def prefix_suffix_feasible(problem_data, verbosity=1, solver=None):
"""
Define and solve a mode-counting synthesis problem
with a prefix-suffix strategy.
Inputs:
* *problem_data*: dictionary with the following fields:
* ``'graph'`` : mode-transition graph G
* ``'init'`` : initial configuration in G
* ``'horizon'`` : length of strategy prefix part
* ``'cycle_set'`` : set of cycles from which suffix part is formed
* ``'mode'`` : mode to count
* ``'lb_suffix'`` : lower mode-counting bound in suffix phase
* ``'ub_suffix'`` : upper mode-counting bound in suffix phase
Optional fields
* ``'lb_prefix'`` : lower mode-counting bound in prefix phase (default: lb_suffix)
* ``'ub_prefix'`` : upper mode-counting bound in prefix phase (default: ub_suffix)
* ``'order_function'`` : a function that is a bijection that maps nodes in G to integers :math:`[0, 1, \ldots , N]` (default: G.nodes().index)
* ``'forbidden_nodes'`` : nodes in G that can not be visited (default: [])
* ``'ilp'`` : if true, solve as ILP (default: ``True``)
* *verbosity*: level of verbosity
Output: a dictionary with the following fields:
* ``'controls'`` : prefix part u of strategy, u[:,t] is control at time t
* ``'states'`` : states x generated by u, x[:,t] is state at time t
* ``'cycles'`` : suffix cycles
* ``'assignments'`` : suffix assignments
Example: see example_simple.py
"""
G, T, N, ilp, order_fcn, forbidden_nodes = _extract_arguments(problem_data)
# clean cycle set from forbidden nodes
cycle_set = _clean_cycle_set(problem_data["cycle_set"], forbidden_nodes)
# variables: u[0], ..., u[T-1], x[0], ..., x[T], a[0], ..., a[C-1],
# lb[0], ..., lb[C-1], ub[0], ... ub[C-1]
N_u = T * N # input vars
N_x = (T + 1) * N # state vars
N_cycle_tot = sum([len(cycle) for cycle in cycle_set]) # cycle vars
N_bound = len(cycle_set) # lb/ub vars
N_tot = N_u + N_x + N_cycle_tot + 2 * N_bound
print "Setting up LP.. \n"
lp_start = time.time()
################################
# Initialize basic constraints #
################################
Aeq, beq, Aiq, biq = _ux_constraints(G, problem_data["init"], T, order_fcn, forbidden_nodes)
Aeq = scipy.sparse.bmat([[Aeq, _coo_zeros(Aeq.shape[0], N_cycle_tot + 2 * N_bound)]])
Aiq = scipy.sparse.bmat([[Aiq, _coo_zeros(Aiq.shape[0], N_cycle_tot + 2 * N_bound)]])
###############################
##### Time T constraints ######
###############################
Psi_mats = [_cycle_indices(G, cycle, order_fcn) for cycle in cycle_set]
Aeq = _sparse_vstack(Aeq, scipy.sparse.bmat([[_stacked_eye(G), -scipy.sparse.bmat([Psi_mats])]]), N_u + N * T)
beq = np.hstack([beq, np.zeros(len(G))])
###############################
##### Prefix mode-count #######
###############################
try:
lb_prefix = problem_data["lb_prefix"]
ub_prefix = problem_data["ub_prefix"]
except:
lb_prefix = problem_data["lb_suffix"]
ub_prefix = problem_data["ub_suffix"]
Aiq_new, biq_new = _prefix_mc(G, T, N, problem_data["mode"], lb_prefix, ub_prefix)
Aiq = _sparse_vstack(Aiq, Aiq_new, N_u)
biq = np.hstack([biq, biq_new])
###############################
##### Suffix mode-count #######
###############################
# Individual cycles bounds
Aiq_new, biq_new = _suffix_mc(G, cycle_set, problem_data["mode"])
Aiq = _sparse_vstack(Aiq, Aiq_new, N_u + N_x)
biq = np.hstack([biq, biq_new])
# Aggregate cycle bounds: sum(ub) < ub_tot, lb_tot < sum(lb)
Aiq_new = scipy.sparse.block_diag((-np.ones([1, N_bound]), np.ones([1, N_bound])))
Aiq = _sparse_vstack(Aiq, Aiq_new, N_u + N_x + N_cycle_tot)
biq = np.hstack([biq, np.array([-problem_data["lb_suffix"], problem_data["ub_suffix"]])])
###############################
#### Positive assignments #####
###############################
Aiq = _sparse_vstack(Aiq, -scipy.sparse.identity(N_cycle_tot), N_u + N_x)
biq = np.hstack([biq, np.zeros(N_cycle_tot)])
if verbosity >= 1:
time.time()
print "It took ", time.time() - lp_start, " to set up (I)LP"
##############################################################
##############################################################
##############################################################
if verbosity >= 1:
print "solving (I)LP..."
