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.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 _getNearestCellID(self, points): """ Test cases >>> from fipy import * >>> m0 = Grid2D(dx=(.1, 1., 10.), dy=(.1, 1., 10.)) >>> m1 = Grid2D(nx=2, ny=2, dx=5., dy=5.) >>> print m0._getNearestCellID(m1.cellCenters.globalValue) [4 5 7 8] """ return numerix.nearest(data=self.cellCenters.globalValue, points=points)
def _getAddedMeshValues(self, other, resolution=1e-2): """Calculate the parameters to define a concatenation of `other` with `self` Parameters ---------- other : ~fipy.meshes.mesh.Mesh The `Mesh` to concatenate with `self` resolution : float How close vertices have to be (relative to the smallest cell-to-cell distance in either mesh) to be considered the same Returns ------- dict (`vertexCoords`, `faceVertexIDs`, `cellFaceIDs`) for the new mesh. """ selfc = self._concatenableMesh otherc = other._concatenableMesh selfNumFaces = selfc.faceVertexIDs.shape[-1] selfNumVertices = selfc.vertexCoords.shape[-1] otherNumFaces = otherc.faceVertexIDs.shape[-1] otherNumVertices = otherc.vertexCoords.shape[-1] ## check dimensions if(selfc.vertexCoords.shape[0] != otherc.vertexCoords.shape[0]): raise MeshAdditionError("Dimensions do not match") ## compute vertex correlates # from fipy.tools.debug import PRINT # PRINT("selfNumFaces", selfNumFaces) # PRINT("otherNumFaces", otherNumVertices) # PRINT("selfNumVertices", selfNumVertices) # PRINT("otherNumVertices", otherNumVertices) # # from fipy.tools.debug import PRINT # from fipy.tools.debug import PRINT # PRINT("otherExt", otherc.exteriorFaces.value) # raw_input() # PRINT("selfExt", selfc.exteriorFaces.value) # # PRINT("self filled", selfc.faceVertexIDs.filled()) # PRINT("othe filled", otherc.faceVertexIDs.filled()) # raw_input() # # PRINT("selfc.faceVertexIDs.filled()\n",selfc.faceVertexIDs.filled()) # PRINT("flat\n",selfc.faceVertexIDs.filled()[..., # selfc.exteriorFaces.value].flatten()) # PRINT("selfc.exteriorFaces.value\n",selfc.exteriorFaces.value) # PRINT("extfaces type", type(selfc.exteriorFaces)) # PRINT("extfaces mesh", selfc.exteriorFaces.mesh) ## only try to match along the operation manifold if hasattr(self, "opManifold"): self_faces = self.opManifold(selfc) else: self_faces = selfc.exteriorFaces.value if hasattr(other, "opManifold"): other_faces = other.opManifold(otherc) else: other_faces = otherc.exteriorFaces.value ## only try to match exterior (X) vertices self_Xvertices = numerix.unique(selfc.faceVertexIDs.filled()[..., self_faces].flatten()) other_Xvertices = numerix.unique(otherc.faceVertexIDs.filled()[..., other_faces].flatten()) self_XvertexCoords = selfc.vertexCoords[..., self_Xvertices] other_XvertexCoords = otherc.vertexCoords[..., other_Xvertices] closest = numerix.nearest(self_XvertexCoords, other_XvertexCoords) # just because they're closest, doesn't mean they're close tmp = self_XvertexCoords[..., closest] - other_XvertexCoords distance = numerix.sqrtDot(tmp, tmp) # only want vertex pairs that are 100x closer than the smallest # cell-to-cell distance close = distance < resolution * min(selfc._cellToCellDistances.min(), otherc._cellToCellDistances.min()) vertexCorrelates = numerix.array((self_Xvertices[closest[close]], other_Xvertices[close])) # warn if meshes don't touch, but allow it if (selfc._numberOfVertices > 0 and otherc._numberOfVertices > 0 and vertexCorrelates.shape[-1] == 0): import warnings warnings.warn("Vertices are not aligned", UserWarning, stacklevel=4) ## compute face correlates # ensure that both sets of faceVertexIDs have the same maximum number of (masked) elements self_faceVertexIDs = selfc.faceVertexIDs other_faceVertexIDs = otherc.faceVertexIDs diff = self_faceVertexIDs.shape[0] - other_faceVertexIDs.shape[0] if diff > 0: other_faceVertexIDs = numerix.append(other_faceVertexIDs, -1 * numerix.ones((diff,) + other_faceVertexIDs.shape[1:], 'l'), axis=0) other_faceVertexIDs = MA.masked_values(other_faceVertexIDs, -1) elif