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https://github.com/wassname/simpeg.git
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rowanc1
562 lines
20 KiB
Python
562 lines
20 KiB
Python
from SimPEG import np, sp, Utils, Solver
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import matplotlib.pyplot as plt
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import matplotlib.colors as colors
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import matplotlib.cm as cmx
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def SortByX0():
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eps = 1e-7
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def mycmp(c1,c2):
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if np.abs(c1.x0[1] - c2.x0[1]) < eps:
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return c1.x0[0] - c2.x0[0]
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return c1.x0[1] - c2.x0[1]
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class K(object):
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def __init__(self, obj, *args):
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self.obj = obj
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def __lt__(self, other):
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return mycmp(self.obj, other.obj) < 0
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def __gt__(self, other):
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return mycmp(self.obj, other.obj) > 0
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def __eq__(self, other):
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return mycmp(self.obj, other.obj) == 0
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def __le__(self, other):
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return mycmp(self.obj, other.obj) <= 0
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def __ge__(self, other):
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return mycmp(self.obj, other.obj) >= 0
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def __ne__(self, other):
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return mycmp(self.obj, other.obj) != 0
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return K
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class TreeObject(object):
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"""docstring for TreeObject"""
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children = None #: children of the tree object
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num = None
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def __init__(self, mesh, parent):
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self.mesh = mesh
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self._parent = parent
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@property
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def parent(self): return self._parent
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@property
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def dim(self): return self.mesh.dim
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@property
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def isleaf(self): return self.children is None
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@property
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def center(self): return self.x0
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class TreeNode(TreeObject):
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"""docstring for TreeNode"""
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def __init__(self, mesh, x0=[0,0], depth=0, parent=None):
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TreeObject.__init__(self, mesh, parent)
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self.x0 = np.array(x0, dtype=float)
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self.mesh.nodes.add(self)
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class TreeEdge(TreeObject):
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"""docstring for TreeEdge"""
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def __init__(self, mesh, x0=[0,0], edgeType=None, sz=[1,], depth=0,
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node0=None, node1=None,
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parent=None):
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TreeObject.__init__(self, mesh, parent)
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self.x0 = np.array(x0, dtype=float)
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self.depth = depth
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self.edgeType = edgeType
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self.sz = np.array(sz, dtype=float)
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mesh.edges.add(self)
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if edgeType is 'x': mesh.edgesX.add(self)
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elif edgeType is 'y': mesh.edgesY.add(self)
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elif edgeType is 'z': mesh.edgesZ.add(self)
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self.node0 = node0
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self.node1 = node1
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class TreeFace(TreeObject):
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"""docstring for TreeFace"""
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def __init__(self, mesh, x0=[0,0], faceType=None, sz=[1,], depth=0,
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node0=None, node1=None, node2=None, node3=None,
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parent=None):
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TreeObject.__init__(self, mesh, parent)
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self.x0 = np.array(x0, dtype=float)
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self.depth = depth
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self.faceType = faceType
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self.sz = np.array(sz, dtype=float)
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mesh.faces.add(self)
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if faceType is 'x': mesh.facesX.add(self)
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elif faceType is 'y': mesh.facesY.add(self)
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elif faceType is 'z': mesh.facesZ.add(self)
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# Add the nodes:
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if self.dim == 2:
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self.node0 = node0 if isinstance(node0,TreeNode) else TreeNode(mesh, x0=self.x0)
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self.node1 = node1 if isinstance(node1,TreeNode) else TreeNode(mesh, x0=self.x0 + self.tangent0*self.sz)
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@property
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def tangent0(self):
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if self.faceType is 'x': t = np.r_[0,1.,0]
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elif self.faceType is 'y': t = np.r_[1.,0,0]
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elif self.faceType is 'z': t = np.r_[1.,0,0]
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return t[:self.dim]
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@property
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def tangent1(self):
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if self.dim == 2: return
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if self.faceType is 'x': t = np.r_[0,0,1.]
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elif self.faceType is 'y': t = np.r_[0,0,1.]
