print("Problem statistics:")
print("----------------------")
print("Number of variables: {:>25d}".format(nlp.nx))
print("Number of equality constraints: {:>14d}".format(nlp.nc))
print("Number of inequality constraints: {:>11d}".format(nlp.nd))
print("Total number of constraints: {:>17d}".format(nlp.ng))
print("Number of nnz in Jacobian: {:>20d}".format(nlp.nnz_jacobian_g))
print("Number of nnz in hessian of Lagrange: {:>8d}".format(
nlp.nnz_hessian_lag))
x = nlp.x_init()
y = nlp.create_vector_y()
y.fill(1.0)
# Evaluate jacobian of all constraints
jac_g = nlp.jacobian_g(x)
plt.spy(jac_g)
plt.title('Jacobian of the all constraints\n')
plt.show()
# Evaluate jacobian of equality constraints
jac_c = nlp.jacobian_c(x)
plt.title('Jacobian of the equality constraints\n')
plt.spy(jac_c)
plt.show()
# Evaluate jacobian of equality constraints
jac_d = nlp.jacobian_d(x)
plt.title('Jacobian of the inequality constraints\n')
plt.spy(jac_d)
plt.show()
def main():
"""
Make the flowsheet object and solve
"""
ss_flowsheet = ss_sim.main()
flowsheet = Flowsheet(name='MB_Model')
# fill in values of IC parameters from steady state solve
setICs(flowsheet, ss_flowsheet)
# Fix variables
setInputs(flowsheet)
# Initialize at steady state
initialize_ss(flowsheet, ss_flowsheet)
mb = flowsheet.MB_fuel
write_differential_equations(flowsheet)
# Then perturb
solid_x_ptb = {'Fe2O3': 0.25, 'Fe3O4': 0.01, 'Al2O3': 0.74}
gas_y_ptb = {'CO2': 0.03999, 'H2O': 0.00001, 'CH4': 0.96}
#perturbInputs(flowsheet,0,Solid_M=691.4,Solid_T=1283,Solid_x=solid_x_ptb,
# Gas_F=150,Gas_T=350,Gas_y=gas_y_ptb)
for t in mb.t:
perturbInputs(flowsheet, t, Solid_M=691.4)
# should put this in a dedicated ~intialize~ function
# that also intelligently initializes the model after perturbation
mb.eq_d4.deactivate()
mb.eq_d5.deactivate()
mb.eq_d8.deactivate()
mb.eq_d9.deactivate()
mb.eq_d10.deactivate()
mb.eq_g7.deactivate()
mb.eq_g8.deactivate()
mb.eq_g10.deactivate()
mb.eq_g11.deactivate()
mb.eq_g12.deactivate()
mb.eq_g13.deactivate()
mb.eq_g14.deactivate()
mb.eq_g4.deactivate()
mb.eq_g5.deactivate()
mb.eq_g2.deactivate()
mb.Tg_GW.fix(0.0)
mb.Tw_GW.fix(0.0)
mb.Tg_refractory.fix(0.0)
mb.Tw_Wamb.fix()
mb.Tw.fix()
mb.Nuw.fix()
mb.Nu_ext.fix()
mb.hw.fix()
mb.hext.fix()
mb.hext2.fix()
mb.U.fix()
mb.Uw.fix()
mb.Pr_ext.fix()
mb.Ra.fix()
mb.Re.fix()
###
# other tentatively unused variables:
mb.mFe_mAl.fix(0.0)
mb.Solid_Out_M_Comp.fix()
mb.eq_c5.deactivate()
# Create a solver
tol = 1e-8
opt = SolverFactory('ipopt')
opt.options = {
'tol': tol,
'linear_solver': 'ma57',
'bound_push': 1e-8,
'max_cpu_time': 600,
'print_level': 5
}
#'halt_on_ampl_error': 'yes'}
# initialized at steady state, works regardless:
flowsheet.strip_bounds()
#for z in mb.z:
# for t in mb.t:
# mb.Cg[z,'CH4',t].setlb(1e-8)
for t in mb.t:
alg_update(flowsheet, t)
update_time_derivatives(flowsheet, t)
print_violated_constraints(flowsheet, tol)
nlp_ss = PyomoNLP(ss_flowsheet)
x_ss = get_vector_from_flowsheet(nlp_ss, ss_flowsheet)
jac_ss = nlp_ss.jacobian_g(x_ss)
print('calculating steady state condition number...')