diff < 0: self_faceVertexIDs = numerix.append(self_faceVertexIDs, -1 * numerix.ones((-diff,) + self_faceVertexIDs.shape[1:], 'l'), axis=0) self_faceVertexIDs = MA.masked_values(self_faceVertexIDs, -1) # want self's Faces for which all faceVertexIDs are in vertexCorrelates self_matchingFaces = numerix.in1d(self_faceVertexIDs, vertexCorrelates[0]).reshape(self_faceVertexIDs.shape).all(axis=0).nonzero()[0] # want other's Faces for which all faceVertexIDs are in vertexCorrelates other_matchingFaces = numerix.in1d(other_faceVertexIDs, vertexCorrelates[1]).reshape(other_faceVertexIDs.shape).all(axis=0).nonzero()[0] # map other's Vertex IDs to new Vertex IDs, # accounting for overlaps with self's Vertex IDs vertex_map = numerix.empty(otherNumVertices, dtype=numerix.INT_DTYPE) verticesToAdd = numerix.delete(numerix.arange(otherNumVertices), vertexCorrelates[1]) vertex_map[verticesToAdd] = numerix.arange(otherNumVertices - len(vertexCorrelates[1])) + selfNumVertices vertex_map[vertexCorrelates[1]] = vertexCorrelates[0] # calculate hashes of faceVertexIDs for comparing Faces if self_matchingFaces.shape[-1] == 0: self_faceHash = numerix.empty(self_matchingFaces.shape[:-1] + (0,), dtype="str") else: # sort each of self's Face's vertexIDs for canonical comparison self_faceHash = numerix.sort(self_faceVertexIDs[..., self_matchingFaces], axis=0) # then hash the Faces for comparison (NumPy set operations are only for 1D arrays) self_faceHash = numerix.apply_along_axis(str, axis=0, arr=self_faceHash) face_sort = numerix.argsort(self_faceHash) self_faceHash = self_faceHash[face_sort] self_matchingFaces = self_matchingFaces[face_sort] if other_matchingFaces.shape[-1] == 0: other_faceHash = numerix.empty(other_matchingFaces.shape[:-1] + (0,), dtype="str") else: # convert each of other's Face's vertexIDs to new IDs other_faceHash = vertex_map[other_faceVertexIDs[..., other_matchingFaces]] # sort each of other's Face's vertexIDs for canonical comparison other_faceHash = numerix.sort(other_faceHash, axis=0) # then hash the Faces for comparison (NumPy set operations are only for 1D arrays) other_faceHash = numerix.apply_along_axis(str, axis=0, arr=other_faceHash) face_sort = numerix.argsort(other_faceHash) other_faceHash = other_faceHash[face_sort] other_matchingFaces = other_matchingFaces[face_sort] self_matchingFaces = self_matchingFaces[numerix.in1d(self_faceHash, other_faceHash)] other_matchingFaces = other_matchingFaces[numerix.in1d(other_faceHash, self_faceHash)] faceCorrelates = numerix.array((self_matchingFaces, other_matchingFaces)) # warn if meshes don't touch, but allow it if (selfc.numberOfFaces > 0 and otherc.numberOfFaces > 0 and faceCorrelates.shape[-1] == 0): import warnings warnings.warn("Faces are not aligned", UserWarning, stacklevel=4) # map other's Face IDs to new Face IDs, # accounting for overlaps with self's Face IDs face_map = numerix.empty(otherNumFaces, dtype=numerix.INT_DTYPE) facesToAdd = numerix.delete(numerix.arange(otherNumFaces), faceCorrelates[1]) face_map[facesToAdd] = numerix.arange(otherNumFaces - len(faceCorrelates[1])) + selfNumFaces face_map[faceCorrelates[1]] = faceCorrelates[0] other_faceVertexIDs = vertex_map[otherc.faceVertexIDs[..., facesToAdd]] # ensure that both sets of cellFaceIDs have the same maximum number of (masked) elements self_cellFaceIDs = selfc.cellFaceIDs other_cellFaceIDs = face_map[otherc.cellFaceIDs] diff = self_cellFaceIDs.shape[0] - other_cellFaceIDs.shape[0] if diff > 0: other_cellFaceIDs = numerix.append(other_cellFaceIDs, -1 * numerix.ones((diff,) + other_cellFaceIDs.shape[1:], 'l'), axis=0) other_cellFaceIDs = MA.masked_values(other_cellFaceIDs, -1) elif diff < 0: self_cellFaceIDs = numerix.append(self_cellFaceIDs, -1 * numerix.ones((-diff,) + self_cellFaceIDs.shape[1:], 'l'), axis=0) self_cellFaceIDs = MA.masked_values(self_cellFaceIDs, -1) # concatenate everything and return return { 'vertexCoords': numerix.concatenate((selfc.vertexCoords, otherc.vertexCoords[..., verticesToAdd]), axis=1), 'faceVertexIDs': numerix.concatenate((self_faceVertexIDs, other_faceVertexIDs), axis=1), 'cellFaceIDs': MA.concatenate((self_cellFaceIDs, other_cellFaceIDs), axis=1) }
