def _getDifferences(self, adjacentValues, cellValues, oldArray, cellToCellIDs, mesh):
dAP = mesh._cellToCellDistances
## adjacentGradient = numerix.take(oldArray.grad, cellToCellIDs)
adjacentGradient = numerix.take(oldArray.grad, mesh._cellToCellIDs, axis=-1)
adjacentNormalGradient = numerix.dot(adjacentGradient, mesh._cellNormals)
adjacentUpValues = cellValues + 2 * dAP * adjacentNormalGradient
cellIDs = numerix.repeat(numerix.arange(mesh.numberOfCells)[numerix.newaxis, ...],
mesh._maxFacesPerCell, axis=0)
cellIDs = MA.masked_array(cellIDs, mask = MA.getmask(mesh._cellToCellIDs))
cellGradient = numerix.take(oldArray.grad, cellIDs, axis=-1)
cellNormalGradient = numerix.dot(cellGradient, mesh._cellNormals)
cellUpValues = adjacentValues - 2 * dAP * cellNormalGradient
cellLaplacian = (cellUpValues + adjacentValues - 2 * cellValues) / dAP**2
adjacentLaplacian = (adjacentUpValues + cellValues - 2 * adjacentValues) / dAP**2
adjacentLaplacian = adjacentLaplacian.filled(0)
cellLaplacian = cellLaplacian.filled(0)
mm = numerix.where(cellLaplacian * adjacentLaplacian < 0.,
0.,
numerix.where(abs(cellLaplacian) > abs(adjacentLaplacian),
adjacentLaplacian,
cellLaplacian))
return FirstOrderAdvectionTerm._getDifferences(self, adjacentValues, cellValues, oldArray, cellToCellIDs, mesh) - mm * dAP / 2.
def _buildMatrix(self, var, SparseMatrix, boundaryConditions=(), dt=1., equation=None):
"""Implicit portion considers
"""
mesh = var.getMesh()
id1, id2 = mesh._getAdjacentCellIDs()
interiorFaces = numerix.nonzero(mesh.getInteriorFaces())[0]
id1 = numerix.take(id1, interiorFaces)
id2 = numerix.take(id2, interiorFaces)
N = len(var)
b = numerix.zeros((N),'d')
L = SparseMatrix(size = N)
if equation is not None:
from fipy.tools.numerix import sign, add
self._diagonalSign.setValue(sign(add.reduce(equation.matrix.takeDiagonal())))
else:
self._diagonalSign.setValue(1)
weight = self._getWeight(mesh, equation=equation)
if weight.has_key('implicit'):
self._implicitBuildMatrix(SparseMatrix, L, id1, id2, b, weight['implicit'], mesh, boundaryConditions, interiorFaces, dt)
if weight.has_key('explicit'):
self._explicitBuildMatrix(SparseMatrix, var.getOld(), id1, id2, b, weight['explicit'], mesh, boundaryConditions, interiorFaces, dt)
return (L, b)
def quiver(self, sparsity=None, scale=None):
var = self.vars[0]
mesh = var.mesh
if isinstance(var, FaceVariable):
N = mesh.numberOfFaces
X, Y = mesh.faceCenters
elif isinstance(var, CellVariable):
N = mesh.numberOfCells
X, Y = mesh.cellCenters
if sparsity is not None and N > sparsity:
XYrand = numerix.random.random((2, sparsity))
XYrand = numerix.array([[min(X)],
[min(Y)]]) + XYrand * numerix.array([[max(X) - min(X)],
[max(Y) - min(Y)]])
self.indices = numerix.nearest(numerix.array([X, Y]), XYrand)
else:
self.indices = numerix.arange(N)
X = numerix.take(X, self.indices)
Y = numerix.take(Y, self.indices)
U = V = numerix.ones(X.shape, 'l')
if hasattr(self, "_quiver"):
self._quiver.remove()
self._quiver = self.axes.quiver(X, Y, U, V, scale=scale, pivot='middle')
def quiver(self, sparsity=None, scale=None):
var = self.vars[0]
mesh = var.getMesh()
if isinstance(var, FaceVariable):
N = mesh._getNumberOfFaces()
V = mesh._getFaceAreas()
X, Y = mesh.getFaceCenters()
elif isinstance(var, CellVariable):
N = mesh.getNumberOfCells()
V = mesh.getCellVolumes()
X, Y = mesh.getCellCenters()
if sparsity is not None and N > sparsity:
self.indices = numerix.random.rand(N) * V
self.indices = self.indices.argsort()[-sparsity:]
else:
self.indices = numerix.arange(N)
X = numerix.take(X, self.indices)
Y = numerix.take(Y, self.indices)
U = V = numerix.ones(X.shape)
import pylab
pylab.ion()
pylab.cla()
self._quiver = pylab.quiver(X, Y, U, V, scale=scale)
pylab.ioff()
def _calcValuePy(self):
dAP = self.mesh._getCellDistances()
id1, id2 = self.mesh._getAdjacentCellIDs()
v1 = take(self.var, id1)
v2 = take(self.var, id2)
for bc in self.bcs:
if isinstance(bc, FixedValue):
v2[bc.faces.getValue()] = bc._getValue()
N = (v2 - v1) / dAP
normals = self.mesh._getOrientedFaceNormals()
tangents1 = self.mesh._getFaceTangents1()
tangents2 = self.mesh._getFaceTangents2()
cellGrad = self.var.getGrad().getValue()
grad1 = take(cellGrad, id1, axis=1)
grad2 = take(cellGrad, id2, axis=1)
t1grad1 = sum(tangents1 * grad1, 0)
t1grad2 = sum(tangents1 * grad2, 0)
t2grad1 = sum(tangents2 * grad1, 0)
t2grad2 = sum(tangents2 * grad2, 0)
T1 = (t1grad1 + t1grad2) / 2.0
T2 = (t2grad1 + t2grad2) / 2.0
T1 = (id1 == id2) * T1
T2 = (id1 == id2) * T2
return normals * N + tangents1 * T1 + tangents2 * T2
def plotMesh(self, filename = None):
self._plot()
faceVertexIDs = self.mesh.faceVertexIDs
vertexCoords = self.mesh.vertexCoords
x0 = numerix.take(vertexCoords[0], faceVertexIDs[0])
y0 = numerix.take(vertexCoords[1], faceVertexIDs[0])
x1 = numerix.take(vertexCoords[0], faceVertexIDs[1])
y1 = numerix.take(vertexCoords[1], faceVertexIDs[1])
