mirror of
https://github.com/wassname/simpeg.git
synced 2026-06-28 23:42:13 +08:00
Rowan Cockett
1207 lines
51 KiB
Python
1207 lines
51 KiB
Python
from SimPEG import np, sp, Utils, Solver
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import matplotlib.pyplot as plt
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import matplotlib
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class ZCurve(object):
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"""
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The Z-order curve is generated by interleaving the bits of an offset.
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See:
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https://github.com/cortesi/scurve
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Aldo Cortesi <aldo@corte.si>
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"""
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def __init__(self, dimension, bits):
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"""
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dimension: Number of dimensions
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bits: The number of bits per co-ordinate. Total number of points is
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2**(bits*dimension).
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"""
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self.dimension, self.bits = dimension, bits
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def bitrange(self, x, width, start, end):
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"""
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Extract a bit range as an integer.
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(start, end) is inclusive lower bound, exclusive upper bound.
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"""
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return x >> (width-end) & ((2**(end-start))-1)
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def index(self, p):
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p.reverse()
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idx = 0
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iwidth = self.bits * self.dimension
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for i in range(iwidth):
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bitoff = self.bits-(i/self.dimension)-1
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poff = self.dimension-(i%self.dimension)-1
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b = self.bitrange(p[poff], self.bits, bitoff, bitoff+1) << i
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idx |= b
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return idx
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def point(self, idx):
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p = [0]*self.dimension
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iwidth = self.bits * self.dimension
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for i in range(iwidth):
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b = self.bitrange(idx, iwidth, i, i+1) << (iwidth-i-1)/self.dimension
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p[i%self.dimension] |= b
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p.reverse()
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return p
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def SortGrid(grid, offset=0):
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"""
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Sorts a grid by the x0 location.
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"""
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eps = 1e-7
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def mycmp(c1,c2):
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c1 = grid[c1-offset]
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c2 = grid[c2-offset]
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if c1.size == 2:
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if np.abs(c1[1] - c2[1]) < eps:
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return c1[0] - c2[0]
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return c1[1] - c2[1]
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elif c1.size == 3:
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if np.abs(c1[2] - c2[2]) < eps:
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if np.abs(c1[1] - c2[1]) < eps:
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return c1[0] - c2[0]
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return c1[1] - c2[1]
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return c1[2] - c2[2]
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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 sorted(range(offset,grid.shape[0]+offset), key=K)
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class NotBalancedException(Exception):
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pass
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class Tree(object):
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def __init__(self, h_in, levels=3):
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assert type(h_in) is list, 'h_in must be a list'
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assert len(h_in) > 1, "len(h_in) must be greater than 1"
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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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elif type(h_i) is list:
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h_i = Utils.meshTensor(h_i)
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assert isinstance(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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assert len(h_i) == 2**levels, "must make h and levels match"
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h[i] = h_i[:] # make a copy.
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self.h = h
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self._levels = levels
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self._levelBits = int(np.ceil(np.sqrt(levels)))+1
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self.__dirty__ = True #: The numbering is dirty!
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self._z = ZCurve(self.dim, 20)
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self._treeInds = set()
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self._treeInds.add(0)
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@property
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def __dirty__(self):
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return self.__dirtyFaces__ or self.__dirtyEdges__ or self.__dirtyNodes__ or self.__dirtyHanging__
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@__dirty__.setter
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def __dirty__(self, val):
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assert val is True
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self.__dirtyFaces__ = True
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self.__dirtyEdges__ = True
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self.__dirtyNodes__ = True
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self.__dirtyHanging__ = True
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@property
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def levels(self): return self._levels
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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._treeInds)
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@property
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def nN(self):
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self._numberNodes()
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return len(self._nodes)
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@property
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def nF(self):
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return self.nFx + self.nFy + (0 if self.dim == 2 else self.nFz)
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@property
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def nFx(self):
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self._numberFaces()
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return len(self._facesX)
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@property
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def nFy(self):
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self._numberFaces()
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return len(self._facesY)
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@property
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def nFz(self):
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if self.dim == 2: return None
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self._numberFaces()
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return len(self._facesZ)
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@property
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def nE(self):
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return self.nEx + self.nEy + (0 if self.dim == 2 else self.nEz)
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@property
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def nEx(self):
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if self.dim == 2:return self.nFy
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self._numberEdges()
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return len(self._edgesX)
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@property
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def nEy(self):
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if self.dim == 2:return self.nFx
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self._numberEdges()
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return len(self._edgesY)
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@property
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def nEz(self):
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if self.dim == 2: return None
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self._numberEdges()
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return len(self._edgesZ)
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@property
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def vol(self):
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self.number()
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return self._vol
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@property
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def area(self):
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self.number()
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return self._area
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@property
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def edge(self):
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self.number()
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if self.dim == 2:
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return np.r_[self._area[self.nFx:], self._area[:self.nFx]]
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@property
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def _sortedInds(self):
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if getattr(self, '__sortedInds', None) is None:
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self.__sortedInds = sorted(self._treeInds)
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return self.__sortedInds
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@property
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def permuteCC(self):
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#TODO: cache these?
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P = SortGrid(self.gridCC)
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return sp.identity(self.nC).tocsr()[P,:]
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@property
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def permuteF(self):
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#TODO: cache these?
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P = SortGrid(self.gridFx)
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P += SortGrid(self.gridFy, offset=self.nFx)
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if self.dim == 3:
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P += SortGrid(self.gridFz, offset=self.nFx+self.nFy)
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return sp.identity(self.nF).tocsr()[P,:]
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@property
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def permuteE(self):
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#TODO: cache these?
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if self.dim == 2:
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P = SortGrid(self.gridFy)
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P += SortGrid(self.gridFx, offset=self.nEx)
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return sp.identity(self.nE).tocsr()[P,:]
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if self.dim == 3:
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raise Exception()
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def _structureChange(self):
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if self.__dirty__: return
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deleteThese = ['__sortedInds', '_gridCC', '_gridFx']
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for p in deleteThese:
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if hasattr(self, p): delattr(self, p)
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self.__dirty__ = True
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def _index(self, pointer):
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assert len(pointer) is self.dim+1
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assert pointer[-1] <= self.levels
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x = self._z.index([p for p in pointer[:-1]]) # copy
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return (x << self._levelBits) + pointer[-1]
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def _pointer(self, index):
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assert type(index) in [int, long]
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n = index & (2**self._levelBits-1)
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p = self._z.point(index >> self._levelBits)
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return p + [n]
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def __contains__(self, v):
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if type(v) in [int, long]:
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return v in self._treeInds
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return self._index(v) in self._treeInds
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def refine(self, function=None, recursive=True, cells=None):
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cells = cells if cells is not None else sorted(self._treeInds)
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recurse = []
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for cell in cells:
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p = self._pointer(cell)
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do = function(self._cellC(cell)) > p[-1]
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if do:
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recurse += self._refineCell(cell)
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if recursive and len(recurse) > 0:
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self.refine(function=function, recursive=True, cells=recurse)
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return recurse
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def _refineCell(self, pointer):
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self._structureChange()
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pointer = self._asPointer(pointer)
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ind = self._asIndex(pointer)
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assert ind in self
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h = self._levelWidth(pointer[-1])/2 # halfWidth
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nL = pointer[-1] + 1 # new level
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add = lambda p:p[0]+p[1]
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added = []
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def addCell(p):
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i = self._index(p+[nL])
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self._treeInds.add(i)
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added.append(i)
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addCell(map(add, zip(pointer[:-1], [0,0,0][:self.dim])))
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addCell(map(add, zip(pointer[:-1], [h,0,0][:self.dim])))
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addCell(map(add, zip(pointer[:-1], [0,h,0][:self.dim])))
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addCell(map(add, zip(pointer[:-1], [h,h,0][:self.dim])))
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if self.dim == 3:
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addCell(map(add, zip(pointer[:-1], [0,0,h])))
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addCell(map(add, zip(pointer[:-1], [h,0,h])))
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addCell(map(add, zip(pointer[:-1], [0,h,h])))
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addCell(map(add, zip(pointer[:-1], [h,h,h])))
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self._treeInds.remove(ind)
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return added
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def _corsenCell(self, pointer):
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self._structureChange()
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raise Exception('Not yet implemented')
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def _asPointer(self, ind):
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if type(ind) in [int, long]:
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return self._pointer(ind)
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if type(ind) is list:
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return ind
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if isinstance(ind, np.ndarray):
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return ind.tolist()
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raise Exception
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def _asIndex(self, pointer):
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if type(pointer) in [int, long]:
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return pointer
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if type(pointer) is list:
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return self._index(pointer)
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raise Exception
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def _parentPointer(self, pointer):
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mod = self._levelWidth(pointer[-1]-1)
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return [p - (p % mod) for p in pointer[:-1]] + [pointer[-1]-1]
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def _cellN(self, p):
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p = self._asPointer(p)
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return [hi[:p[ii]].sum() for ii, hi in enumerate(self.h)]
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def _cellH(self, p):
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p = self._asPointer(p)
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w = self._levelWidth(p[-1])
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return [hi[p[ii]:p[ii]+w].sum() for ii, hi in enumerate(self.h)]
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def _cellC(self, p):
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return (np.array(self._cellH(p))/2.0 + self._cellN(p)).tolist()
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def _levelWidth(self, level):
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return 2**(self.levels - level)
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def _isInsideMesh(self, pointer):
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inside = True
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for p in pointer[:-1]:
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inside = inside and p >= 0 and p < 2**self.levels
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return inside
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def _getNextCell(self, ind, direction=0, positive=True):
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"""
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Returns a None, int, list, or nested list
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The int is the cell number.
