def test_write_non_distributed_npy(self):
cls = self.__class__
rank = cls.comm.getRank()
nproc = cls.comm.getSize()
if nproc > 1:
mvector_filename = 'out_mvector_write_test_' + str(nproc)
else:
mvector_filename = 'out_mvector_write_test'
file_dir = os.path.dirname(__file__)
filename = 'input.yaml'
problem = Utils.createAlbanyProblem(file_dir + '/' + filename,
cls.parallelEnv)
n_cols = 4
parameter_map = problem.getParameterMap(0)
mvector = Tpetra.MultiVector(parameter_map, n_cols, dtype="d")
mvector[0, :] = 1. * (rank + 1)
mvector[1, :] = -1. * (rank + 1)
mvector[2, :] = 3.26 * (rank + 1)
mvector[3, :] = -3.1 * (rank + 1)
Utils.writeMVector(file_dir + '/' + mvector_filename,
mvector,
distributedFile=False,
useBinary=True)
def test_read_non_distributed_non_scattered_txt(self):
cls = self.__class__
rank = cls.comm.getRank()
nproc = cls.comm.getSize()
if nproc > 1:
mvector_filename = 'in_mvector_read_test_' + str(nproc)
else:
mvector_filename = 'in_mvector_read_test'
file_dir = os.path.dirname(__file__)
filename = 'input.yaml'
problem = Utils.createAlbanyProblem(file_dir + '/' + filename,
cls.parallelEnv)
n_cols = 4
parameter_map = problem.getParameterMap(0)
mvector = Utils.loadMVector(file_dir + '/' + mvector_filename,
n_cols,
parameter_map,
distributedFile=False,
useBinary=False,
readOnRankZero=False)
tol = 1e-8
mvector_target = np.array([1., -1, 3.26, -3.1]) * (rank + 1)
for i in range(0, n_cols):
self.assertTrue(np.abs(mvector[i, 0] - mvector_target[i]) < tol)
def test_all(self):
cls = self.__class__
rank = cls.comm.getRank()
file_dir = os.path.dirname(__file__)
# Create an Albany problem:
filename = 'input_conductivity_dist_paramT.yaml'
problem = Utils.createAlbanyProblem(file_dir+'/'+filename, cls.parallelEnv)
n_vecs = 4
parameter_map = problem.getParameterMap(0)
num_elems = parameter_map.getNodeNumElements()
# generate vectors with random entries
omega = Tpetra.MultiVector(parameter_map, n_vecs, dtype="d")
for i in range(n_vecs):
omega[i,:] = np.random.randn(num_elems)
# call the orthonormalization method
wpa.orthogTpMVecs(omega, 2)
# check that the vectors are now orthonormal
tol = 1.e-12
for i in range(n_vecs):
for j in range(i+1):
omegaiTomegaj = Utils.inner(omega[i,:], omega[j,:], cls.comm)
if rank == 0:
if i == j:
self.assertTrue(abs(omegaiTomegaj - 1.0) < tol)
else:
self.assertTrue(abs(omegaiTomegaj-0.0) < tol)
def test_all(self):
cls = self.__class__
rank = cls.comm.getRank()
file_dir = os.path.dirname(__file__)
# Create an Albany problem:
filename = 'input_conductivity_dist_paramT.yaml'
problem = Utils.createAlbanyProblem(file_dir+'/'+filename, cls.parallelEnv)
parameter_map = problem.getParameterMap(0)
parameter = Tpetra.MultiVector(parameter_map, 1, dtype="d")
num_elems = parameter_map.getNodeNumElements()
parameter[0, :] = 2.0*np.ones(num_elems)
problem.performSolve()
state_map = problem.getStateMap()
state = Tpetra.MultiVector(state_map, 1, dtype="d")
state[0, :] = problem.getState()
state_ref = Utils.loadMVector('state_ref', 1, state_map, distributedFile=False, useBinary=False, readOnRankZero=True)
stackedTimer = problem.getStackedTimer()
setup_time = stackedTimer.accumulatedTime("PyAlbany: Setup Time")
print("setup_time = " + str(setup_time))
tol = 1.e-8
self.assertTrue(np.linalg.norm(state_ref[0, :] - state[0,:]) < tol)
def main(parallelEnv):
comm = MPI.COMM_WORLD
myGlobalRank = comm.rank
# Create an Albany problem:
filename = "input_dirichletT.yaml"
parameter = Utils.createParameterList(
filename, parallelEnv
)
problem = Utils.createAlbanyProblem(parameter, parallelEnv)
parameter_map_0 = problem.getParameterMap(0)
parameter_0 = Tpetra.Vector(parameter_map_0, dtype="d")
N = 200
p_min = -2.
p_max = 2.
