def test_linalg():
for mod in list(sys.modules.keys()):
if mod.startswith('pascal_lite'):
del sys.modules[mod]
import pascal_lite as pascal
subspace_dimension = 4
V = pascal.symbolic_array(subspace_dimension)
v = pascal.symbolic_array()
v1 = pascal.dot(V, v)
assert not v1.is_distributed
v2 = pascal.outer(v1, v)
assert v2.is_distributed
v3 = pascal.qr_transpose(V)[0]
assert v3.is_distributed
g = pascal.ComputationalGraph([v1.value, v2.value, v3.value])
n = 16
A = np.random.rand(subspace_dimension, n)
b = np.random.rand(n)
def actual_inputs(x):
if x is V.value:
return A
elif x is v.value:
return b
o1, o2, o3 = g(actual_inputs)
assert np.allclose(o1, np.dot(A, b))
assert np.allclose(o2, np.outer(np.dot(A, b), b))
assert np.allclose(o3, np.linalg.qr(A.T)[0].T)
def test_add_mul():
for mod in list(sys.modules.keys()):
if mod.startswith('pascal_lite'):
del sys.modules[mod]
import pascal_lite as pascal
subspace_dimension = 16
V = pascal.random(subspace_dimension)
V = V.reshape([1, -1]).T.transpose().ravel()
v0 = pascal.ones().copy() + pascal.zeros()
v1 = pascal.symbolic_array()
v2 = pascal.symbolic_array(1)
a = np.ones(subspace_dimension)
V[1:2] = 1
v3 = -v0 / 2 + (V * a).sum() - 2 * v1 + v2[0]
v3 = 0.5 - (-v3) / 2
v3 = -0.5 + v3
v3 *= 2
print(v0, v1, v2, len(v0))
g = pascal.ComputationalGraph([v3.value])
n_for_this_mpi_rank = 100000
actual_inputs = {
pascal.builtin.ZERO:
np.zeros(n_for_this_mpi_rank),
pascal.builtin.RANDOM[0]:
np.ones(pascal.builtin.RANDOM[0].shape + (n_for_this_mpi_rank, )),
v1.value:
np.ones(n_for_this_mpi_rank),
v2.value:
2.5 * np.ones(n_for_this_mpi_rank)
}
actual_output, = g(actual_inputs)
assert actual_output.shape == (n_for_this_mpi_rank, )
assert abs(actual_output - subspace_dimension).max() < 1E-12
# a different interface
def actual_inputs(x):
if x is pascal.builtin.ZERO:
return np.zeros(n_for_this_mpi_rank)
elif x is pascal.builtin.RANDOM[0]:
return np.ones(pascal.builtin.RANDOM[0].shape +
(n_for_this_mpi_rank, ))
elif x is v1.value:
return np.ones(n_for_this_mpi_rank)
elif x is v2.value:
return 2.5 * np.ones(n_for_this_mpi_rank)
actual_output, = g(actual_inputs)
assert actual_output.shape == (n_for_this_mpi_rank, )
assert abs(actual_output - subspace_dimension).max() < 1E-12
def shadowing(run,
u0,
parameter,
subspace_dimension,
num_segments,
steps_per_segment,
runup_steps,
epsilon=1E-6,
checkpoint_path=None,
checkpoint_interval=1,
simultaneous_runs=None,
run_ddt=None,
return_checkpoint=False,
get_host_dir=None,
spawn_compute_job=None):
'''
run: a function in the form
u1, J = run(u0, parameter, steps, run_id, interprocess)
inputs - u0: init solution, a flat numpy array of doubles.
parameter: design parameter, a single number.
steps: number of time steps, an int.
run_id: a unique identifier, a string,
e.g., "segment02_init_perturb003".
interprocess: a tuple of (lock, dict) for
synchronizing between different runs.
lock: a multiprocessing.Manager.Lock object.
dict: a multiprocessing.Manager.dict object.
outputs - u1: final solution, a flat numpy array of doubles,
must be of the same size as u0.
J: quantities of interest, a numpy array of shape
(steps, n_qoi), where n_qoi is an arbitrary
but consistent number, # quantities of interest.
