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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 | )abbrev category NUMINT NumericalIntegrationCategory
++ Author: Brian Dupee
++ Date Created: February 1994
++ Date Last Updated: March 1996
++ Description:
++ \axiomType{NumericalIntegrationCategory} is the \axiom{category} for
++ describing the set of Numerical Integration \axiom{domains} with
++ \axiomFun{measure} and \axiomFun{numericalIntegration}.
NumericalIntegrationCategory() : Category == SIG where
EDFE ==> Expression DoubleFloat
SOCDFE ==> Segment OrderedCompletion DoubleFloat
DFE ==> DoubleFloat
NIAE ==> Record(var:Symbol,fn:EDFE,range:SOCDFE,abserr:DFE,relerr:DFE)
MDNIAE ==> Record(fn:EDFE,range:List SOCDFE,abserr:DFE,relerr:DFE)
SIG ==> SetCategory with
measure : (RoutinesTable,NIAE) -> _
Record(measure:Float,explanations:String,extra:Result)
++ measure(R,args) calculates an estimate of the ability of a particular
++ method to solve a problem.
++
++ This method may be either a specific NAG routine or a strategy (such
++ as transforming the function from one which is difficult to one which
++ is easier to solve).
++
++ It will call whichever agents are needed to perform analysis on the
++ problem in order to calculate the measure. There is a parameter,
++ labelled \axiom{sofar}, which would contain the best compatibility
++ found so far.
numericalIntegration : (NIAE, Result) -> Result
++ numericalIntegration(args,hints) performs the integration of the
++ function given the strategy or method returned by \axiomFun{measure}.
measure : (RoutinesTable,MDNIAE) -> _
Record(measure:Float,explanations:String,extra:Result)
++ measure(R,args) calculates an estimate of the ability of a particular
++ method to solve a problem.
++
++ This method may be either a specific NAG routine or a strategy (such
++ as transforming the function from one which is difficult to one which
++ is easier to solve).
++
++ It will call whichever agents are needed to perform analysis on the
++ problem in order to calculate the measure. There is a parameter,
++ labelled \axiom{sofar}, which would contain the best compatibility
++ found so far.
numericalIntegration : (MDNIAE, Result) -> Result
++ numericalIntegration(args,hints) performs the integration of the
++ function given the strategy or method returned by \axiomFun{measure}.
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