# Generate N samples randomly chosen in [p_min, p_max]:
p = np.random.uniform(p_min, p_max, N)
QoI = np.zeros((N,))
# Loop over the N samples and evaluate the quantity of interest:
for i in range(0, N):
parameter_0[0] = p[i]
problem.setParameter(0, parameter_0)
problem.performSolve()
response = problem.getResponse(0)
QoI[i] = response.getData()[0]
if myGlobalRank == 0:
if printPlot:
f, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(16,6))
ax1.hist(p)
ax1.set_ylabel('Counts')
ax1.set_xlabel('Random parameter')
ax2.scatter(p, QoI)
ax2.set_ylabel('Quantity of interest')
ax2.set_xlabel('Random parameter')
ax3.hist(QoI)
ax3.set_ylabel('Counts')
ax3.set_xlabel('Quantity of interest')
plt.savefig('UQ.jpeg', dpi=800)
plt.close()
def test_all(self):
cls = self.__class__
rank = cls.comm.getRank()
file_dir = os.path.dirname(__file__)
# Create an Albany problem:
filename = 'input_conductivity_dist_paramT.yaml'
problem = Utils.createAlbanyProblem(file_dir+'/'+filename, cls.parallelEnv)
n_directions = 4
parameter_map = problem.getParameterMap(0)
directions = Tpetra.MultiVector(parameter_map, n_directions, dtype="d")
directions[0,:] = 1.
directions[1,:] = -1.
directions[2,:] = 3.
directions[3,:] = -3.
problem.setDirections(0, directions)
problem.performSolve()
response = problem.getResponse(0)
sensitivity = problem.getSensitivity(0, 0)
hessian = problem.getReducedHessian(0, 0)
g_target = 3.23754626955999991e-01
norm_target = 8.94463776843999921e-03
h_target = np.array([0.009195356672103817, 0.009195356672103817, 0.027586070971800013, 0.027586070971800013])
g_data = response.getData()
norm = Utils.norm(sensitivity.getData(0), cls.comm)
print("g_target = " + str(g_target))
print("g_data[0] = " + str(g_data[0]))
print("norm = " + str(norm))
print("norm_target = " + str(norm_target))
hessian_norms = np.zeros((n_directions,))
for i in range(0,n_directions):
hessian_norms[i] = Utils.norm(hessian.getData(i), cls.comm)
tol = 1e-8
if rank == 0:
self.assertTrue(np.abs(g_data[0]-g_target) < tol)
self.assertTrue(np.abs(norm-norm_target) < tol)
for i in range(0,n_directions):
self.assertTrue(np.abs(hessian_norms[i]-h_target[i]) < tol)
def test_all(self):
comm = Teuchos.DefaultComm.getComm()
rank = comm.getRank()
file_dir = os.path.dirname(__file__)
# Create an Albany problem:
filename = 'input_conductivity_dist_paramT.yaml'
problem = Utils.createAlbanyProblem(file_dir + '/' + filename)
n_directions = 4
parameter_map = problem.getParameterMap(0)
directions = Tpetra.MultiVector(parameter_map, n_directions, dtype="d")
directions[0, :] = 1.
directions[1, :] = -1.
directions[2, :] = 3.
directions[3, :] = -3.