import gist
gist.pldj(x0, y0, x1, y1)
if filename is not None:
import os.path
root, ext = os.path.splitext(filename)
if ext.lower() in (".eps", ".epsi"):
gist.eps(root)
else:
gist.hcp_file(filename, dump = 1)
gist.hcp()
gist.hcp_finish(-1)
gist.fma()
def _implicitBuildMatrix_(self, SparseMatrix, L, id1, id2, b, weight, var, boundaryConditions, interiorFaces, dt):
mesh = var.mesh
coeffMatrix = self._getCoeffMatrix_(var, weight)
id1 = self._reshapeIDs(var, id1)
id2 = self._reshapeIDs(var, id2)
L.addAt(numerix.take(coeffMatrix['cell 1 diag'], interiorFaces, axis=-1).ravel(), id1.ravel(), id1.swapaxes(0, 1).ravel())
L.addAt(numerix.take(coeffMatrix['cell 1 offdiag'], interiorFaces, axis=-1).ravel(), id1.ravel(), id2.swapaxes(0, 1).ravel())
L.addAt(numerix.take(coeffMatrix['cell 2 offdiag'], interiorFaces, axis=-1).ravel(), id2.ravel(), id1.swapaxes(0, 1).ravel())
L.addAt(numerix.take(coeffMatrix['cell 2 diag'], interiorFaces, axis=-1).ravel(), id2.ravel(), id2.swapaxes(0, 1).ravel())
N = mesh.numberOfCells
M = mesh._maxFacesPerCell
for boundaryCondition in boundaryConditions:
LL, bb = boundaryCondition._buildMatrix(SparseMatrix, N, M, coeffMatrix)
if 'FIPY_DISPLAY_MATRIX' in os.environ:
self._viewer.title = r"%s %s" % (boundaryCondition.__class__.__name__, self.__class__.__name__)
self._viewer.plot(matrix=LL, RHSvector=bb)
from fipy import raw_input
input()
L += LL
b += bb
def _plot(self):
var = self.vars[0]
mesh = var.mesh
U, V = var.numericValue
U = numerix.take(U, self.indices)
V = numerix.take(V, self.indices)
ang = numerix.arctan2(V, U)
mag = numerix.sqrt(U**2 + V**2)
datamin, datamax = self._autoscale(vars=(mag,),
datamin=self._getLimit('datamin'),
datamax=self._getLimit('datamax'))
mag = numerix.where(mag > datamax, datamax, mag)
mag = numerix.ma.masked_array(mag, mag < datamin)
if self.log:
mag = numerix.log10(mag)
mag = numerix.ma.masked_array(mag, numerix.isnan(mag))
U = mag * numerix.cos(ang)
V = mag * numerix.sin(ang)
self._quiver.set_UVC(U, V)
self.axes.set_xlim(xmin=self._getLimit('xmin'),
xmax=self._getLimit('xmax'))
self.axes.set_ylim(ymin=self._getLimit('ymin'),
ymax=self._getLimit('ymax'))
def _calcValue_(self, alpha, id1, id2):
distance = numerix.array(self.var)
cell1 = numerix.take(distance, id1)
cell2 = numerix.take(distance, id2)
return numerix.where(numerix.logical_or(cell1 < 0, cell2 < 0),
0,
self.diffusionCoeff)
def _orderVertices(vertexCoords, vertices):
coordinates = numerix.take(vertexCoords, vertices, axis=1)
centroid = numerix.add.reduce(coordinates, axis=1) / coordinates.shape[1]
coordinates = coordinates - centroid[..., numerix.newaxis]
coordinates = numerix.where(coordinates == 0, 1.e-10, coordinates) ## to prevent division by zero
angles = numerix.arctan(coordinates[1] / coordinates[0]) + numerix.where(coordinates[0] < 0, numerix.pi, 0) ## angles go from -pi / 2 to 3*pi / 2
sortorder = numerix.argsort(angles)
return numerix.take(vertices, sortorder)
def _calcValue_(self, alpha, id1, id2):
cell1 = numerix.take(self.var,id1, axis=-1)
cell2 = numerix.take(self.var,id2, axis=-1)
return numerix.where((cell1 > 0) & (cell2 > 0),
numerix.minimum(cell1, cell2),
numerix.where((cell1 < 0) & (cell2 < 0),
numerix.maximum(cell1, cell2),
0))
def __getCoefficientMatrix(self, SparseMatrix, var, coeff):
mesh = var.mesh
id1, id2 = mesh._adjacentCellIDs
interiorFaces = numerix.nonzero(mesh.interiorFaces)[0]
id1 = numerix.take(id1, interiorFaces)
id2 = numerix.take(id2, interiorFaces)
id1 = self._reshapeIDs(var, id1)
id2 = self._reshapeIDs(var, id2)
## print 'id1',id1
## print 'id2',id2
coefficientMatrix = SparseMatrix(mesh=mesh, bandwidth = mesh._maxFacesPerCell + 1)
interiorCoeff = numerix.take(coeff, interiorFaces, axis=-1).ravel()
coefficientMatrix.addAt(interiorCoeff, id1.ravel(), id1.swapaxes(0,1).ravel())
coefficientMatrix.addAt(-interiorCoeff, id1.ravel(), id2.swapaxes(0,1).ravel())
coefficientMatrix.addAt(-interiorCoeff, id2.ravel(), id1.swapaxes(0,1).ravel())
coefficientMatrix.addAt(interiorCoeff, id2.ravel(), id2.swapaxes(0,1).ravel())
## print 'coefficientMatrix',coefficientMatrix
## raw_input('stopped')
## interiorCoeff = numerix.array(coeff)
## interiorCoeff[...,mesh.exteriorFaces.value] = 0
## print 'interiorCoeff',interiorCoeff
## interiorCoeff = numerix.take(interiorCoeff, mesh.cellFaceIDs, axis=-1)
## ## print interiorCoeff.shape
## ## print interiorCoeff[:,:,0]
## ## print interiorCoeff[:,:,1]
## coefficientMatrix = SparseMatrix(mesh=mesh, bandwidth = mesh._maxFacesPerCell + 1)
## ## print 'numerix.sum(interiorCoeff, -2)',numerix.sum(interiorCoeff, -2)
## ## print numerix.sum(interiorCoeff, -2).ravel()
## ## raw_input('stopped')
## ## coefficientMatrix.addAtDiagonal(numerix.sum(interiorCoeff, -2).ravel())
## ## print 'coefficientMatrix',coefficientMatrix
## del interiorCoeff
## interiorFaces = mesh.interiorFaceIDs
## interiorFaceCellIDs = mesh.interiorFaceCellIDs
## interiorCoeff = -numerix.take(coeff, interiorFaces, axis=-1)
## print 'interiorCoeff',interiorCoeff
## raw_input('stopped')
## coefficientMatrix.addAt(interiorCoeff, interiorFaceCellIDs[0], interiorFaceCellIDs[1])
## interiorCoeff = -numerix.take(coeff, interiorFaces, axis=-1)
## coefficientMatrix.addAt(interiorCoeff, interiorFaceCellIDs[1], interiorFaceCellIDs[0])
return coefficientMatrix