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"""
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pointer = self._asPointer(ind)
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step = (1 if positive else -1) * self._levelWidth(pointer[-1])
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nextCell = [p if ii is not direction else p + step for ii, p in enumerate(pointer)]
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if not self._isInsideMesh(nextCell): return None
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# it might be the same size as me?
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if nextCell in self: return self._index(nextCell)
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# it might be smaller than me?
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if nextCell[-1] + 1 <= self.levels: # if I am not the smallest.
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nextCell[-1] += 1
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if not positive:
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nextCell[direction] -= step/2 # Get the closer one
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if nextCell in self: # there is at least one
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hw = self._levelWidth(pointer[-1]) / 2
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nextCell = np.array([p if ii is not direction else p + (step/2 if positive else 0) for ii, p in enumerate(pointer)])
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if self.dim == 2:
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if direction == 0: children = [0,0,1], [0,hw,1]
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if direction == 1: children = [0,0,1], [hw,0,1]
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elif self.dim == 3:
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if direction == 0: children = [0,0,0,1], [0,hw,0,1], [0,0,hw,1], [0,hw,hw,1]
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if direction == 1: children = [0,0,0,1], [hw,0,0,1], [0,0,hw,1], [hw,0,hw,1]
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if direction == 2: children = [0,0,0,1], [hw,0,0,1], [0,hw,0,1], [hw,hw,0,1]
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nextCells = []
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for child in children:
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nextCells.append(self._getNextCell(nextCell + child, direction=direction,positive=positive))
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return nextCells
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# it might be bigger than me?
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return self._getNextCell(self._parentPointer(pointer),
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direction=direction, positive=positive)
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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._gridCC = np.zeros((len(self._treeInds),self.dim))
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for ii, ind in enumerate(self._sortedInds):
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p = self._asPointer(ind)
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self._gridCC[ii, :] = self._cellC(p)
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return self._gridCC
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@property
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def gridN(self):
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self._numberNodes()
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return self._gridN
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@property
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def gridFx(self):
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self._numberFaces()
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return self._gridFx
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@property
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def gridFy(self):
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self._numberFaces()
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return self._gridFy
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@property
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def gridFz(self):
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if self.dim < 3: return None
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self._numberFaces()
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return self._gridFz
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@property
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def gridEx(self):
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if self.dim == 2: return self.gridFy
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self._numberEdges()
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return self._gridEx
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@property
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def gridEy(self):
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if self.dim == 2: return self.gridFx
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self._numberEdges()
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return self._gridEy
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@property
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def gridEz(self):
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if self.dim < 3: return None
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self._numberEdges()
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return self._gridEz
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def _onSameLevel(self, i0, i1):
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p0 = self._asPointer(i0)
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p1 = self._asPointer(i1)
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return p0[-1] == p1[-1]
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def _numberNodes(self, force=False):