problem.setDirections(0, directions)
problem.performSolve()
response = problem.getResponse(0)
sensitivity = problem.getSensitivity(0, 0)
hessian = problem.getReducedHessian(0, 0)
g_target = 3.23754626955999991e-01
norm_target = 8.94463776843999921e-03
h_target = np.array([
4.2121719763904516e-05, -4.21216874727712e-05,
0.00012636506241831498, -0.00012636506241831496
])
g_data = response.getData()
norm = Utils.norm(sensitivity.getData(0), comm)
print("g_target = " + str(g_target))
print("g_data[0] = " + str(g_data[0]))
print("norm = " + str(norm))
print("norm_target = " + str(norm_target))
tol = 1e-8
if rank == 0:
self.assertTrue(np.abs(g_data[0] - g_target) < tol)
self.assertTrue(np.abs(norm - norm_target) < tol)
for i in range(0, n_directions):
self.assertTrue(np.abs(hessian[i, 0] - h_target[i]) < tol)
def main(parallelEnv):
comm = Teuchos.DefaultComm.getComm()
filename = 'input_conductivity_dist_paramT.yaml'
problem = Utils.createAlbanyProblem(filename, parallelEnv)
# We can get from the Albany problem the map of a distributed parameter:
parameter_map = problem.getParameterMap(0)
# This map can then be used to construct an RCP to a Tpetra::Multivector:
m_directions = 4
directions = Tpetra.MultiVector(parameter_map, m_directions, dtype="d")
# Numpy operations, such as assignments, can then be performed on the local entries:
directions[0, :] = 1. # Set all entries of v_0 to 1
directions[1, :] = -1. # Set all entries of v_1 to -1
directions[2, :] = 3. # Set all entries of v_2 to 3
directions[3, :] = -3. # Set all entries of v_3 to -3
# Now that we have an RCP to the directions, we provide it to the Albany problem:
problem.setDirections(0, directions)
# Finally, we can solve the problem (which includes applying the Hessian to the directions)
# and get the Hessian-vector products:
problem.performSolve()
hessian = problem.getReducedHessian(0, 0)
def test_all(self):
cls = self.__class__
rank = cls.comm.getRank()
file_dir = os.path.dirname(__file__)
# Create an Albany problem:
filename = "input_dirichlet_mixed_paramsT.yaml"
parameter = Utils.createParameterList(file_dir + "/" + filename,
cls.parallelEnv)
parameter.sublist("Discretization").set("1D Elements", 10)
parameter.sublist("Discretization").set("2D Elements", 10)
problem = Utils.createAlbanyProblem(parameter, cls.parallelEnv)
parameter_map_0 = problem.getParameterMap(0)
para_0_new = Tpetra.Vector(parameter_map_0, dtype="d")
parameter_map_1 = problem.getParameterMap(1)
para_1_new = Tpetra.Vector(parameter_map_1, dtype="d")
para_1_new[:] = 0.333333
n_values = 5
para_0_values = np.linspace(-1, 1, n_values)
responses = np.zeros((n_values, ))
responses_target = np.array(
[0.69247527, 0.48990929, 0.35681844, 0.29320271, 0.2990621])
tol = 1e-8
for i in range(0, n_values):
para_0_new[:] = para_0_values[i]
problem.setParameter(0, para_0_new)
problem.performSolve()
response = problem.getResponse(0)
responses[i] = response.getData()[0]
print("p = " + str(para_0_values))
print("QoI = " + str(responses))
if rank == 0:
self.assertTrue(
np.abs(np.amax(responses - responses_target)) < tol)
def main(parallelEnv):
filename = 'input_conductivity_dist_paramT.yaml'
problem = Utils.createAlbanyProblem(filename, parallelEnv)
# Now that the Albany problem is constructed, we can solve
# it and evaluate the response:
problem.performSolve()
response = problem.getResponse(0)
print(response)
def test_read_non_distributed_npy(self):
comm = Teuchos.DefaultComm.getComm()
rank = comm.getRank()
nproc = comm.getSize()
if nproc > 1:
mvector_filename = 'in_mvector_read_test_' + str(nproc)
else:
mvector_filename ='in_mvector_read_test'
file_dir = os.path.dirname(__file__)
