from SimPEG import np, sp, Utils, Solver from BaseMesh import BaseMesh from InnerProducts import InnerProducts import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D import matplotlib.colors as colors import matplotlib.cm as cmx def SortByX0(): eps = 1e-7 def mycmp(c1,c2): if c1.x0.size == 2: if np.abs(c1.x0[1] - c2.x0[1]) < eps: return c1.x0[0] - c2.x0[0] return c1.x0[1] - c2.x0[1] elif c1.x0.size == 3: if np.abs(c1.x0[2] - c2.x0[2]) < eps: if np.abs(c1.x0[1] - c2.x0[1]) < eps: return c1.x0[0] - c2.x0[0] return c1.x0[1] - c2.x0[1] return c1.x0[2] - c2.x0[2] class K(object): def __init__(self, obj, *args): self.obj = obj def __lt__(self, other): return mycmp(self.obj, other.obj) < 0 def __gt__(self, other): return mycmp(self.obj, other.obj) > 0 def __eq__(self, other): return mycmp(self.obj, other.obj) == 0 def __le__(self, other): return mycmp(self.obj, other.obj) <= 0 def __ge__(self, other): return mycmp(self.obj, other.obj) >= 0 def __ne__(self, other): return mycmp(self.obj, other.obj) != 0 return K class TreeNode(object): """docstring for TreeNode""" __slots__ = ['x0', 'num'] def __init__(self, mesh, x0=[0,0]): self.x0 = np.array(x0, dtype=float) mesh.nodes.add(self) @property def center(self): return self.x0 class TreeEdge(object): """docstring for TreeEdge""" __slots__ = ['mesh', 'children', 'depth', 'x0', 'num', 'edgeType', 'sz', 'node0', 'node1'] def __init__(self, mesh, x0=[0,0], edgeType=None, sz=[1,], depth=0, node0=None, node1=None): self.mesh = mesh self.depth = depth self.x0 = x0 self.sz = sz self.edgeType = edgeType mesh.edges.add(self) if edgeType is 'x': mesh.edgesX.add(self) elif edgeType is 'y': mesh.edgesY.add(self) elif edgeType is 'z': mesh.edgesZ.add(self) self.node0 = node0 if isinstance(node0,TreeNode) else TreeNode(mesh, x0=self.x0) self.node1 = node1 if isinstance(node1,TreeNode) else TreeNode(mesh, x0=self.x0 + self.tangent*self.sz[0]) @property def isleaf(self): return getattr(self, 'children', None) is None def refine(self): if not self.isleaf: return self.mesh.isNumbered = False self.children = np.empty(2,dtype=TreeFace) # Create refined x0's x0r_0 = self.x0 x0r_1 = self.x0+0.5*self.tangent*self.sz self.children[0] = TreeEdge(self.mesh, x0=x0r_0, edgeType=self.edgeType, sz=0.5*self.sz, depth=self.depth+1, node0=self.node0) self.children[1] = TreeEdge(self.mesh, x0=x0r_1, edgeType=self.edgeType, sz=0.5*self.sz, depth=self.depth+1, node0=self.children[0].node1, node1=self.node1) self.mesh.edges.remove(self) if self.edgeType is 'x': self.mesh.edgesX.remove(self) elif self.edgeType is 'y': self.mesh.edgesY.remove(self) elif self.edgeType is 'z': self.mesh.edgesZ.remove(self) @property def tangent(self): if self.edgeType is 'x': return np.r_[1.,0,0] elif self.edgeType is 'y': return np.r_[0,1.,0] elif self.edgeType is 'z': return np.r_[0,0,1.] def plotGrid(self, ax, text=False, lineOpts={'color':'r', 'ls': '-'}): line = np.c_[self.node0.x0, self.node1.x0].T ax.plot(line[:,0], line[:,1], zs=line[:,2], **lineOpts) @property def center(self): return 0.5*(self.node0.x0 + self.node1.x0) @property def length(self): return np.sqrt(((self.node1.x0 - self.node0.x0)**2).sum()) @property def index(self): if self.isleaf: return [self.num] l = [edge.index for edge in self.children.flatten(order='F')] # Flatten the list # e.g. # [[1,3],[4]] --> [1, 3, 4] return [item for sublist in l for item in sublist] class TreeFace(object): """docstring for TreeFace""" __slots__ = ['mesh', 'children', 'depth', 'num', 'faceType', 'sz', 'node0', 'node1', 'node2', 'node3', 'edge0', 'edge1', 'edge2', 'edge3', '_tangent0', '_tangent1'] def __init__(self, mesh, x0=[0,0], faceType=None, sz=[1,], depth=0, node0=None, node1=None, edge0=None, edge1=None, edge2=None, edge3=None): self.mesh = mesh self.depth = depth self.faceType = faceType self.sz = sz mesh.faces.add(self) if faceType is 'x': mesh.facesX.add(self) elif faceType is 'y': mesh.facesY.add(self) elif faceType is 'z': mesh.facesZ.add(self) if self.dim == 2: # Add the nodes: self.node0 = node0 if isinstance(node0,TreeNode) else TreeNode(mesh, x0=x0) self.node1 = node1 if isinstance(node1,TreeNode) else TreeNode(mesh, x0=x0 + self.tangent0*self.sz[0]) if self.dim == 3: #TODO: Change this