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if not self.__dirtyNodes__ and not force: return
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self._nodes = set()
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for ind in self._treeInds:
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p = self._asPointer(ind)
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w = self._levelWidth(p[-1])
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if self.dim == 2:
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self._nodes.add(self._index([p[0] , p[1] , p[2]]))
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self._nodes.add(self._index([p[0] + w, p[1] , p[2]]))
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self._nodes.add(self._index([p[0] , p[1] + w, p[2]]))
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self._nodes.add(self._index([p[0] + w, p[1] + w, p[2]]))
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elif self.dim == 3:
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self._nodes.add(self._index([p[0] , p[1] , p[2] , p[3]]))
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self._nodes.add(self._index([p[0] + w, p[1] , p[2] , p[3]]))
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self._nodes.add(self._index([p[0] , p[1] + w, p[2] , p[3]]))
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self._nodes.add(self._index([p[0] + w, p[1] + w, p[2] , p[3]]))
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self._nodes.add(self._index([p[0] , p[1] , p[2] + w, p[3]]))
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self._nodes.add(self._index([p[0] + w, p[1] , p[2] + w, p[3]]))
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self._nodes.add(self._index([p[0] , p[1] + w, p[2] + w, p[3]]))
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self._nodes.add(self._index([p[0] + w, p[1] + w, p[2] + w, p[3]]))
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gridN = []
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self._n2i = dict()
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for ii, n in enumerate(sorted(self._nodes)):
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self._n2i[n] = ii
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gridN.append( self._cellN( self._pointer(n)[:-1] ) )
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self._gridN = np.array(gridN)
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self.__dirtyNodes__ = False
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def _numberFaces(self, force=False):
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if not self.__dirtyFaces__ and not force: return
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self._facesX = set()
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self._facesY = set()
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if self.dim == 3:
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self._facesZ = set()
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for ind in self._treeInds:
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p = self._asPointer(ind)
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w = self._levelWidth(p[-1])
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if self.dim == 2:
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self._facesX.add(self._index([p[0] , p[1] , p[2]]))
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self._facesX.add(self._index([p[0] + w, p[1] , p[2]]))
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self._facesY.add(self._index([p[0] , p[1] , p[2]]))
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self._facesY.add(self._index([p[0] , p[1] + w, p[2]]))
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elif self.dim == 3:
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self._facesX.add(self._index([p[0] , p[1] , p[2] , p[3]]))
|
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self._facesX.add(self._index([p[0] + w, p[1] , p[2] , p[3]]))
|
|
self._facesY.add(self._index([p[0] , p[1] , p[2] , p[3]]))
|
|
self._facesY.add(self._index([p[0] , p[1] + w, p[2] , p[3]]))
|
|
self._facesZ.add(self._index([p[0] , p[1] , p[2] , p[3]]))
|
|
self._facesZ.add(self._index([p[0] , p[1] , p[2] + w, p[3]]))
|
|
|
|
gridFx = []
|
|
self._fx2i = dict()
|
|
for ii, fx in enumerate(sorted(self._facesX)):
|
|
self._fx2i[fx] = ii
|
|
p = self._pointer(fx)
|
|
n, h = self._cellN(p), self._cellH(p)
|
|
if self.dim == 2:
|
|
gridFx.append( [n[0], n[1] + h[1]/2.0] )
|
|
elif self.dim == 3:
|
|
gridFx.append( [n[0], n[1] + h[1]/2.0, n[2] + h[2]/2.0] )
|
|
self._gridFx = np.array(gridFx)
|
|
|
|
gridFy = []
|
|
self._fy2i = dict()
|
|
for ii, fy in enumerate(sorted(self._facesY)):
|
|
self._fy2i[fy] = ii
|
|
p = self._pointer(fy)
|
|
n, h = self._cellN(p), self._cellH(p)
|
|
if self.dim == 2:
|
|
gridFy.append( [n[0] + h[0]/2.0, n[1]] )
|
|
elif self.dim == 3:
|
|
gridFy.append( [n[0] + h[0]/2.0, n[1], n[2] + h[2]/2.0] )
|
|
self._gridFy = np.array(gridFy)
|
|
|
|
if self.dim == 2:
|
|
self.__dirtyFaces__ = False
|
|
return
|
|
|
|
gridFz = []
|
|
self._fz2i = dict()
|
|
for ii, fz in enumerate(sorted(self._facesZ)):
|
|
self._fz2i[fz] = ii
|
|
p = self._pointer(fz)
|
|
n, h = self._cellN(p), self._cellH(p)
|
|
gridFz.append( [n[0] + h[0]/2.0, n[1] + h[1]/2.0, n[2]] )
|
|
self._gridFz = np.array(gridFz)
|
|
|
|
self.__dirtyFaces__ = False
|
|
|
|
|
|
def _hanging(self, force=False):
|
|
if not self.__dirtyHanging__ and not force: return
|
|
|
|
self._numberNodes()
|
|
self._numberFaces()
|
|
self._numberEdges()
|
|
|
|
self._hangingN = dict()
|
|
self._hangingFx = dict()
|
|
self._hangingFy = dict()
|
|
if self.dim == 3:
|
|
self._hangingFz = dict()
|
|
self._hangingEx = dict()
|
|
self._hangingEy = dict()
|
|
self._hangingEz = dict()
|
|
|
|
# Compute from x faces
|
|
for fx in self._facesX:
|
|
p = self._pointer(fx)
|
|
if p[-1] + 1 > self.levels: continue
|
|
sl = p[-1] + 1 #: small level
|
|
test = self._index(p[:-1] + [sl])
|
|
if test not in self._facesX:
|
|