def _getAddedMeshValues(self, other, resolution=1e-2): """Calculate the parameters to define a concatenation of `other` with `self` :Parameters: - `other`: The :class:`~fipy.meshes.Mesh` to concatenate with `self` - `resolution`: How close vertices have to be (relative to the smallest cell-to-cell distance in either mesh) to be considered the same :Returns: A `dict` with 3 elements: the new mesh vertexCoords, faceVertexIDs, and cellFaceIDs. """ selfc = self._concatenableMesh otherc = other._concatenableMesh selfNumFaces = selfc.faceVertexIDs.shape[-1] selfNumVertices = selfc.vertexCoords.shape[-1] otherNumFaces = otherc.faceVertexIDs.shape[-1] otherNumVertices = otherc.vertexCoords.shape[-1] ## check dimensions if(selfc.vertexCoords.shape[0] != otherc.vertexCoords.shape[0]): raise MeshAdditionError("Dimensions do not match") ## compute vertex correlates """ from fipy.tools.debug import PRINT PRINT("selfNumFaces", selfNumFaces) PRINT("otherNumFaces", otherNumVertices) PRINT("selfNumVertices", selfNumVertices) PRINT("otherNumVertices", otherNumVertices) from fipy.tools.debug import PRINT from fipy.tools.debug import PRINT PRINT("otherExt", otherc.exteriorFaces.value) raw_input() PRINT("selfExt", selfc.exteriorFaces.value) PRINT("self filled", selfc.faceVertexIDs.filled()) PRINT("othe filled", otherc.faceVertexIDs.filled()) raw_input() PRINT("selfc.faceVertexIDs.filled()\n",selfc.faceVertexIDs.filled()) PRINT("flat\n",selfc.faceVertexIDs.filled()[..., selfc.exteriorFaces.value].flatten()) PRINT("selfc.exteriorFaces.value\n",selfc.exteriorFaces.value) PRINT("extfaces type", type(selfc.exteriorFaces)) PRINT("extfaces mesh", selfc.exteriorFaces.mesh) """ ## only try to match along the operation manifold if hasattr(self, "opManifold"): self_faces = self.opManifold(selfc) else: self_faces = selfc.exteriorFaces.value if hasattr(other, "opManifold"): other_faces = other.opManifold(otherc) else: other_faces = otherc.exteriorFaces.value ## only try to match exterior (X) vertices self_Xvertices = numerix.unique(selfc.faceVertexIDs.filled()[..., self_faces].flatten()) other_Xvertices = numerix.unique(otherc.faceVertexIDs.filled()[..., other_faces].flatten()) self_XvertexCoords = selfc.vertexCoords[..., self_Xvertices] other_XvertexCoords = otherc.vertexCoords[..., other_Xvertices] closest = numerix.nearest(self_XvertexCoords, other_XvertexCoords) # just because they're closest, doesn't mean they're close tmp = self_XvertexCoords[..., closest] - other_XvertexCoords distance = numerix.sqrtDot(tmp, tmp) # only want vertex pairs that are 100x closer than the smallest # cell-to-cell distance close = distance < resolution * min(selfc._cellToCellDistances.min(), otherc._cellToCellDistances.min()) vertexCorrelates = numerix.array((self_Xvertices[closest[close]], other_Xvertices[close])) # warn if meshes don't touch, but allow it if (selfc._numberOfVertices > 0 and otherc._numberOfVertices > 0 and vertexCorrelates.shape[-1] == 0): import warnings warnings.warn("Vertices are not aligned", UserWarning, stacklevel=4) ## compute face correlates # ensure that both sets of faceVertexIDs have the same maximum number of (masked) elements self_faceVertexIDs = selfc.faceVertexIDs other_faceVertexIDs = otherc.faceVertexIDs diff = self_faceVertexIDs.shape[0] - other_faceVertexIDs.shape[0] if diff > 0: other_faceVertexIDs = numerix.append(other_faceVertexIDs, -1 * numerix.ones((diff,) + other_faceVertexIDs.shape[1:], 'l'), axis=0) other_faceVertexIDs = MA.masked_values(other_faceVertexIDs, -1) elif diff < 0: self_faceVertexIDs = numerix.append(self_faceVertexIDs, -1 * numerix.ones((-diff,) + self_faceVertexIDs.shape[1:], 'l'), axis=0) self_faceVertexIDs = MA.masked_values(self_faceVertexIDs, -1) # want