filename = 'input.yaml'
problem = Utils.createAlbanyProblem(file_dir+'/'+filename)
n_cols = 4
parameter_map = problem.getParameterMap(0)
mvector = Utils.loadMVector(file_dir+'/'+mvector_filename, n_cols, parameter_map, distributedFile = False)
tol = 1e-8
mvector_target = np.array([1., -1, 3.26, -3.1])*(rank+1)
for i in range(0, n_cols):
self.assertTrue(np.abs(mvector[i,0]-mvector_target[i]) < tol)
def main(parallelEnv):
comm = parallelEnv.comm
filename = 'input_conductivity_dist_paramT.yaml'
problem = Utils.createAlbanyProblem(filename, parallelEnv)
problem.performSolve()
# We can solve the problem and extract the sensitivity w.r.t. a parameter:
sensitivity = problem.getSensitivity(0, 0)
# In this example, we illustrate how to return values as output without
# relying on Kokkos-related object; the local data of the vectors are deeply
# copied to a new numpy array:
sensitivity_out = np.copy(sensitivity[0, :])
return sensitivity_out
def test_all(self):
cls = self.__class__
rank = cls.comm.getRank()
file_dir = os.path.dirname(__file__)
# Create an Albany problem:
filename = "input_dirichlet_mixed_paramsT.yaml"
parameter = Utils.createParameterList(
file_dir + "/" + filename, cls.parallelEnv
)
parameter.sublist("Discretization").set("1D Elements", 10)
parameter.sublist("Discretization").set("2D Elements", 10)
problem = Utils.createAlbanyProblem(parameter, cls.parallelEnv)
g_target_before = 0.35681844
g_target_after = 0.17388298
g_target_2 = 0.19570272
p_0_target = 0.39886689
p_1_norm_target = 5.37319376038225
tol = 1e-8
problem.performSolve()
response_before_analysis = problem.getResponse(0)
problem.performAnalysis()
para_0 = problem.getParameter(0)
para_1 = problem.getParameter(1)
print(para_0.getData())
print(para_1.getData())
para_1_norm = Utils.norm(para_1.getData(), cls.comm)
print(para_1_norm)
if rank == 0:
self.assertTrue(np.abs(para_0[0] - p_0_target) < tol)
self.assertTrue(np.abs(para_1_norm - p_1_norm_target) < tol)
problem.performSolve()
response_after_analysis = problem.getResponse(0)
print("Response before analysis " + str(response_before_analysis.getData()))
print("Response after analysis " + str(response_after_analysis.getData()))
if rank == 0:
self.assertTrue(np.abs(response_before_analysis[0] - g_target_before) < tol)
self.assertTrue(np.abs(response_after_analysis[0] - g_target_after) < tol)
parameter_map_0 = problem.getParameterMap(0)
para_0_new = Tpetra.Vector(parameter_map_0, dtype="d")
para_0_new[:] = 0.0
problem.setParameter(0, para_0_new)
problem.performSolve()
response = problem.getResponse(0)
print("Response after setParameter " + str(response.getData()))
if rank == 0:
self.assertTrue(np.abs(response[0] - g_target_2) < tol)
def setUpClass(cls):
cls.comm = Teuchos.DefaultComm.getComm()
cls.parallelEnv = Utils.createDefaultParallelEnv(cls.comm)
def test_all(self):
debug = True
cls = self.__class__
myGlobalRank = cls.comm.getRank()
nproc = cls.comm.getSize()
# Create an Albany problem:
n_params = 2
filename = "thermal_steady.yaml"
parameter = Utils.createParameterList(
filename, cls.parallelEnv
)
problem = Utils.createAlbanyProblem(parameter, cls.parallelEnv)
# ----------------------------------------------
#
# 1. Evaluation of the theta star
#
# ----------------------------------------------
l_min = 0.
l_max = 2.
n_l = 3
l = np.linspace(l_min, l_max, n_l)
theta_star, I_star, F_star, P_star = ee.evaluateThetaStar(l, problem, n_params)
# ----------------------------------------------
#
# 2. Evaluation of the prefactor using IS
#
# ----------------------------------------------
N_samples = 10
mean = np.array([1., 1.])
cov = np.array([[1., 0.], [0., 1.]])
