def setUp(self):
a = np.array([1, 1, 1])
b = np.array([1, 2])
c = np.array([1, 4])
gridIt = lambda h: [np.cumsum(np.r_[0, x]) for x in h]
X, Y = ndgrid(gridIt([a, b]), vector=False)
self.TM2 = TensorMesh([a, b])
self.Curv2 = CurvilinearMesh([X, Y])
X, Y, Z = ndgrid(gridIt([a, b, c]), vector=False)
self.TM3 = TensorMesh([a, b, c])
self.Curv3 = CurvilinearMesh([X, Y, Z])
def setUp(self):
a = np.array([1, 1, 1])
b = np.array([1, 2])
c = np.array([1, 4])
gridIt = lambda h: [np.cumsum(np.r_[0, x]) for x in h]
X, Y = ndgrid(gridIt([a, b]), vector=False)
self.TM2 = TensorMesh([a, b])
self.Curv2 = CurvilinearMesh([X, Y])
X, Y, Z = ndgrid(gridIt([a, b, c]), vector=False)
self.TM3 = TensorMesh([a, b, c])
self.Curv3 = CurvilinearMesh([X, Y, Z])
def interactive_two_configurations_comparison(log_sig0,log_sig1,log_sig2,R0,R1,xstart,ystart,xend,yend,dipole_number,electrode_spacing,matching_spheres_example):
sig0,sig1 = conductivity_log_wrapper(log_sig0,log_sig1)
sig2 = 10.**log_sig2
E0 = 1. # inducing field strength in V/m
n = 100 #level of discretisation
xr = np.linspace(-200., 200., n) # X-axis discretization
yr = xr.copy() # Y-axis discretization
zr = np.r_[0] # identical to saying `zr = np.array([0])`
XYZ = ndgrid(xr,yr,zr) # Space Definition
PlotOpt = 'Total'
if matching_spheres_example:
sig0 = 10.**(-3)
sig1 = 10.**(-2)
sig2 = 1.310344828 * 10**(-3)
R0 = 20.
R1 = 40.
two_configurations_comparison(XYZ,sig0,sig1,sig2,R0,R1,E0,xstart,ystart,xend,yend,dipole_number,electrode_spacing,PlotOpt)
else:
two_configurations_comparison(XYZ,sig0,sig1,sig2,R0,R1,E0,xstart,ystart,xend,yend,dipole_number,electrode_spacing,PlotOpt)
plt.tight_layout(True)
plt.show()
def _getEdgePxxx(M):
i, j, k = np.arange(M.nCx), np.arange(M.nCy), np.arange(M.nCz)
iijjkk = ndgrid(i, j, k)
ii, jj, kk = iijjkk[:, 0], iijjkk[:, 1], iijjkk[:, 2]
if M._meshType == 'Curv':
eT1 = M.r(M.tangents, 'E', 'Ex', 'M')
eT2 = M.r(M.tangents, 'E', 'Ey', 'M')
eT3 = M.r(M.tangents, 'E', 'Ez', 'M')
def Pxxx(xEdge, yEdge, zEdge):
# no | node | e1 | e2 | e3
# 000 | i ,j ,k | i ,j ,k | i ,j ,k | i ,j ,k
# 100 | i+1,j ,k | i ,j ,k | i+1,j ,k | i+1,j ,k
# 010 | i ,j+1,k | i ,j+1,k | i ,j ,k | i ,j+1,k
# 110 | i+1,j+1,k | i ,j+1,k | i+1,j ,k | i+1,j+1,k
# 001 | i ,j ,k+1 | i ,j ,k+1 | i ,j ,k+1 | i ,j ,k
# 101 | i+1,j ,k+1 | i ,j ,k+1 | i+1,j ,k+1 | i+1,j ,k
# 011 | i ,j+1,k+1 | i ,j+1,k+1 | i ,j ,k+1 | i ,j+1,k
# 111 | i+1,j+1,k+1 | i ,j+1,k+1 | i+1,j ,k+1 | i+1,j+1,k
posX = [0, 0] if xEdge == 'eX0' else [
