def test_Collocation_2():
# Full 2PBVP test problem
# This is calculating the 4th eigenvalue of Mathieu's Equation
# This problem contains an adjustable parameter.
def odefun(t, X, p, const):
return (X[1], -(p[0] - 2 * 5 * np.cos(2 * t)) * X[0])
def bcfun(t0, X0, q0, tf, Xf, qf, p, ndp, aux):
return (X0[1], Xf[1], X0[0] - 1)
algo = Collocation(odefun, None, bcfun)
solinit = Solution()
solinit.t = np.linspace(0, np.pi, 30)
solinit.y = np.vstack(
(np.cos(4 * solinit.t), -4 * np.sin(4 * solinit.t))).T
solinit.dynamical_parameters = np.array([15])
out = algo.solve(solinit)
assert abs(out.t[-1] - np.pi) < tol
assert abs(out.y[0][0] - 1) < tol
assert abs(out.y[0][1]) < tol
assert abs(out.y[-1][0] - 1) < tol
assert abs(out.y[-1][1]) < tol
assert abs(out.dynamical_parameters[0] - 17.09646175) < tol
def guess_mapper(sol):
n_c = len(constants_of_motion)
if n_c == 0:
return sol
sol_out = Solution()
sol_out.t = copy.copy(sol.t)
sol_out.y = np.array([[fn(*sol.y[0]) for fn in states_2_states_fn]])
sol_out.q = sol.q
if len(quads) > 0:
sol_out.q = -0.0 * np.array([np.ones((len(quads)))])
sol_out.dynamical_parameters = sol.dynamical_parameters
sol_out.dynamical_parameters[-n_c:] = np.array(
[fn(*sol.y[0]) for fn in states_2_constants_fn])
sol_out.nondynamical_parameters = sol.nondynamical_parameters
sol_out.aux = sol.aux
return sol_out
def test_Shooting_3():
# This problem contains a parameter, but it is not explicit in the BCs.
# Since time is buried in the ODEs, this tests if the BVP solver calculates
# sensitivities with respect to parameters.
def odefun(t, X, p, const):
return 1 * p[0]
def bcfun(t0, X0, q0, tf, Xf, qf, p, ndp, aux):
return (X0[0] - 0, Xf[0] - 2)
algo = Shooting(odefun, None, bcfun)
solinit = Solution()
solinit.t = np.linspace(0, 1, 2)
solinit.y = np.array([[0], [0]])
solinit.dynamical_parameters = np.array([1])
out = algo.solve(solinit)
assert abs(out.dynamical_parameters - 2) < tol
def test_Shooting_1():
# Full 2PBVP test problem
# This is the simplest BVP
def odefun(t, X, p, const):
return (X[1], -abs(X[0]))
def bcfun(t0, X0, q0, tf, Xf, qf, p, ndp, aux):
return (X0[0], Xf[0]+2)
algo = Shooting(odefun, None, bcfun)
solinit = Solution()
solinit.t = np.linspace(0,4,2)
solinit.y = np.array([[0,1],[0,1]])
out = algo.solve(solinit)
assert out.y[0][0] < tol
assert out.y[0][1] - 2.06641646 < tol
assert out.y[-1][0] + 2 < tol
assert out.y[-1][1] + 2.87588998 < tol
assert out.t[-1] - 4 < tol
assert abs(out.y[0][1] - solinit.y[0][1]) > tol
assert abs(out.y[-1][0] - solinit.y[-1][0]) - 2 < tol
def test_Shooting_4():
# This problem contains a quad and tests if the bvp solver correctly
# integrates the quadfun.
def odefun(t, x, p, const):
return -x[1], x[0]
def quadfun(t, x, p, const):
return x[0]
def bcfun(t0, X0, q0, tf, Xf, qf, params, ndp, aux):
return X0[0], X0[1] - 1, qf[0] - 1.0
algo = Shooting(odefun, quadfun, bcfun)
solinit = Solution()
solinit.t = np.linspace(0, np.pi / 2, 2)
solinit.y = np.array([[1, 0], [1, 0]])
solinit.q = np.array([[0], [0]])
out = algo.solve(solinit)
assert (out.y[0,0] - 0) < tol
assert (out.y[0,1] - 1) < tol
assert (out.q[0,0] - 2) < tol
assert (out.q[-1,0] - 1) < tol
def load(self):
"""
Loads solution data using dill if not already loaded
"""
if not self.is_loaded:
logging.info("Loading datafile " + self.filename + "...")