# Return early without checking the other faces
|
|
continue
|
|
w = self._levelWidth(sl)
|
|
|
|
if self.dim == 2:
|
|
self._hangingFx[self._fx2i[test ]] = ([self._fx2i[fx], 0.5], )
|
|
self._hangingFx[self._fx2i[self._index([p[0] , p[1] + w, sl])]] = ([self._fx2i[fx], 0.5], )
|
|
|
|
n0, n1 = fx, self._index([p[0], p[1] + 2*w, p[-1]])
|
|
self._hangingN[self._n2i[test ]] = ([self._n2i[n0], 1.0], )
|
|
self._hangingN[self._n2i[self._index([p[0] , p[1] + w, sl])]] = ([self._n2i[n0], 0.5], [self._n2i[n1], 0.5])
|
|
self._hangingN[self._n2i[self._index([p[0] , p[1] + 2*w, sl])]] = ([self._n2i[n1], 1.0], )
|
|
|
|
elif self.dim == 3:
|
|
ey0 = fx
|
|
ey1 = self._index([p[0], p[1] , p[2] + 2*w, p[-1]])
|
|
ez0 = fx
|
|
ez1 = self._index([p[0], p[1] + 2*w, p[2] , p[-1]])
|
|
|
|
n0 = fx
|
|
n1 = self._index([p[0], p[1] + 2*w, p[2] , p[-1]])
|
|
n2 = self._index([p[0], p[1] , p[2] + 2*w, p[-1]])
|
|
n3 = self._index([p[0], p[1] + 2*w, p[2] + 2*w, p[-1]])
|
|
|
|
self._hangingFx[self._fx2i[test ]] = ([self._fx2i[fx], 0.25], )
|
|
self._hangingFx[self._fx2i[self._index([p[0], p[1] + w, p[2] , sl])]] = ([self._fx2i[fx], 0.25], )
|
|
self._hangingFx[self._fx2i[self._index([p[0], p[1] , p[2] + w, sl])]] = ([self._fx2i[fx], 0.25], )
|
|
self._hangingFx[self._fx2i[self._index([p[0], p[1] + w, p[2] + w, sl])]] = ([self._fx2i[fx], 0.25], )
|
|
|
|
self._hangingEy[self._ey2i[test ]] = ([self._ey2i[ey0], 0.5], )
|
|
self._hangingEy[self._ey2i[self._index([p[0], p[1] + w, p[2] , sl])]] = ([self._ey2i[ey0], 0.5], )
|
|
self._hangingEy[self._ey2i[self._index([p[0], p[1] , p[2] + w, sl])]] = ([self._ey2i[ey0], 0.25], [self._ey2i[ey1], 0.25])
|
|
self._hangingEy[self._ey2i[self._index([p[0], p[1] + w, p[2] + w, sl])]] = ([self._ey2i[ey0], 0.25], [self._ey2i[ey1], 0.25])
|
|
self._hangingEy[self._ey2i[self._index([p[0], p[1] , p[2] + 2*w, sl])]] = ([self._ey2i[ey1], 0.5], )
|
|
self._hangingEy[self._ey2i[self._index([p[0], p[1] + w, p[2] + 2*w, sl])]] = ([self._ey2i[ey1], 0.5], )
|
|
|
|
self._hangingEz[self._ez2i[test ]] = ([self._ez2i[ez0], 0.5], )
|
|
self._hangingEz[self._ez2i[self._index([p[0], p[1] , p[2] + w, sl])]] = ([self._ez2i[ez0], 0.5], )
|
|
self._hangingEz[self._ez2i[self._index([p[0], p[1] + w, p[2] , sl])]] = ([self._ez2i[ez0], 0.25], [self._ez2i[ez1], 0.25])
|
|
self._hangingEz[self._ez2i[self._index([p[0], p[1] + w, p[2] + w, sl])]] = ([self._ez2i[ez0], 0.25], [self._ez2i[ez1], 0.25])
|
|
self._hangingEz[self._ez2i[self._index([p[0], p[1] + 2*w, p[2] , sl])]] = ([self._ez2i[ez1], 0.5], )
|
|
self._hangingEz[self._ez2i[self._index([p[0], p[1] + 2*w, p[2] + w, sl])]] = ([self._ez2i[ez1], 0.5], )
|
|
|
|
self._hangingN[ self._n2i[ test ]] = ([self._n2i[n0], 1.0], )
|
|
self._hangingN[ self._n2i[ self._index([p[0], p[1] + w, p[2] , sl])]] = ([self._n2i[n0], 0.5], [self._n2i[n1], 0.5])
|
|
self._hangingN[ self._n2i[ self._index([p[0], p[1] + 2*w, p[2] , sl])]] = ([self._n2i[n1], 1.0], )
|
|
self._hangingN[ self._n2i[ self._index([p[0], p[1] , p[2] + w, sl])]] = ([self._n2i[n0], 0.5], [self._n2i[n2], 0.5])
|
|
self._hangingN[ self._n2i[ self._index([p[0], p[1] + w, p[2] + w, sl])]] = ([self._n2i[n0], 0.25], [self._n2i[n1], 0.25], [self._n2i[n2], 0.25], [self._n2i[n3], 0.25])
|
|
self._hangingN[ self._n2i[ self._index([p[0], p[1] + 2*w, p[2] + w, sl])]] = ([self._n2i[n1], 0.5], [self._n2i[n3], 0.5])
|
|
self._hangingN[ self._n2i[ self._index([p[0], p[1] , p[2] + 2*w, sl])]] = ([self._n2i[n2], 1.0], )
|
|
self._hangingN[ self._n2i[ self._index([p[0], p[1] + w, p[2] + 2*w, sl])]] = ([self._n2i[n2], 0.5], [self._n2i[n3], 0.5])
|
|
self._hangingN[ self._n2i[ self._index([p[0], p[1] + 2*w, p[2] + 2*w, sl])]] = ([self._n2i[n3], 1.0], )
|
|
|
|
# Compute from y faces
|
|
for fy in self._facesY:
|
|
p = self._pointer(fy)
|
|
if p[-1] + 1 > self.levels: continue
|
|
sl = p[-1] + 1 #: small level
|
|
test = self._index(p[:-1] + [sl])
|
|
if test not in self._facesY:
|
|
# Return early without checking the other faces
|
|
continue
|
|
w = self._levelWidth(sl)
|
|
|
|
if self.dim == 2:
|
|
self._hangingFy[self._fy2i[test ]] = ([self._fy2i[fy], 0.5], )
|
|
self._hangingFy[self._fy2i[self._index([p[0] + w, p[1] , sl])]] = ([self._fy2i[fy], 0.5], )
|
|
|
|
n0, n1 = fy, self._index([p[0] + 2*w, p[1], p[-1]])
|
|
self._hangingN[self._n2i[test ]] = ([self._n2i[n0], 1.0], )
|
|
self._hangingN[self._n2i[self._index([p[0] + w, p[1] , sl])]] = ([self._n2i[n0], 0.5], [self._n2i[n1], 0.5])
|
|
self._hangingN[self._n2i[self._index([p[0] + 2*w, p[1] , sl])]] = ([self._n2i[n1], 1.0], )
|
|
|
|
elif self.dim == 3:
|
|
ex0 = fy
|
|
ex1 = self._index([p[0] , p[1], p[2] + 2*w, p[-1]])
|
|
ez0 = fy
|
|
ez1 = self._index([p[0] + 2*w, p[1], p[2] , p[-1]])
|
|
|
|
n0 = fy
|
|
n1 = self._index([p[0] + 2*w, p[1], p[2] , p[-1]])
|
|
n2 = self._index([p[0] , p[1], p[2] + 2*w, p[-1]])
|
|
n3 = self._index([p[0] + 2*w, p[1], p[2] + 2*w, p[-1]])
|
|
|
|
self._hangingFy[self._fy2i[test ]] = ([self._fy2i[fy], 0.25], )
|
|
self._hangingFy[self._fy2i[self._index([p[0] + w, p[1], p[2] , sl])]] = ([self._fy2i[fy], 0.25], )
|
|
self._hangingFy[self._fy2i[self._index([p[0] , p[1], p[2] + w, sl])]] = ([self._fy2i[fy], 0.25], )
|
|
self._hangingFy[self._fy2i[self._index([p[0] + w, p[1], p[2] + w, sl])]] = ([self._fy2i[fy], 0.25], )
|
|
|
|
self._hangingEx[self._ex2i[test ]] = ([self._ex2i[ex0], 0.5], )
|
|
self._hangingEx[self._ex2i[self._index([p[0] + w, p[1], p[2] , sl])]] = ([self._ex2i[ex0], 0.5], )
|
|
self._hangingEx[self._ex2i[self._index([p[0] , p[1], p[2] + w, sl])]] = ([self._ex2i[ex0], 0.25], [self._ex2i[ex1], 0.25])
|
|
self._hangingEx[self._ex2i[self._index([p[0] + w, p[1], p[2] + w, sl])]] = ([self._ex2i[ex0], 0.25], [self._ex2i[ex1], 0.25])
|
|
self._hangingEx[self._ex2i[self._index([p[0] , p[1], p[2] + 2*w, sl])]] = ([self._ex2i[ex1], 0.5], )
|
|
self._hangingEx[self._ex2i[self._index([p[0] + w, p[1], p[2] + 2*w, sl])]] = ([self._ex2i[ex1], 0.5], )
|
|
|
|
self._hangingEz[self._ez2i[test ]] = ([self._ez2i[ez0], 0.5], )
|
|
self._hangingEz[self._ez2i[self._index([p[0] , p[1], p[2] + w, sl])]] = ([self._ez2i[ez0], 0.5], )