np.random.seed(41)
samples = np.random.multivariate_normal(mean, cov, N_samples)
angle_1 = 0.49999*np.pi
angle_2 = np.pi - angle_1
P_IS = ee.importanceSamplingEstimator(mean, cov, theta_star, F_star, P_star, samples, problem)
P_mixed = ee.mixedImportanceSamplingEstimator(mean, cov, theta_star, F_star, P_star, samples, problem, angle_1, angle_2)
if myGlobalRank == 0:
expected_theta_star = np.loadtxt('expected_theta_star_steady_'+str(nproc)+'.txt')
expected_I_star = np.loadtxt('expected_I_star_steady_'+str(nproc)+'.txt')
expected_P_star = np.loadtxt('expected_P_star_steady_'+str(nproc)+'.txt')
expected_F_star = np.loadtxt('expected_F_star_steady_'+str(nproc)+'.txt')
expected_P_IS = np.loadtxt('expected_P_steady_IS_'+str(nproc)+'.txt')
expected_P_mixed = np.loadtxt('expected_P_steady_mixed_'+str(nproc)+'.txt')
tol = 1e-8
tol_F = 5e-5
if debug:
for i in range(0, len(expected_theta_star)):
print('i = ' + str(i) + ': theta star: expected value = ' + str(expected_theta_star[i]) + ', computed value = ' + str(theta_star[i]) + ', and diff = ' + str(expected_theta_star[i]-theta_star[i]))
print('i = ' + str(i) + ': I star: expected value = ' + str(expected_I_star[i]) + ', computed value = ' + str(I_star[i]) + ', and diff = ' + str(expected_I_star[i]-I_star[i]))
print('i = ' + str(i) + ': P star: expected value = ' + str(expected_P_star[i]) + ', computed value = ' + str(P_star[i]) + ', and diff = ' + str(expected_P_star[i]-P_star[i]))
print('i = ' + str(i) + ': F star: expected value = ' + str(expected_F_star[i]) + ', computed value = ' + str(F_star[i]) + ', and diff = ' + str(expected_F_star[i]-F_star[i]))
print('i = ' + str(i) + ': P IS: expected value = ' + str(expected_P_IS[i]) + ', computed value = ' + str(P_IS[i]) + ', and diff = ' + str(expected_P_IS[i]-P_IS[i]))
print('i = ' + str(i) + ': P mixed: expected value = ' + str(expected_P_mixed[i]) + ', computed value = ' + str(P_mixed[i]) + ', and diff = ' + str(expected_P_mixed[i]-P_mixed[i]))
self.assertTrue(np.amax(np.abs(expected_theta_star - theta_star)) < tol)
self.assertTrue(np.amax(np.abs(expected_I_star - I_star)) < tol)
self.assertTrue(np.amax(np.abs(expected_P_star - P_star)) < tol)
self.assertTrue(np.amax(np.abs(expected_F_star - F_star)) < tol_F)
self.assertTrue(np.amax(np.abs(expected_P_IS - P_IS)) < tol)
self.assertTrue(np.amax(np.abs(expected_P_mixed - P_mixed)) < tol)
for j in range(0, nTimers):
mean_timers_sec[i, j] = np.mean(timers_sec[i, j, :])
speedUp[i, :] = mean_timers_sec[0, :] / (mean_timers_sec[i, :])
print('timers')
print(mean_timers_sec)
print('speed up')
print(speedUp)
if printPlot:
fig = plt.figure(figsize=(10, 6))
plt.plot(np.arange(1, nMaxProcs + 1), np.arange(1, nMaxProcs + 1),
'--')
for j in range(0, nTimers):
plt.plot(np.arange(1, nMaxProcs + 1),
speedUp[:, j],
'o-',
label=timerNames[j])
plt.ylabel('speed up')
plt.xlabel('number of MPI processes')
plt.grid(True)
plt.legend()
plt.savefig('speedup.jpeg', dpi=800)
plt.close()
if __name__ == "__main__":
comm = Teuchos.DefaultComm.getComm()
parallelEnv = Utils.createDefaultParallelEnv(comm)
main(parallelEnv)
def main(parallelEnv):
comm = MPI.COMM_WORLD
nMaxProcs = comm.Get_size()
myGlobalRank = comm.rank
timerNames = [
"PyAlbany: Create Albany Problem", "PyAlbany: Set directions",
"PyAlbany: Perform Solve", "PyAlbany: Total"
]
nTimers = len(timerNames)
# number of times that the test is repeated for a fixed
# number of MPI processes
N = 10
timers_sec = np.zeros((nMaxProcs, nTimers, N))
mean_timers_sec = np.zeros((nMaxProcs, nTimers))
speedUp = np.zeros((nMaxProcs, nTimers))
for nProcs in range(1, nMaxProcs + 1):
newGroup = comm.group.Incl(np.arange(0, nProcs))
newComm = comm.Create_group(newGroup)
if myGlobalRank < nProcs:
parallelEnv.comm = Teuchos.MpiComm(newComm)
for i_test in range(0, N):
timers = Utils.createTimers(timerNames)
timers[3].start()
timers[0].start()
filename = 'input_conductivity_dist_paramT.yaml'
problem = Utils.createAlbanyProblem(filename, parallelEnv)
timers[0].stop()
timers[1].start()
n_directions = 4
parameter_map = problem.getParameterMap(0)
directions = Tpetra.MultiVector(parameter_map,
n_directions,
dtype="d")
directions[0, :] = 1.