def _explicitBuildMatrixPy(self, oldArray, id1, id2, b, coeffMatrix, mesh, interiorFaces, dt, weight):
oldArrayId1, oldArrayId2 = self._getOldAdjacentValues(oldArray, id1, id2, dt=dt)
cell1diag = numerix.take(coeffMatrix['cell 1 diag'], interiorFaces)
cell1offdiag = numerix.take(coeffMatrix['cell 1 offdiag'], interiorFaces)
cell2diag = numerix.take(coeffMatrix['cell 2 diag'], interiorFaces)
cell2offdiag = numerix.take(coeffMatrix['cell 2 offdiag'], interiorFaces)
vector.putAdd(b, id1, -(cell1diag * oldArrayId1 + cell1offdiag * oldArrayId2))
vector.putAdd(b, id2, -(cell2diag * oldArrayId2 + cell2offdiag * oldArrayId1))
def _calcCellNormals(self):
cellNormals = numerix.take(self.faceNormals, self.cellFaceIDs, axis=1)
cellFaceCellIDs = numerix.take(self.faceCellIDs[0], self.cellFaceIDs)
cellIDs = numerix.repeat(numerix.arange(self.numberOfCells)[numerix.newaxis,...],
self._maxFacesPerCell,
axis=0)
direction = (cellFaceCellIDs == cellIDs) * 2 - 1
if self._maxFacesPerCell > 0:
return direction[numerix.newaxis, ...] * cellNormals
else:
return cellNormals
def _orderVertices(vertexCoords, vertices):
coordinates = numerix.take(vertexCoords, vertices)
centroid = numerix.add.reduce(coordinates) / coordinates.shape[0]
coordinates = coordinates - centroid
# to prevent division by zero
coordinates = numerix.where(coordinates == 0, 1.e-100, coordinates)
# angles go from -pi / 2 to 3*pi / 2
angles = numerix.arctan(coordinates[:, 1] / coordinates[:, 0]) \
+ numerix.where(coordinates[:, 0] < 0, numerix.pi, 0)
sortorder = numerix.argsort(angles)
return numerix.take(vertices, sortorder)
def _calcCellNormals(self):
cellNormals = numerix.take(self._getFaceNormals(), self._getCellFaceIDs(), axis=1)
cellFaceCellIDs = numerix.take(self.faceCellIDs[0], self.cellFaceIDs)
cellIDs = numerix.repeat(numerix.arange(self.getNumberOfCells())[numerix.newaxis,...],
self._getMaxFacesPerCell(),
axis=0)
direction = (cellFaceCellIDs == cellIDs) * 2 - 1
if self._getMaxFacesPerCell() > 0:
self.cellNormals = direction[numerix.newaxis, ...] * cellNormals
else:
self.cellNormals = cellNormals
def _calcValue_(self, alpha, id1, id2):
cell1 = numerix.take(self.var,id1, axis=-1)
cell2 = numerix.take(self.var,id2, axis=-1)
value = ((cell2 - cell1) * alpha + cell1)
eps = 1e-20
value = (value == 0.) * eps + (value != 0.) * value
cell1Xcell2 = cell1 * cell2
value = ((value > eps) | (value < -eps)) * cell1Xcell2 / value
value = (cell1Xcell2 >= 0.) * value
return value
def aspect2D(self):
"""The physical y:x aspect ratio of a 2D mesh
"""
if self.dim != 2:
raise NotImplementedError
else:
vertexIDs = self._orderedCellVertexIDs
xCoords = numerix.take(self.vertexCoords[0], vertexIDs)
yCoords = numerix.take(self.vertexCoords[1], vertexIDs)
return float((yCoords.max() - yCoords.min()) / (xCoords.max() - xCoords.min()))
def _calcOrderedCellVertexIDs(self):
from fipy.tools.numerix import take
NFac = self._maxFacesPerCell
# numpy 1.1's MA.take doesn't like FlatIter. Call ravel() instead.
cellVertexIDs0 = take(self.faceVertexIDs[0], self.cellFaceIDs.ravel())
cellVertexIDs1 = take(self.faceVertexIDs[1], self.cellFaceIDs.ravel())
cellVertexIDs = MA.where(self._cellToFaceOrientations.ravel() > 0,
cellVertexIDs0, cellVertexIDs1)
cellVertexIDs = numerix.reshape(cellVertexIDs, (NFac, -1))
return cellVertexIDs
def _explicitBuildMatrixInline_(self, oldArray, id1, id2, b, coeffMatrix, mesh, interiorFaces, dt, weight):
oldArrayId1, oldArrayId2 = self._getOldAdjacentValues(oldArray, id1, id2, dt=dt)
cell1diag = numerix.take(coeffMatrix['cell 1 diag'], interiorFaces)
cell1offdiag = numerix.take(coeffMatrix['cell 1 offdiag'], interiorFaces)
cell2diag = numerix.take(coeffMatrix['cell 2 diag'], interiorFaces)
cell2offdiag = numerix.take(coeffMatrix['cell 2 offdiag'], interiorFaces)
vector.putAdd(b, id1, -(cell1diag * oldArrayId1 + cell1offdiag * oldArrayId2))
vector.putAdd(b, id2, -(cell2diag * oldArrayId2 + cell2offdiag * oldArrayId1))
def plot_mesh(self):
vertexIDs = self.mesh._orderedCellVertexIDs
vertexCoords = self.mesh.vertexCoords
xCoords = numerix.take(vertexCoords[0], vertexIDs)
yCoords = numerix.take(vertexCoords[1], vertexIDs)
polys = []
for x, y in zip(xCoords.swapaxes(0, 1), yCoords.swapaxes(0, 1)):
polys.append(zip(x, y))
self.collection = PolyCollection(polys)
self.collection.set_linewidth(0.5)
self.axes.add_collection(self.collection)
self.update(self.var)
def _calcOrderedCellVertexIDs(self):