|
|
self._hangingEz[self._ez2i[self._index([p[0] + w, p[1], p[2] , sl])]] = ([self._ez2i[ez0], 0.25], [self._ez2i[ez1], 0.25])
|
|
self._hangingEz[self._ez2i[self._index([p[0] + w, p[1], p[2] + w, sl])]] = ([self._ez2i[ez0], 0.25], [self._ez2i[ez1], 0.25])
|
|
self._hangingEz[self._ez2i[self._index([p[0] + 2*w, p[1], p[2] , sl])]] = ([self._ez2i[ez1], 0.5], )
|
|
self._hangingEz[self._ez2i[self._index([p[0] + 2*w, p[1], p[2] + w, sl])]] = ([self._ez2i[ez1], 0.5], )
|
|
|
|
self._hangingN[ self._n2i[ test ]] = ([self._n2i[n0], 1.0], )
|
|
self._hangingN[ self._n2i[ self._index([p[0] + w, p[1], p[2] , sl])]] = ([self._n2i[n0], 0.5], [self._n2i[n1], 0.5])
|
|
self._hangingN[ self._n2i[ self._index([p[0] + 2*w, p[1], p[2] , sl])]] = ([self._n2i[n1], 1.0], )
|
|
self._hangingN[ self._n2i[ self._index([p[0] , p[1], p[2] + w, sl])]] = ([self._n2i[n0], 0.5], [self._n2i[n2], 0.5])
|
|
self._hangingN[ self._n2i[ self._index([p[0] + w, p[1], p[2] + w, sl])]] = ([self._n2i[n0], 0.25], [self._n2i[n1], 0.25], [self._n2i[n2], 0.25], [self._n2i[n3], 0.25])
|
|
self._hangingN[ self._n2i[ self._index([p[0] + 2*w, p[1], p[2] + w, sl])]] = ([self._n2i[n1], 0.5], [self._n2i[n3], 0.5])
|
|
self._hangingN[ self._n2i[ self._index([p[0] , p[1], p[2] + 2*w, sl])]] = ([self._n2i[n2], 1.0], )
|
|
self._hangingN[ self._n2i[ self._index([p[0] + w, p[1], p[2] + 2*w, sl])]] = ([self._n2i[n2], 0.5], [self._n2i[n3], 0.5])
|
|
self._hangingN[ self._n2i[ self._index([p[0] + 2*w, p[1], p[2] + 2*w, sl])]] = ([self._n2i[n3], 1.0], )
|
|
|
|
if self.dim == 2:
|
|
self.__dirtyHanging__ = False
|
|
return
|
|
|
|
# Compute from z faces
|
|
for fz in self._facesZ:
|
|
p = self._pointer(fz)
|
|
if p[-1] + 1 > self.levels: continue
|
|
sl = p[-1] + 1 #: small level
|
|
test = self._index(p[:-1] + [sl])
|
|
if test not in self._facesZ:
|
|
# Return early without checking the other faces
|
|
continue
|
|
w = self._levelWidth(sl)
|
|
|
|
ex0 = fz
|
|
ex1 = self._index([p[0] , p[1] + 2*w, p[2], p[-1]])
|
|
ey0 = fz
|
|
ey1 = self._index([p[0] + 2*w, p[1] , p[2], p[-1]])
|
|
|
|
n0 = fz
|
|
n1 = self._index([p[0] + 2*w, p[1] , p[2], p[-1]])
|
|
n2 = self._index([p[0] , p[1] + 2*w, p[2], p[-1]])
|
|
n3 = self._index([p[0] + 2*w, p[1] + 2*w, p[2], p[-1]])
|
|
|
|
self._hangingFz[self._fz2i[test ]] = ([self._fz2i[fz], 0.25], )
|
|
self._hangingFz[self._fz2i[self._index([p[0] + w, p[1] , p[2], sl])]] = ([self._fz2i[fz], 0.25], )
|
|
self._hangingFz[self._fz2i[self._index([p[0] , p[1] + w, p[2], sl])]] = ([self._fz2i[fz], 0.25], )
|
|
self._hangingFz[self._fz2i[self._index([p[0] + w, p[1] + w, p[2], sl])]] = ([self._fz2i[fz], 0.25], )
|
|
|
|
self._hangingEx[self._ex2i[test ]] = ([self._ex2i[ex0], 0.5], )
|
|
self._hangingEx[self._ex2i[self._index([p[0] + w, p[1] , p[2], sl])]] = ([self._ex2i[ex0], 0.5], )
|
|
self._hangingEx[self._ex2i[self._index([p[0] , p[1] + w, p[2], sl])]] = ([self._ex2i[ex0], 0.25], [self._ex2i[ex1], 0.25])
|
|
self._hangingEx[self._ex2i[self._index([p[0] + w, p[1] + w, p[2], sl])]] = ([self._ex2i[ex0], 0.25], [self._ex2i[ex1], 0.25])
|
|
self._hangingEx[self._ex2i[self._index([p[0] , p[1] + 2*w, p[2], sl])]] = ([self._ex2i[ex1], 0.5], )
|
|
self._hangingEx[self._ex2i[self._index([p[0] + w, p[1] + 2*w, p[2], sl])]] = ([self._ex2i[ex1], 0.5], )
|
|
|
|
self._hangingEy[self._ey2i[test ]] = ([self._ey2i[ey0], 0.5], )
|
|
self._hangingEy[self._ey2i[self._index([p[0] , p[1] + w, p[2], sl])]] = ([self._ey2i[ey0], 0.5], )
|
|
self._hangingEy[self._ey2i[self._index([p[0] + w, p[1] , p[2], sl])]] = ([self._ey2i[ey0], 0.25], [self._ey2i[ey1], 0.25])
|
|
self._hangingEy[self._ey2i[self._index([p[0] + w, p[1] + w, p[2], sl])]] = ([self._ey2i[ey0], 0.25], [self._ey2i[ey1], 0.25])
|
|
self._hangingEy[self._ey2i[self._index([p[0] + 2*w, p[1] , p[2], sl])]] = ([self._ey2i[ey1], 0.5], )
|
|
self._hangingEy[self._ey2i[self._index([p[0] + 2*w, p[1] + w, p[2], sl])]] = ([self._ey2i[ey1], 0.5], )
|
|
|
|
self._hangingN[ self._n2i[ test ]] = ([self._n2i[n0], 1.0], )
|
|
self._hangingN[ self._n2i[ self._index([p[0] + w, p[1] , p[2], sl])]] = ([self._n2i[n0], 0.5], [self._n2i[n1], 0.5])
|
|
self._hangingN[ self._n2i[ self._index([p[0] + 2*w, p[1] , p[2], sl])]] = ([self._n2i[n1], 1.0], )
|
|
self._hangingN[ self._n2i[ self._index([p[0] , p[1] + w, p[2], sl])]] = ([self._n2i[n0], 0.5], [self._n2i[n2], 0.5])
|
|
self._hangingN[ self._n2i[ self._index([p[0] + w, p[1] + w, p[2], sl])]] = ([self._n2i[n0], 0.25], [self._n2i[n1], 0.25], [self._n2i[n2], 0.25], [self._n2i[n3], 0.25])
|
|
self._hangingN[ self._n2i[ self._index([p[0] + 2*w, p[1] + w, p[2], sl])]] = ([self._n2i[n1], 0.5], [self._n2i[n3], 0.5])
|
|
self._hangingN[ self._n2i[ self._index([p[0] , p[1] + 2*w, p[2], sl])]] = ([self._n2i[n2], 1.0], )
|
|
self._hangingN[ self._n2i[ self._index([p[0] + w, p[1] + 2*w, p[2], sl])]] = ([self._n2i[n2], 0.5], [self._n2i[n3], 0.5])
|
|
self._hangingN[ self._n2i[ self._index([p[0] + 2*w, p[1] + 2*w, p[2], sl])]] = ([self._n2i[n3], 1.0], )
|
|
|
|
self.__dirtyHanging__ = False
|
|
|
|
|
|
def _numberEdges(self, force=False):
|
|
if self.dim == 2: return
|
|
if not self.__dirtyEdges__ and not force: return
|
|
|
|
self._edgesX = set()
|
|
self._edgesY = set()
|
|
self._edgesZ = set()
|
|
|
|
for ind in self._treeInds:
|
|
p = self._asPointer(ind)
|
|
w = self._levelWidth(p[-1])
|
|
self._edgesX.add(self._index([p[0] , p[1] , p[2] , p[3]]))
|
|
self._edgesX.add(self._index([p[0] , p[1] + w, p[2] , p[3]]))
|
|
self._edgesX.add(self._index([p[0] , p[1] , p[2] + w, p[3]]))
|
|
self._edgesX.add(self._index([p[0] , p[1] + w, p[2] + w, p[3]]))
|
|
|
|
self._edgesY.add(self._index([p[0] , p[1] , p[2] , p[3]]))
|
|
self._edgesY.add(self._index([p[0] + w, p[1] , p[2] , p[3]]))
|
|
self._edgesY.add(self._index([p[0] , p[1] , p[2] + w, p[3]]))
|
|
self._edgesY.add(self._index([p[0] + w, p[1] , p[2] + w, p[3]]))
|
|
|
|
self._edgesZ.add(self._index([p[0] , p[1] , p[2] , p[3]]))
|
|
self._edgesZ.add(self._index([p[0] + w, p[1] , p[2] , p[3]]))
|
|
self._edgesZ.add(self._index([p[0] , p[1] + w, p[2] , p[3]]))
