def main():
m = create_model(4.5, 1.0)
opt = pyo.SolverFactory('ipopt')
results = opt.solve(m, tee=True)
nlp = PyomoNLP(m)
x = nlp.init_primals()
y = compute_init_lam(nlp, x=x)
nlp.set_primals(x)
nlp.set_duals(y)
J = nlp.extract_submatrix_jacobian(pyomo_variables=[m.x1, m.x2, m.x3],
pyomo_constraints=[m.const1, m.const2])
H = nlp.extract_submatrix_hessian_lag(
pyomo_variables_rows=[m.x1, m.x2, m.x3],
pyomo_variables_cols=[m.x1, m.x2, m.x3])
M = BlockMatrix(2, 2)
M.set_block(0, 0, H)
M.set_block(1, 0, J)
M.set_block(0, 1, J.transpose())
Np = BlockMatrix(2, 1)
Np.set_block(
0, 0,
nlp.extract_submatrix_hessian_lag(
pyomo_variables_rows=[m.x1, m.x2, m.x3],
pyomo_variables_cols=[m.eta1, m.eta2]))
Np.set_block(
1, 0,
nlp.extract_submatrix_jacobian(pyomo_variables=[m.eta1, m.eta2],
pyomo_constraints=[m.const1, m.const2]))
ds = spsolve(M.tocsc(), -Np.tocsc())
print("ds:\n", ds.todense())
#################################################################
p0 = np.array([pyo.value(m.nominal_eta1), pyo.value(m.nominal_eta2)])
p = np.array([4.45, 1.05])
dp = p - p0
dx = ds.dot(dp)[0:3]
x_indices = nlp.get_primal_indices([m.x1, m.x2, m.x3])
x_names = np.array(nlp.primals_names())
new_x_sens = x[x_indices] + dx
print("dp:", dp)
print("dx:", dx)
print("Variable names: \n", x_names[x_indices])
print("Sensitivity based x:\n", new_x_sens)
#################################################################
m = create_model(4.45, 1.05)
opt = pyo.SolverFactory('ipopt')
results = opt.solve(m, tee=False)
nlp = PyomoNLP(m)
new_x = nlp.init_primals()[nlp.get_primal_indices([m.x1, m.x2, m.x3])]
print("NLP based x:\n", new_x)
return new_x_sens, new_x
def getZ(nlp, parm_vars):
# Get the Z matrix to compute reduced hessian
parm_vars_name = [x.name for x in parm_vars]
non_parm_vars = [
x for x in nlp.get_pyomo_variables() if x.name not in parm_vars_name
]
Ji = nlp.extract_submatrix_jacobian(
pyomo_variables=parm_vars,
pyomo_constraints=nlp.get_pyomo_constraints())
Jd = nlp.extract_submatrix_jacobian(
pyomo_variables=non_parm_vars,
pyomo_constraints=nlp.get_pyomo_constraints())
#print("Ji")
#print(Ji.todense())
#print("Jd")
#print(Jd.todense())
Zd = spsolve(Jd.tocsc(), Ji.tocsc())
Z = BlockMatrix(2, 1)
Z[0, 0] = Zd
Z[1, 0] = identity(len(parm_vars))
#print("Z")
#print(Z.todense())
# reorder variables to the order in hessian
zorder = getvarorder(nlp, parm_vars, non_parm_vars)
Zorder = Z.tocsc()[zorder, :].todense()
#print("Zorder")
#print(Zorder)
return Zorder
J = nlp.evaluate_jacobian()
H = nlp.evaluate_hessian_lag()
M = BlockSymMatrix(2)
M[0, 0] = H
M[1, 0] = J
Np = BlockMatrix(2, 1)
Np[0, 0] = nlp.extract_submatrix_hessian_lag(
pyomo_variables_rows=nlp.get_pyomo_variables(),
pyomo_variables_cols=[m.eta1, m.eta2])
Np[1, 0] = nlp.extract_submatrix_jacobian(
pyomo_variables=[m.eta1, m.eta2],
pyomo_constraints=nlp.get_pyomo_constraints())
ds = spsolve(M.tocsc(), Np.tocsc())
print(nlp.variable_names())
#################################################################
p0 = np.array([pyo.value(m.nominal_eta1), pyo.value(m.nominal_eta2)])
p = np.array([4.45, 1.05])
dp = p - p0
dx = ds.dot(dp)[0:nlp.n_primals()]
new_x = x + dx
print(new_x)
#################################################################
m = create_model(4.45, 1.05)
opt = pyo.SolverFactory('ipopt')
results = opt.solve(m, tee=True)
M = BlockMatrix(2, 2)
M.set_block(0, 0, H)
M.set_block(1, 0, J)
M.set_block(0, 1, J.transpose())
Np = BlockMatrix(2, 1)
Np.set_block(
0, 0,
nlp.extract_submatrix_hessian_lag(pyomo_variables_rows=[m.x1, m.x2, m.x3],
pyomo_variables_cols=[m.eta1, m.eta2]))
Np.set_block(
1, 0,
nlp.extract_submatrix_jacobian(pyomo_variables=[m.eta1, m.eta2],
pyomo_constraints=[m.const1, m.const2]))
ds = spsolve(M.tocsc(), -Np.tocsc())
print("ds:\n", ds.todense())
#################################################################
p0 = np.array([pyo.value(m.nominal_eta1), pyo.value(m.nominal_eta2)])
p = np.array([4.45, 1.05])
dp = p - p0
dx = ds.dot(dp)[0:3]
x_indices = nlp.get_primal_indices([m.x1, m.x2, m.x3])
x_names = np.array(nlp.variable_names())
new_x = x[x_indices] + dx
print("dp:", dp)
print("dx:", dx)
print("Variable names: \n", x_names[x_indices])
print("Sensitivity based x:\n", new_x)