self's Faces for which all faceVertexIDs are in vertexCorrelates self_matchingFaces = numerix.in1d(self_faceVertexIDs, vertexCorrelates[0]).reshape(self_faceVertexIDs.shape).all(axis=0).nonzero()[0] # want other's Faces for which all faceVertexIDs are in vertexCorrelates other_matchingFaces = numerix.in1d(other_faceVertexIDs, vertexCorrelates[1]).reshape(other_faceVertexIDs.shape).all(axis=0).nonzero()[0] # map other's Vertex IDs to new Vertex IDs, # accounting for overlaps with self's Vertex IDs vertex_map = numerix.empty(otherNumVertices, dtype=numerix.INT_DTYPE) verticesToAdd = numerix.delete(numerix.arange(otherNumVertices), vertexCorrelates[1]) vertex_map[verticesToAdd] = numerix.arange(otherNumVertices - len(vertexCorrelates[1])) + selfNumVertices vertex_map[vertexCorrelates[1]] = vertexCorrelates[0] # calculate hashes of faceVertexIDs for comparing Faces if self_matchingFaces.shape[-1] == 0: self_faceHash = numerix.empty(self_matchingFaces.shape[:-1] + (0,), dtype="str") else: # sort each of self's Face's vertexIDs for canonical comparison self_faceHash = numerix.sort(self_faceVertexIDs[..., self_matchingFaces], axis=0) # then hash the Faces for comparison (NumPy set operations are only for 1D arrays) self_faceHash = numerix.apply_along_axis(str, axis=0, arr=self_faceHash) face_sort = numerix.argsort(self_faceHash) self_faceHash = self_faceHash[face_sort] self_matchingFaces = self_matchingFaces[face_sort] if other_matchingFaces.shape[-1] == 0: other_faceHash = numerix.empty(other_matchingFaces.shape[:-1] + (0,), dtype="str") else: # convert each of other's Face's vertexIDs to new IDs other_faceHash = vertex_map[other_faceVertexIDs[..., other_matchingFaces]] # sort each of other's Face's vertexIDs for canonical comparison other_faceHash = numerix.sort(other_faceHash, axis=0) # then hash the Faces for comparison (NumPy set operations are only for 1D arrays) other_faceHash = numerix.apply_along_axis(str, axis=0, arr=other_faceHash) face_sort = numerix.argsort(other_faceHash) other_faceHash = other_faceHash[face_sort] other_matchingFaces = other_matchingFaces[face_sort] self_matchingFaces = self_matchingFaces[numerix.in1d(self_faceHash, other_faceHash)] other_matchingFaces = other_matchingFaces[numerix.in1d(other_faceHash, self_faceHash)] faceCorrelates = numerix.array((self_matchingFaces, other_matchingFaces)) # warn if meshes don't touch, but allow it if (selfc.numberOfFaces > 0 and otherc.numberOfFaces > 0 and faceCorrelates.shape[-1] == 0): import warnings warnings.warn("Faces are not aligned", UserWarning, stacklevel=4) # map other's Face IDs to new Face IDs, # accounting for overlaps with self's Face IDs face_map = numerix.empty(otherNumFaces, dtype=numerix.INT_DTYPE) facesToAdd = numerix.delete(numerix.arange(otherNumFaces), faceCorrelates[1]) face_map[facesToAdd] = numerix.arange(otherNumFaces - len(faceCorrelates[1])) + selfNumFaces face_map[faceCorrelates[1]] = faceCorrelates[0] other_faceVertexIDs = vertex_map[otherc.faceVertexIDs[..., facesToAdd]] # ensure that both sets of cellFaceIDs have the same maximum number of (masked) elements self_cellFaceIDs = selfc.cellFaceIDs other_cellFaceIDs = face_map[otherc.cellFaceIDs] diff = self_cellFaceIDs.shape[0] - other_cellFaceIDs.shape[0] if diff > 0: other_cellFaceIDs = numerix.append(other_cellFaceIDs, -1 * numerix.ones((diff,) + other_cellFaceIDs.shape[1:], 'l'), axis=0) other_cellFaceIDs = MA.masked_values(other_cellFaceIDs, -1) elif diff < 0: self_cellFaceIDs = numerix.append(self_cellFaceIDs, -1 * numerix.ones((-diff,) + self_cellFaceIDs.shape[1:], 'l'), axis=0) self_cellFaceIDs = MA.masked_values(self_cellFaceIDs, -1) # concatenate everything and return return { 'vertexCoords': numerix.concatenate((selfc.vertexCoords, otherc.vertexCoords[..., verticesToAdd]), axis=1), 'faceVertexIDs': numerix.concatenate((self_faceVertexIDs, other_faceVertexIDs), axis=1), 'cellFaceIDs': MA.concatenate((self_cellFaceIDs, other_cellFaceIDs), axis=1) }