def test_compare_evaluations(self): A1 = 5 A2 = 10 c1 = 3 c2 = 4 N = 6 dt = 1 m = create_pyomo_model(A1, A2, c1, c2, N, dt) solver = pyo.SolverFactory('ipopt') solver.options['linear_solver'] = 'mumps' status = solver.solve(m, tee=False) m_nlp = PyomoNLP(m) mex = create_pyomo_external_grey_box_model(A1, A2, c1, c2, N, dt) # mex_nlp = PyomoGreyBoxNLP(mex) mex_nlp = PyomoNLPWithGreyBoxBlocks(mex) # get the variable and constraint order and create the maps # reliable order independent comparisons m_x_order = m_nlp.primals_names() m_c_order = m_nlp.constraint_names() mex_x_order = mex_nlp.primals_names() mex_c_order = mex_nlp.constraint_names() x1list = [ 'h1[0]', 'h1[1]', 'h1[2]', 'h1[3]', 'h1[4]', 'h1[5]', 'h2[0]', 'h2[1]', 'h2[2]', 'h2[3]', 'h2[4]', 'h2[5]', 'F1[1]', 'F1[2]', 'F1[3]', 'F1[4]', 'F1[5]', 'F2[1]', 'F2[2]', 'F2[3]', 'F2[4]', 'F2[5]', 'F12[0]', 'F12[1]', 'F12[2]', 'F12[3]', 'F12[4]', 'F12[5]', 'Fo[0]', 'Fo[1]', 'Fo[2]', 'Fo[3]', 'Fo[4]', 'Fo[5]' ] x2list = [ 'egb.inputs[h1_0]', 'egb.inputs[h1_1]', 'egb.inputs[h1_2]', 'egb.inputs[h1_3]', 'egb.inputs[h1_4]', 'egb.inputs[h1_5]', 'egb.inputs[h2_0]', 'egb.inputs[h2_1]', 'egb.inputs[h2_2]', 'egb.inputs[h2_3]', 'egb.inputs[h2_4]', 'egb.inputs[h2_5]', 'egb.inputs[F1_1]', 'egb.inputs[F1_2]', 'egb.inputs[F1_3]', 'egb.inputs[F1_4]', 'egb.inputs[F1_5]', 'egb.inputs[F2_1]', 'egb.inputs[F2_2]', 'egb.inputs[F2_3]', 'egb.inputs[F2_4]', 'egb.inputs[F2_5]', 'egb.outputs[F12_0]', 'egb.outputs[F12_1]', 'egb.outputs[F12_2]', 'egb.outputs[F12_3]', 'egb.outputs[F12_4]', 'egb.outputs[F12_5]', 'egb.outputs[Fo_0]', 'egb.outputs[Fo_1]', 'egb.outputs[Fo_2]', 'egb.outputs[Fo_3]', 'egb.outputs[Fo_4]', 'egb.outputs[Fo_5]' ] x1_x2_map = dict(zip(x1list, x2list)) x1idx_x2idx_map = { i: mex_x_order.index(x1_x2_map[m_x_order[i]]) for i in range(len(m_x_order)) } c1list = [ 'h1bal[1]', 'h1bal[2]', 'h1bal[3]', 'h1bal[4]', 'h1bal[5]', 'h2bal[1]', 'h2bal[2]', 'h2bal[3]', 'h2bal[4]', 'h2bal[5]', 'F12con[0]', 'F12con[1]', 'F12con[2]', 'F12con[3]', 'F12con[4]', 'F12con[5]', 'Focon[0]', 'Focon[1]', 'Focon[2]', 'Focon[3]', 'Focon[4]', 'Focon[5]', 'min_inflow[1]', 'min_inflow[2]', 'min_inflow[3]', 'min_inflow[4]', 'min_inflow[5]', 'max_outflow[0]', 'max_outflow[1]', 'max_outflow[2]', 'max_outflow[3]', 'max_outflow[4]', 'max_outflow[5]', 'h10', 'h20' ] c2list = [ 'egb.h1bal_1', 'egb.h1bal_2', 'egb.h1bal_3', 'egb.h1bal_4', 'egb.h1bal_5', 'egb.h2bal_1', 'egb.h2bal_2', 'egb.h2bal_3', 'egb.h2bal_4', 'egb.h2bal_5', 'egb.output_constraints[F12_0]', 'egb.output_constraints[F12_1]', 'egb.output_constraints[F12_2]', 'egb.output_constraints[F12_3]', 'egb.output_constraints[F12_4]', 'egb.output_constraints[F12_5]', 'egb.output_constraints[Fo_0]', 'egb.output_constraints[Fo_1]', 'egb.output_constraints[Fo_2]', 'egb.output_constraints[Fo_3]', 'egb.output_constraints[Fo_4]', 'egb.output_constraints[Fo_5]', 'min_inflow[1]', 'min_inflow[2]', 'min_inflow[3]', 'min_inflow[4]', 'min_inflow[5]', 'max_outflow[0]', 'max_outflow[1]', 'max_outflow[2]', 'max_outflow[3]', 'max_outflow[4]', 'max_outflow[5]', 'h10', 'h20' ] c1_c2_map = dict(zip(c1list, c2list)) c1idx_c2idx_map = { i: mex_c_order.index(c1_c2_map[m_c_order[i]]) for i in range(len(m_c_order)) } # get the primals from m and put them in the correct order for mex m_x = m_nlp.get_primals() mex_x = np.zeros(len(m_x)) for i in range(len(m_x)): mex_x[x1idx_x2idx_map[i]] = m_x[i] # get the duals from m and put them in the correct order for mex m_lam = m_nlp.get_duals() mex_lam = np.zeros(len(m_lam)) for i in range(len(m_x)): mex_lam[c1idx_c2idx_map[i]] = m_lam[i] mex_nlp.set_primals(mex_x) mex_nlp.set_duals(mex_lam) m_obj = m_nlp.evaluate_objective() mex_obj = mex_nlp.evaluate_objective() self.assertAlmostEqual(m_obj, mex_obj, places=4) m_gobj = m_nlp.evaluate_grad_objective() mex_gobj = mex_nlp.evaluate_grad_objective() check_vectors_specific_order(self, m_gobj, m_x_order, mex_gobj, mex_x_order, x1_x2_map) m_c = m_nlp.evaluate_constraints() mex_c = mex_nlp.evaluate_constraints() check_vectors_specific_order(self, m_c, m_c_order, mex_c, mex_c_order, c1_c2_map) m_j = m_nlp.evaluate_jacobian() mex_j = mex_nlp.evaluate_jacobian().todense() check_sparse_matrix_specific_order(self, m_j, m_c_order, m_x_order, mex_j, mex_c_order, mex_x_order, c1_c2_map, x1_x2_map) m_h = m_nlp.evaluate_hessian_lag() mex_h = mex_nlp.evaluate_hessian_lag() check_sparse_matrix_specific_order(self, m_h, m_x_order, m_x_order, mex_h, mex_x_order, mex_x_order, x1_x2_map, x1_x2_map) mex_h = 0 * mex_h mex_nlp.evaluate_hessian_lag(out=mex_h) check_sparse_matrix_specific_order(self, m_h, m_x_order, m_x_order, mex_h, mex_x_order, mex_x_order, x1_x2_map, x1_x2_map)
