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rtable_eval - evaluate the entries of an rtable under certain conditions
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Calling Sequence
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rtable_eval(A,inplace)
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Parameters
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A
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rtable object
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inplace
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-
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(optional) BooleanOpt(inplace); specifies if output overwrites input
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Description
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The rtable_eval(A) command, where A is an Array, Matrix, or Vector, returns either a copy of A, or the original input A depending if evaluation is needed. It also changes the way elements are evaluated when the returned rtable is subsequently referenced.
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Evaluation is needed provided the following two conditions are met. Firstly, eval(A[i],1) <> eval(A[i]) for a given element ![A[i]](/support/helpjp/helpview.aspx?si=4806/file00502/math60.png) . Secondly, full evaluation must have been applied to A prior to calling rtable_eval(A).
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Applying eval() to an rtable returns immediately without changing the given rtable. This is unlike a list, which maps eval() onto each element and returns a copy. Evaluation of rtable elements is normally deferred until elements are referenced. If the same elements are repeatedly referenced, evaluation of those elements is also repeated. The rtable_eval(A) command provides a way to evaluate every element once so that future references can bypass evaluation, without necessarily making a copy.
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Applying rtable_eval to any rtable with a hardware datatype always returns the input rtable unchanged.
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Applying rtable_eval to any rtable with a user defined indexing-function always returns the input rtable unchanged.
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The result of rtable_eval is an rtable with the same attributes as the input rtable, including shape, storage, and datatype.
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If the optional second argument, inplace is specified, the input rtable is changed if necessary. No copy is made.
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Thread Safety
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The rtable_eval command is thread-safe as of Maple 15.
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Examples
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Create an rtable that prints something when an element is referenced.
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p := proc(i) printf("eval element %d\n",i); end proc:
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![V := Vector(['p(1)', 'p(2)', 'p(3)'])](/support/helpjp/helpview.aspx?si=4806/file00502/math116.png)
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Reference the first element 4 times. This generates 4 eval()'s.
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f := proc(V) V[1]; V[1]; V[1]; V[1]; end proc:
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eval element 1
eval element 1
eval element 1
eval element 1
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Use rtable_eval() to evaluate every element initially. Subsequent references will already contain the results of evaluating, so V[1] does not print anything.
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f := proc(VV) local V; V := rtable_eval(VV); V[1]; V[1]; V[1]; V[1]; end proc:
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eval element 1
eval element 3
eval element 2
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Generate a Matrix containing polynomials that are expensive to evaluate.
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F := proc(n) option remember; if n <= 2 then n else x*F(n-1)+F(n-2); end if; end proc:
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Compare the cost of an O(N^3) operation with and without rtable_eval().
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dostuff1 := proc(M) local i, j, k, y;
for i from 1 to op([1,1],M) do
for j from 1 to op([1,2],M) do
for k from 1 to op([1,2],M) do
y := M[i,j];
end do;
end do;
end do;
end proc:
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dostuff2 := proc(M) local i, j, k, y;
rtable_eval(M,'inplace');
for i from 1 to op([1,1],M) do
for j from 1 to op([1,2],M) do
for k from 1 to op([1,2],M) do
y := M[i,j];
end do;
end do;
end do;
end proc:
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