from fipy.tools.numerix import take
NFac = self._maxFacesPerCell
# numpy 1.1's MA.take doesn't like FlatIter. Call ravel() instead.
cellVertexIDs0 = take(self.faceVertexIDs[0], self.cellFaceIDs.ravel())
cellVertexIDs1 = take(self.faceVertexIDs[1], self.cellFaceIDs.ravel())
cellVertexIDs = MA.where(self._cellToFaceOrientations.ravel() > 0,
cellVertexIDs0, cellVertexIDs1)
cellVertexIDs = numerix.reshape(cellVertexIDs, (NFac, -1))
return cellVertexIDs
def _calcCellNormals(self):
cellNormals = numerix.take(self.faceNormals, self.cellFaceIDs, axis=1)
cellFaceCellIDs = numerix.take(self.faceCellIDs[0], self.cellFaceIDs)
cellIDs = numerix.repeat(numerix.arange(
self.numberOfCells)[numerix.newaxis, ...],
self._maxFacesPerCell,
axis=0)
direction = (cellFaceCellIDs == cellIDs) * 2 - 1
if self._maxFacesPerCell > 0:
return direction[numerix.newaxis, ...] * cellNormals
else:
return cellNormals
def _calcFaceAreas(self):
faceVertexIDs = MA.filled(self.faceVertexIDs, -1)
substitute = numerix.repeat(faceVertexIDs[numerix.newaxis, 0],
faceVertexIDs.shape[0], axis=0)
faceVertexIDs = numerix.where(MA.getmaskarray(self.faceVertexIDs), substitute, faceVertexIDs)
faceVertexCoords = numerix.take(self.vertexCoords, faceVertexIDs, axis=1)
faceOrigins = numerix.repeat(faceVertexCoords[:,0], faceVertexIDs.shape[0], axis=0)
faceOrigins = numerix.reshape(faceOrigins, MA.shape(faceVertexCoords))
faceVertexCoords = faceVertexCoords - faceOrigins
left = range(faceVertexIDs.shape[0])
right = left[1:] + [left[0]]
cross = numerix.sum(numerix.cross(faceVertexCoords, numerix.take(faceVertexCoords, right, 1), axis=0), 1)
self.faceAreas = numerix.sqrtDot(cross, cross) / 2.
def _calcFaceCellToCellNormals(self):
faceCellCentersUp = numerix.take(self._cellCenters, self.faceCellIDs[1], axis=1)
faceCellCentersDown = numerix.take(self._cellCenters, self.faceCellIDs[0], axis=1)
faceCellCentersUp = numerix.where(MA.getmaskarray(faceCellCentersUp),
self._faceCenters,
faceCellCentersUp)
diff = faceCellCentersDown - faceCellCentersUp
mag = numerix.sqrt(numerix.sum(diff**2))
faceCellToCellNormals = diff / numerix.resize(mag, (self.dim, len(mag)))
orientation = 1 - 2 * (numerix.dot(self.faceNormals, faceCellToCellNormals) < 0)
return faceCellToCellNormals * orientation
def _getOldAdjacentValues(self, oldArray, id1, id2, dt):
oldArray1, oldArray2 = ExplicitUpwindConvectionTerm._getOldAdjacentValues(self, oldArray, id1, id2, dt)
mesh = oldArray.getMesh()
interiorIDs = numerix.nonzero(mesh.getInteriorFaces())[0]
interiorFaceAreas = numerix.take(mesh._getFaceAreas(), interiorIDs)
interiorFaceNormals = numerix.take(mesh._getOrientedFaceNormals(), interiorIDs, axis=-1)
# Courant-Friedrichs-Levy number
interiorCFL = abs(numerix.take(self._getGeomCoeff(mesh), interiorIDs)) * dt
gradUpwind = (oldArray2 - oldArray1) / numerix.take(mesh._getCellDistances(), interiorIDs)
vol1 = numerix.take(mesh.getCellVolumes(), id1)
self.CFL = interiorCFL / vol1
oldArray1 += 0.5 * self._getGradient(numerix.dot(numerix.take(oldArray.getGrad(), id1, axis=-1), interiorFaceNormals), gradUpwind) \
* (vol1 - interiorCFL) / interiorFaceAreas
vol2 = numerix.take(mesh.getCellVolumes(), id2)
self.CFL = numerix.maximum(interiorCFL / vol2, self.CFL)
oldArray2 += 0.5 * self._getGradient(numerix.dot(numerix.take(oldArray.getGrad(), id2, axis=-1), -interiorFaceNormals), -gradUpwind) \
* (vol2 - interiorCFL) / interiorFaceAreas
return oldArray1, oldArray2
def _getOldAdjacentValues(self, oldArray, id1, id2, dt):
oldArray1, oldArray2 = ExplicitUpwindConvectionTerm._getOldAdjacentValues(self, oldArray, id1, id2, dt)
mesh = oldArray.mesh
interiorIDs = numerix.nonzero(mesh.interiorFaces)[0]
interiorFaceAreas = numerix.take(mesh._faceAreas, interiorIDs)
interiorFaceNormals = numerix.take(mesh._orientedFaceNormals, interiorIDs, axis=-1)
# Courant-Friedrichs-Levy number
interiorCFL = abs(numerix.take(self._getGeomCoeff(oldArray), interiorIDs)) * dt
gradUpwind = (oldArray2 - oldArray1) / numerix.take(mesh._cellDistances, interiorIDs)
vol1 = numerix.take(mesh.cellVolumes, id1)
oldArray1 += 0.5 * self._getGradient(numerix.dot(numerix.take(oldArray.grad, id1, axis=-1), interiorFaceNormals), gradUpwind) \
* (vol1 - interiorCFL) / interiorFaceAreas
vol2 = numerix.take(mesh.cellVolumes, id2)
oldArray2 += 0.5 * self._getGradient(numerix.dot(numerix.take(oldArray.grad, id2, axis=-1), -interiorFaceNormals), -gradUpwind) \
* (vol2 - interiorCFL) / interiorFaceAreas
return oldArray1, oldArray2
def _implicitBuildMatrix(self, SparseMatrix, L, id1, id2, b, weight, mesh, boundaryConditions, interiorFaces, dt):
coeffMatrix = self._getCoeffMatrix(mesh, weight)