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elif self.faceType is 'z': t = np.r_[0,1.,0]
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return t[:self.dim]
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@property
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def normal(self):
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if self.faceType is 'x': n = np.r_[1.,0,0]
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elif self.faceType is 'y': n = np.r_[0,1.,0]
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elif self.faceType is 'z': n = np.r_[0,0,1.]
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return n[:self.dim]
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@property
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def index(self):
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if not self.mesh.isNumbered: raise Exception('Mesh is not numbered.')
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if self.isleaf: return np.r_[self.num]
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return np.concatenate([face.index for face in self.children])
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@property
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def area(self):
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"""area of the face"""
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return self.sz.prod()
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def refine(self):
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if not self.isleaf: return
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self.mesh.isNumbered = False
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self.children = np.empty(2,dtype=TreeFace)
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# Create refined x0's
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x0r_0 = self.x0
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x0r_1 = self.x0+0.5*self.tangent0*self.sz
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self.children[0] = TreeFace(self.mesh, x0=x0r_0, faceType=self.faceType, sz=0.5*self.sz, depth=self.depth+1, parent=self, node0=self.node0)
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self.children[1] = TreeFace(self.mesh, x0=x0r_1, faceType=self.faceType, sz=0.5*self.sz, depth=self.depth+1, parent=self, node0=self.children[0].node1, node1=self.node1)
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self.mesh.faces.remove(self)
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if self.faceType is 'x':
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self.mesh.facesX.remove(self)
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elif self.faceType is 'y':
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self.mesh.facesY.remove(self)
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def plotGrid(self, ax, text=True):
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if not self.isleaf: return
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ax.plot(np.r_[self.x0[0],self.x0[0]+self.tangent0[0]*self.sz], np.r_[self.x0[1], self.x0[1]+self.tangent0[1]*self.sz],'r-')
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if text: ax.text(self.x0[0]+0.5*self.tangent0[0]*self.sz, self.x0[1]+0.5*self.tangent0[1]*self.sz,self.num)
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@property
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def center(self):
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return self.x0 + 0.5*self.tangent0*self.sz
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class TreeCell(TreeObject):
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"""docstring for TreeCell"""
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children = None #:
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def __init__(self, mesh, x0=[0,0], depth=0, sz=[1,1],
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fXm=None, fXp=None,
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fYm=None, fYp=None,
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fZm=None, fZp=None,
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parent=None):
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TreeObject.__init__(self, mesh, parent)
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self.x0 = np.array(x0, dtype=float)
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self.sz = np.array(sz, dtype=float)
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self.depth = depth
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if self.dim == 2:
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#
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# 2___________3
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# | fYp |
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# | |
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# fXm| x |fXp y
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# | | ^
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# |___________| |___> x
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# 0 fYm 1
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#
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N = {}
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N["n0"] = getattr(fXm, 'node0', None) or getattr(fYm, 'node0', None)
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N["n1"] = getattr(fXp, 'node0', None) or getattr(fYm, 'node1', None)
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N["n2"] = getattr(fXm, 'node1', None) or getattr(fYp, 'node0', None)
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N["n3"] = getattr(fXp, 'node1', None) or getattr(fYp, 'node1', None)
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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, parent=parent, node0=N['n0'], node1=N['n2'])
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N["n0"], N["n2"] = fXm.node0, fXm.node1
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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, parent=parent, node0=N['n1'], node1=N['n3'])
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N["n1"], N["n3"] = fXp.node0, fXp.node1
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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, parent=parent, node0=N['n0'], node1=N['n1'])
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N["n0"], N["n1"] = fYm.node0, fYm.node1
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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, parent=parent, node0=N['n2'], node1=N['n3'])
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N["n2"], N["n3"] = fYp.node0, fYp.node1
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self.faces = {"fXm":fXm, "fXp":fXp, "fYm":fYm, "fYp":fYp}
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self.nodes = N
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elif self.dim == 3:
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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, parent=parent)
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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, parent=parent)
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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, parent=parent)
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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, parent=parent)
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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, parent=parent)
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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, parent=parent)
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self.faces = {"fXm":fXm, "fXp":fXp, "fYm":fYm, "fYp":fYp, "fZm":fZm, "fZp":fZp}
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mesh.cells.add(self)
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@property
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def branchdepth(self):
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if self.isleaf:
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return self.depth
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else:
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return np.max([node.branchdepth for node in self.children.flatten('F')])
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@property
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def center(self): return self.x0 + 0.5*self.sz
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def refine(self, function=None):
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if not self.isleaf and function is None: return
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if function is not None:
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do = function(self.center) > self.depth
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if not do: return
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if self.dim == 2:
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return self._refine2D()
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# pass the refine function to the children
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if function is not None:
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for child in self.children.flatten():
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child.refine(function)
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def _refine2D(self):
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self.mesh.isNumbered = False
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self.children = np.empty((2,2),dtype=TreeCell)
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x0, sz = self.x0, self.sz
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for faceName in self.faces:
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self.faces[faceName].refine()
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i, j = 0, 0
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x0r = np.r_[x0[0] + 0.5*i*sz[0], x0[1] + 0.5*j*sz[1]]
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fXm, fXp, fYm, fYp = self.faces['fXm'].children[0], None, self.faces['fYm'].children[0], None
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self.children[i,j] = TreeCell(self.mesh, x0=x0r, depth=self.depth+1, sz=0.5*sz, parent=self, fXm=fXm, fXp=fXp, fYm=fYm, fYp=fYp)
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i, j = 1, 0
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x0r = np.r_[x0[0] + 0.5*i*sz[0], x0[1] + 0.5*j*sz[1]]
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fXm, fXp, fYm, fYp = self.children[0,0].faces['fXp'], self.faces['fXp'].children[0], self.faces['fYm'].children[1], None
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self.children[i,j] = TreeCell(self.mesh, x0=x0r, depth=self.depth+1, sz=0.5*sz, parent=self, fXm=fXm, fXp=fXp, fYm=fYm, fYp=fYp)
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i, j = 0, 1
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x0r = np.r_[x0[0] + 0.5*i*sz[0], x0[1] + 0.5*j*sz[1]]
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fXm, fXp, fYm, fYp = self.faces['fXm'].children[1], None, self.children[0,0].faces['fYp'], self.faces['fYp'].children[0]
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self.children[i,j] = TreeCell(self.mesh, x0=x0r, depth=self.depth+1, sz=0.5*sz, parent=self, fXm=fXm, fXp=fXp, fYm=fYm, fYp=fYp)
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i, j = 1, 1
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x0r = np.r_[x0[0] + 0.5*i*sz[0], x0[1] + 0.5*j*sz[1]]
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fXm, fXp, fYm, fYp = self.children[0,1].faces['fXp'], self.faces['fXp'].children[1], self.children[1,0].faces['fYp'], self.faces['fYp'].children[1]
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self.children[i,j] = TreeCell(self.mesh, x0=x0r, depth=self.depth+1, sz=0.5*sz, parent=self, fXm=fXm, fXp=fXp, fYm=fYm, fYp=fYp)
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self.mesh.cells.remove(self)
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@property
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def faceIndex(self):
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#TODO: preallocate
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I, J, V = np.empty(0,dtype=float), np.empty(0,dtype=float), np.empty(0,dtype=float)
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for face in self.faces:
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j = self.faces[face].index
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i = j*0+self.num
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v = j*0+1
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if 'p' in face:
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v *= -1
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I, J, V = np.r_[I,i], np.r_[J,j], np.r_[V,v]
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return I, J, V
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@property
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def vol(self): return self.sz.prod()
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def viz(self, ax, color='none', text=False):
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if not self.isleaf: return
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x0, sz = self.x0, self.sz
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ax.add_patch(plt.Rectangle((x0[0], x0[1]), sz[0], sz[1], facecolor=color, edgecolor='k'))
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if text: ax.text(self.center[0],self.center[1],self.num)
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def plotGrid(self, ax, text=False):
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if not self.isleaf: return
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ax.plot(self.center[0],self.center[1],'b.')