1, 0
] if xEdge == 'eX1' else [0, 1] if xEdge == 'eX2' else [1, 1]
posY = [0, 0] if yEdge == 'eY0' else [
1, 0
] if yEdge == 'eY1' else [0, 1] if yEdge == 'eY2' else [1, 1]
posZ = [0, 0] if zEdge == 'eZ0' else [
1, 0
] if zEdge == 'eZ1' else [0, 1] if zEdge == 'eZ2' else [1, 1]
ind1 = sub2ind(M.vnEx, np.c_[ii, jj + posX[0], kk + posX[1]])
ind2 = sub2ind(M.vnEy, np.c_[ii + posY[0], jj,
kk + posY[1]]) + M.nEx
ind3 = sub2ind(M.vnEz, np.c_[ii + posZ[0], jj + posZ[1],
kk]) + M.nEx + M.nEy
IND = np.r_[ind1, ind2, ind3].flatten()
PXXX = sp.coo_matrix((np.ones(3 * M.nC), (range(3 * M.nC), IND)),
shape=(3 * M.nC, M.nE)).tocsr()
if M._meshType == 'Curv':
I3x3 = inv3X3BlockDiagonal(
getSubArray(eT1[0], [i, j + posX[0], k + posX[1]]),
getSubArray(eT1[1], [i, j + posX[0], k + posX[1]]),
getSubArray(eT1[2], [i, j + posX[0], k + posX[1]]),
getSubArray(eT2[0], [i + posY[0], j, k + posY[1]]),
getSubArray(eT2[1], [i + posY[0], j, k + posY[1]]),
getSubArray(eT2[2], [i + posY[0], j, k + posY[1]]),
getSubArray(eT3[0], [i + posZ[0], j + posZ[1], k]),
getSubArray(eT3[1], [i + posZ[0], j + posZ[1], k]),
getSubArray(eT3[2], [i + posZ[0], j + posZ[1], k]))
PXXX = I3x3 * PXXX
return PXXX
return Pxxx
def test_ndgrid_2D(self):
XY = ndgrid([self.a, self.b])
X1_test = np.array([1, 2, 3, 1, 2, 3])
X2_test = np.array([1, 1, 1, 2, 2, 2])
self.assertTrue(np.all(XY[:, 0] == X1_test))
self.assertTrue(np.all(XY[:, 1] == X2_test))
def test_ndgrid_2D(self):
XY = ndgrid([self.a, self.b])
X1_test = np.array([1, 2, 3, 1, 2, 3])
X2_test = np.array([1, 1, 1, 2, 2, 2])
self.assertTrue(np.all(XY[:, 0] == X1_test))
self.assertTrue(np.all(XY[:, 1] == X2_test))
def test_ndgrid_3D(self):
XYZ = ndgrid([self.a, self.b, self.c])
X1_test = np.array([1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3])
X2_test = np.array([1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2])
X3_test = np.array([1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4])
self.assertTrue(np.all(XYZ[:, 0] == X1_test))
self.assertTrue(np.all(XYZ[:, 1] == X2_test))
self.assertTrue(np.all(XYZ[:, 2] == X3_test))
def test_ndgrid_3D(self):
XYZ = ndgrid([self.a, self.b, self.c])
X1_test = np.array([
1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1,
2, 3
])
X2_test = np.array([
1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2,
2, 2
])
X3_test = np.array([
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4,