class ExternalPyomoModel(ExternalGreyBoxModel): """ This is an ExternalGreyBoxModel used to create an external model from existing Pyomo components. Given a system of variables and equations partitioned into "input" and "external" variables and "residual" and "external" equations, this class computes the residual of the "residual equations," as well as their Jacobian and Hessian, as a function of only the inputs. Pyomo components: f(x, y) == 0 # "Residual equations" g(x, y) == 0 # "External equations", dim(g) == dim(y) Effective constraint seen by this "external model": F(x) == f(x, y(x)) == 0 where y(x) solves g(x, y) == 0 """ def __init__( self, input_vars, external_vars, residual_cons, external_cons, solver=None, ): if solver is None: solver = SolverFactory("ipopt") self._solver = solver # We only need this block to construct the NLP, which wouldn't # be necessary if we could compute Hessians of Pyomo constraints. self._block = create_subsystem_block( residual_cons + external_cons, input_vars + external_vars, ) self._block._obj = Objective(expr=0.0) self._nlp = PyomoNLP(self._block) self._scc_list = list( generate_strongly_connected_components(external_cons, variables=external_vars)) assert len(external_vars) == len(external_cons) self.input_vars = input_vars self.external_vars = external_vars self.residual_cons = residual_cons self.external_cons = external_cons self.residual_con_multipliers = [None for _ in residual_cons] self.residual_scaling_factors = None def n_inputs(self): return len(self.input_vars) def n_equality_constraints(self): return len(self.residual_cons) # I would like to try to get by without using the following "name" methods. def input_names(self): return ["input_%i" % i for i in range(self.n_inputs())] def equality_constraint_names(self): return [ "residual_%i" % i for i in range(self.n_equality_constraints()) ] def set_input_values(self, input_values): solver = self._solver external_cons = self.external_cons external_vars = self.external_vars input_vars = self.input_vars for var, val in zip(input_vars, input_values): var.set_value(val) for block, inputs in self._scc_list: if len(block.vars) == 1: calculate_variable_from_constraint(block.vars[0], block.cons[0]) else: with TemporarySubsystemManager(to_fix=inputs): solver.solve(block) # Send updated variable values to NLP for dervative evaluation primals = self._nlp.get_primals() to_update = input_vars + external_vars indices = self._nlp.get_primal_indices(to_update) values = np.fromiter((var.value for var in to_update), float) primals[indices] = values self._nlp.set_primals(primals) def set_equality_constraint_multipliers(self, eq_con_multipliers): """ Sets multipliers for residual equality constraints seen by the outer solver. """ for i, val in enumerate(eq_con_multipliers): self.residual_con_multipliers[i] = val def set_external_constraint_multipliers(self, eq_con_multipliers): eq_con_multipliers = np.array(eq_con_multipliers) external_multipliers = self.calculate_external_constraint_multipliers( eq_con_multipliers, ) multipliers = np.concatenate( (eq_con_multipliers, external_multipliers)) cons = self.residual_cons + self.external_cons n_con = len(cons) assert n_con == self._nlp.n_constraints() duals = np.zeros(n_con) indices = self._nlp.get_constraint_indices(cons) duals[indices] = multipliers self._nlp.set_duals(duals) def calculate_external_constraint_multipliers(self, resid_multipliers): """ Calculates the