test for the jacobian function: Solve a reaction system and check if the analytical jacobian matches the finite difference jacobian. """ coreSpecies = [self.CH4, self.CH3, self.C2H6, self.C2H5, self.H2] edgeSpecies = [] numCoreSpecies = len(coreSpecies) c0 = {self.CH4: 0.2, self.CH3: 0.1, self.C2H6: 0.35, self.C2H5: 0.15, self.H2: 0.2} edgeReactions = [] rxnList = [] rxnList.append(Reaction( reactants=[self.C2H6], products=[self.CH3, self.CH3], kinetics=Arrhenius(A=(686.375*6, '1/s'), n=4.40721, Ea=(7.82799, 'kcal/mol'), T0=(298.15, 'K')) )) rxnList.append(Reaction( reactants=[self.CH3, self.CH3], products=[self.C2H6], kinetics=Arrhenius(A=(686.375*6, 'm^3/(mol*s)'), n=4.40721, Ea=(7.82799, 'kcal/mol'), T0=(298.15, 'K')) )) rxnList.append(Reaction( reactants=[self.C2H6, self.CH3], products=[self.C2H5, self.CH4], kinetics=Arrhenius(A=(46.375*6, 'm^3/(mol*s)'), n=3.40721, Ea=(6.82799, 'kcal/mol'), T0=(298.15, 'K')) )) rxnList.append(Reaction( reactants=[self.C2H5, self.CH4], products=[self.C2H6, self.CH3], kinetics=Arrhenius(A=(46.375*6, 'm^3/(mol*s)'), n=3.40721, Ea=(6.82799, 'kcal/mol'), T0=(298.15, 'K')) )) rxnList.append(Reaction( reactants=[self.C2H5, self.CH4], products=[self.CH3, self.CH3, self.CH3], kinetics=Arrhenius(A=(246.375*6, 'm^3/(mol*s)'), n=1.40721, Ea=(3.82799, 'kcal/mol'), T0=(298.15, 'K')) )) rxnList.append(Reaction( reactants=[self.CH3, self.CH3, self.CH3], products=[self.C2H5, self.CH4], kinetics=Arrhenius(A=(246.375*6, 'm^6/(mol^2*s)'), n=1.40721, Ea=(3.82799, 'kcal/mol'), T0=(298.15, 'K')) )) rxnList.append(Reaction( reactants=[self.C2H6, self.CH3, self.CH3], products=[self.C2H5, self.C2H5, self.H2], kinetics=Arrhenius(A=(146.375*6, 'm^6/(mol^2*s)'), n=2.40721, Ea=(8.82799, 'kcal/mol'), T0=(298.15, 'K')) )) rxnList.append(Reaction( reactants=[self.C2H5, self.C2H5, self.H2], products=[self.C2H6, self.CH3, self.CH3], kinetics=Arrhenius(A=(146.375*6, 'm^6/(mol^2*s)'), n=2.40721, Ea=(8.82799, 'kcal/mol'), T0=(298.15, 'K')) )) rxnList.append(Reaction( reactants=[self.C2H6, self.C2H6], products=[self.CH3, self.CH4, self.C2H5], kinetics=Arrhenius(A=(1246.375*6, 'm^3/(mol*s)'), n=0.40721, Ea=(8.82799, 'kcal/mol'), T0=(298.15, 'K')) )) rxnList.append(Reaction( reactants=[self.CH3, self.CH4, self.C2H5], products=[self.C2H6, self.C2H6], kinetics=Arrhenius(A=(46.375*6, 'm^6/(mol^2*s)'), n=0.10721, Ea=(8.82799, 'kcal/mol'), T0=(298.15, 'K')) )) # Analytical Jacobian for reaction 6 def jacobian_rxn6(c, kf, kr, s): c1, c2, c3, c4 = c[s[1]], c[s[2]], c[s[3]], c[s[4]] J = numpy.zeros((5, 5)) J[1, 1] = -4 * kf * c1 * c2 J[1, 2] = -2 * kf * c1 * c1 J[1, 3] = 4 * kr * c3 * c4 J[1, 4] = 2 * kr * c3 * c3 J[2, 1:] = 0.5 * J[1, 1:] J[3, 1:] = -J[1, 1:] J[4, 1:] = -0.5 * J[1, 1:] return J # Analytical Jacobian for reaction 7 def jacobian_rxn7(c, kf, kr, s): c1, c2, c3, c4 = c[s[1]], c[s[2]], c[s[3]], c[s[4]] J = numpy.zeros((5, 5)) J[1, 1] = -4 * kr * c1 * c2 J[1, 2] = -2 * kr * c1 * c1 J[1, 3] = 4 * kf * c3 * c4 J[1, 4] = 2 * kf * c3 * c3 J[2, 1:] = 0.5 * J[1, 1:] J[3, 1:] = -J[1, 1:] J[4, 1:] = -0.5 * J[1, 1:] return J for rxn_num, rxn in enumerate(rxnList): coreReactions = [rxn] rxnSystem0 = LiquidReactor(self.T, c0, 1, termination=[]) rxnSystem0.initializeModel(coreSpecies, coreReactions, edgeSpecies, edgeReactions) dydt0 = rxnSystem0.residual(0.0, rxnSystem0.y, numpy.zeros(rxnSystem0.y.shape))[0] dN = .000001*sum(rxnSystem0.y) # Let the solver compute the jacobian solverJacobian = rxnSystem0.jacobian(0.0, rxnSystem0.y, dydt0, 0.0) if rxn_num not in (6, 7): dydt = [] for i in xrange(numCoreSpecies): rxnSystem0.y[i] += dN dydt.append(rxnSystem0.residual(0.0, rxnSystem0.y, numpy.zeros(rxnSystem0.y.shape))[0]) rxnSystem0.y[i] -= dN # reset y # Compute the jacobian using finite differences jacobian = numpy.zeros((numCoreSpecies, numCoreSpecies)) for i in xrange(numCoreSpecies): for j in xrange(numCoreSpecies): jacobian[i, j] = (dydt[j][i]-dydt0[i])/dN self.assertAlmostEqual(jacobian[i, j], solverJacobian[i, j], delta=abs(1e-4*jacobian[i, j])) # The forward finite difference is very unstable for reactions # 6 and 7. Use Jacobians calculated by hand instead. elif rxn_num == 6: kforward = rxn.getRateCoefficient(self.T) kreverse = kforward / rxn.getEquilibriumConstant(self.T) jacobian = jacobian_rxn6(c0, kforward, kreverse, coreSpecies) for i in xrange(numCoreSpecies): for j in xrange(numCoreSpecies): self.assertAlmostEqual(jacobian[i, j], solverJacobian[i, j], delta=abs(1e-4*jacobian[i, j])) elif rxn_num == 7: kforward = rxn.getRateCoefficient(self.T) kreverse = kforward / rxn.getEquilibriumConstant(self.T) jacobian = jacobian_rxn7(c0, kforward, kreverse, coreSpecies) for i in xrange(numCoreSpecies): for j in xrange(numCoreSpecies): self.assertAlmostEqual(jacobian[i, j], solverJacobian[i, j], delta=abs(1e-4*jacobian[i, j]))
def test_jacobian(self): """ Unit test for the jacobian function: Solve a reaction system and check if the analytical jacobian matches the finite difference jacobian """ coreSpecies = [self.CH4, self.CH3, self.C2H6, self.C2H5] edgeSpecies = [] rxn1 = Reaction(reactants=[self.C2H6, self.CH3], products=[self.C2H5, self.CH4], kinetics=Arrhenius(A=(686.375 * 6, 'm^3/(mol*s)'), n=4.40721, Ea=(7.82799, 'kcal/mol'), T0=(298.15, 'K'))) coreReactions = [rxn1] edgeReactions = [] numCoreSpecies = len(coreSpecies) rxnList = [] rxnList.append( Reaction(reactants=[self.C2H6], products=[self.CH3, self.CH3], kinetics=Arrhenius(A=(686.375 * 6, '1/s'), n=4.40721, Ea=(7.82799, 'kcal/mol'), T0=(298.15, 'K')))) rxnList.append( Reaction(reactants=[self.CH3, self.CH3], products=[self.C2H6], kinetics=Arrhenius(A=(686.375 * 6, 'm^3/(mol*s)'), n=4.40721, Ea=(7.82799, 