def main(show_plot=True):
if show_plot:
import matplotlib.pylab as plt
instance = create_problem(0.0, 10.0)
# Discretize model using Orthogonal Collocation
discretizer = pyo.TransformationFactory('dae.collocation')
discretizer.apply_to(instance, nfe=100, ncp=3, scheme='LAGRANGE-RADAU')
discretizer.reduce_collocation_points(instance,
var=instance.u,
ncp=1,
contset=instance.t)
# Interface pyomo model with nlp
nlp = PyomoNLP(instance)
x = nlp.create_new_vector('primals')
x.fill(1.0)
nlp.set_primals(x)
lam = nlp.create_new_vector('duals')
lam.fill(1.0)
nlp.set_duals(lam)
# Evaluate jacobian
jac = nlp.evaluate_jacobian()
if show_plot:
plt.spy(jac)
plt.title('Jacobian of the constraints\n')
plt.show()
# Evaluate hessian of the lagrangian
hess_lag = nlp.evaluate_hessian_lag()
if show_plot:
plt.spy(hess_lag)
plt.title('Hessian of the Lagrangian function\n')
plt.show()
# Build KKT matrix
kkt = BlockMatrix(2, 2)
kkt.set_block(0, 0, hess_lag)
kkt.set_block(1, 0, jac)
kkt.set_block(0, 1, jac.transpose())
if show_plot:
plt.spy(kkt.tocoo())
plt.title('KKT system\n')
plt.show()
m.init_condition_names = ['init_conditions']
return m
instance = create_problem(0.0, 10.0)
# Discretize model using Orthogonal Collocation
discretizer = pyo.TransformationFactory('dae.collocation')
discretizer.apply_to(instance, nfe=100, ncp=3, scheme='LAGRANGE-RADAU')
discretizer.reduce_collocation_points(instance,
var=instance.u,
ncp=1,
contset=instance.t)
# Interface pyomo model with nlp
nlp = PyomoNLP(instance)
x = nlp.create_new_vector('primals')
x.fill(1.0)
nlp.set_primals(x)
lam = nlp.create_new_vector('duals')
lam.fill(1.0)
nlp.set_duals(lam)
# Evaluate jacobian
jac = nlp.evaluate_jacobian()
plt.spy(jac)
plt.title('Jacobian of the constraints\n')
plt.show()
# Evaluate hessian of the lagrangian
hess_lag = nlp.evaluate_hessian_lag()
#instance = create_model(1.0)
nlp = PyomoNLP(instance)
print("\n----------------------")
print("Problem statistics:")
print("----------------------")
print("Number of variables: {:>25d}".format(nlp.n_primals()))
print("Number of equality constraints: {:>14d}".format(nlp.n_eq_constraints()))
print("Number of inequality constraints: {:>11d}".format(
nlp.n_ineq_constraints()))
print("Total number of constraints: {:>17d}".format(nlp.n_constraints()))
print("Number of nnz in Jacobian: {:>20d}".format(nlp.nnz_jacobian()))
print("Number of nnz in hessian of Lagrange: {:>8d}".format(
nlp.nnz_hessian_lag()))
x = nlp.init_primals().copy()
y = nlp.create_new_vector('duals')
y.fill(1.0)
nlp.set_primals(x)
nlp.set_duals(y)
# Evaluate jacobian of all constraints
jac_full = nlp.evaluate_jacobian()
plt.spy(jac_full)
plt.title('Jacobian of the all constraints\n')
plt.show()
# Evaluate jacobian of the equality constraints
jac = nlp.evaluate_jacobian_eq()
plt.title('Jacobian of the equality constraints\n')
plt.spy(jac)
plt.show()