directions[1, :] = -1.
directions[2, :] = 3.
directions[3, :] = -3.
problem.setDirections(0, directions)
timers[1].stop()
timers[2].start()
problem.performSolve()
timers[2].stop()
timers[3].stop()
if myGlobalRank == 0:
for j in range(0, nTimers):
timers_sec[nProcs - 1, j,
i_test] = timers[j].totalElapsedTime()
if myGlobalRank == 0:
for i in range(0, nMaxProcs):
for j in range(0, nTimers):
mean_timers_sec[i, j] = np.mean(timers_sec[i, j, :])
speedUp[i, :] = mean_timers_sec[0, :] / (mean_timers_sec[i, :])
print('timers')
print(mean_timers_sec)
print('speed up')
print(speedUp)
if printPlot:
fig = plt.figure(figsize=(10, 6))
plt.plot(np.arange(1, nMaxProcs + 1), np.arange(1, nMaxProcs + 1),
'--')
for j in range(0, nTimers):
plt.plot(np.arange(1, nMaxProcs + 1),
speedUp[:, j],
'o-',
label=timerNames[j])
plt.ylabel('speed up')
plt.xlabel('number of MPI processes')
plt.grid(True)
plt.legend()
plt.savefig('speedup.jpeg', dpi=800)
plt.close()
def test_all(self):
debug = True
cls = self.__class__
myGlobalRank = cls.comm.getRank()
nproc = cls.comm.getSize()
# Create an Albany problem:
n_params = 2
filename = "thermal_steady_hessian.yaml"
parameter = Utils.createParameterList(
filename, cls.parallelEnv
)
problem = Utils.createAlbanyProblem(parameter, cls.parallelEnv)
# ----------------------------------------------
#
# 1. Evaluation of the theta star
#
# ----------------------------------------------
l_min = 1.
l_max = 2.
n_l = 4
p = 0.25
l = l_min + np.power(np.linspace(0.0, 1.0, n_l), p) * (l_max-l_min)
theta_star, I_star, F_star, P_star = ee.evaluateThetaStar(l, problem, n_params)
# ----------------------------------------------
#
# 2. Evaluation of the prefactor using SO
#
# ----------------------------------------------
mean = np.array([1., 1.])
cov = np.array([[1., 0.], [0., 1.]])
P_SO = ee.secondOrderEstimator(mean, cov, l, theta_star, I_star, F_star, P_star, problem)
if myGlobalRank == 0:
expected_theta_star = np.loadtxt('expected_theta_star_steady_hessian_'+str(nproc)+'.txt')
expected_I_star = np.loadtxt('expected_I_star_steady_hessian_'+str(nproc)+'.txt')
expected_P_star = np.loadtxt('expected_P_star_steady_hessian_'+str(nproc)+'.txt')
expected_F_star = np.loadtxt('expected_F_star_steady_hessian_'+str(nproc)+'.txt')
expected_P_SO = np.loadtxt('expected_P_steady_hessian_SO_'+str(nproc)+'.txt')
tol = 1e-6
if debug:
for i in range(0, len(expected_theta_star)):
print('i = ' + str(i) + ': theta star: expected value = ' + str(expected_theta_star[i]) + ', computed value = ' + str(theta_star[i]) + ', and diff = ' + str(expected_theta_star[i]-theta_star[i]))
print('i = ' + str(i) + ': I star: expected value = ' + str(expected_I_star[i]) + ', computed value = ' + str(I_star[i]) + ', and diff = ' + str(expected_I_star[i]-I_star[i]))
print('i = ' + str(i) + ': P star: expected value = ' + str(expected_P_star[i]) + ', computed value = ' + str(P_star[i]) + ', and diff = ' + str(expected_P_star[i]-P_star[i]))
print('i = ' + str(i) + ': F star: expected value = ' + str(expected_F_star[i]) + ', computed value = ' + str(F_star[i]) + ', and diff = ' + str(expected_F_star[i]-F_star[i]))
print('i = ' + str(i) + ': P SO: expected value = ' + str(expected_P_SO[i]) + ', computed value = ' + str(P_SO[i]) + ', and diff = ' + str(expected_P_SO[i]-P_SO[i]))
self.assertTrue(np.amax(np.abs(expected_theta_star - theta_star)) < tol)
self.assertTrue(np.amax(np.abs(expected_I_star - I_star)) < tol)
self.assertTrue(np.amax(np.abs(expected_P_star - P_star)) < tol)
self.assertTrue(np.amax(np.abs(expected_F_star - F_star)) < tol)
self.assertTrue(np.amax(np.abs(expected_P_SO - P_SO)) < tol)
def main(parallelEnv):
