mirror of
https://github.com/wassname/simpeg.git
synced 2026-06-28 22:04:20 +08:00
Rowan Cockett
493 lines
16 KiB
Python
493 lines
16 KiB
Python
import numpy as np, scipy.sparse as sp
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from SimPEG.Utils import ndgrid, mkvc, sdiag
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NUM, ACTIVE, NX, NY, NZ = range(5)
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NUM, ACTIVE, PARENT, EDIR, ENODE0, ENODE1 = range(6)
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NUM, ACTIVE, PARENT, FDIR, FEDGE0, FEDGE1, FEDGE2, FEDGE3 = range(8)
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NUM, ACTIVE, PARENT, CFACE0, CFACE1, CFACE2, CFACE3, CFACE4, CFACE5 = range(9)
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def SortByX0(grid):
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dtype=[('x',float),('y',float)]
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grid2 = np.zeros(grid.shape[0], dtype=dtype)
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grid2['x'][:] = grid[:,0]
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grid2['y'][:] = grid[:,1]
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P = np.argsort(grid2, order=['y','x'])
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return P
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class TreeMesh(object):
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def __init__(self, h):
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hx, hy = h
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nx = np.r_[0,hx.cumsum()]
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ny = np.r_[0,hy.cumsum()]
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vnC = [nx.size-1, ny.size-1]
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vnN = [nx.size, ny.size]
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XY = ndgrid(nx, ny)
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N = np.c_[np.arange(XY.shape[0]), np.ones(XY.shape[0]), XY]
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I = np.arange(nx.size * ny.size, dtype=int).reshape(vnN, order='F')
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vEx = np.c_[mkvc(I[:-1,:]), mkvc(I[1:,:])]
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vEy = np.c_[mkvc(I[:,:-1]), mkvc(I[:,1:])]
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nEx = np.arange(vEx.shape[0], dtype=int).reshape(nx.size-1, ny.size, order='F')
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nEy = np.arange(vEy.shape[0], dtype=int).reshape(nx.size, ny.size-1, order='F') + vEx.shape[0]
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zEx = np.zeros(nEx.size, dtype=int)
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zEy = np.zeros(nEy.size, dtype=int)
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# # active parent dir, n1,n2
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Ex = np.c_[mkvc(nEx), zEx+1, zEx-1, zEx+0, vEx]
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Ey = np.c_[mkvc(nEy), zEy+1, zEy-1, zEy+1, vEy]
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nC = np.arange(np.prod(vnC), dtype=int)
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C = np.c_[nC, nC*0+1, nC*0-1, nC*0+2, mkvc(nEx[:,:-1]), mkvc(nEx[:,1:]), mkvc(nEy[:-1,:]), mkvc(nEy[1:,:])]
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self._nodes = N
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self._edges = np.r_[Ex, Ey]
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self._faces = C
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self.isNumbered = False
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@property
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def isNumbered(self):
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return self._numberedCC and self._numberedN and self._numberedEx and self._numberedEy
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@isNumbered.setter
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def isNumbered(self, value):
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assert value is False, 'Can only set to False.'