solve_start = time.time()
if ilp:
lp_sln = solve_mip(np.zeros(N_tot), Aiq, biq, Aeq, beq, set(range(N_u)), solver=solver)
else:
lp_sln = solve_lp(np.zeros(N_tot), Aiq, biq, Aeq, beq, solver=solver)
if verbosity >= 1:
print "It took ", time.time() - solve_start, " to solve (I)LP"
sol = _extract_solution(lp_sln["x"], N, T, cycle_set)
if verbosity >= 2:
_print_sol(G, problem_data["mode"], sol)
return sol
def prefix_feasible(problem_data, verbosity=1, solver=None):
"""
Define and solve the prefix part of a mode-counting
synthesis problem (requires a given suffix part)
Inputs:
* *problem_data*: dictionary with the following fields:
* ``'graph'`` : mode-transition graph G
* ``'init'`` : initial configuration in G
* ``'horizon'`` : length of strategy prefix part
* ``'cycle_set'`` : cycles to form suffix part
* ``'assignments'`` : assignments to ``'cycle_set'``
* ``'mode'`` : mode to count
* ``'lb_prefix'`` : lower mode-counting bound in prefix phase
* ``'ub_prefix'`` : upper mode-counting bound in prefix phase
Optional fields
* ``'order_function'`` : a function that is a bijection that maps nodes in G to integers :math:`[0, 1, \ldots , N]` (default: G.nodes().index)
* ``'forbidden_nodes'``: nodes in G that can not be visited (default: [])
* ``'ilp'`` : if true, solve as ILP (default: ``True``)
* *verbosity*: level of verbosity
Output: a dictionary with the following fields:
* ``'controls'`` : prefix part u of strategy, u[:,t] is control at time t
* ``'states'`` : states x generated by u, x[:,t] is state at time t
* ``'cycles'`` : suffix cycles (same as input)
* ``'assignments'`` : suffix assignments (same as input)
"""
G, T, N, ilp, order_fcn, forbidden_nodes = _extract_arguments(problem_data)
# variables: u[0], ..., u[T-1], x[0], ..., x[T]
N_u = T * N # input vars
N_x = (T + 1) * N # state vars
N_tot = N_u + N_x
if verbosity:
lp_start = time.time()
print "Setting up LP.."
################################
# Initialize basic constraints #
################################
Aeq, beq, Aiq, biq = _ux_constraints(G, problem_data["init"], T, order_fcn, forbidden_nodes)
###############################
##### Time T constraints ######
###############################
Psi_mats = [_cycle_indices(G, cycle, order_fcn) for cycle in problem_data["cycle_set"]]
Aeq = _sparse_vstack(Aeq, _stacked_eye(G), N_u + N * T)
beq = np.hstack(
[
beq,
np.sum(
[
_cycle_indices(G, cycle, order_fcn).dot(ass)
for cycle, ass in zip(problem_data["cycle_set"], problem_data["assignments"])
],
0,
),
]
)
###############################
##### Prefix mode-count #######
###############################
Aiq_new, biq_new = _prefix_mc(G, T, N, problem_data["mode"], problem_data["lb_prefix"], problem_data["ub_prefix"])
Aiq = _sparse_vstack(Aiq, Aiq_new, N_u)
biq = np.hstack([biq, biq_new])
if verbosity >= 1:
print "It took ", time.time() - lp_start, " to set up (I)LP"
##############################################################
##############################################################
##############################################################
if verbosity >= 1:
print "solving (I)LP..."
solve_start = time.time()
if ilp:
lp_sln = solve_mip(np.zeros(N_tot), Aiq, biq, Aeq, beq, set(range(N_u)), solver=solver)
else:
lp_sln = solve_lp(np.zeros(N_tot), Aiq, biq, Aeq, beq, solver=solver)
if verbosity >= 1:
print "It took ", time.time() - solve_start, " to solve (I)LP"
sol = _extract_solution_state(lp_sln["x"], N, T)
sol["assignments"] = problem_data["assignments"]
sol["cycles"] = problem_data["cycle_set"]
if verbosity >= 2:
_print_sol(G, problem_data["mode"], sol)
return sol