fig.suptitle('Eigenvectors of KLE', fontsize=20)
fig.subplots_adjust(right=0.8)
cbar_ax = fig.add_axes([0.85, 0.15, 0.05, 0.7])
fig.colorbar(im, cax=cbar_ax)
plt.savefig('figs/square.png')
plt.show()
return
if __name__ == '__main__':
from dolfin import *
mesh = UnitSquare(20, 20) #really a 101 x 101 grid
mesh.coordinates()[:] = 2. * mesh.coordinates() - 1.
kernel = Matern(p=0, l=1.) #Exponential covariance kernel
kle = KLE(mesh, kernel, verbose=True)
kle.compute_eigendecomposition(k=20)
print kle.l
import matplotlib.pyplot as plt
plt.close('all')
#ploteigenvectors(kle)
#Generate realizations
real = kle.realizations()
#Gaussian field with correlation length l
p, l = np.inf, 1
#number of terms in expansion
k = 20
kernel = Matern(p=p, l=l) #0,1Exponential covariance kernel
kle = KLE(mesh, kernel, verbose=True)
kle.compute_eigendecomposition(k=k) #20 by default
print "eigenvalues:", kle.l
plt.close('all')
#ploteigenvectors(kle)
#Generate realizations
noise = kle.realizations()
# The markers are stored within the mesh
#ffun = MeshFunction("size_t", mesh, 2, mesh.domains())
# The facet function contains some very large number,
# so if you want plot it you need to surpress those values
#ffun.array()[ffun.array() == max(ffun.array())] = 0
#plot(ffun,mesh, interactive =True))
#plotting the field
V = FunctionSpace(mesh, "CG", 1)
random_field = Function(V)
random_f = np.zeros((mesh.num_vertices()), dtype=float)
random_f = noise
random_field.vector()[:] = random_f[dof_to_vertex_map(V)]
plot(random_field, mesh, interactive=True)
sffmean = Function(model.projection_space)
sffstdv = Function(model.projection_space)
sffsai1 = Function(model.projection_space)
sffsait = Function(model.projection_space)
random_field = Function(FunctionSpace(model.mesh, "CG", 1))
# Evaluate model in sample points
solves1 = []
solves2 = []
solves3 = []
nnan = 0
for s in nodes.T:
alpha_noise = kle.realizations(s)
model.update_randomfield( alpha_noise = alpha_noise)
pressure = pi
while pressure <= pressures[len(pressures)-1]:
print "----------------"
print "PRESSURE", pressure
print "----------------"
qoi = model.run(pressure)
while np.isnan(qoi[0]) == True:
print "WARNING: NaN"
newsample = joint.sample(1, rule = "R")
model = problem()
model.update_params(*newsample.T[0])
nnan = nnan + 1
sffmean = Function(model.projection_space)
sffstdv = Function(model.projection_space)
sffsai1 = Function(model.projection_space)
sffsait = Function(model.projection_space)
random_field = Function(FunctionSpace(model.mesh, "CG", 1))
# Evaluate model in sample points
solves1 = []
solves2 = []
solves3 = []
nnan, i = 0, 0
model = problem()
for s in nodes.T:
model = problem()
alpha_noise = kle.realizations(s)[dof_to_vertex_map(model.fiber_space)]
model.update_randomfield(alpha_noise=alpha_noise)
pressure = pi
while pressure <= pressures[len(pressures) - 1]:
print
"----------------"
print
"PRESSURE", pressure, pressures[len(pressures) - 1]
print
"----------------"
qoi = model.run(pressure)
if (i == 0) & (pressure == 0.0):
txt_file.write("--------------------------------- \n")
txt_file.write("PCE: Random Field \n")
txt_file.write("Nkl terms: %i \n" % int(nkl))