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self._numberedCC = False
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self._numberedN = False
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self._numberedEx = False
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self._numberedEy = False
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for name in ['vol', 'area', 'edge', 'gridCC', 'gridN', 'gridEx', 'gridEy', 'gridEz', 'gridFx', 'gridFy', 'gridFz']:
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if hasattr(self, '_'+name):
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delattr(self, '_'+name)
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@property
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def dim(self):
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return 2
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def _push(self, attr, rows):
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self.isNumbered = False
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rows = np.atleast_2d(rows)
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X = getattr(self, attr)
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offset = X.shape[0]
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rowNumer = np.arange(rows.shape[0], dtype=int) + offset
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rows[:,0] = rowNumer*0-1
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setattr(self, attr, np.vstack((X, rows)).astype(X.dtype))
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if rows.shape[0] == 1:
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return offset, rows.flatten()
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return rowNumer, rows
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def addNode(self, between):
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"""Add a node between the node in list between"""
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between = np.array(between).flatten()
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nodes = self._nodes[between.astype(int), :]
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newNode = np.mean(nodes, axis=0)
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newNode[ACTIVE] = 1
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return self._push('_nodes', newNode)
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def refineEdge(self, index):
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e = self._edges[index,:]
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if e[ACTIVE] == 0:
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# search for the children up to one level deep
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subInds = np.argwhere(self._edges[:,PARENT] == index).flatten()
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return subInds, self._edges[subInds,:]
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self._edges[index, ACTIVE] = 0
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newNode, node = self.addNode(e[[ENODE0, ENODE1]])
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Es = np.zeros((2, 6))
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Es[:, ACTIVE] = 1
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Es[:, PARENT] = index
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Es[:, EDIR] = e[EDIR]
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Es[0, ENODE0] = e[ENODE0]
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Es[0, ENODE1] = newNode
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Es[1, ENODE0] = newNode
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Es[1, ENODE1] = e[ENODE1]
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return self._push('_edges', Es)
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def refineFace(self, index):
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f = self._faces[index,:]
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nodeNums = self._edges[f[[FEDGE0, FEDGE1]],:][:,[ENODE0, ENODE1]]
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self._faces[index, ACTIVE] = 0
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# new faces and edges
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# 2_______________3 _______________
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# | e1--> | | | |
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# ^ | | ^ | 2 3 3 | y z z
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# | | | | | | | ^ ^ ^
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# | | x | | ---> |---0---+---1---| | | |
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# e2 | | e3 | | | | | |
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# | | | 0 2 1 | z-----> x y-----> x x-----> y
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# |_______________| |_______|_______|
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# 0 e0--> 1
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# Refine the outer edges
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E0i, E0 = self.refineEdge(f[FEDGE0])
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E1i, E1 = self.refineEdge(f[FEDGE1])
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E2i, E2 = self.refineEdge(f[FEDGE2])
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E3i, E3 = self.refineEdge(f[FEDGE3])
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newNode, node = self.addNode(nodeNums)
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# Refine the inner edges
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nE = np.zeros((4,6))
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nE[:, ACTIVE] = 1
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nE[:, PARENT] = -1
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nE[:, EDIR] = [0,0,1,1] if f[FDIR] == 2 else [0,0,2,2] if f[FDIR] == 1 else [1,1,2,2]
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nE[0, ENODE0] = E2[0, ENODE1]
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nE[0, ENODE1] = newNode
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nE[1, ENODE0] = newNode
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nE[1, ENODE1] = E3[0, ENODE1]
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nE[2, ENODE0] = E0[0, ENODE1]
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nE[2, ENODE1] = newNode
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nE[3, ENODE0] = newNode
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nE[3, ENODE1] = E1[0, ENODE1]
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nEi, nE = self._push('_edges', nE)
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# Add four new faces
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Fs = np.zeros((4,8))
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Fs[:, ACTIVE] = 1
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Fs[:, PARENT] = index
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Fs[:, FDIR] = f[FDIR]
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fInds = [FEDGE0,FEDGE1,FEDGE2,FEDGE3]
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Fs[0, fInds] = [E0i[0], nEi[0], E2i[0], nEi[2]]
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Fs[1, fInds] = [E0i[1], nEi[1], nEi[2], E3i[0]]
