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Innerproduct work. Testing, visualization, and 2D - NOTE there are bugs in anything but a uniform LOM

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Not very helpful yet!
This commit is contained in:
Rowan Cockett
2013-08-05 11:51:03 -07:00
parent e2e38074fc
commit e073eaeb8b
9 changed files with 465 additions and 116 deletions
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SimPEG/InnerProducts.py
+91 -3
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@@ -1,5 +1,5 @@
from scipy import sparse as sp
from sputils import sdiag, inv3X3BlockDiagonal
from sputils import sdiag, inv3X3BlockDiagonal, inv2X2BlockDiagonal
from utils import sub2ind, ndgrid, mkvc, getSubArray
import numpy as np
@@ -16,7 +16,10 @@ class InnerProducts(object):
pass
elif self._meshType == 'LOM':
pass # todo: we should be doing something slightly different here!
return getFaceInnerProduct(self, mu, returnP)
if self.dim == 2:
return getFaceInnerProduct2D(self, mu, returnP)
elif self.dim == 3:
return getFaceInnerProduct(self, mu, returnP)
def getEdgeInnerProduct(self, sigma=None, returnP=False):
if self._meshType == 'TENSOR':
@@ -59,6 +62,11 @@ def getFaceInnerProduct(mesh, mu=None, returnP=False):
iijjkk = ndgrid(i, j, k)
ii, jj, kk = iijjkk[:, 0], iijjkk[:, 1], iijjkk[:, 2]
if mesh._meshType == 'LOM':
fN1 = mesh.r(mesh.normals, 'F', 'Fx', 'M')
fN2 = mesh.r(mesh.normals, 'F', 'Fy', 'M')
fN3 = mesh.r(mesh.normals, 'F', 'Fz', 'M')
def Pxxx(pos):
ind1 = sub2ind(mesh.nFx, np.c_[ii + pos[0][0], jj + pos[0][1], kk + pos[0][2]])
ind2 = sub2ind(mesh.nFy, np.c_[ii + pos[1][0], jj + pos[1][1], kk + pos[1][2]]) + mesh.nF[0]
@@ -66,7 +74,15 @@ def getFaceInnerProduct(mesh, mu=None, returnP=False):
IND = np.r_[ind1, ind2, ind3].flatten()
return sp.coo_matrix((np.ones(3*nc), (range(3*nc), IND)), shape=(3*nc, np.sum(mesh.nF))).tocsr()
PXXX = sp.coo_matrix((np.ones(3*nc), (range(3*nc), IND)), shape=(3*nc, np.sum(mesh.nF))).tocsr()
if mesh._meshType == 'LOM':
I3x3 = inv3X3BlockDiagonal(getSubArray(fN1[0], [i + pos[0][0], j + pos[0][1], k + pos[0][2]]), getSubArray(fN1[1], [i + pos[0][0], j + pos[0][1], k + pos[0][2]]), getSubArray(fN1[2], [i + pos[0][0], j + pos[0][1], k + pos[0][2]]),
getSubArray(fN2[0], [i + pos[1][0], j + pos[1][1], k + pos[1][2]]), getSubArray(fN2[1], [i + pos[1][0], j + pos[1][1], k + pos[1][2]]), getSubArray(fN2[2], [i + pos[1][0], j + pos[1][1], k + pos[1][2]]),
getSubArray(fN3[0], [i + pos[2][0], j + pos[2][1], k + pos[2][2]]), getSubArray(fN3[1], [i + pos[2][0], j + pos[2][1], k + pos[2][2]]), getSubArray(fN3[2], [i + pos[2][0], j + pos[2][1], k + pos[2][2]]))
PXXX = I3x3 * PXXX
return PXXX
# no | node | f1 | f2 | f3
# 000 | i ,j ,k | i , j, k | i, j , k | i, j, k
@@ -110,6 +126,78 @@ def getFaceInnerProduct(mesh, mu=None, returnP=False):
return A
def getFaceInnerProduct2D(mesh, mu=None, returnP=False):
if mu is None: # default is ones
mu = np.ones((mesh.nC, 1))
m = np.array([mesh.nCx, mesh.nCy])
nc = mesh.nC
i, j = np.int64(range(m[0])), np.int64(range(m[1]))
iijj = ndgrid(i, j)
ii, jj = iijj[:, 0], iijj[:, 1]
if mesh._meshType == 'LOM':
fN1 = mesh.r(mesh.normals, 'F', 'Fx', 'M')
fN2 = mesh.r(mesh.normals, 'F', 'Fy', 'M')
def Pxx(pos):
ind1 = sub2ind(mesh.nFx, np.c_[ii + pos[0][0], jj + pos[0][1]])
ind2 = sub2ind(mesh.nFy, np.c_[ii + pos[1][0], jj + pos[1][1]]) + mesh.nF[0]
IND = np.r_[ind1, ind2].flatten()
PXX = sp.coo_matrix((np.ones(2*nc), (range(2*nc), IND)), shape=(2*nc, np.sum(mesh.nF))).tocsr()
if mesh._meshType == 'LOM':
# print fN1[0].shape
# print fN2[0].shape
# print np.c_[i+pos[0][0],j+pos[0][1],i+pos[1][0],j+pos[1][1]]
# print fN1[1].shape
I2x2 = inv2X2BlockDiagonal(getSubArray(fN1[0], [i + pos[0][0], j + pos[0][1]]), getSubArray(fN1[1], [i + pos[0][0], j + pos[0][1]]),
getSubArray(fN2[0], [i + pos[1][0], j + pos[1][1]]), getSubArray(fN2[1], [i + pos[1][0], j + pos[1][1]]))
PXX = I2x2 * PXX
# import matplotlib.pyplot as plt
# plt.spy(PXX)
# plt.show()
return PXX
# no | node | f1 | f2
# 00 | i ,j | i , j | i, j
# 10 | i+1,j | i+1, j | i, j
# 01 | i ,j+1 | i , j | i, j+1
# 11 | i+1,j+1 | i+1, j | i, j+1
# Square root of cell volume multiplied by 1/4
v = np.sqrt(0.25*mesh.vol)
V2 = sdiag(np.r_[v, v]) # We will multiply on each side to keep symmetry
P00 = V2*Pxx([[0, 0], [0, 0]])
P10 = V2*Pxx([[1, 0], [0, 0]])
P01 = V2*Pxx([[0, 0], [0, 1]])
P11 = V2*Pxx([[1, 0], [0, 1]])
if mu.size == mesh.nC: # Isotropic!
mu = mkvc(mu) # ensure it is a vector.
Mu = sdiag(np.r_[mu, mu])
elif mu.shape[1] == 2: # Diagonal tensor
Mu = sdiag(np.r_[mu[:, 0], mu[:, 1]])
elif mu.shape[1] == 3: # Fully anisotropic
row1 = sp.hstack((sdiag(mu[:, 0]), sdiag(mu[:, 2])))
row2 = sp.hstack((sdiag(mu[:, 2]), sdiag(mu[:, 1])))
Mu = sp.vstack((row1, row2))
A = P00.T*Mu*P00 + P10.T*Mu*P10 + P01.T*Mu*P01 + P11.T*Mu*P11
P = [P00, P10, P01, P11]
if returnP:
return A, P
else:
return A
def getEdgeInnerProduct(mesh, sigma=None, returnP=False):
if sigma is None: # default is ones