to edges # # 2___________3 # | e1 | # | | # e2| x |e3 t1 # | | ^ # |___________| |___> t0 # 0 e0 1 # N = {} n0 = getattr(edge0, 'node0', None) or getattr(edge2, 'node0', None) n1 = getattr(edge0, 'node1', None) or getattr(edge3, 'node0', None) n2 = getattr(edge1, 'node0', None) or getattr(edge2, 'node1', None) n3 = getattr(edge1, 'node1', None) or getattr(edge3, 'node1', None) eType = ['x', 'y'] if self.faceType == 'z' else ['x', 'z'] if self.faceType == 'y' else ['y', 'z'] e0 = edge0 if isinstance(edge0,TreeEdge) else TreeEdge(mesh, x0=x0, edgeType=eType[0], sz=np.r_[sz[0]], depth=depth, node0=n0, node1=n1) n0, n1 = e0.node0, e0.node1 e1 = edge1 if isinstance(edge1,TreeEdge) else TreeEdge(mesh, x0=x0 + self.tangent1*self.sz[1], edgeType=eType[0], sz=np.r_[sz[0]], depth=depth, node0=n2, node1=n3) n2, n3 = e1.node0, e1.node1 e2 = edge2 if isinstance(edge2,TreeEdge) else TreeEdge(mesh, x0=x0, edgeType=eType[1], sz=np.r_[sz[1]], depth=depth, node0=n0, node1=n2) n0, n2 = e2.node0, e2.node1 e3 = edge3 if isinstance(edge3,TreeEdge) else TreeEdge(mesh, x0=x0 + self.tangent0*self.sz[0], edgeType=eType[1], sz=np.r_[sz[1]], depth=depth, node0=n1, node1=n3) n1, n3 = e3.node0, e3.node1 # self.nodes = N self.node0, self.node1, self.node2, self.node3 = n0, n1, n2, n3 self.edge0, self.edge1, self.edge2, self.edge3 = e0, e1, e2, e3 # self.edges = {'e0':e0, 'e1':e1, 'e2':e2, 'e3':e3} @property def dim(self): return self.mesh.dim @property def x0(self): return self.node0.x0 @property def isleaf(self): return getattr(self, 'children', None) is None @property def branchdepth(self): if self.isleaf: return self.depth else: return np.max([node.branchdepth for node in self.children.flatten('F')]) @property def tangent0(self): if getattr(self,'_tangent0',None) is None: if self.faceType is 'x': t = np.r_[0,1.,0] elif self.faceType is 'y': t = np.r_[1.,0,0] elif self.faceType is 'z': t = np.r_[1.,0,0] self._tangent0 = t[:self.dim] return self._tangent0 @property def tangent1(self): if self.dim == 2: return if getattr(self,'_tangent1',None) is None: if self.faceType is 'x': t = np.r_[0,0,1.] elif self.faceType is 'y': t = np.r_[0,0,1.] elif self.faceType is 'z': t = np.r_[0,1.,0] self._tangent1 = t return self._tangent1 @property def normal(self): if self.faceType is 'x': n = np.r_[1.,0,0] elif self.faceType is 'y': n = np.r_[0,1.,0] elif self.faceType is 'z': n = np.r_[0,0,1.] return n[:self.dim] @property def index(self): if self.isleaf: return [self.num] l = [face.index for face in self.children.flatten(order='F')] # Flatten the list # e.g. # [[1,3],[4]] --> [1, 3, 4] return [item for sublist in l for item in sublist] @property def area(self): """area of the face""" return self.sz.prod() @property def length(self): if self.dim == 3: raise Exception('face.length is not defined for 2D face') return np.sqrt(((self.node1.x0 - self.node0.x0)**2).sum()) def refine(self): if not self.isleaf: return self.mesh.isNumbered = False if self.dim == 2: self._refine2D() elif self.dim == 3: self._refine3D() def _refine2D(self): self.children = np.empty(2,dtype=TreeFace) # Create refined x0's x0r_0 = self.x0 x0r_1 = self.x0+0.5*self.tangent0*self.sz self.children[0] = TreeFace(self.mesh, x0=x0r_0, faceType=self.faceType, sz=0.5*self.sz, depth=self.depth+1, node0=self.node0) self.children[1] = TreeFace(self.mesh, x0=x0r_1, faceType=self.faceType, sz=0.5*self.sz, depth=self.depth+1, node0=self.children[0].node1, node1=self.node1) self.mesh.faces.remove(self) if self.faceType is 'x': self.mesh.facesX.remove(self) elif self.faceType is 'y': self.mesh.facesY.remove(self) def _refine3D(self): # # 2_______________3 _______________ # | e1--> | | | | # ^ | | ^ | (0,1) | (1,1) | # | | | | | | | # | | x | | ---> |-------+-------| # e2 | | e3 | | | # | | | (0,0) | (1,0) | # |_______________| |_______|_______| # 0 e0--> 1 order = [{'c':[0,0], 'e0': ('p', 'e0', [0]), 'e1': 'new' , 'e2': ('p', 'e2', [0]), 'e3': 'new' }, {'c':[1,0], 'e0': ('p', 'e0', [1]), 'e1': 'new' , 'e2': ('c', 'e3', [0,0]), 'e3': ('p', 'e3', [0])}, {'c':[0,1], 'e0': ('c', 'e1', [0,0]), 'e1': ('p', 'e1', [0]), 'e2': ('p', 'e2', [1]), 'e3': 'new' }, {'c':[1,1], 'e0': ('c', 'e1', [1,0]), 'e1': ('p', 'e1', [1]), 'e2': ('c', 'e3', [0,1]), 