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Fs[2, fInds] = [nEi[0], E1i[0], E2i[1], nEi[3]]
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Fs[3, fInds] = [nEi[1], E1i[1], nEi[3], E3i[1]]
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return self._push('_faces', Fs)
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@property
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def nC(self):
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if self.dim == 2:
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return np.sum(self._faces[:,ACTIVE] == 1)
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return np.sum(self._cells[:,ACTIVE] == 1)
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@property
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def nN(self):
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return np.sum(self._cells[:,ACTIVE] == 1)
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@property
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def nE(self):
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return np.sum(self._edges[:,ACTIVE] == 1)
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@property
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def nF(self):
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if self.dim == 2:
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return self.nFx + self.nFy
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return np.sum(self._faces[:,ACTIVE] == 1)
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@property
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def nEx(self):
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return np.sum((self._edges[:,ACTIVE] == 1) & (self._edges[:,EDIR] == 0))
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@property
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def nEy(self):
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return np.sum((self._edges[:,ACTIVE] == 1) & (self._edges[:,EDIR] == 1))
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@property
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def nEz(self):
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if self.dim == 2:
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return None
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return np.sum((self._edges[:,ACTIVE] == 1) & (self._edges[:,EDIR] == 2))
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@property
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def nFx(self):
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if self.dim == 2:
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return self.nEy
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return np.sum((self._faces[:,ACTIVE] == 1) & (self._faces[:,FDIR] == 0))
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@property
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def nFy(self):
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if self.dim == 2:
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return self.nEx
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return np.sum((self._faces[:,ACTIVE] == 1) & (self._faces[:,FDIR] == 1))
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@property
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def nFz(self):
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if self.dim == 2:
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return None
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return np.sum((self._faces[:,ACTIVE] == 1) & (self._faces[:,FDIR] == 1))
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@property
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def edge(self):
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if getattr(self, '_edge', None) is None:
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self.number()
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N = self._nodes
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E = self._edges
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activeEdges = E[:,ACTIVE] == 1
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e0xy = N[E[activeEdges,ENODE0],:][:,[NX,NY]]
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e1xy = N[E[activeEdges,ENODE1],:][:,[NX,NY]]
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A = np.sum((e1xy - e0xy)**2,axis=1)**0.5
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P = np.argsort(E[activeEdges,NUM])
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self._edge = A[P]
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return self._edge
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@property
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def area(self):
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if getattr(self, '_area', None) is None:
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self.number()
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if self.dim == 2:
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self._area = np.r_[self.edge[self.nEx:], self.edge[:self.nEx]]
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return self._area
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@property
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def vol(self):
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if getattr(self, '_vol', None) is None:
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self.number()
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N = self._nodes
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E = self._edges
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C = self._faces
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activeCells = C[:,ACTIVE] == 1
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nInds1 = E[C[activeCells,FEDGE0],:][:,[ENODE0,ENODE1]]
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nInds2 = E[C[activeCells,FEDGE1],:][:,[ENODE0,ENODE1]]
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n0 = N[nInds1[:,0],:][:,[NX,NY]] # 2------3 3------2
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n1 = N[nInds1[:,1],:][:,[NX,NY]] # | | --> | |
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n3 = N[nInds2[:,0],:][:,[NX,NY]] # | | | |
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n2 = N[nInds2[:,1],:][:,[NX,NY]] # 0------1 0------1
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a = np.sum((n1 - n0)**2,axis=1)**0.5
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b = np.sum((n2 - n1)**2,axis=1)**0.5
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c = np.sum((n3 - n2)**2,axis=1)**0.5
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d = np.sum((n0 - n3)**2,axis=1)**0.5
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p = np.sum((n2 - n0)**2,axis=1)**0.5
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q = np.sum((n3 - n1)**2,axis=1)**0.5
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# Area of an arbitrary quadrilateral (in a plane)
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V = 0.25 * (4.0*(p**2)*(q**2) - (a**2 + c**2 - b**2 - d**2)**2)**0.5
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P = np.argsort(C[activeCells,NUM])
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self._vol = V[P]