# This example illustrates how PyAlbany can be used to compute
# reduced Hessian-vector products w.r.t to the basal friction.
comm = parallelEnv.comm
rank = comm.getRank()
nprocs = comm.getSize()
file_dir = os.path.dirname(__file__)
filename = 'input_fo_gis_analysis_beta_smbT.yaml'
parameter_index = 0
response_index = 0
timers = Utils.createTimers([
"PyAlbany: Create Albany Problem",
"PyAlbany: Read multivector directions", "PyAlbany: Set directions",
"PyAlbany: Perform Solve", "PyAlbany: Get Reduced Hessian",
"PyAlbany: Write Reduced Hessian", "PyAlbany: Total"
])
timers[6].start()
timers[0].start()
problem = Utils.createAlbanyProblem(filename, parallelEnv)
timers[0].stop()
timers[1].start()
n_directions = 4
parameter_map = problem.getParameterMap(0)
directions = Utils.loadMVector('random_directions',
n_directions,
parameter_map,
distributedFile=False,
useBinary=True)
timers[1].stop()
timers[2].start()
problem.setDirections(parameter_index, directions)
timers[2].stop()
timers[3].start()
problem.performSolve()
timers[3].stop()
timers[4].start()
hessian = problem.getReducedHessian(response_index, parameter_index)
timers[4].stop()
timers[5].start()
Utils.writeMVector("hessian_nprocs_" + str(nprocs),
hessian,
distributedFile=True,
useBinary=False)
Utils.writeMVector("hessian_all_nprocs_" + str(nprocs),
hessian,
distributedFile=False,
useBinary=False)
timers[5].stop()
print(hessian[0, 0])
print(hessian[1, 0])
print(hessian[2, 0])
print(hessian[3, 0])
timers[6].stop()
Utils.printTimers(timers, "timers_nprocs_" + str(nprocs) + ".txt")
# First, some Python packages are imported:
from PyTrilinos import Tpetra
from PyTrilinos import Teuchos
import numpy as np
from PyAlbany import Utils
# Then, the parallel environment is initialized (including Kokkos):
comm = Teuchos.DefaultComm.getComm()
parallelEnv = Utils.createDefaultParallelEnv(comm,
n_threads=-1,
n_numa=-1,
device_id=-1)
# (Kokkos finalize will be called during the destruction of parallelEnv;
# we will have to enforce that this destructor is called after the destruction
# of every object which relies on Kokkos.)
# Finally, given a filename and the parallel environment, an Albany problem is constructed:
filename = 'input_conductivity_dist_paramT.yaml'
problem = Utils.createAlbanyProblem(filename, parallelEnv)
# Now, we call the problem destructor first (by setting the RCP to null):
problem = None
# And we call the parallelEnv destructor:
parallelEnv = None
comm = Teuchos.DefaultComm.getComm()
rank = comm.getRank()
nprocs = comm.getSize()
file_dir = os.path.dirname(__file__)
filename = 'input_fo_gis_analysis_beta_smbT.yaml'
parameter_index = 0
response_index = 0
timers = Utils.createTimers(["PyAlbany: Create Albany Problem",
"PyAlbany: Read multivector directions",
"PyAlbany: Set directions",
"PyAlbany: Perform Solve",
"PyAlbany: Get Reduced Hessian",
"PyAlbany: Write Reduced Hessian",
"PyAlbany: Total"])
timers[6].start()
timers[0].start()
problem = Utils.createAlbanyProblem(filename)
timers[0].stop()
timers[1].start()
n_directions=4
parameter_map = problem.getParameterMap(0)
directions = Utils.loadMVector('random_directions', n_directions, parameter_map, distributedFile = False, useBinary = True)
timers[1].stop()
