UFL Specification and User Manual 0.3 - FEniCS Project

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UFL Specification and User Manual 0.3Martin S. Alnæs, Anders LoggSubclasses of Terminal represent atomic quantities which terminate the expressiontree, e.g. they have no subexpressions. Subclasses of Operatorrepresent operations on one or more other expressions, which may usually beExpr subclasses of arbitrary type. Different Operators may have restrictionson some properties of their arguments.All the types mentioned here are conceptually immutable, i.e. they shouldnever be modified over the course of their entire lifetime. When a modifiedexpression, measure, integral, or form is needed, a new instance must becreated, possibly sharing some data with the old one. Since the shared datais also immutable, sharing can cause no problems.4.2 General properties of expressionsAny UFL expression has certain properties, defined by functions that everyExpr subclass must implement. In the following, u represents an arbitraryUFL expression, i.e. an instance of an arbitrary Expr subclass.4.2.1 operandsu.operands() returns a tuple with all the operands of u, which should allbe Expr instances.4.2.2 reconstructu.reconstruct(operands) returns a new Expr instance representing thesame operation as u but with other operands. Terminal objects may simplyreturn self since all Expr instance are immutable. An important invariantis that u.reconstruct(u.operands()) == u.76
UFL Specification and User Manual 0.3Martin S. Alnæs, Anders Logg4.2.3 cellu.cell() returns the first Cell instance found in u. It is currently assumedinUFLthatnotwodifferentcellsareusedinasingleform. Notallexpressiondefine a cell, in which case this returns None and u is spatially constant. Notethat this property is used in some algorithms.4.2.4 shapeu.shape() returns a tuple of integers, which is the tensor shape of u.4.2.5 free indicesu.free indices() returns a tuple of Index objects, which are the unassigned,free indices of u.4.2.6 index dimensionsu.index dimensions() returns a dict mapping from each Index instancein u.free indices() to the integer dimension of the value space each indexcan range over.4.2.7 str(u)str(u) returns a human-readable string representation of u.4.2.8 repr(u)repr(u)returnsaPythonstringrepresentationof u,suchthateval(repr(u))== u holds in Python.77
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UFL Specification and User Manual 0
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ContentsAbout this manual 111 Intro
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2.8.10 skew . . . . . . . . . . . .
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4 Internal Representation Details 7
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B Installation 97B.1 Installing fro
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Page 93: Bibliography[1] M. Alnæs and K.-A.
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