L.addAt(numerix.take(coeffMatrix['cell 1 diag'], interiorFaces), id1, id1)
L.addAt(numerix.take(coeffMatrix['cell 1 offdiag'], interiorFaces), id1, id2)
L.addAt(numerix.take(coeffMatrix['cell 2 offdiag'], interiorFaces), id2, id1)
L.addAt(numerix.take(coeffMatrix['cell 2 diag'], interiorFaces), id2, id2)
N = mesh.getNumberOfCells()
M = mesh._getMaxFacesPerCell()
for boundaryCondition in boundaryConditions:
LL, bb = boundaryCondition._buildMatrix(SparseMatrix, N, M, coeffMatrix)
L += LL
b += bb
def _calcCellToCellIDs(self):
cellToCellIDs = numerix.take(self.faceCellIDs,
self.cellFaceIDs,
axis=1)
cellToCellIDs = MA.where(self._cellToFaceOrientations == 1,
cellToCellIDs[1], cellToCellIDs[0])
return cellToCellIDs
def _calcCellDistAndVec(self):
tmp = numerix.take(self._cellCenters, self.faceCellIDs, axis=1)
tmp = tmp[...,1,:] - tmp[...,0,:]
tmp = MA.filled(MA.where(MA.getmaskarray(tmp), self._cellToFaceDistanceVectors[:,0], tmp))
cellDistanceVectors = tmp
cellDistances = MA.filled(MA.sqrt(MA.sum(tmp * tmp, 0)))
return cellDistances, cellDistanceVectors
def _calcValue(self):
ids = self.mesh.cellFaceIDs
contributions = numerix.take(self.faceVariable, ids, axis=-1)
s = (numerix.newaxis, ) * (len(contributions.shape) - 2) + (slice(
0, None, None), ) + (slice(0, None, None), )
faceContributions = contributions * self.mesh._cellToFaceOrientations[
s] #just changes sign
temp = faceContributions.copy()
maskedValues = np.vstack(
([not isinstance(xi, float) for xi in temp[0]
], [not isinstance(xi, float) for xi in temp[1]
], [not isinstance(xi, float) for xi in temp[2]],
[not isinstance(xi, float) for xi in temp[3]]))
faceAreas = np.take(self.mesh._faceAreas, ids)
faceAreas = MA.masked_where(maskedValues, faceAreas)
if (len(temp) > 1):
temp = temp * faceAreas
temp[2] = numerix.MA.filled(temp[2], temp[0])
temp[3] = numerix.MA.filled(temp[3], temp[1])
faceAreas[2] = numerix.MA.filled(faceAreas[2], faceAreas[0])
faceAreas[3] = numerix.MA.filled(faceAreas[3], faceAreas[1])
faceAreas[0] = (faceAreas[0] + faceAreas[2])
faceAreas[1] = (faceAreas[1] + faceAreas[3])
temp[0] = (temp[0] + temp[2]) / faceAreas[0]
temp[1] = (temp[1] + temp[3]) / faceAreas[1]
temp = numerix.vstack(
(numerix.array(temp[0]), numerix.array(temp[1])))
return numerix.tensordot(numerix.ones(temp.shape[-2], 'd'), temp,
(0, -2)) / self.mesh.cellVolumes
def _calcValue(self):
flag = MA.filled(
numerix.take(self.distanceVar._interfaceFlag,
self.mesh.cellFaceIDs), 0)
flag = numerix.sum(flag, axis=0)
return numerix.where(
numerix.logical_and(self.distanceVar.value > 0, flag > 0), 1, 0)
def interiorFaceCellIDs(self):
if not hasattr(self, '_interiorFaceCellIDs'):
## Commented line is better, but doesn't work for zero length arrays
## self.interiorFaceCellIDs = self.getFaceCellIDs()[..., self.getInteriorFaceIDs()]
self._interiorFaceCellIDs = numerix.take(self.faceCellIDs,
self.interiorFaceIDs, axis=1)
return self._interiorFaceCellIDs
def _calcFaceToCellDistances(self):
tmp = MA.repeat(self.faceCenters[...,numerix.NewAxis,:], 2, 1)
# array -= masked_array screws up masking for on numpy 1.1
tmp = tmp - numerix.take(self.cellCenters, self.faceCellIDs, axis=1)
self.cellToFaceDistanceVectors = tmp
self.faceToCellDistances = MA.sqrt(MA.sum(tmp * tmp,0))
def interiorFaceCellIDs(self):
if not hasattr(self, '_interiorFaceCellIDs'):
## Commented line is better, but doesn't work for zero length arrays
## self.interiorFaceCellIDs = self.getFaceCellIDs()[..., self.getInteriorFaceIDs()]
self._interiorFaceCellIDs = numerix.take(self.faceCellIDs,
self.interiorFaceIDs, axis=1)
return self._interiorFaceCellIDs
def _buildMatrix(self, var, SparseMatrix, boundaryCondtions=(), dt=None, equation=None):
oldArray = var.getOld()
mesh = var.getMesh()
NCells = mesh.getNumberOfCells()
NCellFaces = mesh._getMaxFacesPerCell()
cellValues = numerix.repeat(oldArray[numerix.newaxis, ...], NCellFaces, axis = 0)
cellIDs = numerix.repeat(numerix.arange(NCells)[numerix.newaxis, ...], NCellFaces, axis = 0)
cellToCellIDs = mesh._getCellToCellIDs()
if NCells > 0:
cellToCellIDs = MA.where(MA.getmask(cellToCellIDs), cellIDs, cellToCellIDs)
adjacentValues = numerix.take(oldArray, cellToCellIDs)
differences = self._getDifferences(adjacentValues, cellValues, oldArray, cellToCellIDs, mesh)
differences = MA.filled(differences, 0)
minsq = numerix.sqrt(numerix.sum(numerix.minimum(differences, numerix.zeros((NCellFaces, NCells)))**2, axis=0))
maxsq = numerix.sqrt(numerix.sum(numerix.maximum(differences, numerix.zeros((NCellFaces, NCells)))**2, axis=0))
coeff = numerix.array(self._getGeomCoeff(mesh))
coeffXdiffereneces = coeff * ((coeff > 0.) * minsq + (coeff < 0.) * maxsq)
else:
coeffXdiffereneces = 0.