'kcal/mol'), T0=(298.15, 'K')))) rxnList.append( Reaction(reactants=[self.C2H6, self.CH3], products=[self.C2H5, self.CH4], kinetics=Arrhenius(A=(46.375 * 6, 'm^3/(mol*s)'), n=3.40721, Ea=(6.82799, 'kcal/mol'), T0=(298.15, 'K')))) rxnList.append( Reaction(reactants=[self.C2H5, self.CH4], products=[self.C2H6, self.CH3], kinetics=Arrhenius(A=(46.375 * 6, 'm^3/(mol*s)'), n=3.40721, Ea=(6.82799, 'kcal/mol'), T0=(298.15, 'K')))) rxnList.append( Reaction(reactants=[self.C2H5, self.CH4], products=[self.CH3, self.CH3, self.CH3], kinetics=Arrhenius(A=(246.375 * 6, 'm^3/(mol*s)'), n=1.40721, Ea=(3.82799, 'kcal/mol'), T0=(298.15, 'K')))) rxnList.append( Reaction(reactants=[self.CH3, self.CH3, self.CH3], products=[self.C2H5, self.CH4], kinetics=Arrhenius(A=(246.375 * 6, 'm^6/(mol^2*s)'), n=1.40721, Ea=(3.82799, 'kcal/mol'), T0=(298.15, 'K')))) # rxnList.append( Reaction(reactants=[self.C2H6, self.CH3, self.CH3], products=[self.C2H5, self.C2H5, self.H2], kinetics=Arrhenius(A=(146.375 * 6, 'm^6/(mol^2*s)'), n=2.40721, Ea=(8.82799, 'kcal/mol'), T0=(298.15, 'K')))) rxnList.append( Reaction(reactants=[self.C2H5, self.C2H5, self.H2], products=[self.C2H6, self.CH3, self.CH3], kinetics=Arrhenius(A=(146.375 * 6, 'm^6/(mol^2*s)'), n=2.40721, Ea=(8.82799, 'kcal/mol'), T0=(298.15, 'K')))) rxnList.append( Reaction(reactants=[self.C2H6, self.C2H6], products=[self.CH3, self.CH4, self.C2H5], kinetics=Arrhenius(A=(1246.375 * 6, 'm^3/(mol*s)'), n=0.40721, Ea=(8.82799, 'kcal/mol'), T0=(298.15, 'K')))) rxnList.append( Reaction(reactants=[self.CH3, self.CH4, self.C2H5], products=[self.C2H6, self.C2H6], kinetics=Arrhenius(A=(46.375 * 6, 'm^6/(mol^2*s)'), n=0.10721, Ea=(8.82799, 'kcal/mol'), T0=(298.15, 'K')))) for rxn in rxnList: coreSpecies = [self.CH4, self.CH3, self.C2H6, self.C2H5, self.H2] edgeSpecies = [] coreReactions = [rxn] c0 = { self.CH4: 0.2, self.CH3: 0.1, self.C2H6: 0.35, self.C2H5: 0.15, self.H2: 0.2 } rxnSystem0 = LiquidReactor(self.T, c0, termination=[]) rxnSystem0.initializeModel(coreSpecies, coreReactions, edgeSpecies, edgeReactions) dydt0 = rxnSystem0.residual(0.0, rxnSystem0.y, numpy.zeros(rxnSystem0.y.shape))[0] dN = .000001 * sum(rxnSystem0.y) dN_array = dN * numpy.eye(numCoreSpecies) dydt = [] for i in xrange(numCoreSpecies): rxnSystem0.y[i] += dN dydt.append( rxnSystem0.residual(0.0, rxnSystem0.y, numpy.zeros(rxnSystem0.y.shape))[0]) rxnSystem0.y[i] -= dN # reset y to original y0 # Let the solver compute the jacobian solverJacobian = rxnSystem0.jacobian(0.0, rxnSystem0.y, dydt0, 0.0) # Compute the jacobian using finite differences jacobian = numpy.zeros((numCoreSpecies, numCoreSpecies)) for i in xrange(numCoreSpecies): for j in xrange(numCoreSpecies): jacobian[i, j] = (dydt[j][i] - dydt0[i]) / dN self.assertAlmostEqual(jacobian[i, j], solverJacobian[i, j], delta=abs(1e-4 * jacobian[i, j]))