'''
u0 = pascal.symbolic_array(field=u0)
run = RunWrapper(run)
manager = Manager()
interprocess = (manager.Lock(), manager.dict())
if runup_steps > 0:
u0, _ = run(u0.field, parameter, runup_steps, 'runup', interprocess)
u0 = pascal.symbolic_array(field=u0)
#print u0.field
V, v = tangent_initial_condition(subspace_dimension)
lss = LssTangent()
checkpoint = Checkpoint(u0, V, v, lss, [], [], [], [], [])
return continue_shadowing(run, parameter, checkpoint, num_segments,
steps_per_segment, epsilon, checkpoint_path,
checkpoint_interval, simultaneous_runs, run_ddt,
return_checkpoint, get_host_dir,
spawn_compute_job)
def test_add_mul():
for mod in list(sys.modules.keys()):
if mod.startswith('pascal_lite'):
del sys.modules[mod]
import pascal_lite as pascal
subspace_dimension = 16
V = pascal.random(subspace_dimension)
V = V.reshape([1, -1]).T.transpose().ravel()
v0 = pascal.ones().copy() + pascal.zeros()
v1 = pascal.symbolic_array()
v2 = pascal.symbolic_array(1)
a = np.ones(subspace_dimension)
V[1:2] = 1
v3 = -v0 / 2 + (V * a).sum() - 2 * v1 + v2[0]
v3 = 0.5 - (-v3) / 2
v3 = -0.5 + v3
v3 *= 2
print(v0, v1, v2, len(v0))
g = pascal.ComputationalGraph([v3.value])
n_for_this_mpi_rank = 100000
actual_inputs = {
pascal.builtin.ZERO: np.zeros(n_for_this_mpi_rank),
pascal.builtin.RANDOM[0]:
np.ones(pascal.builtin.RANDOM[0].shape +
(n_for_this_mpi_rank,)),
v1.value: np.ones(n_for_this_mpi_rank),
v2.value: 2.5 * np.ones(n_for_this_mpi_rank)
}
actual_output, = g(actual_inputs)
assert actual_output.shape == (n_for_this_mpi_rank,)
assert abs(actual_output - subspace_dimension).max() < 1E-12
# a different interface
def actual_inputs(x):
if x is pascal.builtin.ZERO:
return np.zeros(n_for_this_mpi_rank)
elif x is pascal.builtin.RANDOM[0]:
return np.ones(pascal.builtin.RANDOM[0].shape +
(n_for_this_mpi_rank,))
elif x is v1.value:
return np.ones(n_for_this_mpi_rank)
elif x is v2.value:
return 2.5 * np.ones(n_for_this_mpi_rank)
actual_output, = g(actual_inputs)
assert actual_output.shape == (n_for_this_mpi_rank,)
assert abs(actual_output - subspace_dimension).max() < 1E-12
def shadowing(
run, u0, parameter, subspace_dimension, num_segments,
steps_per_segment, runup_steps, epsilon=1E-6,
checkpoint_path=None, checkpoint_interval=1, simultaneous_runs=None,
run_ddt=None, return_checkpoint=False, get_host_dir=None, spawn_compute_job=None):
'''
run: a function in the form
u1, J = run(u0, parameter, steps, run_id, interprocess)
inputs - u0: init solution, a flat numpy array of doubles.
parameter: design parameter, a single number.
steps: number of time steps, an int.
run_id: a unique identifier, a string,
e.g., "segment02_init_perturb003".
interprocess: a tuple of (lock, dict) for
synchronizing between different runs.
lock: a multiprocessing.Manager.Lock object.
dict: a multiprocessing.Manager.dict object.
outputs - u1: final solution, a flat numpy array of doubles,
must be of the same size as u0.
J: quantities of interest, a numpy array of shape
(steps, n_qoi), where n_qoi is an arbitrary
but consistent number, # quantities of interest.