return (SparseMatrix(mesh=var.getMesh()), -coeffXdiffereneces * mesh.getCellVolumes())
def _calcValue(self):
Nfaces = self.mesh.numberOfFaces
M = self.mesh._maxFacesPerCell
dim = self.mesh.dim
cellFaceIDs = self.mesh.cellFaceIDs
faceNormalAreas = self.distanceVar._levelSetNormals * self.mesh._faceAreas
cellFaceNormalAreas = numerix.array(MA.filled(numerix.take(faceNormalAreas, cellFaceIDs, axis=-1), 0))
norms = numerix.array(MA.filled(MA.array(self.mesh._cellNormals), 0))
alpha = numerix.dot(cellFaceNormalAreas, norms)
alpha = numerix.where(alpha > 0, alpha, 0)
alphasum = numerix.sum(alpha, axis=0)
alphasum += (alphasum < 1e-100) * 1.0
alpha = alpha / alphasum
phi = numerix.repeat(self.distanceVar[numerix.newaxis, ...], M, axis=0)
alpha = numerix.where(phi > 0., 0, alpha)
volumes = numerix.array(self.mesh.cellVolumes)
alpha = alpha * volumes * norms
value = numerix.zeros((dim, Nfaces), 'd')
vector._putAdd(value, cellFaceIDs, alpha, mask=MA.getmask(MA.array(cellFaceIDs)))
## value = numerix.reshape(value, (dim, Nfaces, dim))
return -value / self.mesh._faceAreas
def _buildMatrix(self, var, SparseMatrix, boundaryConditions=(), dt=None, equation=None, transientGeomCoeff=None, diffusionGeomCoeff=None):
oldArray = var.old
mesh = var.mesh
NCells = mesh.numberOfCells
NCellFaces = mesh._maxFacesPerCell
cellValues = numerix.repeat(oldArray[numerix.newaxis, ...], NCellFaces, axis = 0)
cellIDs = numerix.repeat(numerix.arange(NCells)[numerix.newaxis, ...], NCellFaces, axis = 0)
cellToCellIDs = mesh._cellToCellIDs
if NCells > 0:
cellToCellIDs = MA.where(MA.getmask(cellToCellIDs), cellIDs, cellToCellIDs)
adjacentValues = numerix.take(oldArray, cellToCellIDs)
differences = self._getDifferences(adjacentValues, cellValues, oldArray, cellToCellIDs, mesh)
differences = MA.filled(differences, 0)
minsq = numerix.sqrt(numerix.sum(numerix.minimum(differences, numerix.zeros((NCellFaces, NCells), 'l'))**2, axis=0))
maxsq = numerix.sqrt(numerix.sum(numerix.maximum(differences, numerix.zeros((NCellFaces, NCells), 'l'))**2, axis=0))
coeff = numerix.array(self._getGeomCoeff(var))
coeffXdiffereneces = coeff * ((coeff > 0.) * minsq + (coeff < 0.) * maxsq)
else:
coeffXdiffereneces = 0.
return (var, SparseMatrix(mesh=var.mesh), -coeffXdiffereneces * mesh.cellVolumes)
def plot(self, filename=None):
"""
Plot the `CellVariable` as a contour plot.
"""
self._plot()
datamin = self._getLimit(('datamin', 'zmin'))
datamax = self._getLimit(('datamax', 'zmax'))
if datamin == 'e':
datamin = None
if datamax == 'e':
datamax = None
datamin, datamax = self._autoscale(vars=self.vars,
datamin=datamin,
datamax=datamax)
if datamax == datamin:
datamax = datamin + 1e-10
vertexIDs = self.mesh._orderedCellVertexIDs
vertexCoords = self.mesh.vertexCoords
xCoords = numerix.take(vertexCoords[0], vertexIDs).flatten("FORTRAN")
yCoords = numerix.take(vertexCoords[1], vertexIDs).flatten("FORTRAN")
import gist
import Numeric
gist.plfp(Numeric.array(numerix.array(self.vars[0])),
yCoords,
xCoords,
self.mesh._numberOfFacesPerCell,
cmin=datamin,
cmax=datamax)
import fipy.viewers.gistViewer.colorbar
colorbar._color_bar(minz=datamin,
maxz=datamax,
ncol=240,
zlabel=self.vars[0].name)
_GistViewer.plot(self, filename=filename)
def _calcFaceTangents(self):
faceVertexCoord = numerix.array(
numerix.take(self.vertexCoords, self.faceVertexIDs[0], axis=1))
tmp = self._faceCenters - faceVertexCoord
faceTangents1 = tmp / numerix.sqrtDot(tmp, tmp)
tmp = numerix.cross(faceTangents1, self.faceNormals, axis=0)
faceTangents2 = tmp / numerix.sqrtDot(tmp, tmp)
return faceTangents1, faceTangents2
def _calcFaceAreas(self):
faceVertexIDs = MA.filled(self.faceVertexIDs, -1)
substitute = numerix.repeat(faceVertexIDs[numerix.newaxis, 0],
faceVertexIDs.shape[0], axis=0)
faceVertexIDs = numerix.where(MA.getmaskarray(self.faceVertexIDs),
substitute, faceVertexIDs)
faceVertexCoords = numerix.take(self.vertexCoords, faceVertexIDs, axis=1)
faceOrigins = numerix.repeat(faceVertexCoords[:,0], faceVertexIDs.shape[0], axis=0)
faceOrigins = numerix.reshape(faceOrigins, MA.shape(faceVertexCoords))
faceVertexCoords = faceVertexCoords - faceOrigins
left = range(faceVertexIDs.shape[0])
right = left[1:] + [left[0]]
cross = numerix.sum(numerix.cross(faceVertexCoords,
numerix.take(faceVertexCoords, right, 1),
axis=0),
1)
return numerix.sqrtDot(cross, cross) / 2.
def _calcFaceToCellDistAndVec(self):
tmp = MA.repeat(self._faceCenters[..., numerix.NewAxis, :], 2, 1)
# array -= masked_array screws up masking for on numpy 1.1
tmp = tmp - numerix.take(self._cellCenters, self.faceCellIDs, axis=1)
cellToFaceDistanceVectors = tmp
faceToCellDistances = MA.sqrt(MA.sum(tmp * tmp, 0))
return faceToCellDistances, cellToFaceDistanceVectors
def _calcValueNoInline(self):
dAP = self.mesh._cellDistances
id1, id2 = self.mesh._adjacentCellIDs
N2 = numerix.take(self.var.value, id2, axis=-1)
faceMask = numerix.array(self.mesh.exteriorFaces)