4, 4
])
self.assertTrue(np.all(XYZ[:, 0] == X1_test))
self.assertTrue(np.all(XYZ[:, 1] == X2_test))
self.assertTrue(np.all(XYZ[:, 2] == X3_test))
def _getEdgePxx(M):
i, j = np.arange(M.nCx), np.arange(M.nCy)
iijj = ndgrid(i, j)
ii, jj = iijj[:, 0], iijj[:, 1]
if M._meshType == 'Curv':
eT1 = M.r(M.tangents, 'E', 'Ex', 'M')
eT2 = M.r(M.tangents, 'E', 'Ey', 'M')
def Pxx(xEdge, yEdge):
# no | node | e1 | e2
# 00 | i ,j | i ,j | i ,j
# 10 | i+1,j | i ,j | i+1,j
# 01 | i ,j+1 | i ,j+1 | i ,j
# 11 | i+1,j+1 | i ,j+1 | i+1,j
posX = 0 if xEdge == 'eX0' else 1
posY = 0 if yEdge == 'eY0' else 1
ind1 = sub2ind(M.vnEx, np.c_[ii, jj + posX])
ind2 = sub2ind(M.vnEy, np.c_[ii + posY, jj]) + M.nEx
IND = np.r_[ind1, ind2].flatten()
PXX = sp.coo_matrix((np.ones(2 * M.nC), (range(2 * M.nC), IND)),
shape=(2 * M.nC, M.nE)).tocsr()
if M._meshType == 'Curv':
I2x2 = inv2X2BlockDiagonal(getSubArray(eT1[0], [i, j + posX]),
getSubArray(eT1[1], [i, j + posX]),
getSubArray(eT2[0], [i + posY, j]),
getSubArray(eT2[1], [i + posY, j]))
PXX = I2x2 * PXX
return PXX
return Pxx
def interact_conductiveSphere(R,log_sig0,log_sig1,Figure1a,Figure1b,Figure2a,Figure2b):
sig0,sig1 = conductivity_log_wrapper(log_sig0,log_sig1)
E0 = 1. # inducing field strength in V/m
n = 100 #level of discretisation
xr = np.linspace(-200., 200., n) # X-axis discretization
yr = xr.copy() # Y-axis discretization
zr = np.r_[0] # identical to saying `zr = np.array([0])`
XYZ = ndgrid(xr,yr,zr) # Space Definition
fig, ax = plt.subplots(1,2,figsize=(18,6))
#Setup figure 1 with options Configuration, Total or Secondary,
#then Potential, ElectricField, Current Density or Charges Density
if Figure1a == 'Configuration':
ax[0] = get_Setup(XYZ,sig0,sig1,R,E0,ax[0],True,[0.1,0.1,0.6])
elif Figure1a == 'Total':
if Figure1b == 'Potential':
ax[0] = Plot_Total_Potential(XYZ,sig0,sig1,R,E0,ax[0])
elif Figure1b == 'ElectricField':
ax[0] = Plot_Total_ElectricField(XYZ,sig0,sig1,R,E0,ax[0])
elif Figure1b == 'CurrentDensity':
ax[0] = Plot_Total_Currents(XYZ,sig0,sig1,R,E0,ax[0])
elif Figure1b == 'ChargesDensity':
ax[0] = Plot_ChargesDensity(XYZ,sig0,sig1,R,E0,ax[0])
elif Figure1a == 'Secondary':
if Figure1b == 'Potential':
ax[0] = Plot_Secondary_Potential(XYZ,sig0,sig1,R,E0,ax[0])
elif Figure1b == 'ElectricField':
ax[0] = Plot_Secondary_ElectricField(XYZ,sig0,sig1,R,E0,ax[0])
elif Figure1b == 'CurrentDensity':
ax[0] = Plot_Secondary_Currents(XYZ,sig0,sig1,R,E0,ax[0])
