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