multipliers of the external constraints from the multipliers of the residual constraints (which are provided by the "outer" solver). """ # NOTE: This method implicitly relies on the value of inputs stored # in the nlp. Should we also rely on the multiplier that are in # the nlp? # We would then need to call nlp.set_duals twice. Once with the # residual multipliers and once with the full multipliers. # I like the current approach better for now. nlp = self._nlp y = self.external_vars f = self.residual_cons g = self.external_cons jfy = nlp.extract_submatrix_jacobian(y, f) jgy = nlp.extract_submatrix_jacobian(y, g) jgy_t = jgy.transpose() jfy_t = jfy.transpose() dfdg = -sps.linalg.splu(jgy_t.tocsc()).solve(jfy_t.toarray()) resid_multipliers = np.array(resid_multipliers) external_multipliers = dfdg.dot(resid_multipliers) return external_multipliers def get_full_space_lagrangian_hessians(self): """ Calculates terms of Hessian of full-space Lagrangian due to external and residual constraints. Note that multipliers are set by set_equality_constraint_multipliers. These matrices are used to calculate the Hessian of the reduced-space Lagrangian. """ nlp = self._nlp x = self.input_vars y = self.external_vars hlxx = nlp.extract_submatrix_hessian_lag(x, x) hlxy = nlp.extract_submatrix_hessian_lag(x, y) hlyy = nlp.extract_submatrix_hessian_lag(y, y) return hlxx, hlxy, hlyy def calculate_reduced_hessian_lagrangian(self, hlxx, hlxy, hlyy): """ Performs the matrix multiplications necessary to get the reduced space Hessian-of-Lagrangian term from the full-space terms. """ # Converting to dense is faster for the distillation # example. Does this make sense? hlxx = hlxx.toarray() hlxy = hlxy.toarray() hlyy = hlyy.toarray() dydx = self.evaluate_jacobian_external_variables() term1 = hlxx prod = hlxy.dot(dydx) term2 = prod + prod.transpose() term3 = hlyy.dot(dydx).transpose().dot(dydx) hess_lag = term1 + term2 + term3 return hess_lag def evaluate_equality_constraints(self): return self._nlp.extract_subvector_constraints(self.residual_cons) def evaluate_jacobian_equality_constraints(self): nlp = self._nlp x = self.input_vars y = self.external_vars f = self.residual_cons g = self.external_cons jfx = nlp.extract_submatrix_jacobian(x, f) jfy = nlp.extract_submatrix_jacobian(y, f) jgx = nlp.extract_submatrix_jacobian(x, g) jgy = nlp.extract_submatrix_jacobian(y, g) nf = len(f) nx = len(x) n_entries = nf * nx # TODO: Does it make sense to cast dydx to a sparse matrix? # My intuition is that it does only if jgy is "decomposable" # in the strongly connected component sense, which is probably # not usually the case. dydx = -1 * sps.linalg.splu(jgy.tocsc()).solve(jgx.toarray()) # NOTE: PyNumero block matrices require this to be a sparse matrix # that contains coordinates for every entry that could possibly # be nonzero. Here, this is all of the entries. dfdx = jfx + jfy.dot(dydx) return _dense_to_full_sparse(dfdx) def evaluate_jacobian_external_variables(self): nlp = self._nlp x = self.input_vars y = self.external_vars g = self.external_cons jgx = nlp.extract_submatrix_jacobian(x, g) jgy = nlp.extract_submatrix_jacobian(y, g) jgy_csc = jgy.tocsc() dydx = -1 * sps.linalg.splu(jgy_csc).solve(jgx.toarray()) return dydx def evaluate_hessian_external_variables(self): nlp = self._nlp x = self.input_vars y = self.external_vars g = self.external_cons jgx = nlp.extract_submatrix_jacobian(x, g) jgy = nlp.extract_submatrix_jacobian(y, g) jgy_csc = jgy.tocsc() jgy_fact = sps.linalg.splu(jgy_csc) dydx = -1 * jgy_fact.solve(jgx.toarray()) ny = len(y) nx = len(x) hgxx = np.array([ get_hessian_of_constraint(con, x, nlp=nlp).toarray() for con in g ]) hgxy = np.array([ get_hessian_of_constraint(con, x, y, nlp=nlp).toarray() for con in g ]) hgyy = np.array([ get_hessian_of_constraint(con, y, nlp=nlp).toarray() for con in g ]) # This term is sparse, but we do not exploit it. term1 = hgxx # This is what we want. # prod[i,j,k] = sum(hgxy[i,:,j] * dydx[:,k]) prod = hgxy.dot(dydx) # Swap the second and third axes of the tensor term2 = prod + prod.transpose((0, 2, 1)) # The term2 tensor could have some sparsity worth exploiting. # matrix.dot(tensor) is not what we want, so we reverse the order of the # product. Exploit symmetry of hgyy to only perform one transpose. term3 = hgyy.dot(dydx).transpose((0, 2, 1)).dot(dydx) rhs = term1 + term2 + term3 rhs.shape = (ny, nx * nx) sol = jgy_fact.solve(rhs) sol.shape = (ny, nx, nx) d2ydx2 = -sol return d2ydx2 def evaluate_hessians_of_residuals(self): """ This method computes the Hessian matrix of each equality constraint individually, rather than the sum of Hessians times multipliers. """ nlp = self._nlp x = self.input_vars y = self.external_vars f = self.residual_cons g = self.external_cons jfx = nlp.extract_submatrix_jacobian(x, f) jfy = nlp.extract_submatrix_jacobian(y, f) dydx = self.evaluate_jacobian_external_variables() ny = len(y) nf = len(f) nx = len(x) hfxx = np.array([ get_hessian_of_constraint(con, x, nlp=nlp).toarray() for con in f ]) hfxy = np.array([ get_hessian_of_constraint(con, x, y, nlp=nlp).toarray() for con in f ]) hfyy = np.array([ get_hessian_of_constraint(con, y, nlp=nlp).toarray() for con in f ]) d2ydx2 = self.evaluate_hessian_external_variables() term1 = hfxx prod = hfxy.dot(dydx) term2 = prod + prod.transpose((0, 2, 1)) term3 = hfyy.dot(dydx).transpose((0, 2, 1)).dot(dydx) d2ydx2.shape = (ny, nx * nx) term4 = jfy.dot(d2ydx2) term4.shape = (nf, nx, nx) d2fdx2 = term1 + term2 + term3 + term4 return d2fdx2 def evaluate_hessian_equality_constraints(self): """ This method actually evaluates the sum of Hessians times multipliers, i.e. the term in the Hessian of the Lagrangian due to these equality constraints. """ # External multipliers must be calculated after both primals and duals # are set, and are only necessary for this Hessian calculation. # We know this Hessian calculation wants to use the most recently # set primals and duals, so we can safely calculate external # multipliers here. eq_con_multipliers = self.residual_con_multipliers self.set_external_constraint_multipliers(eq_con_multipliers) # These are full-space Hessian-of-Lagrangian terms hlxx, hlxy, hlyy = self.get_full_space_lagrangian_hessians() # These terms can be used to calculate the corresponding # Hessian-of-Lagrangian term in the full space. hess_lag = self.calculate_reduced_hessian_lagrangian(hlxx, hlxy, hlyy) sparse = _dense_to_full_sparse(hess_lag) return sps.tril(sparse) def set_equality_constraint_scaling_factors(self, scaling_factors): """ Set scaling factors for the equality constraints that are exposed to a solver. These are the "residual equations" in this class. """ self.residual_scaling_factors = np.array(scaling_factors) def get_equality_constraint_scaling_factors(self): """ Get scaling factors for the equality constraints that are exposed to a solver. These are the "residual equations" in this class. """ return self.residual_scaling_factors
class ExternalPyomoModel(ExternalGreyBoxModel): """ This is an ExternalGreyBoxModel used to create an external model from existing Pyomo components. Given a system of variables and equations partitioned into "input" and "external" variables and "residual" and "external" equations, this class computes the residual of the "residual equations," as well as their Jacobian and Hessian, as a function of only the inputs. Pyomo components: f(x, y) == 0 # "Residual equations" g(x, y) == 0 # "External equations", dim(g) == dim(y) Effective constraint seen by this "external model": F(x) == f(x, y(x)) == 0 where y(x) solves g(x, y) == 0 """ def __init__( self, input_vars, external_vars, residual_cons, external_cons, use_cyipopt=None, solver=None, ): """ Arguments: ---------- input_vars: list List of variables sent to this system by the outer solver external_vars: list List of variables that are solved for internally by this system residual_cons: list List of equality constraints whose residuals are exposed to the outer solver external_cons: list List of equality constraints used to solve for the external variables use_cyipopt: bool Whether to use CyIpopt