'''
u0 = pascal.symbolic_array(field=u0)
run = RunWrapper(run)
manager = Manager()
interprocess = (manager.Lock(), manager.dict())
if runup_steps > 0:
u0, _ = run(u0.field, parameter, runup_steps, 'runup', interprocess)
u0 = pascal.symbolic_array(field=u0)
#print u0.field
V, v = tangent_initial_condition(subspace_dimension)
lss = LssTangent()
checkpoint = Checkpoint(u0, V, v, lss, [], [], [], [], [])
return continue_shadowing(
run, parameter, checkpoint,
num_segments, steps_per_segment, epsilon,
checkpoint_path, checkpoint_interval,
simultaneous_runs, run_ddt, return_checkpoint, get_host_dir, spawn_compute_job)
def __init__(self, run, u0, parameter, run_id,
simultaneous_runs, interprocess):
threads = Pool(simultaneous_runs)
res = []
for steps in range(1, self.order_of_accuracy + 1):
run_id_steps = run_id + '_{0}steps'.format(steps)
res.append(threads.apply_async(
run, (u0.field, parameter, steps, run_id_steps, interprocess)))
u = [res_i.get()[0] for res_i in res]
u = [u0] + [pascal.symbolic_array(field=ui) for ui in u]
threads.close()
threads.join()
self.dxdt = compute_dxdt(u)
self.dxdt_normalized = self.dxdt / pascal.norm(self.dxdt)
def __init__(self, run, u0, parameter, run_id,
simultaneous_runs, interprocess):
threads = Pool(simultaneous_runs)
res = []
for steps in range(1, self.order_of_accuracy + 1):
run_id_steps = run_id + '_{0}steps'.format(steps)
# set_trace()
res.append(threads.apply_async(
run, (u0.field, parameter, steps, run_id_steps, interprocess)))
u = [res_i.get()[0] for res_i in res]
u = [u0] + [pascal.symbolic_array(field=ui) for ui in u]
threads.close()
threads.join()
self.dxdt = compute_dxdt(u)
self.dxdt_normalized = self.dxdt / pascal.norm(self.dxdt)
def run_segment(run,
u0,
V,
v,
parameter,
i_segment,
steps,
epsilon,
simultaneous_runs,
interprocess,
get_host_dir=None,
compute_outputs=None,
spawn_compute_job=None):
'''
Run Time Segement i_segment, starting from
u0: nonlinear solution
V: homogeneous tangents
v: inhomogeneous tangent
for steps time steps, and returns afterwards
u0: nonlinear solution
V: homogeneous tangents
v: inhomogeneous tangent
J0: history of quantities of interest for the nonlinear solution
G: sensitivities of the homogeneous tangents
g: sensitivity of the inhomogeneous tangent
'''
if get_host_dir is None:
get_host_dir = lambda x: x
if compute_outputs is None:
compute_outputs = []
threads = Pool(simultaneous_runs)
run_id = 'segment{0:02d}_baseline'.format(i_segment)
# run homogeneous tangents
res_h = []
subspace_dimension = len(V)
u1i = u0 + v * epsilon
run_ids = [
'segment{0:02d}_param_perturb{1:03d}'.format(i_segment,
subspace_dimension)
]
u1i.value.field = os.path.join(get_host_dir(run_ids[0]), 'input.h5')
u1h = []
for j in range(subspace_dimension):
u1h.append(u0 + V[j] * epsilon)
run_ids.append('segment{0:02d}_init_perturb{1:03d}'.format(
i_segment, j))
u1h[-1].value.field = os.path.join(get_host_dir(run_ids[-1]),
'input.h5')
# compute all outputs
run_compute([u1i] + u1h + compute_outputs,
spawn_compute_job=spawn_compute_job,
interprocess=interprocess)
res_0 = threads.apply_async(
run, (u0.field, parameter, steps, run_id, interprocess))
for j in range(subspace_dimension):
res_h.append(
threads.apply_async(run, (u1h[j].field, parameter, steps,
run_ids[1 + j], interprocess)))
# run inhomogeneous tangent
res_i = threads.apply_async(
run, (u1i.field, parameter + epsilon, steps, run_ids[0], interprocess))
u0p, J0 = res_0.get()
u0p = pascal.symbolic_array(field=u0p)
# get homogeneous tangents
G = []
V = pascal.random(subspace_dimension)
for j in range(subspace_dimension):
u1p, J1 = res_h[j].get()
u1p = pascal.symbolic_array(field=u1p)
V[j] = (u1p - u0p) / epsilon
G.append(trapez_mean(J1 - J0, 0) / epsilon)
# get inhomogeneous tangent
u1p, J1 = res_i.get()
u1p = pascal.symbolic_array(field=u1p)
v, g = (u1p - u0p) / epsilon, trapez_mean(J1 - J0, 0) / epsilon
threads.close()
threads.join()
return u0p, V, v, J0, G, g