out = loadmat(self.filename)
if 'output' in out:
out = out['output']['result'][0][0][0][0]
soldata = out['solution']['phase'][0][0][0][0]
# if 'solution' not in self._data:
# self.is_loaded = False
# logging.error("Solution missing in data file :"+self.filename)
# raise RuntimeError("Solution missing in data file :"+self.filename)
# if 'problem_data' not in self._data:
# self.is_loaded = False
# logging.error("Problem data missing in data file :"+self.filename)
# raise RuntimeError("Problem data missing in data file :"+self.filename)
#
_sol = Solution()
tf = max(soldata['time'])
_sol.x = soldata['time'][:, 0] / tf
_sol.y = np.r_[soldata['state'].T, soldata['costate'].T,
np.ones_like(soldata['time']).T * tf]
_sol.u = soldata['control'].T
if 'tf' not in self.problem_data['state_list']:
self.problem_data['state_list'] = tuple(
self.problem_data['state_list']) + ('tf', )
_sol.arcs = ((0, len(_sol.x) - 1), )
if self._const is not None:
_sol.aux = {'const': self._const}
self._sol = [[_sol]]
logging.info('Loaded solution from data file')
self.is_loaded = True
def solve(ocp, method, bvp_algorithm, steps, guess_generator):
"""
Solves the OCP using specified method
"""
output_file = config['output_file']
logging.info("Computing the necessary conditions of optimality")
if method.lower() == 'traditional' or method.lower() == 'brysonho':
ocp_ws = BH_ocp_to_bvp(ocp, guess_generator)
elif method.lower() == 'icrm':
ocp_ws = ICRM_ocp_to_bvp(ocp, guess_generator)
else:
raise NotImplementedError
ocp_ws['problem'] = ocp
ocp_ws['guess'] = guess_generator
ocp_ws['problem_data']['custom_functions'] = ocp.custom_functions()
solinit = Solution()
solinit.aux['const'] = OrderedDict(
(str(const.name), float(const.value)) for const in ocp_ws['constants'])
solinit.aux['dynamical_parameters'] = [
str(p) for p in ocp_ws['problem_data']['dynamical_parameters']
]
solinit.aux['nondynamical_parameters'] = [
str(p) for p in ocp_ws['problem_data']['nondynamical_parameters']
]
bvp = preprocess(ocp_ws['problem_data'])
solinit = ocp_ws['guess'].generate(bvp, solinit)
state_names = ocp_ws['problem_data']['state_list']
initial_states = solinit.y[0, :]
terminal_states = solinit.y[-1, :]
initial_bc = dict(zip(state_names, initial_states))
terminal_bc = dict(zip(state_names, terminal_states))
solinit.aux['initial'] = initial_bc
solinit.aux['terminal'] = terminal_bc
tic()
