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)abbrev domain D01FCFA d01fcfAnnaType
++ Author: Brian Dupee
++ Date Created: March 1994
++ Date Last Updated: December 1997
++ References:
++ Dupe95 Using Computer Algebra to Choose and Apply Numerical Routines
++ Dewa92 Using Computer Algebra to Select Numerical Algorithms
++ Description:
++ \axiomType{d01fcfAnnaType} is a domain of
++ \axiomType{NumericalIntegrationCategory}
++ for the NAG routine D01FCF, a numerical integration routine which can
++ handle multi-dimensional quadrature over a finite region.  The 
++ function \axiomFun{measure} measures the usefulness of the routine D01GBF
++ for the given problem.  The function \axiomFun{numericalIntegration}
++ performs the integration by using \axiomType{NagIntegrationPackage}.

d01fcfAnnaType() : SIG == CODE where

  EF2  ==> ExpressionFunctions2
  EDF  ==> Expression DoubleFloat
  LDF  ==> List DoubleFloat
  SDF  ==> Stream DoubleFloat
  DF  ==> DoubleFloat
  FI  ==> Fraction Integer
  EFI  ==> Expression Fraction Integer
  SOCDF  ==> Segment OrderedCompletion DoubleFloat
  NIA  ==> Record(var:Symbol,fn:EDF,range:SOCDF,abserr:DF,relerr:DF)
  MDNIA  ==> Record(fn:EDF,range:List SOCDF,abserr:DF,relerr:DF)
  INT  ==> Integer
  BOP  ==> BasicOperator
  S  ==> Symbol
  ST  ==> String
  LST  ==> List String
  RT  ==> RoutinesTable

  SIG ==> NumericalIntegrationCategory 

  CODE ==> Result add

    Rep:=Result
    import Rep, d01AgentsPackage, NagIntegrationPackage

    measure(R:RT,args:MDNIA) ==
      ext:Result := empty()$Result
      segs := args.range
      vars := variables(args.fn)$EDF
      for i in 1..# vars repeat
        nia:NIA := [vars.i,args.fn,segs.i,args.abserr,args.relerr]
        not rangeIsFinite(nia) case finite => return
          [0.0,"d01fcf is not a suitable routine for infinite integrals",ext]
      [getMeasure(R,d01fcf@S)$RT, "Recommended is d01fcf", ext]

    numericalIntegration(args:MDNIA,hints:Result) ==
      import Integer
      segs := args.range
      dim := # segs
      err := args.relerr
      low:Matrix DF := matrix([[getlo(segs.i) for i in 1..dim]])$(Matrix DF)
      high:Matrix DF := matrix([[gethi(segs.i) for i in 1..dim]])$(Matrix DF)
      b:Float:=getButtonValue("d01fcf","functionEvaluations")$AttributeButtons
      a:Float:= exp(1.1513*(1.0/(2.0*(1.0-b))))
      alpha:INT := 2**dim+2*dim**2+2*dim+1
      d:Float := max(1.e-3,nthRoot(convert(err)@Float,4))$Float
      minpts:INT := (fEvals := wholePart(a))*wholePart(alpha::Float/d)
      maxpts:INT := 5*minpts
      lenwrk:INT := (dim+2)*(1+(33*fEvals))
      ArgsFn := map(x+->convert(x)$DF,args.fn)$EF2(DF,Float)
      f : Union(fn:FileName,fp:Asp4(FUNCTN)) := [retract(ArgsFn)$Asp4(FUNCTN)]
      out:Result := d01fcf(dim,low,high,maxpts,err,lenwrk,minpts,-1,f)
      changeName(finval@Symbol,result@Symbol,out)