to solve strongly connected components of the implicit function that have dimension greater than one. solver: Pyomo solver object Used to solve strongly connected components of the implicit function that have dimension greater than one. Only used if use_cyipopt is False. """ if use_cyipopt is None: use_cyipopt = cyipopt_available if use_cyipopt and not cyipopt_available: raise RuntimeError( "Constructing an ExternalPyomoModel with CyIpopt unavailable. " "Please set the use_cyipopt argument to False.") if solver is not None and use_cyipopt: raise RuntimeError( "Constructing an ExternalPyomoModel with a solver specified " "and use_cyipopt set to True. Please set use_cyipopt to False " "to use the desired solver.") elif solver is None and not use_cyipopt: solver = SolverFactory("ipopt") # If use_cyipopt is True, this solver is None and will not be used. self._solver = solver self._use_cyipopt = use_cyipopt # We only need this block to construct the NLP, which wouldn't # be necessary if we could compute Hessians of Pyomo constraints. self._block = create_subsystem_block( residual_cons + external_cons, input_vars + external_vars, ) self._block._obj = Objective(expr=0.0) self._nlp = PyomoNLP(self._block) self._scc_list = list( generate_strongly_connected_components(external_cons, variables=external_vars)) if use_cyipopt: # Using CyIpopt allows us to solve inner problems without # costly rewriting of the nl file. It requires quite a bit # of preprocessing, however, to construct the ProjectedNLP # for each block of the decomposition. # Get "vector-valued" SCCs, those of dimension > 0. # We will solve these with a direct IPOPT interface, which requires # some preprocessing. self._vector_scc_list = [(scc, inputs) for scc, inputs in self._scc_list if len(scc.vars) > 1] # Need a dummy objective to create an NLP for scc, inputs in self._vector_scc_list: scc._obj = Objective(expr=0.0) # I need scaling_factor so Pyomo NLPs I create from these blocks # don't break when ProjectedNLP calls get_primals_scaling scc.scaling_factor = Suffix(direction=Suffix.EXPORT) # HACK: scaling_factor just needs to be nonempty. scc.scaling_factor[scc._obj] = 1.0 # These are the "original NLPs" that will be projected self._vector_scc_nlps = [ PyomoNLP(scc) for scc, inputs in self._vector_scc_list ] self._vector_scc_var_names = [[ var.name for var in scc.vars.values() ] for scc, inputs in self._vector_scc_list] self._vector_proj_nlps = [ ProjectedNLP(nlp, names) for nlp, names in zip( self._vector_scc_nlps, self._vector_scc_var_names) ] # We will solve the ProjectedNLPs rather than the original NLPs self._cyipopt_nlps = [ CyIpoptNLP(nlp) for nlp in self._vector_proj_nlps ] self._cyipopt_solvers = [ CyIpoptSolver(nlp) for nlp in self._cyipopt_nlps ] self._vector_scc_input_coords = [ nlp.get_primal_indices(inputs) for nlp, (scc, inputs) in zip( self._vector_scc_nlps, self._vector_scc_list) ] assert len(external_vars) == len(external_cons) self.input_vars = input_vars self.external_vars = external_vars self.residual_cons = residual_cons self.external_cons = external_cons self.residual_con_multipliers = [None for _ in residual_cons] self.residual_scaling_factors = None def n_inputs(self): return len(self.input_vars) def n_equality_constraints(self): return len(self.residual_cons) # I would like to try to get by without using the following "name" methods. def input_names(self): return ["input_%i" % i for i in range(self.n_inputs())] def equality_constraint_names(self): return [ "residual_%i" % i for i in range(self.n_equality_constraints()) ] def set_input_values(self, input_values): solver = self._solver external_cons = self.external_cons external_vars = self.external_vars input_vars = self.input_vars for var, val in zip(input_vars, input_values): var.set_value(val, skip_validation=True) vector_scc_idx = 0 for block, inputs in self._scc_list: if len(block.vars) == 1: calculate_variable_from_constraint(block.vars[0], block.cons[0]) else: if self._use_cyipopt: # Transfer variable values into the projected NLP, solve, # and