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Grid updates for TreeMesh, initial generalizations for OcTree

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rowanc1
2014-02-07 16:28:03 -08:00
parent 3d21f690cc
commit 2f52e15e41
3 changed files with 159 additions and 56 deletions
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SimPEG/mesh/QuadTreeMesh.py → SimPEG/Mesh/TreeMesh.py
+131 -50
View File
@@ -1,4 +1,4 @@
from SimPEG import np, sp, utils
from SimPEG import np, sp, Utils, Solver
import matplotlib.pyplot as plt
import matplotlib.colors as colors
import matplotlib.cm as cmx
@@ -35,14 +35,16 @@ class TreeFace(object):
self.mesh = mesh
self.children = None
self.numFace = None
self.x0 = np.array(x0, dtype=float)
self.faceType = faceType
self.sz = sz
self.sz = np.array(sz, dtype=float)
self.dim = dim
self.depth = depth
mesh.faces.add(self)
if faceType is 'x': self.mesh.faceX.add(self)
elif faceType is 'y': self.mesh.faceY.add(self)
if faceType is 'x': self.mesh.facesX.add(self)
elif faceType is 'y': self.mesh.facesY.add(self)
elif faceType is 'z': self.mesh.facesZ.add(self)
self.tangent = np.zeros(dim)
self.tangent[1 if faceType is 'x' else 0] = 1
self.normal = np.zeros(dim)
@@ -53,12 +55,15 @@ class TreeFace(object):
@property
def index(self):
if not self.mesh.isNumbered: raise Exception('Mesh is not numbered.')
if self.isleaf: return np.r_[self.numFace]
return np.concatenate([face.index for face in self.children])
@property
def area(self): return self.sz
@property
def area(self):
"""area of the face"""
return self.sz.prod()
def refine(self):
if not self.isleaf: return
@@ -68,32 +73,30 @@ class TreeFace(object):
# Create refined x0's
x0r_0 = self.x0
x0r_1 = self.x0+0.5*self.tangent*self.sz
self.children[0] = TreeFace(self.mesh, x0=x0r_0, faceType=self.faceType, dim=self.dim, sz=0.5*self.sz, depth=self.depth+1,parent=self)
self.children[1] = TreeFace(self.mesh, x0=x0r_1, faceType=self.faceType, dim=self.dim, sz=0.5*self.sz, depth=self.depth+1,parent=self)
self.children[0] = TreeFace(self.mesh, x0=x0r_0, faceType=self.faceType, dim=self.dim, sz=0.5*self.sz, depth=self.depth+1, parent=self)
self.children[1] = TreeFace(self.mesh, x0=x0r_1, faceType=self.faceType, dim=self.dim, sz=0.5*self.sz, depth=self.depth+1, parent=self)
self.mesh.faces.remove(self)
if self.faceType is 'x':
self.mesh.faceX.remove(self)
self.mesh.facesX.remove(self)
elif self.faceType is 'y':
self.mesh.faceY.remove(self)
self.mesh.facesY.remove(self)
def viz(self, ax, text=True):
if not self.isleaf: return
ax.plot(np.r_[self.x0[0],self.x0[0]+self.tangent[0]*self.sz], np.r_[self.x0[1], self.x0[1]+self.tangent[1]*self.sz],'r-')
if text: ax.text(self.x0[0]+0.5*self.tangent[0]*self.sz, self.x0[1]+0.5*self.tangent[1]*self.sz,self.numFace)
@property
def center(self):
return self.x0 + 0.5*self.tangent*self.sz
class TreeNode(object):
"""docstring for TreeNode"""
def __init__(self, mesh, x0=[0,0], dim=2, depth=0, sz=[1,1], parent=None, fXm=None, fXp=None, fYm=None, fYp=None):
children = None #:
numCell = None
fXm = fXm if fXm is not None else TreeFace(mesh, x0=np.r_[x0[0] , x0[1] ], faceType='x', dim=dim, sz=sz[1], depth=depth, parent=parent)
fXp = fXp if fXp is not None else TreeFace(mesh, x0=np.r_[x0[0]+sz[0], x0[1] ], faceType='x', dim=dim, sz=sz[1], depth=depth, parent=parent)
fYm = fYm if fYm is not None else TreeFace(mesh, x0=np.r_[x0[0] , x0[1] ], faceType='y', dim=dim, sz=sz[0], depth=depth, parent=parent)
fYp = fYp if fYp is not None else TreeFace(mesh, x0=np.r_[x0[0] , x0[1]+sz[1]], faceType='y', dim=dim, sz=sz[0], depth=depth, parent=parent)
