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leastSquaresCellGradVariable.py
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leastSquaresCellGradVariable.py
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#!/usr/bin/env python
## -*-Pyth-*-
# ###################################################################
# FiPy - Python-based finite volume PDE solver
#
# FILE: "leastSquaresCellGradVariable.py"
#
# Author: Jonathan Guyer <guyer@nist.gov>
# Author: Daniel Wheeler <daniel.wheeler@nist.gov>
# Author: James Warren <jwarren@nist.gov>
# mail: NIST
# www: http://www.ctcms.nist.gov/fipy/
#
# ========================================================================
# This software was developed at the National Institute of Standards
# and Technology by employees of the Federal Government in the course
# of their official duties. Pursuant to title 17 Section 105 of the
# United States Code this software is not subject to copyright
# protection and is in the public domain. FiPy is an experimental
# system. NIST assumes no responsibility whatsoever for its use by
# other parties, and makes no guarantees, expressed or implied, about
# its quality, reliability, or any other characteristic. We would
# appreciate acknowledgement if the software is used.
#
# This software can be redistributed and/or modified freely
# provided that any derivative works bear some notice that they are
# derived from it, and any modified versions bear some notice that
# they have been modified.
# ========================================================================
# See the file "license.terms" for information on usage and redistribution
# of this file, and for a DISCLAIMER OF ALL WARRANTIES.
#
# ###################################################################
##
__docformat__ = 'restructuredtext'
__all__ = []
from fipy.variables.cellVariable import CellVariable
from fipy.tools import numerix
from fipy.tools.decorators import getsetDeprecated
class _LeastSquaresCellGradVariable(CellVariable):
"""
Look at CellVariable.leastSquarseGrad for documentation
"""
def __init__(self, var, name = ''):
CellVariable.__init__(self, mesh=var.mesh, name=name, rank=var.rank + 1)
self.var = self._requires(var)
@getsetDeprecated
def _getNeighborValue(self):
return self._neighborValue
@property
def _neighborValue(self):
return numerix.take(numerix.array(self.var), self.mesh._cellToCellIDs)
def _calcValue(self):
cellToCellDistances = self.mesh._cellToCellDistances
cellNormals = self.mesh._cellNormals
neighborValue = self._neighborValue
value = numerix.array(self.var)
cellDistanceNormals = cellToCellDistances * cellNormals
N = self.mesh.numberOfCells
M = self.mesh._maxFacesPerCell
D = self.mesh.dim
mat = numerix.zeros((D, D, M, N), 'd')
## good god! numpy.outer should have an axis argument!!!
for i in range(D):
for j in range(D):
mat[i,j] = cellDistanceNormals[i] * cellDistanceNormals[j]
mat = numerix.sum(mat, axis=2)
vec = numerix.array(numerix.sum((neighborValue - value) * cellDistanceNormals, axis=1))
if D == 1:
vec[0] = vec[0] / mat[0, 0]
elif D == 2:
divisor = mat[0,0] * mat[1,1] - mat[0,1] * mat[1,0]
gradx = (vec[0] * mat[1,1] - vec[1] * mat[1,0]) / divisor
grady = (vec[1] * mat[0,0] - vec[0] * mat[0,1]) / divisor
vec[0] = gradx
vec[1] = grady
else:
## very stuppy! numerix.linalg.solve should have an axis argument!!!
for i in range(N):
vec[...,i] = numerix.linalg.solve(mat[...,i],vec[...,i])
return vec