'e3': ('p', 'e3', [1])}] def getEdge(pointer): if pointer is 'new': return if pointer[0] == 'p': return getattr(self, 'edg' + pointer[1]).children[pointer[2][0]] if pointer[0] == 'c': f = self.children[pointer[2][0],pointer[2][1]] return getattr(f, 'edg' + pointer[1]) self.children = np.empty((2,2), dtype=TreeFace) for edge in [self.edge0, self.edge1, self.edge2, self.edge3]: edge.refine() for O in order: i, j = O['c'] x0r = self.x0 + 0.5*i*self.tangent0*self.sz[0] + 0.5*j*self.tangent1*self.sz[1] e0, e1, e2, e3 = getEdge(O['e0']), getEdge(O['e1']), getEdge(O['e2']), getEdge(O['e3']) self.children[i,j] = TreeFace(self.mesh, x0=x0r, faceType=self.faceType, depth=self.depth+1, sz=0.5*self.sz, edge0=e0, edge1=e1, edge2=e2, edge3=e3) self.mesh.faces.remove(self) if self.faceType is 'x': self.mesh.facesX.remove(self) elif self.faceType is 'y': self.mesh.facesY.remove(self) elif self.faceType is 'z': self.mesh.facesZ.remove(self) def plotGrid(self, ax, text=True): if not self.isleaf: return if self.dim == 2: line = np.c_[self.node0.x0, self.node1.x0].T ax.plot(line[:,0], line[:,1],'b-') if text: ax.text(self.center[0], self.center[1],self.num) elif self.dim == 3: if text: ax.text(self.center[0], self.center[1], self.center[2], self.num) @property def center(self): if self.dim == 2: return self.x0 + 0.5*self.tangent0*self.sz[0] elif self.dim == 3: return self.x0 + 0.5*self.tangent0*self.sz[0] + 0.5*self.tangent1*self.sz[1] class TreeCell(object): __slots__ = ['mesh', 'children', 'depth', 'num', 'sz', 'node0', 'node1', 'node2', 'node3', 'node4', 'node5', 'node6', 'node7', 'fXm', 'fXp', 'fYm', 'fYp', 'fZm', 'fZp', 'eX0','eX1','eX2','eX3', 'eY0','eY1','eY2','eY3', 'eZ0','eZ1','eZ2','eZ3'] def __init__(self, mesh, x0=[0,0], depth=0, sz=[1,1], fXm=None, fXp=None, fYm=None, fYp=None, fZm=None, fZp=None): self.mesh = mesh self.depth = depth self.sz = np.array(sz, dtype=float) if self.dim == 2: # # 2___________3 # | fYp | # | | # fXm| x |fXp y # | | ^ # |___________| |___> x # 0 fYm 1 # n0 = getattr(fXm, 'node0', None) or getattr(fYm, 'node0', None) n1 = getattr(fXp, 'node0', None) or getattr(fYm, 'node1', None) n2 = getattr(fXm, 'node1', None) or getattr(fYp, 'node0', None) n3 = getattr(fXp, 'node1', None) or getattr(fYp, 'node1', None) self.fXm = fXm if isinstance(fXm, TreeFace) else TreeFace(mesh, x0=np.r_[x0[0] , x0[1] ], faceType='x', sz=np.r_[sz[1]], depth=depth, node0=n0, node1=n2) n0, n2 = self.fXm.node0, self.fXm.node1 self.fXp = fXp if isinstance(fXp, TreeFace) else TreeFace(mesh, x0=np.r_[x0[0]+sz[0], x0[1] ], faceType='x', sz=np.r_[sz[1]], depth=depth, node0=n1, node1=n3) n1, n3 = self.fXp.node0, self.fXp.node1 self.fYm = fYm if isinstance(fYm, TreeFace) else TreeFace(mesh, x0=np.r_[x0[0] , x0[1] ], faceType='y', sz=np.r_[sz[0]], depth=depth, node0=n0, node1=n1) n0, n1 = self.fYm.node0, self.fYm.node1 self.fYp = fYp if isinstance(fYp, TreeFace) else TreeFace(mesh, x0=np.r_[x0[0] , x0[1]+sz[1]], faceType='y', sz=np.r_[sz[0]], depth=depth, node0=n2, node1=n3) n2, n3 = self.fYp.node0, self.fYp.node1 self.node0, self.node1, self.node2, self.node3 = n0, n1, n2, n3 elif self.dim == 3: # fZp # | # 6 ------eX3------ 7 # /| | / | # /eZ2 . / eZ3 # eY2 | fYp eY3 | # / | / fXp| # 4 ------eX2----- 5 | # |fXm 2 -----eX1--|---- 3 z # eZ0 / | eY1 ^ y # | eY0 . fYm eZ1 / | / # | / | | / | / # 0 ------eX0------1 o----> x # | # fZm # # # fX fY fZ # 2___________3 2___________3 2___________3 # | e1 | | e1 | | e1 | # | | | | | | # e2 | x | e3 z e2 | x | e3 z e2 | x | e3 y # | | ^ | | ^ | | ^ # |___________| |___> y |___________| |___> x |___________| |___> x # 0 e0 1 0 e0 1 0 e0 1 # # Mapping Nodes: numOnFace > numOnCell # # fXm 0>0, 1>2, 2>4, 3>6 fYm 0>0, 1>1, 2>4, 3>5 fZm 0>0, 1>1, 2>2, 3>3 # fXp 0>1, 1>3, 2>5, 3>7 fYp 0>2, 1>3, 2>6, 3>7 fZp 0>4, 1>5, 2>6, 3>7 def getEdge(face, key): if face is None: return return getattr(face, key) E = {} eX0 = getEdge(fYm, 'edge0') or getEdge(fZm, 'edge0') eX1 = getEdge(fYp, 'edge0') or getEdge(fZm, 'edge1') eX2 = getEdge(fYm, 'edge1') or getEdge(fZp, 'edge0') eX3 = getEdge(fYp, 'edge1') or getEdge(fZp, 'edge1') eY0 = getEdge(fXm, 'edge0') or getEdge(fZm, 'edge2') eY1 = getEdge(fXp, 'edge0') or getEdge(fZm, 'edge3') eY2 = getEdge(fXm, 'edge1') or getEdge(fZp, 'edge2') eY3 = getEdge(fXp, 'edge1') or getEdge(fZp, 'edge3') eZ0 = getEdge(fXm, 'edge2') or getEdge(fYm, 'edge2') eZ1 = getEdge(fXp, 'edge2') or getEdge(fYm, 'edge3') eZ2 = getEdge(fXm, 'edge3') or getEdge(fYp, 'edge2') eZ3 = getEdge(fXp, 'edge3') or getEdge(fYp, 'edge3') self.fXm = fXm if isinstance(fXm, TreeFace) else TreeFace(mesh, x0=np.r_[x0[0] , x0[1] , x0[2] ], faceType='x', sz=np.r_[sz[1], sz[2]], depth=depth, edge0=eY0, edge1=eY2, edge2=eZ0, edge3=eZ2) eY0, eY2, eZ0, eZ2 = self.fXm.edge0, self.fXm.edge1, self.fXm.edge2, self.fXm.edge3 self.fXp = fXp if isinstance(fXp, TreeFace) else TreeFace(mesh, x0=np.r_[x0[0]+sz[0], x0[1] , x0[2] ], faceType='x', sz=np.r_[sz[1], sz[2]], depth=depth, edge0=eY1, edge1=eY3, edge2=eZ1, edge3=eZ3) eY1, eY3, eZ1, eZ3 = self.fXp.edge0, self.fXp.edge1, self.fXp.edge2, self.fXp.edge3 self.fYm = fYm if isinstance(fYm, TreeFace) else TreeFace(mesh, x0=np.r_[x0[0] , x0[1] , x0[2] ], faceType='y', sz=np.r_[sz[0], sz[2]], depth=depth, edge0=eX0, edge1=eX2, edge2=eZ0, edge3=eZ1) eX0, eX2, eZ0, eZ1 = self.fYm.edge0, self.fYm.edge1, self.fYm.edge2, self.fYm.edge3 self.fYp = fYp if isinstance(fYp, TreeFace) else TreeFace(mesh, x0=np.r_[x0[0] , x0[1]+sz[1], x0[2] ], faceType='y', sz=np.r_[sz[0], sz[2]], depth=depth, edge0=eX1, edge1=eX3, edge2=eZ2, edge3=eZ3) eX1, eX3, eZ2, eZ3 = self.fYp.edge0, self.fYp.edge1, self.fYp.edge2, self.fYp.edge3 self.fZm = fZm if isinstance(fZm, TreeFace) else TreeFace(mesh, x0=np.r_[x0[0] , x0[1] , x0[2] ], faceType='z', sz=np.r_[sz[0], sz[1]], depth=depth, edge0=eX0, edge1=eX1, edge2=eY0, edge3=eY1) eX0, eX1, eY0, eY1 = self.fZm.edge0, self.fZm.edge1, self.fZm.edge2, self.fZm.edge3 self.fZp = fZp if isinstance(fZp, TreeFace) else TreeFace(mesh, x0=np.r_[x0[0] , x0[1] , x0[2]+sz[2]], faceType='z', sz=np.r_[sz[0], sz[1]], depth=depth, edge0=eX2, edge1=eX3, edge2=eY2, edge3=eY3) eX2, eX3, eY2, eY3 = self.fZp.edge0, self.fZp.edge1, self.fZp.edge2, self.fZp.edge3 self.eX0, self.eX1, self.eX2, self.eX3, self.eY0, self.eY1, self.eY2, self.eY3, self.eZ0, self.eZ1, self.eZ2, self.eZ3 = eX0, eX1, eX2, eX3, eY0, eY1, eY2, eY3, eZ0, eZ1, eZ2, eZ3 self.node0, self.node1, self.node2, self.node3, self.node4, self.node5, self.node6, self.node7 = self.fZm.node0, self.fZm.node1, self.fZm.node2, self.fZm.node3, self.fZp.node0, self.fZp.node1, self.fZp.node2, self.fZp.node3 mesh.cells.add(self) @property def x0(self): return self.node0.x0 @property def center(self): return self.x0 + 0.5*self.sz @property def dim(self): return self.mesh.dim @property def faceDict(self): d = {"fXm":self.fXm, "fXp":self.fXp, "fYm":self.fYm, "fYp":self.fYp} if self.dim == 3: d["fZm"] = self.fZm d["fZp"] = self.fZp return d @property def edgeDict(self): if self.dim == 2: return None return {'eX0': self.eX0, 'eX1': self.eX1, 'eX2': self.eX2, 'eX3': self.eX3, 'eY0': self.eY0, 'eY1': self.eY1, 'eY2': self.eY2, 'eY3': self.eY3, 'eZ0': self.eZ0, 'eZ1': self.eZ1, 'eZ2': self.eZ2, 'eZ3': self.eZ3} @property def faceList(self): l = [self.fXm, self.fXp, self.fYm, self.fYp] if self.dim == 3: l += [self.fZm, self.fZp] return l @property def edgeList(self): if self.dim == 2: return None return [self.eX0, self.eX1, self.eX2, self.eX3, self.eY0, self.eY1, self.eY2, self.eY3, self.eZ0, self.eZ1, self.eZ2, self.eZ3] @property def isleaf(self): return getattr(self, 'children', None) is None def refine(self, function=None): if not self.isleaf and function is None: return if function is not None: do = function(self.center) > self.depth if not do: return if self.dim == 2: self._refine2D() elif self.dim == 3: self._refine3D() # pass the refine function to the children if function is not None: for child in self.children.flatten(): child.refine(function) def _refine2D(self): self.mesh.isNumbered = False self.children = np.empty((2,2), dtype=TreeCell) x0, sz = self.x0, self.sz for face in self.faceList: face.refine() order = [{'c':[0,0], 'fXm': ('p', 'fXm', [0]), 'fXp': 'new' , 'fYm': ('p', 'fYm', [0]), 'fYp': 'new' }, {'c':[1,0], 'fXm': ('c', 'fXp', [0,0]), 'fXp': ('p', 'fXp', [0]), 'fYm': ('p', 'fYm', [1]), 'fYp': 'new' }, {'c':[0,1], 'fXm': ('p', 'fXm', [1]), 'fXp': 'new' , 'fYm': ('c', 'fYp', [0,0]), 