import numpy as np
from PyAlbany import Utils
# As discussed in example_0.py parallelEnv should be destructed
# after the destruction of all the other variables which rely on
# Kokkos.
# A better way to enforce this than calling the destructor explicitly
# for all the variables is to rely on the garbage collector capability
# of python using the scope of a function.
# At the end of the function all the internal objects (all objects which
# are not inputs or outputs) are destructed.
# Therefore, we can create a function which takes parallelEnv as input in which
# all Kokkos-related objects will be created and will not be passed as output;
# they will necessarily be destructed before parallelEnv.
# This example revisits example_0.py with the above-mentioned approach.
def main(parallelEnv):
filename = 'input_conductivity_dist_paramT.yaml'
problem = Utils.createAlbanyProblem(filename, parallelEnv)
if __name__ == "__main__":
comm = Teuchos.DefaultComm.getComm()
parallelEnv = Utils.createDefaultParallelEnv(comm,
n_threads=-1,
n_numa=-1,
device_id=-1)
main(parallelEnv)
def main(parallelEnv):
filename = 'input_conductivity_dist_paramT.yaml'
problem = Utils.createAlbanyProblem(filename, parallelEnv)
def main(parallelEnv):
comm = MPI.COMM_WORLD
myGlobalRank = comm.rank
# Create an Albany problem:
n_params = 2
filename = "thermal_steady_2.yaml"
parameter = Utils.createParameterList(filename, parallelEnv)
problem = Utils.createAlbanyProblem(parameter, parallelEnv)
# ----------------------------------------------
#
# 1. Evaluation of the theta star
#
# ----------------------------------------------
l_min = 8.
l_max = 20.
n_l = 5
p = 1.
l = l_min + np.power(np.linspace(0.0, 1.0, n_l), p) * (l_max - l_min)
theta_star, I_star, F_star, P_star = ee.evaluateThetaStar(
l, problem, n_params)
np.savetxt('theta_star_steady_2.txt', theta_star)
np.savetxt('I_star_steady_2.txt', I_star)
np.savetxt('P_star_steady_2.txt', P_star)
np.savetxt('F_star_steady_2.txt', F_star)
# ----------------------------------------------
#
# 2. Evaluation of the prefactor using IS
#
# ----------------------------------------------
N_samples = 100
mean = np.array([1., 1.])
cov = np.array([[1., 0.], [0., 1.]])
samples = np.random.multivariate_normal(mean, cov, N_samples)
angle_1 = 0.49999 * np.pi
angle_2 = np.pi - angle_1
P_IS = ee.importanceSamplingEstimator(mean, cov, theta_star, F_star,
P_star, samples, problem)
P_mixed = ee.mixedImportanceSamplingEstimator(mean, cov, theta_star,
F_star, P_star, samples,
problem, angle_1, angle_2)
P_SO = ee.secondOrderEstimator(mean, cov, l, theta_star, I_star, F_star,
P_star, problem)
np.savetxt('P_steady_IS_2.txt', P_IS)
np.savetxt('P_steady_mixed_2.txt', P_mixed)
np.savetxt('P_steady_SO_2.txt', P_SO)
problem.reportTimers()
# ----------------------------------------------
#
# 3. Plots
#
# ----------------------------------------------
if n_params == 2:
X = np.arange(1, 7, 0.2)
Y = np.arange(1, 7, 0.25)
Z1, Z2 = evaluate_responses(X, Y, problem, True)
X, Y = np.meshgrid(X, Y)
if myGlobalRank == 0:
if printPlot:
plt.figure()
plt.semilogy(F_star, P_star, 'k*-')
plt.semilogy(F_star, P_IS, 'b*-')
plt.semilogy(F_star, P_mixed, 'r*--')
plt.semilogy(F_star, P_SO, 'g*-')
plt.savefig('extreme_steady_2.jpeg', dpi=800)
plt.close()
if n_params == 2:
plt.figure()
plt.plot(theta_star[:, 0], theta_star[:, 1], '*-')
plt.contour(X, Y, Z1, levels=I_star, colors='g')
plt.contour(X, Y, Z2, levels=F_star, colors='r')
plt.savefig('theta_star_2.jpeg', dpi=800)
plt.close()
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot_surface(X, Y, Z1)
plt.savefig('Z1_2.jpeg', dpi=800)
plt.close()
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot_surface(X, Y, Z2)
plt.savefig('Z2_2.jpeg', dpi=800)
plt.close()