|
|
self._edgesZ.add(self._index([p[0] + w, p[1] + w, p[2] , p[3]]))
|
|
|
|
gridEx = []
|
|
self._ex2i = dict()
|
|
for ii, ex in enumerate(sorted(self._edgesX)):
|
|
self._ex2i[ex] = ii
|
|
p = self._pointer(ex)
|
|
n, h = self._cellN(p), self._cellH(p)
|
|
gridEx.append( [n[0] + h[0]/2.0, n[1], n[2]] )
|
|
self._gridEx = np.array(gridEx)
|
|
|
|
gridEy = []
|
|
self._ey2i = dict()
|
|
for ii, ey in enumerate(sorted(self._edgesY)):
|
|
self._ey2i[ey] = ii
|
|
p = self._pointer(ey)
|
|
n, h = self._cellN(p), self._cellH(p)
|
|
gridEy.append( [n[0], n[1] + h[1]/2.0, n[2]] )
|
|
self._gridEy = np.array(gridEy)
|
|
|
|
gridEz = []
|
|
self._ez2i = dict()
|
|
for ii, ez in enumerate(sorted(self._edgesZ)):
|
|
self._ez2i[ez] = ii
|
|
p = self._pointer(ez)
|
|
n, h = self._cellN(p), self._cellH(p)
|
|
gridEz.append( [n[0], n[1], n[2] + h[2]/2.0] )
|
|
self._gridEz = np.array(gridEz)
|
|
|
|
self.__dirtyEdges__ = False
|
|
|
|
|
|
def number(self, force=False):
|
|
if not self.__dirty__ and not force: return
|
|
self._hanging()
|
|
return
|
|
|
|
facesX, facesY, facesZ = [], [], []
|
|
areaX, areaY, areaZ = [], [], []
|
|
hangingFacesX, hangingFacesY, hangingFacesZ = [], [], []
|
|
hangingNodes = []
|
|
faceXCount, faceYCount, faceZCount = -1, -1, -1
|
|
nodeCount = -1
|
|
fXm,fXp,fYm,fYp,fZm,fZp = range(6)
|
|
vol, nodes = [], []
|
|
|
|
def addXFace(count, p, positive=True):
|
|
n = self._cellN(p)
|
|
w = self._cellH(p)
|
|
areaX.append(w[1] if self.dim == 2 else w[1]*w[2])
|
|
if self.dim == 2:
|
|
facesX.append([n[0] + (w[0] if positive else 0), n[1] + w[1]/2.0])
|
|
elif self.dim == 3:
|
|
facesX.append([n[0] + (w[0] if positive else 0), n[1] + w[1]/2.0, n[2] + w[2]/2.0])
|
|
return count + 1
|
|
def addYFace(count, p, positive=True):
|
|
n = self._cellN(p)
|
|
w = self._cellH(p)
|
|
areaY.append(w[0] if self.dim == 2 else w[0]*w[2])
|
|
if self.dim == 2:
|
|
facesY.append([n[0] + w[0]/2.0, n[1] + (w[1] if positive else 0)])
|
|
elif self.dim == 3:
|
|
facesY.append([n[0] + w[0]/2.0, n[1] + (w[1] if positive else 0), n[2] + w[2]/2.0])
|
|
return count + 1
|
|
def addZFace(count, p, positive=True):
|
|
n = self._cellN(p)
|
|
w = self._cellH(p)
|
|
areaZ.append(w[0]*w[1])
|
|
facesZ.append([n[0] + w[0]/2.0, n[1] + w[1]/2.0, n[2] + (w[2] if positive else 0)])
|
|
return count + 1
|
|
|
|
def addNode(count, p, loc=[0,0,0]):
|
|
"""loc=[0,0]"""
|
|
n = self._cellN(p)
|
|
w = self._cellH(p)
|
|
if self.dim == 2:
|
|
nodes.append([n[0] + w[0]*loc[0], n[1] + w[1]*loc[1]])
|
|
elif self.dim == 3:
|
|
nodes.append([n[0] + w[0]*loc[0], n[1] + w[1]*loc[1], n[2] + w[2]*loc[2]])
|
|
return count + 1
|
|
# c2cn = dict()
|
|
c2f = dict()
|
|
def gc2f(ind):
|
|
if ind in c2f: return c2f[ind]
|
|
c2f_ind = [list() for _ in xrange(2*self.dim)]
|
|
c2f[ind] = c2f_ind
|
|
return c2f_ind
|
|
c2n = dict()
|
|
def gc2n(ind):
|
|
if ind in c2n: return c2n[ind]
|
|
c2n_ind = [list() for _ in xrange(2**self.dim)]
|
|
c2n[ind] = c2n_ind
|
|
return c2n_ind
|
|
|
|
def processCellFace(ind, faceCount, addFace, hangingFaces, DIR=0):
|
|
|
|
fM,fP=(0,1) if DIR == 0 else (2,3) if DIR == 1 else (4,5)
|
|
p = self._asPointer(ind)
|
|
if self._getNextCell(p, direction=DIR, positive=False) is None:
|
|
faceCount = addFace(faceCount, p, positive=False)
|
|
gc2f(ind)[fM] += [faceCount]
|
|
|
|
nextCell = self._getNextCell(p, direction=DIR)
|
|
|
|
# Add the next Xface
|
|
if nextCell is None:
|
|
# on the boundary
|
|
faceCount = addFace(faceCount, p)
|
|
gc2f(ind)[fP] += [faceCount]
|
|
elif type(nextCell) in [int, long] and self._onSameLevel(p,nextCell):
|
|
# same sized cell
|
|
faceCount = addFace(faceCount, p)
|
|
gc2f(ind)[fP] += [faceCount]
|
|
gc2f(nextCell)[fM] += [faceCount]
|
|
elif type(nextCell) in [int, long] and not self._onSameLevel(p,nextCell):
|
|
# the cell is bigger than me
|
|
faceCount = addFace(faceCount, p)
|
|
gc2f(ind)[fP] += [faceCount]
|
|
gc2f(nextCell)[fM] += [faceCount]
|
|
hangingFaces.append(faceCount)
|
|
elif type(nextCell) is list:
|
|
# the cell is smaller than me
|
|
|
|
# TODO: ensure that things are balanced.
|
|
p0 = self._pointer(nextCell[0])
|
|
p1 = self._pointer(nextCell[1])
|
|
|
|
faceCount = addFace(faceCount, p0, positive=False)
|
|
gc2f(nextCell[0])[fM] += [faceCount]
|
|
faceCount = addFace(faceCount, p1, positive=False)
|
|
gc2f(nextCell[1])[fM] += [faceCount]
|
|
|
|
gc2f(ind)[fP] += [faceCount-1,faceCount]
|
|
|
|
hangingFaces += [faceCount-1, faceCount]
|
|
|
|
return faceCount
|
|
|
|
|
|
def processCellNode(ind, nodeCount):
|
|
|
|
MMM, PMM, MPM, PPM, MMP, PMP, MPP, PPP = range(8)
|
|
p = self._asPointer(ind)
|
|
|
|
xM = self._getNextCell(p, direction=0, positive=False)
|
|
yM = self._getNextCell(p, direction=1, positive=False)
|
|
zM = None if self.dim == 2 else self._getNextCell(p, direction=2, positive=False)
|
|
|
|
xP = self._getNextCell(p, direction=0, positive=True)
|
|
yP = self._getNextCell(p, direction=1, positive=True)
|
|
zP = None if self.dim == 2 else self._getNextCell(p, direction=2, positive=True)
|
|
|
|
if xM is None and yM is None and zM is None:
|
|
nodeCount = addNode(nodeCount, p, loc=[0,0,0])
|
|
gc2n(ind)[MMM] += [nodeCount]
|
|
if yM is None:
|
|
nodeCount = addNode(nodeCount, p, loc=[1,0,0])
|
|
gc2n(ind)[PMM] += [nodeCount]
|
|
if xM is None:
|
|
nodeCount = addNode(nodeCount, p, loc=[0,1,0])
|
|
gc2n(ind)[MPM] += [nodeCount]
|
|
|
|
# Add the next Xface
|
|
if nextCell is None:
|
|
# on the boundary
|
|
pass
|
|
# nodeCount = addFace(nodeCount, p)
|
|
# gc2f(ind)[fP] += [nodeCount]
|
|
elif type(nextCell) in [int, long] and self._onSameLevel(p,nextCell):
|
|
# same sized cell
|
|
pass
|
|
# nodeCount = addFace(nodeCount, p)
|
|
# gc2f(ind)[fP] += [nodeCount]
|
|
# gc2f(nextCell)[fM] += [nodeCount]
|
|
elif type(nextCell) in [int, long] and not self._onSameLevel(p,nextCell):
|
|
# the cell is bigger than me
|
|
pass
|
|
# nodeCount = addFace(nodeCount, p)
|
|
# gc2f(ind)[fP] += [nodeCount]
|
|
# gc2f(nextCell)[fM] += [nodeCount]
|
|
# hangingFaces.append(nodeCount)
|
|
elif type(nextCell) is list:
|
|
# the cell is smaller than me
|
|
pass
|
|
# TODO: ensure that things are balanced.
|
|
# p0 = self._pointer(nextCell[0])
|
|
# p1 = self._pointer(nextCell[1])
|
|
|
|
# nodeCount = addFace(nodeCount, p0, positive=False)
|
|
# gc2f(nextCell[0])[fM] += [nodeCount]
|
|
# nodeCount = addFace(nodeCount, p1, positive=False)
|
|
# gc2f(nextCell[1])[fM] += [nodeCount]
|
|
|
|
# gc2f(ind)[fP] += [nodeCount-1,nodeCount]
|
|
|
|
# hangingFaces += [nodeCount-1, nodeCount]
|
|
|
|
return nodeCount
|
|
|
|
for ii, ind in enumerate(self._sortedInds):
|
|
# c2cn[ind] = ii
|
|
vol.append(np.prod(self._cellH(ind)))
|
|
|
|
# nodeCount = processCellNode(ind, nodeCount)
|
|
|
|
faceXCount = processCellFace(ind, faceXCount, addXFace, hangingFacesX, DIR=0)
|
|
faceYCount = processCellFace(ind, faceYCount, addYFace, hangingFacesY, DIR=1)
|
|
if self.dim == 3:
|
|
faceZCount = processCellFace(ind, faceZCount, addZFace, hangingFacesZ, DIR=2)
|
|
|
|
self._c2f = c2f
|
|
self._area = np.array(areaX + areaY + (areaZ if self.dim == 3 else []))
|
|
self._vol = np.array(vol)
|
|
self._gridFx = np.array(facesX)
|
|
self._gridFy = np.array(facesY)
|
|
self._gridN = np.array(nodes)
|
|
self._hangingFx = hangingFacesX
|
|
self._hangingFy = hangingFacesY
|
|
if self.dim == 3:
|
|
self._gridFz = np.array(facesZ)
|
|
self._nFz = self._gridFz.shape[0]
|
|
self._hangingFz = hangingFacesZ
|
|
|
|
self._nC = len(self._sortedInds)
|
|
self._nN = self._gridN.shape[0]
|
|
self._nFx = self._gridFx.shape[0]
|
|
self._nFy = self._gridFy.shape[0]
|
|
self._nF = self._nFx + self._nFy + (self._nFz if self.dim == 3 else 0)
|
|
|
|
# self.__dirty__ = False
|
|
|
|
|
|
def _deflationMatrix(self, theSet, theHang, theIndex):
|
|
reducedInd = dict() # final reduced index
|
|
ii = 0
|
|
I,J,V = [],[],[]
|
|
for fx in sorted(theSet):
|
|
if theIndex[fx] not in theHang:
|
|
reducedInd[theIndex[fx]] = ii
|
|
I += [theIndex[fx]]
|
|
J += [ii]
|
|
V += [1.0]
|
|
ii += 1
|
|
for hfkey in theHang.keys():
|
|
hf = theHang[hfkey]
|
|
I += [hfkey]*len(hf)
|
|
J += [_[0] for _ in hf]
|
|
V += [_[1] for _ in hf]
|
|
return sp.csr_matrix((V,(I,J)), shape=(len(theSet), len(reducedInd)))
|
|
|
|
@property
|
|
def faceDiv(self):
|
|
# print self._c2f
|
|
if getattr(self, '_faceDiv', None) is None:
|
|
self.number()
|
|
# TODO: Preallocate!
|
|
I, J, V = [], [], []
|
|
PM = [-1,1]*self.dim # plus / minus
|
|
offset = [0,0,self.nFx,self.nFx,self.nFx+self.nFy,self.nFx+self.nFy]
|
|
|
|
for ii, ind in enumerate(self._sortedInds):
|
|
|
|
p = self._pointer(ind)
|
|
w = self._levelWidth(p[-1])
|
|
|
|
if self.dim == 2:
|
|
faces = [
|
|
self._fx2i[self._index([ p[0] , p[1] , p[2]])],
|
|
self._fx2i[self._index([ p[0] + w, p[1] , p[2]])],
|
|
self._fy2i[self._index([ p[0] , p[1] , p[2]])],
|
|
self._fy2i[self._index([ p[0] , p[1] + w, p[2]])]
|
|
]
|
|
elif self.dim == 3:
|
|
faces = [
|
|
self._fx2i[self._index([ p[0] , p[1] , p[2] , p[3]])],
|
|
self._fx2i[self._index([ p[0] + w, p[1] , p[2] , p[3]])],
|
|
self._fy2i[self._index([ p[0] , p[1] , p[2] , p[3]])],
|
|
self._fy2i[self._index([ p[0] , p[1] + w, p[2] , p[3]])],
|
|
self._fz2i[self._index([ p[0] , p[1] , p[2] , p[3]])],
|
|
self._fz2i[self._index([ p[0] , p[1] , p[2] + w, p[3]])]
|
|
]
|
|
|
|
for off, pm, face in zip(offset,PM,faces):
|
|
I += [ii]
|
|
J += [face + off]
|
|
V += [pm]
|
|
|
|
# total number of faces
|
|
tnF = len(self._facesX) + len(self._facesY) + (0 if self.dim == 2 else len(self._facesZ))
|
|
|
|
D = sp.csr_matrix((V,(I,J)), shape=(self.nC, tnF))
|
|
Rlist = [0]*self.dim
|
|
Rlist[0] = self._deflationMatrix(self._facesX, self._hangingFx, self._fx2i)
|
|
Rlist[1] = self._deflationMatrix(self._facesY, self._hangingFy, self._fy2i)
|
|
if self.dim == 3:
|
|
Rlist[2] = self._deflationMatrix(self._facesZ, self._hangingFz, self._fz2i)
|
|
R = sp.block_diag(Rlist)
|
|
# VOL = self.vol
|
|
# S = self.area
|
|
self._faceDiv = D * R
|
|
# self._faceDiv = Utils.sdiag(1.0/VOL)*D*Utils.sdiag(S)
|
|
return self._faceDiv
|
|
|
|
def plotGrid(self, ax=None, showIt=False, grid=True):
|
|
|
|
self.number()
|
|
|
|
axOpts = {'projection':'3d'} if self.dim == 3 else {}
|
|
if ax is None:
|
|
ax = plt.subplot(111, **axOpts)
|
|
else:
|
|
assert isinstance(ax,matplotlib.axes.Axes), "ax must be an Axes!"
|
|
fig = ax.figure
|
|
|
|
if grid:
|
|
for ind in self._sortedInds:
|
|
p = self._asPointer(ind)
|
|
n = self._cellN(p)
|
|
h = self._cellH(p)
|
|
x = [n[0] , n[0] + h[0], n[0] + h[0], n[0] , n[0]]
|
|
y = [n[1] , n[1] , n[1] + h[1], n[1] + h[1], n[1]]
|
|
if self.dim == 2:
|
|
ax.plot(x,y, 'b-')
|
|
elif self.dim == 3:
|
|
ax.plot(x,y, 'b-', zs=[n[2]]*5)
|
|
z = [n[2] + h[2], n[2] + h[2], n[2] + h[2], n[2] + h[2], n[2] + h[2]]
|
|
ax.plot(x,y, 'b-', zs=z)
|
|
sides = [0,0], [h[0],0], [0,h[1]], [h[0],h[1]]
|
|
for s in sides:
|
|
x = [n[0] + s[0], n[0] + s[0]]
|
|
y = [n[1] + s[1], n[1] + s[1]]
|
|
z = [n[2] , n[2] + h[2]]
|
|
ax.plot(x,y, 'b-', zs=z)
|
|
|
|
if self.dim == 2:
|
|
ax.plot(self.gridCC[[0,-1],0], self.gridCC[[0,-1],1], 'ro')
|
|
ax.plot(self.gridCC[:,0], self.gridCC[:,1], 'r.')