'fYp': ('p', 'fYp', [0])}, {'c':[1,1], 'fXm': ('c', 'fXp', [0,1]), 'fXp': ('p', 'fXp', [1]), 'fYm': ('c', 'fYp', [1,0]), 'fYp': ('p', 'fYp', [1])}] def getFace(pointer): if pointer is 'new': return None if pointer[0] == 'p': return self.faceDict[pointer[1]].children[pointer[2][0],] if pointer[0] == 'c': return self.children[pointer[2][0],pointer[2][1]].faceDict[pointer[1]] for O in order: i, j = O['c'] x0r = np.r_[x0[0] + 0.5*i*sz[0], x0[1] + 0.5*j*sz[1]] fXm, fXp, fYm, fYp = getFace(O['fXm']), getFace(O['fXp']), getFace(O['fYm']), getFace(O['fYp']) self.children[i,j] = TreeCell(self.mesh, x0=x0r, depth=self.depth+1, sz=0.5*sz, fXm=fXm, fXp=fXp, fYm=fYm, fYp=fYp) self.mesh.cells.remove(self) def _refine3D(self): # .----------------.----------------. # /| /| /| # / | / | / | # / | 011 / | 111 / | # / | / | / | # .----------------.----+-----------. | # /| . ---------/|----.----------/|----. # / | /| / | /| / | /| # / | / | 001 / | / | 101 / | / | # / | / | / | / | / | / | # . -------------- .----------------. |/ | # | . ---+------|----.----+------|----. | # | /| .______|___/|____.______|___/|____. # | / | / 010 | / | / 110| / | / # | / | / | / | / | / | / # . ---+---------- . ---+---------- . | / # | |/ | |/ | |/ z # | . ----------|----.-----------|----. ^ y # | / 000 | / 100 | / | / # | / | / | / | / # | / | / | / o----> x # . -------------- . -------------- . # # # Face Refinement: # # 2_______________3 _______________ # | | | | | # ^ | | | (0,1) | (1,1) | # | | | | | | # | | x | ---> |-------+-------| # t1 | | | | | # | | | (0,0) | (1,0) | # |_______________| |_______|_______| # 0 t0--> 1 order = [{'c':[0,0,0], 'fXm': ('p', 'fXm', [0,0]), 'fXp': 'new' , 'fYm': ('p', 'fYm', [0,0]), 'fYp': 'new' , 'fZm': ('p', 'fZm', [0,0]), 'fZp': 'new' ,}, {'c':[1,0,0], 'fXm': ('c', 'fXp', [0,0,0]), 'fXp': ('p', 'fXp', [0,0]), 'fYm': ('p', 'fYm', [1,0]), 'fYp': 'new' , 'fZm': ('p', 'fZm', [1,0]), 'fZp': 'new' }, {'c':[0,1,0], 'fXm': ('p', 'fXm', [1,0]), 'fXp': 'new' , 'fYm': ('c', 'fYp', [0,0,0]), 'fYp': ('p', 'fYp', [0,0]), 'fZm': ('p', 'fZm', [0,1]), 'fZp': 'new' }, {'c':[1,1,0], 'fXm': ('c', 'fXp', [0,1,0]), 'fXp': ('p', 'fXp', [1,0]), 'fYm': ('c', 'fYp', [1,0,0]), 'fYp': ('p', 'fYp', [1,0]), 'fZm': ('p', 'fZm', [1,1]), 'fZp': 'new' }, {'c':[0,0,1], 'fXm': ('p', 'fXm', [0,1]), 'fXp': 'new' , 'fYm': ('p', 'fYm', [0,1]), 'fYp': 'new' , 'fZm': ('c', 'fZp', [0,0,0]), 'fZp': ('p', 'fZp', [0,0])}, {'c':[1,0,1], 'fXm': ('c', 'fXp', [0,0,1]), 'fXp': ('p', 'fXp', [0,1]), 'fYm': ('p', 'fYm', [1,1]), 'fYp': 'new' , 'fZm': ('c', 'fZp', [1,0,0]), 'fZp': ('p', 'fZp', [1,0])}, {'c':[0,1,1], 'fXm': ('p', 'fXm', [1,1]), 'fXp': 'new' , 'fYm': ('c', 'fYp', [0,0,1]), 'fYp': ('p', 'fYp', [0,1]), 'fZm': ('c', 'fZp', [0,1,0]), 'fZp': ('p', 'fZp', [0,1])}, {'c':[1,1,1], 'fXm': ('c', 'fXp', [0,1,1]), 'fXp': ('p', 'fXp', [1,1]), 'fYm': ('c', 'fYp', [1,0,1]), 'fYp': ('p', 'fYp', [1,1]), 'fZm': ('c', 'fZp', [1,1,0]), 'fZp': ('p', 'fZp', [1,1])}] self.mesh.isNumbered = False self.children = np.empty((2,2,2), dtype=TreeCell) x0, sz = self.x0, self.sz for face in self.faceList: face.refine() def getFace(pointer): if pointer is 'new': return None if pointer[0] == 'p': return self.faceDict[pointer[1]].children[pointer[2][0],pointer[2][1]] if pointer[0] == 'c': return self.children[pointer[2][0],pointer[2][1],pointer[2][2]].faceDict[pointer[1]] for O in order: i, j, k = O['c'] x0r = np.r_[x0[0] + 0.5*i*sz[0], x0[1] + 0.5*j*sz[1], x0[2] + 0.5*k*sz[2]] fXm, fXp, fYm, fYp, fZm, fZp = getFace(O['fXm']), getFace(O['fXp']), getFace(O['fYm']), getFace(O['fYp']), getFace(O['fZm']), getFace(O['fZp']) self.children[i,j,k] = TreeCell(self.mesh, x0=x0r, depth=self.depth+1, sz=0.5*sz, fXm=fXm, fXp=fXp, fYm=fYm, fYp=fYp, fZm=fZm, fZp=fZp) self.mesh.cells.remove(self) @property def faceIndex(self): F = {} for face in self.faces: F[face] = self.faces[face].index return F @property def vol(self): return self.sz.prod() def viz(self, ax, color='none', text=False): if not self.isleaf: return x0, sz = self.x0, self.sz ax.add_patch(plt.Rectangle((x0[0], x0[1]), sz[0], sz[1], facecolor=color, edgecolor='k')) if text: ax.text(self.center[0],self.center[1],self.num) def plotGrid(self, ax, text=False): if not self.isleaf: return if self.dim == 2: ax.plot(self.center[0],self.center[1],'ro') if text: ax.text(self.center[0],self.center[1],self.num) elif self.dim == 3: ax.plot([self.center[0]],[self.center[1]],'ro', zs=[self.center[2]]) if text: ax.text(self.center[0], self.center[1], self.center[2], self.num) class TreeMesh(InnerProducts, BaseMesh): """TreeMesh""" _meshType = 'TREE' def __init__(self, h_in, x0=None): assert type(h_in) is list, 'h_in must be a list' assert len(h_in) > 1, "len(h_in) must be greater than 1" h = range(len(h_in)) for i, h_i in enumerate(h_in): if type(h_i) in [int, long, float]: # This gives you something over the unit cube. h_i = np.ones(int(h_i))/int(h_i) assert isinstance(h_i, np.ndarray), ("h[%i] is not a numpy array." % i) assert len(h_i.shape) == 1, ("h[%i] must be a 1D numpy array." % i) h[i] = h_i[:] # make a copy. self.h = h if x0 is None: x0 = np.zeros(self.dim) else: assert type(x0) in [list, np.ndarray], 'x0 must be a numpy array or a list' x0 = np.array(x0, dtype=float) assert len(x0) == self.dim, 'x0 must have the same dimensions as the mesh' # TODO: this has a lot of stuff which doesn't work for this style of mesh... BaseMesh.__init__(self, np.array([x.size for x in h]), x0) # set the sets for holding the cells, nodes, faces, and edges self.cells = set() self.nodes = set() self.faces = set() self.facesX = set() self.facesY = set() if self.dim == 3: self.facesZ = set() self.edges = set() self.edgesX = set() self.edgesY = set() self.edgesZ = set() self.children = np.empty([hi.size for hi in h],dtype=TreeCell) if self.dim == 2: for i in range(h[0].size): for j in range(h[1].size): fXm = None if i is 0 else self.children[i-1][j].fXp fYm = None if j is 0 else self.children[i][j-1].fYp x0i = (np.r_[x0[0], h[0][:i]]).sum() x0j = (np.r_[x0[1], h[1][:j]]).sum() self.children[i][j] = TreeCell(self, x0=[x0i, x0j], depth=0, sz=[h[0][i], h[1][j]], fXm=fXm, fYm=fYm) elif self.dim == 3: for i in range(h[0].size): for j in range(h[1].size): for k in range(h[2].size): fXm = None if i is 0 else self.children[i-1][j][k].fXp fYm = None if j is 0 else self.children[i][j-1][k].fYp fZm = None if k is 0 else self.children[i][j][k-1].fZp x0i = (np.r_[x0[0], h[0][:i]]).sum() x0j = (np.r_[x0[1], h[1][:j]]).sum() x0k = (np.r_[x0[2], h[2][:k]]).sum() self.children[i][j][k] = TreeCell(self, x0=[x0i, x0j, x0k], depth=0, sz=[h[0][i], h[1][j], h[2][k]], fXm=fXm, fYm=fYm, fZm=fZm) isNumbered = Utils.dependentProperty('_isNumbered', False, ['_faceDiv'], 'Setting this to False will delete all operators.') @property def branchdepth(self): return np.max([node.branchdepth for node in self.children.flatten('F')]) def refine(self, function): for cell in self.children.flatten(): cell.refine(function) def number(self): if self.isNumbered: return self.sortedCells = sorted(self.cells,key=SortByX0()) for i, sC in enumerate(self.sortedCells): sC.num = i self.sortedNodes = sorted(self.nodes,key=SortByX0()) for i, sN in enumerate(self.sortedNodes): sN.num = i self.sortedFaceX = sorted(self.facesX,key=SortByX0()) for i, sFx in enumerate(self.sortedFaceX): sFx.num = i self.sortedFaceY = sorted(self.facesY,key=SortByX0()) for i, sFy in enumerate(self.sortedFaceY): sFy.num = i + self.nFx if self.dim == 3: self.sortedFaceZ = sorted(self.facesZ,key=SortByX0()) for i, sFz in enumerate(self.sortedFaceZ): sFz.num = i + self.nFx + self.nFy self.sortedEdgeX = sorted(self.edgesX,key=SortByX0()) for i, sEx in enumerate(self.sortedEdgeX): sEx.num = i self.sortedEdgeY = sorted(self.edgesY,key=SortByX0()) for i, sEy in enumerate(self.sortedEdgeY): sEy.num = i + self.nEx self.sortedEdgeZ = sorted(self.edgesZ,key=SortByX0()) for i, sEz in enumerate(self.sortedEdgeZ): sEz.num = i + self.nEx + self.nEy self.isNumbered = True @property def dim(self): return len(self.h) @property def nC(self): return len(self.cells) @property def nN(self): return len(self.nodes) @property def nF(self): return len(self.faces) @property def nFx(self): return len(self.facesX) @property def nFy(self): return len(self.facesY) @property def nFz(self): return None if self.dim < 3 else len(self.facesZ) @property def nE(self): if self.dim == 2: return len(self.faces) elif self.dim == 3: return len(self.edges) @property