self.faces = {"fXm":fXm, "fXp":fXp, "fYm":fYm, "fYp":fYp}
def __init__(self, mesh, x0=[0,0], dim=2, depth=0, sz=[1,1], parent=None, fXm=None, fXp=None, fYm=None, fYp=None, fZm=None, fZp=None):
self.mesh = mesh
self.x0 = np.array(x0, dtype=float)
@@ -101,8 +104,22 @@ class TreeNode(object):
self.dim = dim
self.depth = depth
self.parent = parent
self.children = None
self.numCell = None
if dim == 2:
fXm = fXm if fXm is not None else TreeFace(mesh, x0=np.r_[x0[0] , x0[1] ], faceType='x', dim=dim, sz=np.r_[sz[1]], depth=depth, parent=parent)
fXp = fXp if fXp is not None else TreeFace(mesh, x0=np.r_[x0[0]+sz[0], x0[1] ], faceType='x', dim=dim, sz=np.r_[sz[1]], depth=depth, parent=parent)
fYm = fYm if fYm is not None else TreeFace(mesh, x0=np.r_[x0[0] , x0[1] ], faceType='y', dim=dim, sz=np.r_[sz[0]], depth=depth, parent=parent)
fYp = fYp if fYp is not None else TreeFace(mesh, x0=np.r_[x0[0] , x0[1]+sz[1]], faceType='y', dim=dim, sz=np.r_[sz[0]], depth=depth, parent=parent)
self.faces = {"fXm":fXm, "fXp":fXp, "fYm":fYm, "fYp":fYp}
elif dim == 3:
fXm = fXm if fXm is not None else TreeFace(mesh, x0=np.r_[x0[0] , x0[1] , x0[2] ], faceType='x', dim=dim, sz=np.r_[sz[1], sz[2]], depth=depth, parent=parent)
fXp = fXp if fXp is not None else TreeFace(mesh, x0=np.r_[x0[0]+sz[0], x0[1] , x0[2] ], faceType='x', dim=dim, sz=np.r_[sz[1], sz[2]], depth=depth, parent=parent)
fYm = fYm if fYm is not None else TreeFace(mesh, x0=np.r_[x0[0] , x0[1] , x0[2] ], faceType='y', dim=dim, sz=np.r_[sz[0], sz[2]], depth=depth, parent=parent)
fYp = fYp if fYp is not None else TreeFace(mesh, x0=np.r_[x0[0] , x0[1]+sz[1], x0[2] ], faceType='y', dim=dim, sz=np.r_[sz[0], sz[2]], depth=depth, parent=parent)
fZm = fZm if fZm is not None else TreeFace(mesh, x0=np.r_[x0[0] , x0[1] , x0[2] ], faceType='z', dim=dim, sz=np.r_[sz[0], sz[1]], depth=depth, parent=parent)
fZp = fZp if fZp is not None else TreeFace(mesh, x0=np.r_[x0[0] , x0[1] , x0[2]+sz[2]], faceType='z', dim=dim, sz=np.r_[sz[0], sz[1]], depth=depth, parent=parent)
self.faces = {"fXm":fXm, "fXp":fXp, "fYm":fYm, "fYp":fYp, "fZm":fZm, "fZp":fZp}
mesh.cells.add(self)
@property
@@ -120,13 +137,17 @@ class TreeNode(object):
return np.max([node.branchdepth for node in self.children.flatten('F')])
@property
def gridCC(self): return self.x0 + 0.5*self.sz
def center(self): return self.x0 + 0.5*self.sz
def refine(self, function=None):
if self.dim == 2:
return self._refine2D(function=function)
def _refine2D(self, function=None):
if not self.isleaf and function is None: return
if function is not None:
do = function(self.gridCC) > self.depth
do = function(self.center) > self.depth
if not do: return
self.mesh.isNumbered = False
@@ -187,20 +208,32 @@ class TreeNode(object):
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.gridCC[0],self.gridCC[1],self.numCell)
if text: ax.text(self.center[0],self.center[1],self.numCell)
class QuadTreeMesh(object):
"""docstring for QuadTreeMesh"""
def __init__(self, h, x0=[0,0]):
self.faces = set()
self.faceX = set()
self.faceY = set()
self.cells = set()
self.x0 = np.array(x0,dtype=float)
class TreeMesh(object):
"""TreeMesh"""
def __init__(self, h, x0=None):
assert type(h) is list, 'h must be a list'
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'
assert len(x0) == self.dim, 'x0 must have the same dimensions as the mesh'
self.x0 = np.array(x0, dtype=float)
# set the sets for holding the faces and cells
self.cells = set()
self.faces = set()
self.facesX = set()
self.facesY = set()
if self.dim == 3: self.facesZ = set()
self.children = np.empty([hi.size for hi in h],dtype=TreeNode)