ss_condition = np.linalg.cond(jac_ss.toarray())
print('steady state condition number: ', ss_condition)
fig1, ax1 = plt.subplots()
ax1.jac_ss = plt.spy(jac_ss)
ax1.set_facecolor('none')
fig1.savefig('jac_ss.png', facecolor='none',
edgecolor='none') #'#f2f2f2',edgecolor='none')
nlp = PyomoNLP(flowsheet)
v_order = nlp.variable_order()
c_order = nlp.constraint_order()
x = get_vector_from_flowsheet(nlp, flowsheet)
lam = nlp.create_vector_y()
jac_c = nlp.jacobian_g(x)
hess_lag = nlp.hessian_lag(x, lam)
kkt = BlockSymMatrix(2)
kkt[0, 0] = hess_lag
kkt[1, 0] = jac_c
fig2, ax2 = plt.subplots()
ax2.jac_c = plt.spy(jac_c)
ax2.set_facecolor('none')
fig2.savefig('jac_c.png', facecolor='none', edgecolor='none')
#MA27 = hsl.MA27_LinearSolver()
#jac_row_fortran = np.zeros(jac_c.nnz,dtype=np.intc)
#jac_col_fortran = np.zeros(jac_c.nnz,dtype=np.intc)
#values = jac_c.data
#for i in range(0,jac_c.nnz):
# jac_row_fortran[i] = int(jac_c.row[i] + 1)
# jac_col_fortran[i] = int(jac_c.col[i] + 1)
#print('Doing symbolic factorization...')
#MA27.DoSymbolicFactorization(nlp.nx,jac_row_fortran,jac_col_fortran)
#print(jac_row_fortran)
#print(jac_col_fortran)
#print('Doing numeric factorization...')
#num_status = MA27.DoNumericFactorization(nlp.nx,values)
#print('Status: ',num_status)
#jac_indices = range(0,jac_c.nnz)
#for i in range(0,jac_c.nnz):
# if np.abs(values[i]) <= 1e-6:
# print('%0.2e'%values[i],str(jac_indices[i])+'-th nonzero.',jac_c.row[i],jac_c.col[i],
# c_order[jac_c.row[i]],v_order[jac_c.col[i]])
#plot_switch = 0
#if plot_switch == 1:
# fig,ax = plt.subplots()
# jac_value_plot = ax.bar(jac_indices,values)
# ax.set_yscale('log')
# fig.savefig('plots/jac_values.png')
print('calculating condition number...')
condition = np.linalg.cond(jac_c.toarray())
print('condition number: ', condition)
#mb.input_objective = Objective(expr=sum((mb.Solid_In_M[t] -601.4)**2 for t in mb.t))
flowsheet.write('fs_dyn.nl')
#with open('factorized_fs.txt','w') as f:
# flowsheet.display(ostream=f)
return flowsheet
print("\n----------------------")
print("Problem statistics:")
print("----------------------")
print("Number of variables: {:>25d}".format(nlp.nx))
print("Number of equality constraints: {:>14d}".format(nlp.nc))
print("Number of inequality constraints: {:>11d}".format(nlp.nd))
print("Total number of constraints: {:>17d}".format(nlp.ng))
print("Number of nnz in Jacobian: {:>20d}".format(nlp.nnz_jacobian_g))
print("Number of nnz in hessian of Lagrange: {:>8d}".format(nlp.nnz_hessian_lag))
x = nlp.x_init()
y = nlp.create_vector_y()
y.fill(1.0)
# Evaluate jacobian of all constraints
jac_g = nlp.jacobian_g(x)
plt.spy(jac_g)
plt.title('Jacobian of the all constraints\n')
plt.show()
# Evaluate jacobian of equality constraints
jac_c = nlp.jacobian_c(x)
plt.title('Jacobian of the equality constraints\n')
plt.spy(jac_c)
plt.show()
# Evaluate jacobian of equality constraints
jac_d = nlp.jacobian_d(x)
plt.title('Jacobian of the inequality constraints\n')
plt.spy(jac_d)
plt.show()