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# Written by Robert C. Kirby
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# Copyright 2005 by The University of Chicago
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# Distributed under the LGPL license
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# This work is partially supported by the US Department of Energy
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# under award number DE-FG02-04ER25650
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# Last modified 10 May 2005 by RCK
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import functional, Numeric
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#class DualBasis( functional.FunctionalList ):
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class DualBasis( object ):
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'''Creates the basis P\' which is dual to some space P.
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ls is a list of functionals or a FunctionalList.
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entity_ids is a dictionary mapping each mesh component to
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the associated vertex numbers. The keys are integers for
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the topological dimension, and each value is itself a
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dictionary mapping the id of each entity of that topological
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dimension to a list of ids for functionals associated with that
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entity. E.g. for linear Lagrange elements on triangles, entity_ids
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{ 0: {0: [0], 1: [1], 2: [2]}, \
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1: {0: [] , 2: [], 2: []}, \
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since there are three vertices (dimension 0),
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each with one node each, and there are no nodes on the edges or
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interior. Similarly, cubics would look like:
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{ 0: {0: [0], 1:[1], 2:[2]}, \
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1: {0: [3,4], 1:[5,6], 2:[7,8]}, \
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num_reps is used to indicate a vector-valued space where
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entity_ids is used for the first component and then
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replicated num_reps-1 times additional times.
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def __init__( self, node_set , entity_ids , num_reps = 1 ):
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self.node_set = node_set
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self.entity_ids = entity_ids
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self.num_reps = num_reps
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# self.mat is the matrix whose rows are the vectors
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# associated with each functional
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# Now, all the dual basis can be applied to a single
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# item by a matrix-vector multiply
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def get_functional_set( self ): return self.node_set
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def getNodeIDs(self, dim):
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return self.entity_ids[ dim ].values()
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raise RuntimeError, "Illegal dimension for this dual basis"
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FIAT/dualbasis.py
