def test_perfect_matching(self):
model = make_gas_expansion_model()
# These are the variables and constraints of the square,
# nonsingular subsystem
variables = []
variables.extend(model.P.values())
variables.extend(model.T[i] for i in model.streams
if i != model.streams.first())
variables.extend(model.rho[i] for i in model.streams
if i != model.streams.first())
variables.extend(model.F[i] for i in model.streams
if i != model.streams.first())
constraints = list(model.component_data_objects(pyo.Constraint))
imat = get_numeric_incidence_matrix(variables, constraints)
con_idx_map = ComponentMap((c, i) for i, c in enumerate(constraints))
n_var = len(variables)
matching = maximum_matching(imat)
matching = ComponentMap(
(c, variables[matching[con_idx_map[c]]]) for c in constraints)
values = ComponentSet(matching.values())
self.assertEqual(len(matching), n_var)
self.assertEqual(len(values), n_var)
# The subset of variables and equations we have identified
# do not have a unique perfect matching. But we at least know
# this much.
self.assertIs(matching[model.ideal_gas[0]], model.P[0])
def test_imperfect_matching(self):
model = make_gas_expansion_model()
all_vars = list(model.component_data_objects(pyo.Var))
all_cons = list(model.component_data_objects(pyo.Constraint))
imat = get_numeric_incidence_matrix(all_vars, all_cons)
n_eqn = len(all_cons)
matching = maximum_matching(imat)
values = set(matching.values())
self.assertEqual(len(matching), n_eqn)
self.assertEqual(len(values), n_eqn)
def test_triangularize(self):
N = 5
model = make_gas_expansion_model(N)
# These are the variables and constraints of the square,
# nonsingular subsystem
variables = []
variables.extend(model.P.values())
variables.extend(model.T[i] for i in model.streams
if i != model.streams.first())
variables.extend(model.rho[i] for i in model.streams
if i != model.streams.first())
variables.extend(model.F[i] for i in model.streams
if i != model.streams.first())
constraints = list(model.component_data_objects(pyo.Constraint))
imat = get_numeric_incidence_matrix(variables, constraints)
con_idx_map = ComponentMap((c, i) for i, c in enumerate(constraints))
var_idx_map = ComponentMap((v, i) for i, v in enumerate(variables))
row_block_map, col_block_map = block_triangularize(imat)
var_block_map = ComponentMap(
(v, col_block_map[var_idx_map[v]]) for v in variables)
con_block_map = ComponentMap(
(c, row_block_map[con_idx_map[c]]) for c in constraints)
var_values = set(var_block_map.values())
con_values = set(con_block_map.values())
self.assertEqual(len(var_values), N + 1)
self.assertEqual(len(con_values), N + 1)
self.assertEqual(var_block_map[model.P[0]], 0)
for i in model.streams:
if i != model.streams.first():
self.assertEqual(var_block_map[model.rho[i]], i)
self.assertEqual(var_block_map[model.T[i]], i)
self.assertEqual(var_block_map[model.P[i]], i)
self.assertEqual(var_block_map[model.F[i]], i)
self.assertEqual(con_block_map[model.ideal_gas[i]], i)
self.assertEqual(con_block_map[model.expansion[i]], i)
self.assertEqual(con_block_map[model.mbal[i]], i)
self.assertEqual(con_block_map[model.ebal[i]], i)
def test_incidence_matrix(self):
N = 5
model = make_gas_expansion_model(N)
all_vars = list(model.component_data_objects(pyo.Var))
all_cons = list(model.component_data_objects(pyo.Constraint))
imat = get_numeric_incidence_matrix(all_vars, all_cons)
n_var = 4 * (N + 1)
n_con = 4 * N + 1
self.assertEqual(imat.shape, (n_con, n_var))
var_idx_map = ComponentMap((v, i) for i, v in enumerate(all_vars))
con_idx_map = ComponentMap((c, i) for i, c in enumerate(all_cons))