|
|
ax.plot(self.gridCC[:,0], self.gridCC[:,1], 'r:')
|
|
ax.plot(self.gridN[:,0], self.gridN[:,1], 'ms')
|
|
ax.plot(self.gridN[self._hangingN.keys(),0], self.gridN[self._hangingN.keys(),1], 'ms', ms=10, mfc='none', mec='m')
|
|
ax.plot(self.gridFx[self._hangingFx.keys(),0], self.gridFx[self._hangingFx.keys(),1], 'gs', ms=10, mfc='none', mec='g')
|
|
ax.plot(self.gridFx[:,0], self.gridFx[:,1], 'g>')
|
|
ax.plot(self.gridFy[self._hangingFy.keys(),0], self.gridFy[self._hangingFy.keys(),1], 'gs', ms=10, mfc='none', mec='g')
|
|
ax.plot(self.gridFy[:,0], self.gridFy[:,1], 'g^')
|
|
elif self.dim == 3:
|
|
ax.plot(self.gridCC[[0,-1],0], self.gridCC[[0,-1],1], 'ro', zs=self.gridCC[[0,-1],2])
|
|
ax.plot(self.gridCC[:,0], self.gridCC[:,1], 'r.', zs=self.gridCC[:,2])
|
|
ax.plot(self.gridCC[:,0], self.gridCC[:,1], 'r:', zs=self.gridCC[:,2])
|
|
|
|
ax.plot(self.gridN[:,0], self.gridN[:,1], 'ms', zs=self.gridN[:,2])
|
|
ax.plot(self.gridN[self._hangingN.keys(),0], self.gridN[self._hangingN.keys(),1], 'ms', ms=10, mfc='none', mec='m', zs=self.gridN[self._hangingN.keys(),2])
|
|
for key in self._hangingN.keys():
|
|
for hf in self._hangingN[key]:
|
|
ind = [key, hf[0]]
|
|
ax.plot(self.gridN[ind,0], self.gridN[ind,1], 'm:', zs=self.gridN[ind,2])
|
|
|
|
ax.plot(self.gridFx[:,0], self.gridFx[:,1], 'g>', zs=self.gridFx[:,2])
|
|
ax.plot(self.gridFx[self._hangingFx.keys(),0], self.gridFx[self._hangingFx.keys(),1], 'gs', ms=10, mfc='none', mec='g', zs=self.gridFx[self._hangingFx.keys(),2])
|
|
for key in self._hangingFx.keys():
|
|
for hf in self._hangingFx[key]:
|
|
ind = [key, hf[0]]
|
|
ax.plot(self.gridFx[ind,0], self.gridFx[ind,1], 'g:', zs=self.gridFx[ind,2])
|
|
|
|
ax.plot(self.gridFy[:,0], self.gridFy[:,1], 'g^', zs=self.gridFy[:,2])
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ax.plot(self.gridFy[self._hangingFy.keys(),0], self.gridFy[self._hangingFy.keys(),1], 'gs', ms=10, mfc='none', mec='g', zs=self.gridFy[self._hangingFy.keys(),2])
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for key in self._hangingFy.keys():
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for hf in self._hangingFy[key]:
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ind = [key, hf[0]]
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ax.plot(self.gridFy[ind,0], self.gridFy[ind,1], 'g:', zs=self.gridFy[ind,2])
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|
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ax.plot(self.gridFz[:,0], self.gridFz[:,1], 'g^', zs=self.gridFz[:,2])
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ax.plot(self.gridFz[self._hangingFz.keys(),0], self.gridFz[self._hangingFz.keys(),1], 'gs', ms=10, mfc='none', mec='g', zs=self.gridFz[self._hangingFz.keys(),2])
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for key in self._hangingFz.keys():
|
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for hf in self._hangingFz[key]:
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ind = [key, hf[0]]
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ax.plot(self.gridFz[ind,0], self.gridFz[ind,1], 'g:', zs=self.gridFz[ind,2])
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|
|
|
|
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ax.plot(self.gridEx[:,0], self.gridEx[:,1], 'k>', zs=self.gridEx[:,2])
|
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ax.plot(self.gridEx[self._hangingEx.keys(),0], self.gridEx[self._hangingEx.keys(),1], 'ks', ms=10, mfc='none', mec='k', zs=self.gridEx[self._hangingEx.keys(),2])
|
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for key in self._hangingEx.keys():
|
|
for hf in self._hangingEx[key]:
|
|
ind = [key, hf[0]]
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ax.plot(self.gridEx[ind,0], self.gridEx[ind,1], 'k:', zs=self.gridEx[ind,2])
|
|
|
|
|
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ax.plot(self.gridEy[:,0], self.gridEy[:,1], 'k<', zs=self.gridEy[:,2])
|
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ax.plot(self.gridEy[self._hangingEy.keys(),0], self.gridEy[self._hangingEy.keys(),1], 'ks', ms=10, mfc='none', mec='k', zs=self.gridEy[self._hangingEy.keys(),2])
|
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for key in self._hangingEy.keys():
|
|
for hf in self._hangingEy[key]:
|
|
ind = [key, hf[0]]
|
|
ax.plot(self.gridEy[ind,0], self.gridEy[ind,1], 'k:', zs=self.gridEy[ind,2])
|
|
|
|
ax.plot(self.gridEz[:,0], self.gridEz[:,1], 'k^', zs=self.gridEz[:,2])
|
|
ax.plot(self.gridEz[self._hangingEz.keys(),0], self.gridEz[self._hangingEz.keys(),1], 'ks', ms=10, mfc='none', mec='k', zs=self.gridEz[self._hangingEz.keys(),2])
|
|
for key in self._hangingEz.keys():
|
|
for hf in self._hangingEz[key]:
|
|
ind = [key, hf[0]]
|
|
ax.plot(self.gridEz[ind,0], self.gridEz[ind,1], 'k:', zs=self.gridEz[ind,2])
|
|
|
|
|
|
ax.axis('equal')
|
|
if showIt:plt.show()
|
|
|
|
|
|
|
|
if __name__ == '__main__':
|
|
|
|
|
|
def function(xc):
|
|
r = xc - np.r_[0.5,0.5]
|
|
dist = np.sqrt(r.dot(r))
|
|
# if dist < 0.05:
|
|
# return 5
|
|
if dist < 0.1:
|
|
return 4
|
|
if dist < 0.3:
|
|
return 3
|
|
if dist < 1.0:
|
|
return 2
|
|
else:
|
|
return 0
|
|
|
|
# T = Tree([[(1,8)],[(1,8)],[(1,8)]],levels=3)
|
|
T = Tree([[(1,16)],[(1,16)]],levels=4)
|
|
T.refine(lambda xc:1)
|
|
T._refineCell([0,0,1])
|
|
T._refineCell([8,8,1])
|
|
# T._refineCell([4,4,4,1])
|
|
|
|
ax = plt.subplot(211)
|
|
ax.spy(T.faceDiv)
|
|
|
|
|
|
|
|
# R = deflationMatrix(T._facesX, T._hangingFx, T._fx2i)
|
|
# print R
|
|
|
|
ax = plt.subplot(212)
|
|
# ax.spy(R)
|
|
|
|
# ax = plt.subplot(313)
|
|
# ax.spy(T.faceDiv[:,:T.nFx] * R)
|
|
|
|
|
|
|
|
T.plotGrid(ax=ax)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
# print T.nN
|
|
|
|
plt.show()
|
|
|