for i in range(h[0].size):
for j in range(h[1].size):
@@ -210,7 +243,7 @@ class QuadTreeMesh(object):
x0j = (np.r_[x0[1], h[1][:j]]).sum()
self.children[i][j] = TreeNode(self, x0=[x0i, x0j], dim=len(h), depth=0, sz=[h[0][i], h[1][j]], fXm=fXm, fYm=fYm)
isNumbered = utils.dependentProperty('_isNumbered', False, ['_faceDiv'], 'Setting this to False will delete all operators.')
isNumbered = Utils.dependentProperty('_isNumbered', False, ['_faceDiv'], 'Setting this to False will delete all operators.')
@property
def branchdepth(self):
@@ -223,41 +256,81 @@ class QuadTreeMesh(object):
def number(self):
if self.isNumbered: return
sortedCells = sorted(M.cells,key=SortByX0())
sortedFaceX = sorted(M.faceX,key=SortByX0())
sortedFaceY = sorted(M.faceY,key=SortByX0())
nFx = len(sortedFaceX)
for i, sc in enumerate(sortedCells): sc.numCell = i
for i, sfx in enumerate(sortedFaceX): sfx.numFace = i
for i, sfy in enumerate(sortedFaceY): sfy.numFace = i + nFx
self.sortedCells = sorted(self.cells,key=SortByX0())
for i, sc in enumerate(self.sortedCells): sc.numCell = i
self.sortedCells = sortedCells
self.sortedFaceX = sortedFaceX
self.sortedFaceY = sortedFaceY
self.sortedFaceX = sorted(self.facesX,key=SortByX0())
for i, sfx in enumerate(self.sortedFaceX): sfx.numFace = i
self.sortedFaceY = sorted(self.facesY,key=SortByX0())
for i, sfy in enumerate(self.sortedFaceY): sfy.numFace = i + self.nFx
if self.dim == 3:
self.sortedFaceZ = sorted(self.facesZ,key=SortByX0())
for i, sfz in enumerate(self.sortedFaceZ): sfz.numFace = i + self.nFx + self.nFy
self.isNumbered = True
@property
def dim(self): return len(self.h)
@property
def dim(self): return len(self.x0)
@property
def nC(self): return len(self.cells)
@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 len(self.facesZ)
@property
def nE(self): return len(self.faces)
@property
def nEx(self):
if self.dim == 2:
return len(self.facesY)
else: raise NotImplementedError('nEx')
@property
def nEy(self):
if self.dim == 2:
return len(self.facesX)
else: raise NotImplementedError('nEy')
@property
def gridCC(self):
if getattr(self, '_gridCC', None) is None:
self.number()
self._gridCC = np.empty((self.nC,self.dim))
for ii, cell in enumerate(self.sortedCells):
self._gridCC[ii,:] = cell.gridCC
self._gridCC[ii,:] = cell.center
return self._gridCC
@property
def gridFx(self):
if getattr(self, '_gridFx', None) is None:
self.number()
self._gridFx = np.empty((self.nFx,self.dim))
for ii, face in enumerate(self.sortedFaceX):
self._gridFx[ii,:] = face.center
return self._gridFx
@property
def gridFy(self):
if getattr(self, '_gridFy', None) is None:
self.number()
self._gridFy = np.empty((self.nFy,self.dim))
for ii, face in enumerate(self.sortedFaceY):
self._gridFy[ii,:] = face.center
return self._gridFy
@property
def vol(self):
self.number()
@@ -280,20 +353,27 @@ class QuadTreeMesh(object):
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)
self._faceDiv = Utils.sdiag(1/VOL)*D*Utils.sdiag(S)
return self._faceDiv
def plotGrid(self, ax=None, text=True, plotC=True, plotF=False):
def plotGrid(self, ax=None, text=True, plotC=True, plotF=False, showIt=False):
if ax is None: ax = plt.subplot(111)
if plotC: [node.viz(ax, text=text) for node in self.cells]
if plotF: [node.viz(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):
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())
@@ -304,11 +384,12 @@ class QuadTreeMesh(object):
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 = QuadTreeMesh([np.ones(x) for x in [4,10]])
M = TreeMesh([np.ones(x) for x in [4,10]])
def function(xc):
r = xc - np.r_[2.,6.]