# TODO: Start from specific step for restart capability
# TODO: Make class to store result from continuation set?
out = dict()
out['problem_data'] = ocp_ws['problem_data']
ocp._scaling.initialize(ocp_ws)
ocp_ws['scaling'] = ocp._scaling
out['solution'] = run_continuation_set(ocp_ws, bvp_algorithm, steps,
solinit, bvp)
total_time = toc()
logging.info('Continuation process completed in %0.4f seconds.\n' %
total_time)
bvp_algorithm.close()
# Final time is appended as a parameter, so scale the output x variables to show the correct time
for continuation_set in out['solution']:
for sol in continuation_set:
tf_ind = [
i for i, s in enumerate(out['problem_data']
['dynamical_parameters'])
if str(s) is 'tf'
][0]
tf = sol.dynamical_parameters[tf_ind]
sol.t = sol.t * tf
# Save data
# del out['problem_data']['s_list']
del out['problem_data']['states']
del out['problem_data']['costates']
qvars = out['problem_data']['quantity_vars']
qvars = {str(k): str(v) for k, v in qvars.items()}
out['problem_data']['quantity_vars'] = qvars
with open(output_file, 'wb') as outfile:
pickle.dump(out, outfile)
return out['solution'][-1][-1]
def solve(ocp, method, bvp_algorithm, steps, guess_generator, output_file='data.dill'):
"""
Solves the OCP using specified method
"""
# Initialize necessary conditions of optimality object
# print("Computing the necessary conditions of optimality")
logging.info("Computing the necessary conditions of optimality")
from beluga.optimlib import methods
# TODO: Load oc method by name
wf = methods[method]
# wf = brysonho.BrysonHo
# workspace = brysonho.init_workspace(ocp)
# ocp_ws = wf(workspace)
ocp_ws = wf({'problem': ocp, 'guess': guess_generator})
solinit = Solution()
solinit.aux['const'] = dict((str(const.name),float(const.value))
for const in ocp_ws['constants'])
solinit.aux['parameters'] = ocp_ws['problem_data']['parameter_list']
# For path constraints
solinit.aux['constraint'] = cl.defaultdict(float)
solinit.aux['constraints'] = dict((s['name'], {'unit':str(s['unit']),
'expr':str(s['expr']),
'direction': s['direction'],
'arc_type': i,
'pi_list':[str(_) for _ in s['pi_list']]})
for i, s in enumerate(ocp_ws['problem_data']['s_list'],1))
solinit.aux['arc_seq'] = (0,)
solinit.aux['pi_seq'] = (None,)
bvp_fn = bvp_algorithm.preprocess(ocp_ws['problem_data'])
# The initial guess is automatically stored in the bvp object
# solinit is just a reference to it
solinit = ocp_ws['guess'].generate(bvp_fn, solinit)
# # includes costates
state_names = ocp_ws['problem_data']['state_list']
initial_states = solinit.y[:,0] # First column
terminal_states = solinit.y[:,-1] # Last column
initial_bc = dict(zip(state_names,initial_states))
terminal_bc = dict(zip(state_names,terminal_states))
solinit.aux['initial'] = initial_bc
solinit.aux['terminal'] = terminal_bc
solinit2= copy.deepcopy(solinit)
tic()
# TODO: Start from specific step for restart capability
# TODO: Make class to store result from continuation set?
out = {};
out['problem_data'] = ocp_ws['problem_data'];
ocp._scaling.initialize(ocp_ws)
ocp_ws['scaling'] = ocp._scaling
out['solution'] = run_continuation_set(ocp_ws, bvp_algorithm, steps, bvp_fn, solinit)
total_time = toc()
# tic()
# out['solution'] = run_continuation_set(ocp_ws, bvp_algorithm, steps, bvp_fn, solinit2)
# total_time = toc()
logging.info('Continuation process completed in %0.4f seconds.\n' % total_time)
bvp_algorithm.close()
# Save data
# del out['problem_data']['s_list']
del out['problem_data']['states']
del out['problem_data']['costates']
qvars = out['problem_data']['quantity_vars']
qvars = {str(k):str(v) for k,v in qvars.items()}
out['problem_data']['quantity_vars'] = qvars
with open(output_file, 'wb') as outfile:
dill.settings['recurse'] = True
dill.dump(out, outfile) # Dill Beluga object only
def solve(ocp, method, bvp_algorithm, steps, guess_generator, **kwargs):
"""
Solves the OCP using specified method
+------------------------+-----------------+-----------------+
| Valid kwargs | Default Value | Valid Values |
+========================+=================+=================+
| autoscale | True | bool |
+------------------------+-----------------+-----------------+
| n_cpus | 1 | integer |
+------------------------+-----------------+-----------------+
"""
autoscale = kwargs.get('autoscale', True)
n_cpus = int(kwargs.get('n_cpus', 1))
if n_cpus < 1:
raise ValueError('Number of cpus must be greater than 1.')