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return self._vol
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@property
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def gridN(self):
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N = self._nodes
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activeNodes = N[:,ACTIVE] == 1
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Nx = N[activeNodes,NX]
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Ny = N[activeNodes,NY]
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P = SortByX0(np.c_[Nx, Ny])
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if not self._numberedN:
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cnt = np.zeros(P.size, dtype=int)
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cnt[P] = np.arange(P.size)
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self._nodes[activeNodes, NUM] = cnt
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self._numberedN = True
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return np.c_[Nx, Ny][P, :]
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@property
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def gridCC(self):
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N = self._nodes
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E = self._edges
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C = self._faces
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activeCells = C[:,ACTIVE] == 1
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nInds1 = E[C[activeCells,FEDGE0],:][:,[ENODE0,ENODE1]]
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nInds2 = E[C[activeCells,FEDGE1],:][:,[ENODE0,ENODE1]]
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Cx = (N[nInds1[:,0],NX] + N[nInds1[:,1],NX] + N[nInds2[:,0],NX] + N[nInds2[:,1],NX])/4.0
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Cy = (N[nInds1[:,0],NY] + N[nInds1[:,1],NY] + N[nInds2[:,0],NY] + N[nInds2[:,1],NY])/4.0
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P = SortByX0(np.c_[N[nInds1[:,0],NX], N[nInds1[:,0],NY]])
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if not self._numberedCC:
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cnt = np.zeros(P.size, dtype=int)
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cnt[P] = np.arange(P.size)
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self._faces[activeCells, NUM] = cnt
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self._numberedCC = True
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return np.c_[Cx, Cy][P, :]
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@property
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def gridEx(self):
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N = self._nodes
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E = self._edges
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C = self._faces
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activeEdges = (E[:,ACTIVE] == 1) & (E[:,EDIR] == 0)
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nInds = E[activeEdges,:][:,[ENODE0,ENODE1]]
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Ex = (N[nInds[:,0],NX] + N[nInds[:,1],NX])/2.0
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Ey = (N[nInds[:,0],NY] + N[nInds[:,1],NY])/2.0
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P = SortByX0(np.c_[N[nInds[:,0],NX], N[nInds[:,0],NY]])
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if not self._numberedEx:
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cnt = np.zeros(P.size, dtype=int)
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cnt[P] = np.arange(P.size)
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self._edges[activeEdges, NUM] = cnt
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self._numberedEx = True
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return np.c_[Ex, Ey][P, :]
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@property
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def gridEy(self):
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N = self._nodes
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E = self._edges
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C = self._faces
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activeEdges = (E[:,ACTIVE] == 1) & (E[:,EDIR] == 1)
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nInds = E[activeEdges,:][:,[ENODE0,ENODE1]]
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Ex = (N[nInds[:,0],NX] + N[nInds[:,1],NX])/2.0
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Ey = (N[nInds[:,0],NY] + N[nInds[:,1],NY])/2.0
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P = SortByX0(np.c_[N[nInds[:,0],NX], N[nInds[:,0],NY]])
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if not self._numberedEy:
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cnt = np.zeros(P.size, dtype=int)
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cnt[P] = np.arange(P.size)
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self._edges[activeEdges, NUM] = cnt + self.nEx
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self._numberedEy = True
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return np.c_[Ex, Ey][P, :]
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@property
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def gridFx(self):
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if self.dim == 2:
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return self.gridEy
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@property
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def gridFy(self):
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if self.dim == 2:
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return self.gridEx
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def _index(self, attr, index):
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index = [index] if np.isscalar(index) else list(index)
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C = getattr(self, attr)
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cSub = []
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iSub = []
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for I in index:
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if C[I, ACTIVE] == 1:
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iSub += [I]
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cSub += [C[I, :]]
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else:
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subInds = np.argwhere(C[:,PARENT] == I).flatten()
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i, c = self._index(attr, subInds)
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iSub += i
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cSub += [c]
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return iSub, np.vstack(cSub)
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@property
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def faceDiv(self):
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if getattr(self, '_faceDiv', None) is None:
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self.number()
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# TODO: Preallocate!