# Map constraints to the variables they contain.
csr_map = ComponentMap()
csr_map.update((model.mbal[i],
ComponentSet([
model.F[i],
model.F[i - 1],
model.rho[i],
model.rho[i - 1],
])) for i in model.streams
if i != model.streams.first())
csr_map.update((model.ebal[i],
ComponentSet([
model.F[i],
model.F[i - 1],
model.rho[i],
model.rho[i - 1],
model.T[i],
model.T[i - 1],
])) for i in model.streams
if i != model.streams.first())
csr_map.update((model.expansion[i],
ComponentSet([
model.rho[i],
model.rho[i - 1],
model.P[i],
model.P[i - 1],
])) for i in model.streams
if i != model.streams.first())
csr_map.update((model.ideal_gas[i],
ComponentSet([
model.P[i],
model.rho[i],
model.T[i],
])) for i in model.streams)
# Map constraint and variable indices to the values of the derivatives
# Note that the derivative values calculated here depend on the model's
# canonical form.
deriv_lookup = {}
m = model # for convenience
for s in model.streams:
# Ideal gas:
i = con_idx_map[model.ideal_gas[s]]
j = var_idx_map[model.P[s]]
deriv_lookup[i, j] = 1.0
j = var_idx_map[model.rho[s]]
deriv_lookup[i, j] = -model.R.value * model.T[s].value
j = var_idx_map[model.T[s]]
deriv_lookup[i, j] = -model.R.value * model.rho[s].value
if s != model.streams.first():
# Expansion:
i = con_idx_map[model.expansion[s]]
j = var_idx_map[model.P[s]]
deriv_lookup[i, j] = 1 / model.P[s - 1].value
j = var_idx_map[model.P[s - 1]]
deriv_lookup[i, j] = -model.P[s].value / model.P[s - 1]**2
j = var_idx_map[model.rho[s]]
deriv_lookup[i, j] = pyo.value(
-m.gamma * (m.rho[s] / m.rho[s - 1])**(m.gamma - 1) /
m.rho[s - 1])
j = var_idx_map[model.rho[s - 1]]
deriv_lookup[i, j] = pyo.value(
-m.gamma * (m.rho[s] / m.rho[s - 1])**(m.gamma - 1) *
(-m.rho[s] / m.rho[s - 1]**2))
# Energy balance:
i = con_idx_map[m.ebal[s]]
j = var_idx_map[m.rho[s - 1]]
deriv_lookup[i, j] = pyo.value(m.F[s - 1] * m.T[s - 1])
j = var_idx_map[m.F[s - 1]]
deriv_lookup[i, j] = pyo.value(m.rho[s - 1] * m.T[s - 1])
j = var_idx_map[m.T[s - 1]]
deriv_lookup[i, j] = pyo.value(m.F[s - 1] * m.rho[s - 1])
j = var_idx_map[m.rho[s]]
deriv_lookup[i, j] = pyo.value(-m.F[s] * m.T[s])
j = var_idx_map[m.F[s]]
deriv_lookup[i, j] = pyo.value(-m.rho[s] * m.T[s])
j = var_idx_map[m.T[s]]
deriv_lookup[i, j] = pyo.value(-m.F[s] * m.rho[s])
# Mass balance:
i = con_idx_map[m.mbal[s]]
j = var_idx_map[m.rho[s - 1]]
deriv_lookup[i, j] = pyo.value(m.F[s - 1])
j = var_idx_map[m.F[s - 1]]
deriv_lookup[i, j] = pyo.value(m.rho[s - 1])
j = var_idx_map[m.rho[s]]
deriv_lookup[i, j] = pyo.value(-m.F[s])
j = var_idx_map[m.F[s]]
deriv_lookup[i, j] = pyo.value(-m.rho[s])
# Want to test that the columns have the rows we expect.
i = model.streams.first()
for i, j, e in zip(imat.row, imat.col, imat.data):
con = all_cons[i]
var = all_vars[j]
self.assertIn(var, csr_map[con])
csr_map[con].remove(var)
self.assertAlmostEqual(deriv_lookup[i, j], e, 8)
# And no additional rows
for con in csr_map:
self.assertEqual(len(csr_map[con]), 0)