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if text: ax.text(self.center[0],self.center[1],self.num)
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class TreeMesh(object):
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"""TreeMesh"""
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def __init__(self, h_in, x0=None):
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assert type(h_in) is list, 'h_in must be a list'
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h = range(len(h_in))
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for i, h_i in enumerate(h_in):
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if type(h_i) in [int, long, float]:
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# This gives you something over the unit cube.
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h_i = np.ones(int(h_i))/int(h_i)
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assert type(h_i) == np.ndarray, ("h[%i] is not a numpy array." % i)
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assert len(h_i.shape) == 1, ("h[%i] must be a 1D numpy array." % i)
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h[i] = h_i[:] # make a copy.
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self.h = h
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if x0 is None:
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x0 = np.zeros(self.dim)
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else:
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assert type(x0) in [list, np.ndarray], 'x0 must be a numpy array or a list'
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assert len(x0) == self.dim, 'x0 must have the same dimensions as the mesh'
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self.x0 = np.array(x0, dtype=float)
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# set the sets for holding the faces and cells
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self.cells = set()
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self.nodes = set()
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self.faces = set()
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self.facesX = set()
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self.facesY = set()
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if self.dim == 3: self.facesZ = set()
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self.edges = set()
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self.edgesX = set()
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self.edgesY = set()
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if self.dim == 3: self.edgesZ = set()
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self.children = np.empty([hi.size for hi in h],dtype=TreeCell)
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for i in range(h[0].size):
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for j in range(h[1].size):
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fXm = None if i is 0 else self.children[i-1][j].faces['fXp']
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fYm = None if j is 0 else self.children[i][j-1].faces['fYp']
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x0i = (np.r_[x0[0], h[0][:i]]).sum()
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x0j = (np.r_[x0[1], h[1][:j]]).sum()
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self.children[i][j] = TreeCell(self, x0=[x0i, x0j], depth=0, sz=[h[0][i], h[1][j]], fXm=fXm, fYm=fYm)
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isNumbered = Utils.dependentProperty('_isNumbered', False, ['_faceDiv'], 'Setting this to False will delete all operators.')
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@property
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def branchdepth(self):
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return np.max([node.branchdepth for node in self.children.flatten('F')])
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def refine(self, function):
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for node in self.children.flatten():
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node.refine(function)
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def number(self):
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if self.isNumbered: return
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self.sortedCells = sorted(self.cells,key=SortByX0())
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for i, sc in enumerate(self.sortedCells): sc.num = i
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self.sortedNodes = sorted(self.nodes,key=SortByX0())
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for i, sn in enumerate(self.sortedNodes): sn.num = i
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self.sortedFaceX = sorted(self.facesX,key=SortByX0())
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for i, sfx in enumerate(self.sortedFaceX): sfx.num = i
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self.sortedFaceY = sorted(self.facesY,key=SortByX0())
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for i, sfy in enumerate(self.sortedFaceY): sfy.num = i + self.nFx
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if self.dim == 3:
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self.sortedFaceZ = sorted(self.facesZ,key=SortByX0())
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for i, sfz in enumerate(self.sortedFaceZ): sfz.num = i + self.nFx + self.nFy
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self.isNumbered = True
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@property
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def dim(self): return len(self.h)
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@property
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def nC(self): return len(self.cells)
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@property
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def nN(self): return len(self.nodes)
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@property
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def nF(self): return len(self.faces)
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@property
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def nFx(self): return len(self.facesX)
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@property