def nEx(self): if self.dim == 2: return len(self.facesY) elif self.dim == 3: return len(self.edgesX) @property def nEy(self): if self.dim == 2: return len(self.facesX) elif self.dim == 3: return len(self.edgesY) @property def nEz(self): return None if self.dim < 3 else len(self.edgesZ) def _grid(self, key): self.number() sObjs = {'CC':self.sortedCells, 'N':self.sortedNodes, 'Fx': self.sortedFaceX, 'Fy': self.sortedFaceY, 'Fz': getattr(self,'sortedFaceZ', None), 'Ex': getattr(self,'sortedEdgeX', self.sortedFaceY), 'Ey': getattr(self,'sortedEdgeY', self.sortedFaceX), 'Ez': getattr(self,'sortedEdgeZ', None)}[key] G = np.empty((len(sObjs),self.dim)) for ii, obj in enumerate(sObjs): G[ii,:] = obj.center return G @property def gridCC(self): if getattr(self, '_gridCC', None) is None: self._gridCC = self._grid('CC') return self._gridCC @property def gridN(self): if getattr(self, '_gridN', None) is None: self._gridN = self._grid('N') return self._gridN @property def gridFx(self): if getattr(self, '_gridFx', None) is None: self._gridFx = self._grid('Fx') return self._gridFx @property def gridFy(self): if getattr(self, '_gridFy', None) is None: self._gridFy = self._grid('Fy') return self._gridFy @property def gridFz(self): if self.dim == 2: return None if getattr(self, '_gridFz', None) is None: self._gridFz = self._grid('Fz') return self._gridFz @property def gridEx(self): if self.dim == 2: return self.gridFy if getattr(self, '_gridEx', None) is None: self._gridEx = self._grid('Ex') return self._gridEx @property def gridEy(self): if self.dim == 2: return self.gridFx if getattr(self, '_gridEy', None) is None: self._gridEy = self._grid('Ey') return self._gridEy @property def gridEz(self): if self.dim == 2: return None if getattr(self, '_gridEz', None) is None: self._gridEz = self._grid('Ez') return self._gridEz @property def vol(self): self.number() return np.array([cell.vol for cell in self.sortedCells]) @property def area(self): self.number() faces = self.sortedFaceX + self.sortedFaceY if self.dim == 3: faces += self.sortedFaceZ return np.array([face.area for face in faces], dtype=float) @property def edge(self): self.number() if self.dim == 2: edges = self.sortedFaceY + self.sortedFaceX elif self.dim == 3: edges = self.sortedEdgeX + self.sortedEdgeY + self.sortedEdgeZ return np.array([e.length for e in edges], dtype=float) @property def faceDiv(self): if getattr(self, '_faceDiv', None) is None: self.number() # TODO: Preallocate! I, J, V = [], [], [] for cell in self.sortedCells: faces = cell.faceDict for face in faces: j = faces[face].index I += [cell.num]*len(j) J += j V += [-1 if 'm' in face else 1]*len(j) VOL = self.vol D = sp.csr_matrix((V,(I,J)), shape=(self.nC, self.nF)) S = self.area self._faceDiv = Utils.sdiag(1/VOL)*D*Utils.sdiag(S) return self._faceDiv @property def edgeCurl(self): """Construct the 3D curl operator.""" assert self.dim > 2, "Edge Curl only programed for 3D." if getattr(self, '_edgeCurl', None) is None: self.number() # TODO: Preallocate! I, J, V = [], [], [] for face in self.faces: for ii, edge in enumerate([face.edge0, face.edge1, face.edge2, face.edge3]): j = edge.index I += [face.num]*len(j) J += j isNeg = [True, False, True, False] V += [-1 if isNeg[ii] else 1]*len(j) C = sp.csr_matrix((V,(I,J)), shape=(self.nF, self.nE)) S = self.area L = self.edge self._edgeCurl = Utils.sdiag(1/S)*C*Utils.sdiag(L) return self._edgeCurl @property def nodalGrad(self): if getattr(self, '_nodalGrad', None) is None: self.number() # TODO: Preallocate! I, J, V = [], [], [] # kinda a hack for the 2D gradient # because edges are not stored edges = self.faces if self.dim == 2 else self.edges for edge in edges: if self.dim == 3: I += [edge.num, edge.num] elif self.dim == 2 and edge.faceType == 'x': I += [edge.num + self.nFy, edge.num + self.nFy] elif self.dim == 2 and edge.faceType == 'y': I += [edge.num - self.nFx, edge.num - self.nFx] J += [edge.node0.num, edge.node1.num] V += [-1, 1] G = sp.csr_matrix((V,(I,J)), shape=(self.nE, self.nN)) L = self.edge self._nodalGrad = Utils.sdiag(1/L)*G return self._nodalGrad def _getFaceP(self, face0, face1, face2): I, J, V = [], [], [] for cell in self.sortedCells: face = cell.faceDict[face0] if face.isleaf: j = face.index elif self.dim == 2: j = face.children[0 if 'm' in face1 else 1].index elif self.dim == 3: j = face.children[0 if 'm' in face1 else 1, 0 if 'm' in face2 else 1].index lenj = len(j) I += [cell.num]*lenj J += j V += [1./lenj]*lenj return sp.csr_matrix((V,(I,J)), shape=(self.nC, self.nF)) def _getEdgeP(self, edge0, edge1, edge2): I, J, V = [], [], [] for cell in self.sortedCells: if self.dim == 2: e2f = lambda e: ('f' + {'X':'Y','Y':'X'}[e[1]] + {'0':'m','1':'p'}[e[2]]) face = cell.faceDict[e2f(edge0)] if face.isleaf: j = face.index else: j = face.children[0 if 'm' in e2f(edge1) else 1].index # Need to flip the numbering for edges if 'X' in edge0: j = [jj - self.nFx for jj in j] elif 'Y' in edge0: j = [jj + self.nFy for jj in j] elif self.dim == 3: edge = cell.edgeDict[edge0] if edge.isleaf: j = edge.index else: mSide = lambda e: {'0':True,'1':True,'2':False,'3':False}[e[2]] j = edge.children[0 if mSide(edge1) else 1, 0 if mSide(edge2) else 1].index lenj = len(j) I += [cell.num]*lenj J += j V += [1./lenj]*lenj return sp.csr_matrix((V,(I,J)), shape=(self.nC, self.nE)) def _getFacePxx(self): def Pxx(xFace, yFace): self.number() xP = self._getFaceP(xFace, yFace, None) yP = self._getFaceP(yFace, xFace, None) return sp.vstack((xP, yP)) return Pxx def _getEdgePxx(self): def Pxx(xEdge, yEdge): self.number() xP = self._getEdgeP(xEdge, yEdge, None) yP = self._getEdgeP(yEdge, xEdge, None) return sp.vstack((xP, yP)) return Pxx def _getFacePxxx(self): def Pxxx(xFace, yFace, zFace): self.number() xP = self._getFaceP(xFace, yFace, zFace) yP = self._getFaceP(yFace, xFace, zFace) zP = self._getFaceP(zFace, xFace, yFace) return sp.vstack((xP, yP, zP)) return Pxxx def _getEdgePxxx(self): def Pxxx(xEdge, yEdge, zEdge): self.number() xP = self._getEdgeP(xEdge, yEdge, zEdge) yP = self._getEdgeP(yEdge, xEdge, zEdge) zP = self._getEdgeP(zEdge, xEdge, yEdge) return sp.vstack((xP, yP, zP)) return Pxxx def plotGrid(self, ax=None, text=False, centers=False, faces=False, edges=False, lines=True, nodes=False, showIt=False): self.number() axOpts = {'projection':'3d'} if self.dim == 3 else {} if ax is None: ax = plt.subplot(111, **axOpts) if lines: [f.plotGrid(ax, text=text) for f in self.faces] if centers: [c.plotGrid(ax, text=text) for c in self.cells] if faces: fX = np.array([f.center for f in self.sortedFaceX]) ax.plot(fX[:,0],fX[:,1],'g>') fY = np.array([f.center for f in self.sortedFaceY]) ax.plot(fY[:,0],fY[:,1],'g^') if edges: eX = np.array([e.center for e in self.sortedFaceY]) ax.plot(eX[:,0],eX[:,1],'c>') eY = np.array([e.center for e in self.sortedFaceX]) ax.plot(eY[:,0],eY[:,1],'c^') if nodes: ns = np.array([n.x0 for n in self.sortedNodes]) ax.plot(ns[:,0],ns[:,1],'bs') ax.set_xlim((self.x0[0], self.h[0].sum())) ax.set_ylim((self.x0[1], self.h[1].sum())) if self.dim == 3: ax.set_zlim((self.x0[2], self.h[2].sum())) ax.grid(True) ax.hold(False) ax.set_xlabel('x1') ax.set_ylabel('x2') if showIt: plt.show() def plotImage(self, I, ax=None, showIt=True): if self.dim == 2: self._plotImage2D(I, ax=ax, showIt=showIt) elif self.dim == 3: raise NotImplementedError('3D visualization is not yet implemented.') def _plotImage2D(self, I, ax=None, showIt=True): if ax is None: ax = plt.subplot(111) jet = cm = plt.get_cmap('jet') cNorm = colors.Normalize(vmin=I.min(), vmax=I.max()) scalarMap = cmx.ScalarMappable(norm=cNorm, cmap=jet) ax.set_xlim((self.x0[0], self.h[0].sum())) ax.set_ylim((self.x0[1], self.h[1].sum())) for ii, node in enumerate(self.sortedCells): node.viz(ax=ax, color=scalarMap.to_rgba(I[ii])) scalarMap._A = [] # http://stackoverflow.com/questions/8342549/matplotlib-add-colorbar-to-a-sequence-of-line-plots plt.colorbar(scalarMap) if showIt: plt.show() if __name__ == '__main__': M = TreeMesh([np.ones(x) for x in [4,10]]) def function(xc): r = xc - np.r_[2.,6.] dist = np.sqrt(r.dot(r)) if dist < 1.0: return 3 if dist < 1.5: return 2 else: return 1 M.refine(function) DIV = M.faceDiv Mf = M.getFaceInnerProduct() # plt.subplot(211) # plt.spy(DIV) M.plotGrid(ax=plt.subplot(111),text=True,showIt=True) q = np.zeros(M.nC) q[208] = -1.0 q[291] = 1.0 b = Solver(-DIV*Mf*DIV.T) * (q) plt.figure() M.plotImage(b) # plt.gca().invert_yaxis() print M.vol plt.show()