extract values. nlp = self._vector_scc_nlps[vector_scc_idx] proj_nlp = self._vector_proj_nlps[vector_scc_idx] input_coords = self._vector_scc_input_coords[ vector_scc_idx] cyipopt = self._cyipopt_solvers[vector_scc_idx] _, local_inputs = self._vector_scc_list[vector_scc_idx] primals = nlp.get_primals() variables = nlp.get_pyomo_variables() # Set values and bounds from inputs to the SCC. # This works because values have been set in the original # pyomo model, either by a previous SCC solve, or from the # "global inputs" for i, var in zip(input_coords, local_inputs): # Set primals (inputs) in the original NLP primals[i] = var.value # This affects future evaluations in the ProjectedNLP nlp.set_primals(primals) x0 = proj_nlp.get_primals() sol, _ = cyipopt.solve(x0=x0) # Set primals from solution in projected NLP. This updates # values in the original NLP proj_nlp.set_primals(sol) # I really only need to set new primals for the variables in # the ProjectedNLP. However, I can only get a list of variables # from the original Pyomo NLP, so here some of the values I'm # setting are redundant. new_primals = nlp.get_primals() assert len(new_primals) == len(variables) for var, val in zip(variables, new_primals): var.set_value(val, skip_validation=True) else: # Use a Pyomo solver to solve this strongly connected # component. with TemporarySubsystemManager(to_fix=inputs): solver.solve(block) vector_scc_idx += 1 # Send updated variable values to NLP for dervative evaluation primals = self._nlp.get_primals() to_update = input_vars + external_vars indices = self._nlp.get_primal_indices(to_update) values = np.fromiter((var.value for var in to_update), float) primals[indices] = values self._nlp.set_primals(primals) def set_equality_constraint_multipliers(self, eq_con_multipliers): """ Sets multipliers for residual equality constraints seen by the outer solver. """ for i, val in enumerate(eq_con_multipliers): self.residual_con_multipliers[i] = val def set_external_constraint_multipliers(self, eq_con_multipliers): eq_con_multipliers = np.array(eq_con_multipliers) external_multipliers = self.calculate_external_constraint_multipliers( eq_con_multipliers, ) multipliers = np.concatenate( (eq_con_multipliers, external_multipliers)) cons = self.residual_cons + self.external_cons n_con = len(cons) assert n_con == self._nlp.n_constraints() duals = np.zeros(n_con) indices = self._nlp.get_constraint_indices(cons) duals[indices] = multipliers self._nlp.set_duals(duals) def calculate_external_constraint_multipliers(self, resid_multipliers): """ Calculates the multipliers of the external constraints from the multipliers of the residual constraints (which are provided by the "outer" solver). """ # NOTE: This method implicitly relies on the value of inputs stored # in the nlp. Should we also rely on the multiplier that are in # the nlp? # We would then need to call nlp.set_duals twice. Once with the # residual multipliers and once with the full multipliers. # I like the current approach better for now. nlp = self._nlp y = self.external_vars f = self.residual_cons g = self.external_cons jfy = nlp.extract_submatrix_jacobian(y, f) jgy = nlp.extract_submatrix_jacobian(y, g) jgy_t = jgy.transpose() jfy_t = jfy.transpose() dfdg = -sps.linalg.splu(jgy_t.tocsc()).solve(jfy_t.toarray()) resid_multipliers = np.array(resid_multipliers) external_multipliers = dfdg.dot(resid_multipliers) return external_multipliers def get_full_space_lagrangian_hessians(self): """ Calculates terms of Hessian of full-space Lagrangian due to external and residual constraints. Note that multipliers are set by set_equality_constraint_multipliers. These matrices are used to calculate the Hessian of the reduced-space Lagrangian. """ nlp = self._nlp x = self.input_vars y = self.external_vars hlxx = nlp.extract_submatrix_hessian_lag(x, x) hlxy = nlp.extract_submatrix_hessian_lag(x, y) hlyy = nlp.extract_submatrix_hessian_lag(y, y) return hlxx, hlxy, hlyy def calculate_reduced_hessian_lagrangian(self, hlxx, hlxy, hlyy): """ Performs the matrix multiplications