## The following conditional is required because empty
## indexing is not altogether functional. This
## numpy.empty((0,))[[]] and this numpy.empty((0,))[...,[]]
## both work, but this numpy.empty((3, 0))[...,[]] is
## broken.
if self.var.faceValue.shape[-1] != 0:
s = (Ellipsis, faceMask)
else:
s = (faceMask, )
N2[s] = self.var.faceValue[s]
N = (N2 - numerix.take(self.var, id1, axis=-1)) / dAP
normals = self.mesh._orientedFaceNormals
tangents1 = self.mesh._faceTangents1
tangents2 = self.mesh._faceTangents2
cellGrad = self.var.grad.numericValue
grad1 = numerix.take(cellGrad, id1, axis=-1)
grad2 = numerix.take(cellGrad, id2, axis=-1)
s = (slice(0, None,
None), ) + (numerix.newaxis, ) * (len(grad1.shape) - 2) + (
slice(0, None, None), )
t1grad1 = numerix.sum(tangents1[s] * grad1, 0)
t1grad2 = numerix.sum(tangents1[s] * grad2, 0)
t2grad1 = numerix.sum(tangents2[s] * grad1, 0)
t2grad2 = numerix.sum(tangents2[s] * grad2, 0)
T1 = (t1grad1 + t1grad2) / 2.
T2 = (t2grad1 + t2grad2) / 2.
return normals[s] * N[numerix.newaxis] + tangents1[s] * T1[
numerix.newaxis] + tangents2[s] * T2[numerix.newaxis]
def extents(self):
ext = dict(min=[], max=[])
for d in range(self.dim):
X = numerix.take(self.vertexCoords[d], self._orderedCellVertexIDs)
ext['min'].append(X.min())
ext['max'].append(X.max())
return ext
def _calcValue_(self, alpha, id1, id2):
cell1 = take(self.var,id1)
cell2 = take(self.var,id2)
delta = cell1 - cell2
eps = 1e-14
value = where(abs(delta) < eps, 1. / exp(delta), 0.)
delta = where(abs(delta) < eps, eps, delta)
value = where((abs(delta) > eps) & (delta < 100),
delta / (exp(delta) - 1), value)
value *= exp(cell1)
for bc in self.bcs:
if isinstance(bc, FixedValue):
value[bc.faces.value] = bc._value
return value
def _calcFaceNormals(self):
faceVertexCoords = numerix.take(self.vertexCoords, self.faceVertexIDs, axis=1)
t1 = faceVertexCoords[:, 1,:] - faceVertexCoords[:, 0,:]
faceNormals = t1.copy()
mag = numerix.sqrt(t1[1]**2 + t1[0]**2)
faceNormals[0] = -t1[1] / mag
faceNormals[1] = t1[0] / mag
orientation = 1 - 2 * (numerix.dot(faceNormals, self.cellDistanceVectors) < 0)
return faceNormals * orientation
def _implicitBuildMatrix_(self, SparseMatrix, L, id1, id2, b, weight, var,
boundaryConditions, interiorFaces, dt):
mesh = var.mesh
coeffMatrix = self._getCoeffMatrix_(var, weight)
id1 = self._reshapeIDs(var, id1)
id2 = self._reshapeIDs(var, id2)
L.addAt(
numerix.take(coeffMatrix['cell 1 diag'], interiorFaces,
axis=-1).ravel(), id1.ravel(),
id1.swapaxes(0, 1).ravel())
L.addAt(
numerix.take(coeffMatrix['cell 1 offdiag'], interiorFaces,
axis=-1).ravel(), id1.ravel(),
id2.swapaxes(0, 1).ravel())
L.addAt(
numerix.take(coeffMatrix['cell 2 offdiag'], interiorFaces,
axis=-1).ravel(), id2.ravel(),
id1.swapaxes(0, 1).ravel())
L.addAt(
numerix.take(coeffMatrix['cell 2 diag'], interiorFaces,
axis=-1).ravel(), id2.ravel(),
id2.swapaxes(0, 1).ravel())
N = mesh.numberOfCells
M = mesh._maxFacesPerCell
for boundaryCondition in boundaryConditions:
LL, bb = boundaryCondition._buildMatrix(SparseMatrix, N, M,
coeffMatrix)
if 'FIPY_DISPLAY_MATRIX' in os.environ:
self._viewer.title = r"%s %s" % (
boundaryCondition.__class__.__name__,
self.__class__.__name__)
self._viewer.plot(matrix=LL, RHSvector=bb)
from fipy import raw_input
input()
L += LL
b += bb
def _nonOrthogonality(self):
exteriorFaceArray = numerix.zeros((self.faceCellIDs.shape[1], ), 'l')
numerix.put(exteriorFaceArray, numerix.nonzero(self.exteriorFaces), 1)
unmaskedFaceCellIDs = MA.filled(self.faceCellIDs, 0)
# what we put in for the "fill" doesn't matter because only exterior
# faces have anything masked, and exterior faces have their displacement
# vectors set to zero.
#
# if it's an exterior face, make the "displacement vector" equal to zero
# so the cross product will be zero.
faceDisplacementVectors = \
numerix.where(numerix.array(zip(exteriorFaceArray, exteriorFaceArray)),
0.0,
numerix.take(self._scaledCellCenters.swapaxes(0,1),
unmaskedFaceCellIDs[1, :]) \
- numerix.take(self._scaledCellCenters.swapaxes(0,1),
unmaskedFaceCellIDs[0, :]))
faceDisplacementVectors = faceDisplacementVectors.swapaxes(0, 1)
faceCrossProducts = (faceDisplacementVectors[0, :] * self.faceNormals[1,:]) \
- (faceDisplacementVectors[1, :] * self.faceNormals[0, :])
faceDisplacementVectorLengths = numerix.maximum(((faceDisplacementVectors[0, :] ** 2) \
+ (faceDisplacementVectors[1, :] ** 2)) ** 0.5, 1.e-100)
faceWeightedNonOrthogonalities = abs(
faceCrossProducts /
faceDisplacementVectorLengths) * self._faceAreas
cellFaceWeightedNonOrthogonalities = numerix.take(
faceWeightedNonOrthogonalities, self.cellFaceIDs)
cellFaceAreas = numerix.take(self._faceAreas, self.cellFaceIDs)
cellTotalWeightedValues = numerix.add.reduce(
cellFaceWeightedNonOrthogonalities, axis=0)
cellTotalFaceAreas = numerix.add.reduce(cellFaceAreas, axis=0)
return (cellTotalWeightedValues / cellTotalFaceAreas)
def _interfaceFlag(self):
"""
Returns 1 for faces on boundary and 0 otherwise.