@@ -330,7 +411,7 @@ if __name__ == '__main__':
q = np.zeros(M.nC)
q[208] = -1.0
q[291] = 1.0
b = utils.Solver(-DIV*DIV.T).solve(q)
b = Solver(-DIV*DIV.T).solve(q)
plt.figure()
M.plotImage(b)
# plt.gca().invert_yaxis()
SimPEG/Mesh/__init__.py
+1 -1
View File
@@ -1,6 +1,6 @@
from Cyl1DMesh import Cyl1DMesh
from TensorMesh import TensorMesh
from QuadTreeMesh import QuadTreeMesh
from TreeMesh import TreeMesh
from LogicallyOrthogonalMesh import LogicallyOrthogonalMesh
from BaseMesh import BaseMesh
from TensorView import TensorView
SimPEG/tests/test_QuadTree.py
+27 -5
View File
@@ -1,19 +1,41 @@
from SimPEG import mesh, np
from SimPEG import Mesh, np
import unittest
class TestCheckDerivative(unittest.TestCase):
class TestQuadTreeMesh(unittest.TestCase):
def setUp(self):
M = mesh.QuadTreeMesh([3,2],[1,2])
M = Mesh.TreeMesh([np.ones(x) for x in [3,2]])
for ii in range(1):
M.children[ii,ii].refine()
self.M = M
M.number()
# M.plotGrid(showIt=True)
def test_MeshSizes(self):
self.assertTrue(len(self.M.faces)==25)
self.assertTrue(len(self.M.cells)==9)
self.assertTrue(self.M.nC==9)
self.assertTrue(self.M.nF==25)
self.assertTrue(self.M.nFx==12)
self.assertTrue(self.M.nFy==13)
self.assertTrue(self.M.nE==25)
self.assertTrue(self.M.nEx==13)
self.assertTrue(self.M.nEy==12)
def test_gridCC(self):
x = np.r_[0.25,0.75,1.5,2.5,0.25,0.75,0.5,1.5,2.5]
y = np.r_[0.25,0.25,0.5,0.5,0.75,0.75,1.5,1.5,1.5]
self.assertTrue(np.linalg.norm((np.c_[x,y]-self.M.gridCC).flatten()) == 0)
def test_gridFx(self):
x = np.r_[0.0,0.5,1.0,2.0,3.0,0.0,0.5,1.0,0.0,1.0,2.0,3.0]
y = np.r_[0.25,0.25,0.25,0.5,0.5,0.75,0.75,0.75,1.5,1.5,1.5,1.5]
self.assertTrue(np.linalg.norm((np.c_[x,y]-self.M.gridFx).flatten()) == 0)
def test_gridFy(self):
x = np.r_[0.25,0.75,1.5,2.5,0.25,0.75,0.25,0.75,1.5,2.5,0.5,1.5,2.5]
y = np.r_[0,0,0,0,0.5,0.5,1,1,1,1,2,2,2]
self.assertTrue(np.linalg.norm((np.c_[x,y]-self.M.gridFy).flatten()) == 0)