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https://github.com/wassname/simpeg.git
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Initial implementation of interpolation matrix generation for TensorMesh (3D ONLY)
This commit is contained in:
Dave Marchant
+109
-1
@@ -1,9 +1,10 @@
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import numpy as np
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import scipy.sparse as sp
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from BaseMesh import BaseMesh
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from TensorView import TensorView
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from DiffOperators import DiffOperators
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from InnerProducts import InnerProducts
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from SimPEG.utils import ndgrid, mkvc
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from SimPEG.utils import ndgrid, mkvc, spzeros, interpmat
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class TensorMesh(BaseMesh, TensorView, DiffOperators, InnerProducts):
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@@ -312,6 +313,113 @@ class TensorMesh(BaseMesh, TensorView, DiffOperators, InnerProducts):
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_edge = None
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edge = property(**edge())
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# --------------- Methods ---------------------
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def isInside(self, pts):
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"""
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Determines if a set of points are inside a mesh.
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:param numpy.ndarray pts: Location of points to test
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:rtype numpy.ndarray
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:return inside, numpy array of booleans
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"""
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pts = np.atleast_2d(pts)
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inside = (pts[:,0] >= self.vectorNx.min()) & (pts[:,0] <= self.vectorNx.max())
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if self.dim > 1:
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inside = inside & ((pts[:,1] >= self.vectorNy.min()) & (pts[:,1] <= self.vectorNy.max()))
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if self.dim > 2:
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inside = inside & ((pts[:,2] >= self.vectorNz.min()) & (pts[:,2] <= self.vectorNz.max()))
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return inside
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def getInterpolationMat(self, loc, locType):
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""" Produces interpolation matrix
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:param numpy.ndarray loc: Location of points to interpolate to
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:param str locType: What to interpolate (see below)
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:rtype: scipy.sparse.csr.csr_matrix
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:return: M, the interpolation matrix
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locType can be::
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'ex' -> x-component of field defined on edges
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'ey' -> y-component of field defined on edges
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'ez' -> z-component of field defined on edges
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'fx' -> x-component of field defined on edges
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'fy' -> y-component of field defined on edges
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'fz' -> z-component of field defined on edges
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'n' -> scalar field defined on nodes
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'cc' -> scalar field defined on cell centres
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"""
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loc = np.atleast_2d(loc)
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assert np.all(self.isInside(loc)), "Points outside of mesh"
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if self.dim == 3:
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if locType == 'fx':
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Qx = interpmat(self.vectorNx,
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self.vectorCCy,
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self.vectorCCz,
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loc[:,0], loc[:,1], loc[:,2])
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Qy = spzeros(loc.shape[0], self.nF[1])
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Qz = spzeros(loc.shape[0], self.nF[2])
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Q = sp.hstack([Qx, Qy, Qz])
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elif locType == 'fy':
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Qx = spzeros(loc.shape[0], self.nF[0])
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Qy = interpmat(self.vectorCCx,
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self.vectorNy,
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self.vectorCCz,
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loc[:,0], loc[:,1], loc[:,2])
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Qz = spzeros(loc.shape[0], self.nF[2])
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Q = sp.hstack([Qx, Qy, Qz])
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elif locType == 'fz':
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Qx = spzeros(loc.shape[0], self.nF[0])
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Qy = spzeros(loc.shape[0], self.nF[1])
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Qz = interpmat(self.vectorCCx,
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self.vectorCCy,
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self.vectorNz,
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loc[:,0], loc[:,1], loc[:,2])
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Q = sp.hstack([Qx, Qy, Qz])
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elif locType == 'ex':
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Qx = interpmat(self.vectorCCx,
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self.vectorNy,
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self.vectorNz,
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loc[:,0], loc[:,1], loc[:,2])
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Qy = spzeros(loc.shape[0], self.nF[1])
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Qz = spzeros(loc.shape[0], self.nF[2])
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Q = sp.hstack([Qx, Qy, Qz])
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elif locType == 'ey':
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Qx = spzeros(loc.shape[0], self.nF[0])
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Qy = interpmat(self.vectorNx,
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self.vectorCCy,
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self.vectorNz,
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loc[:,0], loc[:,1], loc[:,2])
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Qz = spzeros(loc.shape[0], self.nF[2])
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Q = sp.hstack([Qx, Qy, Qz])
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elif locType == 'ez':
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Qx = spzeros(loc.shape[0], self.nF[0])
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Qy = spzeros(loc.shape[0], self.nF[1])
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Qz = interpmat(self.vectorNx,
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self.vectorNy,
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self.vectorCCz,
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loc[:,0], loc[:,1], loc[:,2])
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Q = sp.hstack([Qx, Qy, Qz])
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elif locType == 'n':
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Q = interpmat(self.vectorNx,
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self.vectorNy,
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self.vectorNz,
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loc[:,0], loc[:,1], loc[:,2])
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elif locType == 'cc':
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Q = interpmat(self.vectorCCx,
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self.vectorCCy,
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self.vectorCCz,
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loc[:,0], loc[:,1], loc[:,2])
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else:
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raise NotImplementedError('getInterpolationMat: locType=='+locType)
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else:
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raise NotImplementedError('getInterpolationMat: dim=='+str(m.dim))
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return Q
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if __name__ == '__main__':
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print('Welcome to tensor mesh!')