>>> from fipy.meshes import Grid2D
>>> from fipy.variables.faceVariable import FaceVariable
>>> mesh = Grid2D(dx = .5, dy = .5, nx = 2, ny = 2)
>>> distanceVariable = DistanceVariable(mesh = mesh,
... value = (-0.5, 0.5, 0.5, 1.5))
>>> answer = FaceVariable(mesh=mesh,
... value=(0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0))
>>> print numerix.allclose(distanceVariable._interfaceFlag, answer)
True
"""
adjacentCellIDs = self.mesh._adjacentCellIDs
val0 = numerix.take(numerix.array(self._value), adjacentCellIDs[0])
val1 = numerix.take(numerix.array(self._value), adjacentCellIDs[1])
return numerix.where(val1 * val0 < 0, 1, 0)
def _getDifferences(self, adjacentValues, cellValues, oldArray,
cellToCellIDs, mesh):
dAP = mesh._cellToCellDistances
## adjacentGradient = numerix.take(oldArray.grad, cellToCellIDs)
adjacentGradient = numerix.take(oldArray.grad,
mesh._cellToCellIDs,
axis=-1)
adjacentNormalGradient = numerix.dot(adjacentGradient,
mesh._cellNormals)
adjacentUpValues = cellValues + 2 * dAP * adjacentNormalGradient
cellIDs = numerix.repeat(numerix.arange(
mesh.numberOfCells)[numerix.newaxis, ...],
mesh._maxFacesPerCell,
axis=0)
cellIDs = MA.masked_array(cellIDs,
mask=MA.getmask(mesh._cellToCellIDs))
cellGradient = numerix.take(oldArray.grad, cellIDs, axis=-1)
cellNormalGradient = numerix.dot(cellGradient, mesh._cellNormals)
cellUpValues = adjacentValues - 2 * dAP * cellNormalGradient
cellLaplacian = (cellUpValues + adjacentValues -
2 * cellValues) / dAP**2
adjacentLaplacian = (adjacentUpValues + cellValues -
2 * adjacentValues) / dAP**2
adjacentLaplacian = adjacentLaplacian.filled(0)
cellLaplacian = cellLaplacian.filled(0)
mm = numerix.where(
cellLaplacian * adjacentLaplacian < 0., 0.,
numerix.where(
abs(cellLaplacian) > abs(adjacentLaplacian), adjacentLaplacian,
cellLaplacian))
return FirstOrderAdvectionTerm._getDifferences(
self, adjacentValues, cellValues, oldArray, cellToCellIDs,
mesh) - mm * dAP / 2.
def _calcValue(self):
dAP = self.mesh._cellDistances
id1, id2 = self.mesh._adjacentCellIDs
N = (numerix.take(self.var, id2) -
numerix.take(self.var, id1)) / dAP
normals = self.mesh._orientedFaceNormals
tangents1 = self.mesh._faceTangents1
tangents2 = self.mesh._faceTangents2
cellGrad = self.var.grad.numericValue
grad1 = numerix.take(cellGrad, id1, axis=1)
grad2 = numerix.take(cellGrad, id2, axis=1)
t1grad1 = numerix.sum(tangents1 * grad1, 0)
t1grad2 = numerix.sum(tangents1 * grad2, 0)
t2grad1 = numerix.sum(tangents2 * grad1, 0)
t2grad2 = numerix.sum(tangents2 * grad2, 0)
T1 = (t1grad1 + t1grad2) / 2.
T2 = (t2grad1 + t2grad2) / 2.
return normals * N + tangents1 * T1 + tangents2 * T2
def _rightHandOrientation(self):
faceVertexIDs = MA.filled(self.faceVertexIDs, 0)
faceVertexCoords = numerix.take(self.vertexCoords, faceVertexIDs, axis=1)
t1 = faceVertexCoords[:,1,:] - faceVertexCoords[:,0,:]
t2 = faceVertexCoords[:,2,:] - faceVertexCoords[:,1,:]
norm = numerix.cross(t1, t2, axis=0)
## reordering norm's internal memory for inlining
norm = norm.copy()
norm = norm / numerix.sqrtDot(norm, norm)
faceNormals = -norm
return 1 - 2 * (numerix.dot(faceNormals, self.cellDistanceVectors) < 0)
def _buildMatrix(self, var, SparseMatrix, boundaryConditions=(), dt=None, transientGeomCoeff=None, diffusionGeomCoeff=None):
"""Implicit portion considers
"""
mesh = var.mesh
id1, id2 = mesh._adjacentCellIDs
interiorFaces = numerix.nonzero(mesh.interiorFaces)[0]
id1 = numerix.take(id1, interiorFaces)
id2 = numerix.take(id2, interiorFaces)
b = numerix.zeros(var.shape, 'd').ravel()
L = SparseMatrix(mesh=mesh)
weight = self._getWeight(var, transientGeomCoeff, diffusionGeomCoeff)
if 'implicit' in weight:
self._implicitBuildMatrix_(SparseMatrix, L, id1, id2, b, weight['implicit'], var, boundaryConditions, interiorFaces, dt)
if 'explicit' in weight:
self._explicitBuildMatrix_(SparseMatrix, var.old, id1, id2, b, weight['explicit'], var, boundaryConditions, interiorFaces, dt)
return (var, L, b)
def _calcFaceCenters(self):
maskedFaceVertexIDs = MA.filled(self.faceVertexIDs, 0)
faceVertexCoords = numerix.take(self.vertexCoords, maskedFaceVertexIDs, axis=1)
if MA.getmask(self.faceVertexIDs) is False:
faceVertexCoordsMask = numerix.zeros(numerix.shape(faceVertexCoords), 'l')
else:
faceVertexCoordsMask = \
numerix.repeat(MA.getmaskarray(self.faceVertexIDs)[numerix.newaxis,...],
self.dim, axis=0)
faceVertexCoords = MA.array(data=faceVertexCoords, mask=faceVertexCoordsMask)
return MA.filled(MA.average(faceVertexCoords, axis=1))
def _calcValueNoInline(self):
ids = self.mesh.cellFaceIDs
contributions = numerix.take(self.faceVariable, ids, axis=-1)
# FIXME: numerix.MA.filled casts away dimensions
s = (numerix.newaxis, ) * (len(contributions.shape) - 2) + (slice(
0, None, None), ) + (slice(0, None, None), )
faceContributions = contributions * self.mesh._cellToFaceOrientations[s]
return numerix.tensordot(
numerix.ones(faceContributions.shape[-2], 'd'),
numerix.MA.filled(faceContributions, 0.),
(0, -2)) / self.mesh.cellVolumes