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I, J, V = [], [], []
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offset = np.r_[self.nFx, -self.nEx] # this switches from edge to face numbering
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C = self._faces
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activeCells = C[:,ACTIVE] == 1
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for cell in C[activeCells]:
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for sign, face in zip([-1,1,-1,1],[FEDGE0, FEDGE1, FEDGE2, FEDGE3]):
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ij, jrow = self._index('_edges', cell[face])
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I += [cell[NUM]]*len(ij)
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J += list(jrow[:,0] + offset[jrow[:,EDIR]])
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V += [sign]*len(ij)
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VOL = self.vol
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D = sp.csr_matrix((V,(I,J)), shape=(self.nC, self.nF))
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S = self.area
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self._faceDiv = sdiag(1/VOL)*D*sdiag(S)
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return self._faceDiv
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def number(self):
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if self.isNumbered:
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return
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self._nodes[:,NUM] = -1
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self._edges[:,NUM] = -1
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self._faces[:,NUM] = -1
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# self._cells[:,NUM] = -1
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self.gridCC
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self.gridN
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self.gridEx
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self.gridEy
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def plotGrid(self, ax=None, text=True, showIt=False):
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import matplotlib.pyplot as plt
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axOpts = {'projection':'3d'} if self.dim == 3 else {}
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if ax is None: ax = plt.subplot(111, **axOpts)
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N = self._nodes
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E = self._edges
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C = self._faces
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plt.plot(N[:,1], N[:,2], 'b.')
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activeCells = C[:,ACTIVE] == 1
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for FEDGE in [FEDGE0, FEDGE1, FEDGE2, FEDGE3]:
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nInds = E[C[activeCells,FEDGE],:][:,[ENODE0,ENODE1]]
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eX = np.c_[N[nInds[:,0],NX], N[nInds[:,1],NX], [np.nan]*nInds.shape[0]]
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eY = np.c_[N[nInds[:,0],NY], N[nInds[:,1],NY], [np.nan]*nInds.shape[0]]
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plt.plot(eX.flatten(), eY.flatten(), 'b-')
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gridCC = self.gridCC
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if text:
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[ax.text(cc[0], cc[1],i) for i, cc in enumerate(gridCC)]
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plt.plot(gridCC[:,0], gridCC[:,1], 'r.')
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gridFx = self.gridFx
|
|
gridFy = self.gridFy
|
|
if text:
|
|
[ax.text(cc[0], cc[1],i) for i, cc in enumerate(np.vstack((gridFx,gridFy)))]
|
|
gridEx = self.gridEx
|
|
gridEy = self.gridEy
|
|
# if text:
|
|
# [ax.text(cc[0], cc[1],i) for i, cc in enumerate(np.vstack((gridEx,gridEy)))]
|
|
|
|
# for E in self._edges:
|
|
# if E[ACTIVE] == 0: continue
|
|
# ex = N[E[[ENODE0,ENODE1]],NX]
|
|
# ey = N[E[[ENODE0,ENODE1]],NY]
|
|
# ax.plot(ex, ey, 'b-')
|
|
# ax.text(ex.mean(), ey.mean(), E[NUM])
|
|
|
|
if showIt:
|
|
plt.show()
|
|
|
|
if __name__ == '__main__':
|
|
from SimPEG import Mesh, Utils
|
|
import matplotlib.pyplot as plt
|
|
|
|
tM = TreeMesh([np.ones(3),np.ones(2)])
|
|
|
|
tM.refineFace(0)
|
|
tM.refineFace(1)
|
|
tM.refineFace(3)
|
|
tM.refineFace(9)
|
|
|
|
# print tM._faces
|
|
# print tM._edges[0,:]
|
|
# print tM.area
|
|
|
|
|
|
# tM.number()
|
|
# print tM._index('_edges',3)[1]
|
|
|
|
|
|
# print tM._edges[:,[0,1,3, 4,5 ]]
|
|
|
|
plt.subplot(211)
|
|
plt.spy(tM.faceDiv)
|
|
tM.plotGrid(ax=plt.subplot(212))
|
|
|
|
|
|
print tM.vol
|
|
print tM.area
|
|
print tM.edge
|
|
|
|
# plt.figure(2)
|
|
# plt.plot(SortByX0(tM.gridCC),'b.')
|
|
plt.show()
|
|
|
|
|
|
|