elif Figure1b == 'ChargesDensity':
ax[0] = Plot_ChargesDensity(XYZ,sig0,sig1,R,E0,ax[0])
if Figure1a== 'Configuration':
ax[1] = Plot_Primary_Potential(XYZ,sig0,sig1,R,E0,ax[1])
print 'While figure1 is plotting Configuration, figure2 plots the primary field'
elif Figure2a == 'Total':
if Figure2b == 'Potential':
ax[1] = Plot_Total_Potential(XYZ,sig0,sig1,R,E0,ax[1])
elif Figure2b == 'ElectricField':
ax[1] = Plot_Total_ElectricField(XYZ,sig0,sig1,R,E0,ax[1])
elif Figure2b == 'CurrentDensity':
ax[1]=Plot_Total_Currents(XYZ,sig0,sig1,R,E0,ax[1])
elif Figure2b == 'ChargesDensity':
ax[1] = Plot_ChargesDensity(XYZ,sig0,sig1,R,E0,ax[1])
elif Figure2a == 'Secondary':
if Figure2b == 'Potential':
ax[1] = Plot_Secondary_Potential(XYZ,sig0,sig1,R,E0,ax[1])
elif Figure2b == 'ElectricField':
ax[1] = Plot_Secondary_ElectricField(XYZ,sig0,sig1,R,E0,ax[1])
elif Figure2b == 'CurrentDensity':
ax[1] = Plot_Secondary_Currents(XYZ,sig0,sig1,R,E0,ax[1])
elif Figure2b == 'ChargesDensity':
ax[1] = Plot_ChargesDensity(XYZ,sig0,sig1,R,E0,ax[1])
plt.tight_layout(True)
plt.show()
plt.tight_layout(True)
plt.show()
if __name__ == '__main__':
sig0 = -3. # conductivity of the wholespace
sig1 = -1. # conductivity of the sphere
sig0, sig1 = conductivity_log_wrapper(sig0,sig1)
R = 50. # radius of the sphere
E0 = 1. # inducing field strength
n = 100 #level of discretisation
xr = np.linspace(-2.*R, 2.*R, n) # X-axis discretization
yr = xr.copy() # Y-axis discretization
zr = np.r_[0] # identical to saying `zr = np.array([0])`
XYZ = ndgrid(xr,yr,zr) # Space Definition
fig, ax = plt.subplots(2,5,figsize=(50,10))
ax[0,0] = get_Setup(XYZ,sig0,sig1,R,E0,ax[0,0],True,[0.6,0.1,0.1])
ax[1,0] = Plot_Primary_Potential(XYZ,sig0,sig1,R,E0,ax[1,0])
ax[0,1] = Plot_Total_Potential(XYZ,sig0,sig1,R,E0,ax[0,1])
ax[1,1] = Plot_Secondary_Potential(XYZ,sig0,sig1,R,E0,ax[1,1])
ax[0,2] = Plot_Total_ElectricField(XYZ,sig0,sig1,R,E0,ax[0,2])
ax[1,2] = Plot_Secondary_ElectricField(XYZ,sig0,sig1,R,E0,ax[1,2])
ax[0,3] = Plot_Total_Currents(XYZ,sig0,sig1,R,E0,ax[0,3])
ax[1,3] = Plot_Secondary_Currents(XYZ,sig0,sig1,R,E0,ax[1,3])
ax[0,4] = Plot_Primary_Potential(XYZ,sig0,sig1,R,E0,ax[0,4])
ax[1,4] = Plot_ChargesDensity(XYZ,sig0,sig1,R,E0,ax[1,4])
plt.show()
def _getFacePxxx(M):
"""returns a function for creating projection matrices
Mats takes you from faces a subset of all faces on only the
faces that you ask for.
These are centered around a single nodes.