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def nFy(self): return len(self.facesY)
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@property
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def nFz(self): return len(self.facesZ)
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@property
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def nE(self): return len(self.faces)
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@property
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def nEx(self):
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if self.dim == 2:
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return len(self.facesY)
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else: raise NotImplementedError('nEx')
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@property
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def nEy(self):
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if self.dim == 2:
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return len(self.facesX)
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else: raise NotImplementedError('nEy')
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@property
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def gridCC(self):
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if getattr(self, '_gridCC', None) is None:
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self.number()
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self._gridCC = np.empty((self.nC,self.dim))
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for ii, cell in enumerate(self.sortedCells):
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self._gridCC[ii,:] = cell.center
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return self._gridCC
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@property
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def gridN(self):
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if getattr(self, '_gridN', None) is None:
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self.number()
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self._gridN = np.empty((self.nN,self.dim))
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for ii, node in enumerate(self.sortedNodes):
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self._gridN[ii,:] = node.center
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return self._gridN
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@property
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def gridFx(self):
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if getattr(self, '_gridFx', None) is None:
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self.number()
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self._gridFx = np.empty((self.nFx,self.dim))
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for ii, face in enumerate(self.sortedFaceX):
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self._gridFx[ii,:] = face.center
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return self._gridFx
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@property
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def gridFy(self):
|
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if getattr(self, '_gridFy', None) is None:
|
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self.number()
|
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self._gridFy = np.empty((self.nFy,self.dim))
|
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for ii, face in enumerate(self.sortedFaceY):
|
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self._gridFy[ii,:] = face.center
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return self._gridFy
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|
|
@property
|
|
def gridFz(self):
|
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if self.dim == 2: return None
|
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if getattr(self, '_gridFz', None) is None:
|
|
self.number()
|
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self._gridFz = np.emptz((self.nFz,self.dim))
|
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for ii, face in enumerate(self.sortedFaceZ):
|
|
self._gridFz[ii,:] = face.center
|
|
return self._gridFz
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|
|
@property
|
|
def gridEx(self):
|
|
if self.dim == 2: return self.gridFy
|
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else: raise NotImplementedError('Edge Grid not yet implemented')
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|
|
|
@property
|
|
def gridEy(self):
|
|
if self.dim == 2: return self.gridFx
|
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else: raise NotImplementedError('Edge Grid not yet implemented')
|
|
|
|
@property
|
|
def gridEz(self):
|
|
if self.dim == 2: return None
|
|
else: raise NotImplementedError('Edge Grid not yet implemented')
|
|
|
|
@property
|
|
def vol(self):
|
|
self.number()
|
|
return np.array([cell.vol for cell in self.sortedCells])
|
|
|
|
@property
|
|
def area(self):
|
|
self.number()
|
|
return np.concatenate(([face.area for face in self.sortedFaceX],[face.area for face in self.sortedFaceY]))
|
|
|
|
@property
|
|
def faceDiv(self):
|
|
if getattr(self, '_faceDiv', None) is None:
|
|
self.number()
|
|
I, J, V = np.empty(0), np.empty(0), np.empty(0)
|
|
for cell in M.sortedCells:
|
|
i, j, v = cell.faceIndex
|
|
I, J, V = np.r_[I,i], np.r_[J,j], np.r_[V,v]
|
|
|
|
VOL = self.vol
|
|
D = sp.csr_matrix((V,(I,J)), shape=(M.nC, M.nF))
|
|
S = self.area
|
|
self._faceDiv = Utils.sdiag(1/VOL)*D*Utils.sdiag(S)
|
|
return self._faceDiv
|
|
|
|
def plotGrid(self, ax=None, text=True, plotC=True, plotF=True, showIt=False):
|
|
if ax is None: ax = plt.subplot(111)
|
|
|
|
if plotC: [node.plotGrid(ax, text=text) for node in self.cells]
|
|
if plotF: [node.plotGrid(ax, text=text) for node in self.faces]
|
|
ax.set_xlim((self.x0[0], self.h[0].sum()))
|
|
ax.set_ylim((self.x0[1], self.h[1].sum()))
|
|
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
|
|
# plt.subplot(211)
|
|
# plt.spy(DIV)
|
|
M.plotGrid(ax=plt.subplot(111),text=True)
|
|
|
|
q = np.zeros(M.nC)
|
|
q[208] = -1.0
|
|
q[291] = 1.0
|
|
b = Solver(-DIV*DIV.T).solve(q)
|
|
plt.figure()
|
|
M.plotImage(b)
|
|
# plt.gca().invert_yaxis()
|
|
print M.vol
|
|
plt.show()
|