necessary to get the reduced space Hessian-of-Lagrangian term from the full-space terms. """ # Converting to dense is faster for the distillation # example. Does this make sense? hlxx = hlxx.toarray() hlxy = hlxy.toarray() hlyy = hlyy.toarray() dydx = self.evaluate_jacobian_external_variables() term1 = hlxx prod = hlxy.dot(dydx) term2 = prod + prod.transpose() term3 = hlyy.dot(dydx).transpose().dot(dydx) hess_lag = term1 + term2 + term3 return hess_lag def evaluate_equality_constraints(self): return self._nlp.extract_subvector_constraints(self.residual_cons) def evaluate_jacobian_equality_constraints(self): nlp = self._nlp x = self.input_vars y = self.external_vars f = self.residual_cons g = self.external_cons jfx = nlp.extract_submatrix_jacobian(x, f) jfy = nlp.extract_submatrix_jacobian(y, f) jgx = nlp.extract_submatrix_jacobian(x, g) jgy = nlp.extract_submatrix_jacobian(y, g) nf = len(f) nx = len(x) n_entries = nf * nx # TODO: Does it make sense to cast dydx to a sparse matrix? # My intuition is that it does only if jgy is "decomposable" # in the strongly connected component sense, which is probably # not usually the case. dydx = -1 * sps.linalg.splu(jgy.tocsc()).solve(jgx.toarray()) # NOTE: PyNumero block matrices require this to be a sparse matrix # that contains coordinates for every entry that could possibly # be nonzero. Here, this is all of the entries. dfdx = jfx + jfy.dot(dydx) return _dense_to_full_sparse(dfdx) def evaluate_jacobian_external_variables(self): nlp = self._nlp x = self.input_vars y = self.external_vars g = self.external_cons jgx = nlp.extract_submatrix_jacobian(x, g) jgy = nlp.extract_submatrix_jacobian(y, g) jgy_csc = jgy.tocsc() dydx = -1 * sps.linalg.splu(jgy_csc).solve(jgx.toarray()) return dydx def evaluate_hessian_external_variables(self): nlp = self._nlp x = self.input_vars y = self.external_vars g = self.external_cons jgx = nlp.extract_submatrix_jacobian(x, g) jgy = nlp.extract_submatrix_jacobian(y, g) jgy_csc = jgy.tocsc() jgy_fact = sps.linalg.splu(jgy_csc) dydx = -1 * jgy_fact.solve(jgx.toarray()) ny = len(y) nx = len(x) hgxx = np.array([ get_hessian_of_constraint(con, x, nlp=nlp).toarray() for con in g ]) hgxy = np.array([ get_hessian_of_constraint(con, x, y, nlp=nlp).toarray() for con in g ]) hgyy = np.array([ get_hessian_of_constraint(con, y, nlp=nlp).toarray() for con in g ]) # This term is sparse, but we do not exploit it. term1 = hgxx # This is what we want. # prod[i,j,k] = sum(hgxy[i,:,j] * dydx[:,k]) prod = hgxy.dot(dydx) # Swap the second and third axes of the tensor term2 = prod + prod.transpose((0, 2, 1)) # The term2 tensor could have some sparsity worth exploiting. # matrix.dot(tensor) is not what we want, so we reverse the order of the # product. Exploit symmetry of hgyy to only perform one transpose. term3 = hgyy.dot(dydx).transpose((0, 2, 1)).dot(dydx) rhs = term1 + term2 + term3 rhs.shape = (ny, nx * nx) sol = jgy_fact.solve(rhs) sol.shape = (ny, nx, nx) d2ydx2 = -sol return d2ydx2 def evaluate_hessians_of_residuals(self): """ This method computes the Hessian matrix of each equality constraint individually, rather than the sum of Hessians times multipliers. """ nlp = self._nlp x = self.input_vars y = self.external_vars f = self.residual_cons g = self.external_cons jfx = nlp.extract_submatrix_jacobian(x, f) jfy = nlp.extract_submatrix_jacobian(y, f) dydx = self.evaluate_jacobian_external_variables() ny = len(y) nf = len(f) nx = len(x) hfxx = np.array([ get_hessian_of_constraint(con, x, nlp=nlp).toarray() for con in f ]) hfxy = np.array([ get_hessian_of_constraint(con, x, y, nlp=nlp).toarray() for con in f ]) hfyy = np.array([ get_hessian_of_constraint(con, y, nlp=nlp).toarray() for con in f ]) d2ydx2 = self.evaluate_hessian_external_variables() term1 = hfxx prod = hfxy.dot(dydx) term2 = prod + prod.transpose((0, 2, 1)) term3 = hfyy.dot(dydx).transpose((0, 2, 1)).dot(dydx) d2ydx2.shape = (ny, nx * nx) term4 = jfy.dot(d2ydx2) term4.shape = (nf, nx, nx) d2fdx2 = term1 + term2 + term3 + term4 return d2fdx2 def