"""
i, j, k = np.arange(M.nCx), np.arange(M.nCy), np.arange(M.nCz)
iijjkk = ndgrid(i, j, k)
ii, jj, kk = iijjkk[:, 0], iijjkk[:, 1], iijjkk[:, 2]
if M._meshType == 'Curv':
fN1 = M.r(M.normals, 'F', 'Fx', 'M')
fN2 = M.r(M.normals, 'F', 'Fy', 'M')
fN3 = M.r(M.normals, 'F', 'Fz', 'M')
def Pxxx(xFace, yFace, zFace):
"""
xFace is 'fXp' or 'fXm'
yFace is 'fYp' or 'fYm'
zFace is 'fZp' or 'fZm'
"""
# no | node | f1 | f2 | f3
# 000 | i ,j ,k | i , j, k | i, j , k | i, j, k
# 100 | i+1,j ,k | i+1, j, k | i, j , k | i, j, k
# 010 | i ,j+1,k | i , j, k | i, j+1, k | i, j, k
# 110 | i+1,j+1,k | i+1, j, k | i, j+1, k | i, j, k
# 001 | i ,j ,k+1 | i , j, k | i, j , k | i, j, k+1
# 101 | i+1,j ,k+1 | i+1, j, k | i, j , k | i, j, k+1
# 011 | i ,j+1,k+1 | i , j, k | i, j+1, k | i, j, k+1
# 111 | i+1,j+1,k+1 | i+1, j, k | i, j+1, k | i, j, k+1
posX = 0 if xFace == 'fXm' else 1
posY = 0 if yFace == 'fYm' else 1
posZ = 0 if zFace == 'fZm' else 1
ind1 = sub2ind(M.vnFx, np.c_[ii + posX, jj, kk])
ind2 = sub2ind(M.vnFy, np.c_[ii, jj + posY, kk]) + M.nFx
ind3 = sub2ind(M.vnFz, np.c_[ii, jj, kk + posZ]) + M.nFx + M.nFy
IND = np.r_[ind1, ind2, ind3].flatten()
PXXX = sp.coo_matrix((np.ones(3 * M.nC), (range(3 * M.nC), IND)),
shape=(3 * M.nC, M.nF)).tocsr()
if M._meshType == 'Curv':
I3x3 = inv3X3BlockDiagonal(
getSubArray(fN1[0], [i + posX, j, k]),
getSubArray(fN1[1], [i + posX, j, k]),
getSubArray(fN1[2], [i + posX, j, k]),
getSubArray(fN2[0], [i, j + posY, k]),
getSubArray(fN2[1], [i, j + posY, k]),
getSubArray(fN2[2], [i, j + posY, k]),
getSubArray(fN3[0], [i, j, k + posZ]),
getSubArray(fN3[1], [i, j, k + posZ]),
getSubArray(fN3[2], [i, j, k + posZ]))
PXXX = I3x3 * PXXX
return PXXX
return Pxxx
def _getFacePxx(M):
"""returns a function for creating projection matrices
Mats takes you from faces a subset of all faces on only the
faces that you ask for.
These are centered around a single nodes.
For example, if this was your entire mesh:
f3(Yp)
2_______________3
| |
| |
| |
f0(Xm) | x | f1(Xp)
| |
| |
|_______________|
0 1
f2(Ym)
Pxx('fXm','fYm') = | 1, 0, 0, 0 |
| 0, 0, 1, 0 |
Pxx('fXp','fYm') = | 0, 1, 0, 0 |
| 0, 0, 1, 0 |
"""
i, j = np.arange(M.nCx), np.arange(M.nCy)
iijj = ndgrid(i, j)
ii, jj = iijj[:, 0], iijj[:, 1]
if M._meshType == 'Curv':
fN1 = M.r(M.normals, 'F', 'Fx', 'M')
fN2 = M.r(M.normals, 'F', 'Fy', 'M')
def Pxx(xFace, yFace):
"""
xFace is 'fXp' or 'fXm'
yFace is 'fYp' or 'fYm'
"""
# 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
posFx = 0 if xFace == 'fXm' else 1
posFy = 0 if yFace == 'fYm' else 1
ind1 = sub2ind(M.vnFx, np.c_[ii + posFx, jj])
ind2 = sub2ind(M.vnFy, np.c_[ii, jj + posFy]) + M.nFx
IND = np.r_[ind1, ind2].flatten()
PXX = sp.csr_matrix((np.ones(2 * M.nC), (range(2 * M.nC), IND)),
shape=(2 * M.nC, M.nF))
if M._meshType == 'Curv':
I2x2 = inv2X2BlockDiagonal(getSubArray(fN1[0], [i + posFx, j]),
getSubArray(fN1[1], [i + posFx, j]),
getSubArray(fN2[0], [i, j + posFy]),
getSubArray(fN2[1], [i, j + posFy]))
PXX = I2x2 * PXX
return PXX
return Pxx