def KLE1D(a=1, c=1, k=10):
from kle import KLE
mesh = UnitInterval(1000)
mesh.coordinates()[:] = 2. * a * mesh.coordinates()[:] - a
def kernel(R):
return np.exp(-c * R)
kle = KLE(mesh, kernel)
from time import time
start = time()
la, va = kle.compute_eigendecomposition(k=k)
la = la[::-1]
va = va[:, ::-1]
print "Time for arpack %g " % (time() - start)
return la, va
def KLE1D(a = 1, c = 1, k = 10):
from kle import KLE
mesh = UnitInterval(1000)
mesh.coordinates()[:] = 2.*a*mesh.coordinates()[:] - a
def kernel(R): return np.exp(-c*R)
kle = KLE(mesh,kernel)
from time import time
start = time()
la, va = kle.compute_eigendecomposition(k = k)
la = la[::-1]
va = va[:,::-1]
print "Time for arpack %g " %(time()-start)
return la, va
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.
print mesh.coordinates()
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)
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()
Polynomials = cp.orth_ttr(order, joint_KL)
# Generate samples by quasi-random samples
qmc_scheme = "H"
nnodes = 2*len(Polynomials)
nodes = joint_KL.sample(nnodes, qmc_scheme)
# Regression method in Point Collocation
rgm_rule ="T" #Orthogonal Matching Pursuit#"LS"
# Random Field
p , l = np.inf, 1
k = nkl
kernel = Matern(p = p,l = l) #0,1Exponential covariance kernel
kle = KLE(model.mesh, kernel, verbose = True)
kle.compute_eigendecomposition(k = k)#20 by default
#real = kle.realizations(epsilon)
# range of pressure
pi = 0.0
pf = 0.03
dp = 0.01
pressures = np.arange(pi, pf+dp, dp)
print "---------------------------------"
print "PCE-Random Field"
print "Nkl terms:", int(nkl)
print "Order:", order
print "Sampling Method:", qmc_scheme
print "Number of nodes:", nnodes
from kle import KLE
from covariance import Matern
from dolfin import *
import numpy as np
def view(kle):
#Write in pvd format. Can be opened in Paraview or MayaVi
file = File("figs/kle.pvd","compressed")
v = Function(kle.V)
for i in np.arange(kle.l.size):
v.vector()[:] = np.copy(kle.v[:,i])
file << (v,float(i))
return
if __name__ == '__main__':
mesh = Mesh("meshes/aneurysm.xml.gz")
kernel = Matern(p = 2, l = 20.)
kle = KLE(mesh, kernel, verbose = True)
kle.compute_eigendecomposition(k = 6)
view(kle)
order = 3 Polynomials = cp.orth_ttr(order, joint_KL) # Generate samples by quasi-random samples qmc_scheme = "S" # "H" nnodes = 3 * len(Polynomials) nodes = joint_KL.sample(nnodes, qmc_scheme) # Regression method in Point Collocation rgm_rule = "T" # Orthogonal Matching Pursuit#"LS" # Random Field sigma = 0.5 # 10.*np.pi/180. p, l = np.inf, 10 k = nkl kernel = Matern(p=p, l=l, s=sigma) # 0,1Exponential covariance kernel kle = KLE(model.mesh, kernel, verbose=True) kle.compute_eigendecomposition(k=k) # 20 by default # real = kle.realizations(epsilon) # range of pressure pi = 0.0 pf = 2.0 dp = 0.05 pressures = np.arange(pi, pf + dp, dp) print "---------------------------------" print "PCE-Random Field" print "Nkl terms:", int(nkl)