evaluate_hessian_equality_constraints(self): """ This method actually evaluates the sum of Hessians times multipliers, i.e. the term in the Hessian of the Lagrangian due to these equality constraints. """ # External multipliers must be calculated after both primals and duals # are set, and are only necessary for this Hessian calculation. # We know this Hessian calculation wants to use the most recently # set primals and duals, so we can safely calculate external # multipliers here. eq_con_multipliers = self.residual_con_multipliers self.set_external_constraint_multipliers(eq_con_multipliers) # These are full-space Hessian-of-Lagrangian terms hlxx, hlxy, hlyy = self.get_full_space_lagrangian_hessians() # These terms can be used to calculate the corresponding # Hessian-of-Lagrangian term in the full space. hess_lag = self.calculate_reduced_hessian_lagrangian(hlxx, hlxy, hlyy) sparse = _dense_to_full_sparse(hess_lag) return sps.tril(sparse) def set_equality_constraint_scaling_factors(self, scaling_factors): """ Set scaling factors for the equality constraints that are exposed to a solver. These are the "residual equations" in this class. """ self.residual_scaling_factors = np.array(scaling_factors) def get_equality_constraint_scaling_factors(self): """ Get scaling factors for the equality constraints that are exposed to a solver. These are the "residual equations" in this class. """ return self.residual_scaling_factors
def main(): model = create_basic_model() solver = pyo.SolverFactory('ipopt') solver.solve(model, tee=True) # build nlp initialized at the solution nlp = PyomoNLP(model) # get initial point print(nlp.primals_names()) x0 = nlp.get_primals() # vectors of lower and upper bounds xl = nlp.primals_lb() xu = nlp.primals_ub() # demonstrate use of compression from full set of bounds # to only finite bounds using masks xlb_mask = build_bounds_mask(xl) xub_mask = build_bounds_mask(xu) # get the compressed vector compressed_xl = full_to_compressed(xl, xlb_mask) compressed_xu = full_to_compressed(xu, xub_mask) # we can also build compression matrices Cx_xl = build_compression_matrix(xlb_mask) Cx_xu = build_compression_matrix(xub_mask) # lower and upper bounds residual res_xl = Cx_xl * x0 - compressed_xl res_xu = compressed_xu - Cx_xu * x0 print("Residuals lower bounds x-xl:", res_xl) print("Residuals upper bounds xu-x:", res_xu) # set the value of the primals (we can skip the duals) # here we set them to the initial values, but we could # set them to anything nlp.set_primals(x0) # evaluate residual of equality constraints print(nlp.constraint_names()) res_eq = nlp.evaluate_eq_constraints() print("Residuals of equality constraints:", res_eq) # evaluate residual of inequality constraints res_ineq = nlp.evaluate_ineq_constraints() # demonstrate the use of compression from full set of # lower and upper bounds on the inequality constraints # to only the finite values using masks ineqlb_mask = build_bounds_mask(nlp.ineq_lb()) inequb_mask = build_bounds_mask(nlp.ineq_ub()) # get the compressed vector compressed_ineq_lb = full_to_compressed(nlp.ineq_lb(), ineqlb_mask) compressed_ineq_ub = full_to_compressed(nlp.ineq_ub(), inequb_mask) # we can also build compression matrices Cineq_ineqlb = build_compression_matrix(ineqlb_mask) Cineq_inequb = build_compression_matrix(inequb_mask) # lower and upper inequalities residual res_ineq_lb = Cineq_ineqlb * res_ineq - compressed_ineq_lb res_ineq_ub = compressed_ineq_ub - Cineq_inequb * res_ineq print("Residuals of inequality constraints lower bounds:", res_ineq_lb) print("Residuals of inequality constraints upper bounds:", res_ineq_ub) feasible = False if np.all(res_xl >= 0) and np.all(res_xu >= 0) \ and np.all(res_ineq_lb >= 0) and np.all(res_ineq_ub >= 0) and \ np.allclose(res_eq, np.zeros(nlp.n_eq_constraints()), atol=1e-5): feasible = True print("Is x0 feasible:", feasible) return feasible
def load_solution(m: pe.ConcreteModel(), nlp: PyomoNLP): primals = nlp.get_primals() pyomo_vars = nlp.get_pyomo_variables() for v, val in zip(pyomo_vars, primals): v.value = val