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Re: How to remove unneeded constraints

  • To: mathgroup at
  • Subject: [mg87977] Re: How to remove unneeded constraints
  • From: Albert Retey <awnl at>
  • Date: Mon, 21 Apr 2008 06:39:33 -0400 (EDT)
  • References: <fueeo7$b82$>


> The problem I am working on is a pretty large problem, which I am solving by dividing it into a lot of subproblems.
> As such, I have a large list of constraints that apply to the entire problem, but are not relevant for each individual subproblem.
> This becomes a problem when I use Refine, as it takes a very long time when you have a lot of conditions, even though the conditions don't pertain to the problem. Example:
> In[25]:= Table[Timing@Refine[p>q,Map[Subscript[x,#]>0&,Range[i]]],{i,1000,5000,1000}]
> Out[25]= {{0.547,p>q},{1.797,p>q},{3.875,p>q},{8.594,p>q},{10.468,p>q}}
> And it only gets worse.
> However, for each individual call to Refine I make, I only need a small subset of the total constraints.
> So what I want to do is something like this:
> expr = some expression of n different variables;
> cond = DeleteCases[totalConstraints, all cases which do not contain a variable from expr];
> result = Refine[expr,cond];
> I have no idea how to construct a pattern powerful enough to do what is required for the DeleteCases call, though.
> All of the variables are of the form Subscript[s,_,_,_] or Subscript[b,_,_] and the conditions can also contain expressions of several variables.
> I'd be most grateful for any help. Thank you.

here is a toy problem I used to test the code below, hope it isn't to 

expr = Total@
   Table[Random[]*ToExpression["x" <> ToString[i]]^i, {i, 1, 100, 5}]

conditions =
  Table[ToExpression["x" <> ToString[i - 1]] < Random[] <
    ToExpression["x" <> ToString[i]], {i, 1, 100}]

This will construct a pattern that matches all variables in expr (maybe 
you need some fine tuning to extract only those symbols which represent 
variables in your problem):

varpattern = Alternatives @@ Cases[expr, _Symbol,Infinity]

Now you can use that pattern to extract the relevant conditions:

DeleteCases[conditions, _?(FreeQ[#, varpattern] &)]

If you haven't seen this kind of pattern yet, search for PatternTest in 
the documentation.

In cases where a pattern where such a PatternTest using a pure function 
is necessary, I usually prefere to use Select instead of 
DeleteCases/Cases, but in this case it isn't much clearer or shorter:

Select[conditions, MemberQ[#, varpattern, Infinity] &]



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