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@@ -1,7 +1,9 @@
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import matutils
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import sputils
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import lomutils
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import interputils
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import ModelBuilder
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from matutils import getSubArray, mkvc, ndgrid, ind2sub, sub2ind
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from sputils import spzeros, kron3, speye, sdiag
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from lomutils import volTetra, faceInfo, inv2X2BlockDiagonal, inv3X3BlockDiagonal, indexCube, exampleLomGird
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from interputils import interpmat
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@@ -0,0 +1,77 @@
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import numpy as np
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import scipy.sparse as sp
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from sputils import spzeros
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from matutils import mkvc, sub2ind
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def interpmat(x,y,z,xr,yr,zr):
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""" Local interpolation computed for each receiver point in turn """
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nx = max(x.shape)
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ny = max(y.shape)
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nz = max(z.shape)
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npts = max(xr.shape)
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Q = sp.lil_matrix((npts, nx*ny*nz))
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for i in range(npts):
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# in x-direction
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im = np.argmin(abs(x-xr[i]))
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if xr[i] - x[im] >= 0: # Point on the left
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ind_x1 = im
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ind_x2 = im+1
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elif xr[i] - x[im] < 0: # Point on the right
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ind_x1 = im-1
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ind_x2 = im
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dx1 = xr[i] - x[ind_x1]
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dx2 = x[ind_x2] - xr[i]
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# in y-direction
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im = np.argmin(abs(y-yr[i]))
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if yr[i] - y[im] >= 0: # Point on the left
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ind_y1 = im
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ind_y2 = im+1
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elif yr[i] - y[im] < 0: # Point on the right
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ind_y1 = im-1
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ind_y2 = im
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dy1 = yr[i] - y[ind_y1]
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dy2 = y[ind_y2] - yr[i]
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# in z-direction
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im = np.argmin(abs(z-zr[i]))
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if zr[i] - z[im] >= 0: # Point on the left
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ind_z1 = im
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ind_z2 = im+1
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elif zr[i] - z[im] < 0: # Point on the right
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ind_z1 = im-1
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ind_z2 = im
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dz1 = zr[i] - z[ind_z1]
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dz2 = z[ind_z2] - zr[i]
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dv = (x[ind_x2] - x[ind_x1]) * (y[ind_y2] - y[ind_y1]) *(z[ind_z2] - z[ind_z1])
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Dx = x[ind_x2] - x[ind_x1]
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Dy = y[ind_y2] - y[ind_y1]
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Dz = z[ind_z2] - z[ind_z1]
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# Get the row in the matrix
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inds = sub2ind((nx,ny,nz),[
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( ind_x1, ind_y2, ind_z1),
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( ind_x1, ind_y1, ind_z1),
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( ind_x2, ind_y1, ind_z1),
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( ind_x2, ind_y2, ind_z1),
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( ind_x1, ind_y1, ind_z2),
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( ind_x1, ind_y2, ind_z2),
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( ind_x2, ind_y1, ind_z2),
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( ind_x2, ind_y2, ind_z2)])
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vals = [(1-dx1/Dx)*(1-dy2/Dy)*(1-dz1/Dz),
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(1-dx1/Dx)*(1-dy1/Dy)*(1-dz1/Dz),
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(1-dx2/Dx)*(1-dy1/Dy)*(1-dz1/Dz),
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(1-dx2/Dx)*(1-dy2/Dy)*(1-dz1/Dz),
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(1-dx1/Dx)*(1-dy1/Dy)*(1-dz2/Dz),
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(1-dx1/Dx)*(1-dy2/Dy)*(1-dz2/Dz),
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(1-dx2/Dx)*(1-dy1/Dy)*(1-dz2/Dz),
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(1-dx2/Dx)*(1-dy2/Dy)*(1-dz2/Dz)]
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Q[i, mkvc(inds)] = vals
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Q = Q.tocsr()
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return Q
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