if n_cpus > 1:
logging.debug('Starting processing pool with ' + str(n_cpus) +
'cpus... ')
pool = pathos.multiprocessing.Pool(processes=n_cpus)
logging.debug('Done.')
else:
pool = None
output_file = config['output_file']
logging.info("Computing the necessary conditions of optimality")
if method.lower() == 'traditional' or method.lower() == 'brysonho':
bvp_ws, guess_mapper = BH_ocp_to_bvp(ocp)
elif method.lower() == 'icrm':
bvp_ws, guess_mapper = ICRM_ocp_to_bvp(ocp)
elif method.lower() == 'diffyg':
bvp_ws, guess_mapper = DIFFYG_ocp_to_bvp(ocp)
else:
raise NotImplementedError
logging.debug('Resulting BVP problem:')
for key in bvp_ws.keys():
logging.debug(str(key) + ': ' + str(bvp_ws[key]))
bvp_ws['problem'] = ocp
bvp_ws['guess'] = guess_generator
bvp_ws['custom_functions'] = ocp.custom_functions()
solinit = Solution()
solinit.aux['const'] = OrderedDict(
(const, val)
for const, val in zip(bvp_ws['constants'], bvp_ws['constants_values']))
for const in bvp_ws['constants']:
if not str(const) in solinit.aux['const'].keys():
solinit.aux['const'][str(const)] = 0
solinit.aux['dynamical_parameters'] = bvp_ws['dynamical_parameters']
solinit.aux['nondynamical_parameters'] = bvp_ws['nondynamical_parameters']
bvp = preprocess(bvp_ws)
solinit = bvp_ws['guess'].generate(bvp, solinit, guess_mapper)
state_names = bvp_ws['states']
initial_states = solinit.y[0, :]
terminal_states = solinit.y[-1, :]
initial_bc = dict(zip(state_names, initial_states))
terminal_bc = dict(zip(state_names, terminal_states))
for ii in initial_bc:
if ii + '_0' in solinit.aux['const'].keys():
solinit.aux['const'][ii + '_0'] = initial_bc[ii]
for ii in terminal_bc:
if ii + '_f' in solinit.aux['const'].keys():
solinit.aux['const'][ii + '_f'] = terminal_bc[ii]
quad_names = bvp_ws['quads']
n_quads = len(quad_names)
if n_quads > 0:
initial_quads = solinit.q[0, :]
terminal_quads = solinit.q[-1, :]
initial_bc = dict(zip(quad_names, initial_quads))
terminal_bc = dict(zip(quad_names, terminal_quads))
for ii in initial_bc:
if ii + '_0' in solinit.aux['const'].keys():
solinit.aux['const'][ii + '_0'] = initial_bc[ii]
for ii in terminal_bc:
if ii + '_f' in solinit.aux['const'].keys():
solinit.aux['const'][ii + '_f'] = terminal_bc[ii]
time0 = time.time()
out = dict()
out['problem_data'] = bvp_ws
ocp._scaling.initialize(bvp_ws)
bvp_ws['scaling'] = ocp._scaling
out['solution'] = run_continuation_set(bvp_ws, bvp_algorithm, steps,
solinit, bvp, pool, autoscale)
total_time = time.time() - time0
logging.info('Continuation process completed in %0.4f seconds.\n' %
total_time)
bvp_algorithm.close()
# Final time is appended as a parameter, so scale the output x variables to show the correct time
for continuation_set in out['solution']:
for sol in continuation_set:
tf_ind = [
i for i, s in enumerate(out['problem_data']
['dynamical_parameters'])
if str(s) is 'tf'
][0]
tf = sol.dynamical_parameters[tf_ind]
sol.t = sol.t * tf
if pool is not None:
pool.close()
# Save data
with open(output_file, 'wb') as outfile:
pickle.dump(out, outfile)
return out['solution'][-1][-1]