Status: Valid
Owner: ----
Labels: Type-Defect Priority-Medium Cache
New issue 3205 by [email protected]: Apply proper caching for the Bell
incomplete polynomials (of the second kind).
http://code.google.com/p/sympy/issues/detail?id=3205
Bell incomplete polynomials [2], [3] are implemented in [1] as a method
`_bell_incomplete_poly` of the class `bell(Function)`
This function is recursive.
1. First problem
Now this function is cached partially , since the method "__new__" of base
class "Function" is wrapped by @cacheit.
But this common wrapper cached the whole list of arguments.
X = symbols("x:101"); Y = symbols("y:101");
bell(100, 3, X)
2 sec
bell(100, 3, X)
0 sec
bell(100, 3, Y)
Again 2 sec
It is needed that regardless of X and Y arguments, internal coefficients of
bell(100, 3, ...) themselves would be cached.
2. Second problem.
As this function is recursive then for e.g. bell(500, 3,...) the stack will
overflow, if the cache is empty initially.
To avoid this the enveloping from recursive to plane circle must be used.
For ordinary recursion poly and numbers the "@recurrence_memo" is used, but
Bell incomplete poly has 2D recursion, so either "@assoc_recurrence_memo"
must be used or another special method.
Notes:
Possibly, the algorithm
May be the lower level seems to be a perspective direction (for this
recursive method), with some internal structure.
2-d kind Bell polynomials, as yo can see, have property that the "order" of
monomials (if we weight-ed the x_1, x_2 variables) are the same
$j_1+2j_2+3j_2+\dotsb=n$. So the structure is sparse. But may be exists
another combinatorial method
[1] sympy/functions/combinatorial/numbers.py
[2] http://en.wikipedia.org/wiki/Bell_polynomials
[3] http://mathworld.wolfram.com/BellPolynomial.html
--
You received this message because you are subscribed to the Google Groups
"sympy-issues" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sympy-issues?hl=en.
