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authordos-reis <gdr@axiomatics.org>2011-09-20 06:29:26 +0000
committerdos-reis <gdr@axiomatics.org>2011-09-20 06:29:26 +0000
commit255be06767355e3b41acd75990c6b90270b8f2bd (patch)
tree0a032d40d7cb2213e206d70beb23dc74ccf4a230 /src/algebra/d01Package.spad.pamphlet
parent12c856f9901ef3d6d82fb99855ecdf3e0b91484b (diff)
downloadopen-axiom-255be06767355e3b41acd75990c6b90270b8f2bd.tar.gz
* algebra/asp.spad.pamphlet: Remove.
* algebra/c02.spad.pamphlet: Likewise. * algebra/c05.spad.pamphlet: Likewise. * algebra/c06.spad.pamphlet: Likewise. * algebra/d01.spad.pamphlet: Likewise. * algebra/d02.spad.pamphlet: Likewise. * algebra/d03.spad.pamphlet: Likewise. * algebra/e01.spad.pamphlet: Likewise. * algebra/e02.spad.pamphlet: Likewise. * algebra/e04.spad.pamphlet: Likewise. * algebra/f01.spad.pamphlet: Likewise. * algebra/f02.spad.pamphlet: Likewise. * algebra/f04.spad.pamphlet: Likewise. * algebra/f07.spad.pamphlet: Likewise. * algebra/s.spad.pamphlet: Likewise. * algebra/d01Package.spad.pamphlet: Likewise. * algebra/d02Package.spad.pamphlet: Likewise. * algebra/d03Package.spad.pamphlet: Likewise. * algebra/e04Package.spad.pamphlet: Likewise. * algebra/d01agents.spad.pamphlet: Likewise. * algebra/d01routine.spad.pamphlet: Likewise. * algebra/d01transform.spad.pamphlet: Likewise. * algebra/d01weights.spad.pamphlet: Likewise. * algebra/d02agents.spad.pamphlet: Likewise. * algebra/d02routine.spad.pamphlet: Likewise. * algebra/d03agents.spad.pamphlet: Likewise. * algebra/d03routine.spad.pamphlet: Likewise. * algebra/e04agents.spad.pamphlet: Likewise. * algebra/e04routine.spad.pamphlet: Likewise.
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-\documentclass{article}
-\usepackage{open-axiom}
-\begin{document}
-\title{\$SPAD/src/algebra d01Package.spad}
-\author{Brian Dupee}
-\maketitle
-\begin{abstract}
-\end{abstract}
-\eject
-\tableofcontents
-\eject
-\section{package INTPACK AnnaNumericalIntegrationPackage}
-<<package INTPACK AnnaNumericalIntegrationPackage>>=
-)abbrev package INTPACK AnnaNumericalIntegrationPackage
-++ Author: Brian Dupee
-++ Date Created: August 1994
-++ Date Last Updated: December 1997
-++ Basic Operations: integrate, measure
-++ Related Constructors: Result, RoutinesTable
-++ Also See:
-++ AMS Classifications:
-++ Keywords:
-++ References:
-++ Description:
-++ \axiomType{AnnaNumericalIntegrationPackage} is a \axiom{package}
-++ of functions for the \axiom{category} \axiomType{NumericalIntegrationCategory}
-++ with \axiom{measure}, and \axiom{integrate}.
-EDF ==> Expression DoubleFloat
-DF ==> DoubleFloat
-EF ==> Expression Float
-F ==> Float
-INT ==> Integer
-SOCDF ==> Segment OrderedCompletion DoubleFloat
-OCDF ==> OrderedCompletion DoubleFloat
-SBOCF ==> SegmentBinding OrderedCompletion Float
-LSOCF ==> List Segment OrderedCompletion Float
-SOCF ==> Segment OrderedCompletion Float
-OCF ==> OrderedCompletion Float
-LS ==> List Symbol
-S ==> Symbol
-LST ==> List String
-ST ==> String
-RT ==> RoutinesTable
-NIA ==> Record(var:S, fn:EDF, range:SOCDF, abserr:DF, relerr:DF)
-MDNIA ==> Record(fn:EDF,range:List SOCDF,abserr:DF,relerr:DF)
-IFL ==> List(Record(ifail:Integer,instruction:String))
-Entry ==> Record(chapter:String, type:String, domainName: String,
- defaultMin:F, measure:F, failList:IFL, explList:List String)
-Measure ==> Record(measure:F, name:ST, explanations:LST, extra:Result)
-
-
-AnnaNumericalIntegrationPackage(): with
-
- integrate: (EF,SOCF,F,F,RT) -> Result
- ++ integrate(exp, a..b, epsrel, routines) is a top level ANNA function
- ++ to integrate an expression, {\tt exp}, over a given range {\tt a}
- ++ to {\tt b} to the required absolute and relative accuracy using
- ++ the routines available in the RoutinesTable provided.
- ++
- ++ It iterates over the \axiom{domains} of
- ++ \axiomType{NumericalIntegrationCategory}
- ++ to get the name and other
- ++ relevant information of the the (domain of the) numerical
- ++ routine likely to be the most appropriate,
- ++ i.e. have the best \axiom{measure}.
- ++
- ++ It then performs the integration of the given expression
- ++ on that \axiom{domain}.
- integrate: NumericalIntegrationProblem -> Result
- ++ integrate(IntegrationProblem) is a top level ANNA function
- ++ to integrate an expression over a given range or ranges
- ++ to the required absolute and relative accuracy.
- ++
- ++ It iterates over the \axiom{domains} of
- ++ \axiomType{NumericalIntegrationCategory} to get the name and other
- ++ relevant information of the the (domain of the) numerical
- ++ routine likely to be the most appropriate,
- ++ i.e. have the best \axiom{measure}.
- ++
- ++ It then performs the integration of the given expression
- ++ on that \axiom{domain}.
-
- integrate: (EF,SOCF,F,F) -> Result
- ++ integrate(exp, a..b, epsabs, epsrel) is a top level ANNA function
- ++ to integrate an expression, {\tt exp}, over a given range {\tt a}
- ++ to {\tt b} to the required absolute and relative accuracy.
- ++
- ++ It iterates over the \axiom{domains} of
- ++ \axiomType{NumericalIntegrationCategory} to get the name and other
- ++ relevant information of the the (domain of the) numerical
- ++ routine likely to be the most appropriate,
- ++ i.e. have the best \axiom{measure}.
- ++
- ++ It then performs the integration of the given expression
- ++ on that \axiom{domain}.
-
- integrate: (EF,SOCF,F) -> Result
- ++ integrate(exp, a..b, epsrel) is a top level ANNA
- ++ function to integrate an expression, {\tt exp}, over a given
- ++ range {\tt a} to {\tt b} to the required relative accuracy.
- ++
- ++ It iterates over the \axiom{domains} of
- ++ \axiomType{NumericalIntegrationCategory} to get the name and other
- ++ relevant information of the the (domain of the) numerical
- ++ routine likely to be the most appropriate,
- ++ i.e. have the best \axiom{measure}.
- ++
- ++ It then performs the integration of the given expression
- ++ on that \axiom{domain}.
- ++
- ++ If epsrel = 0, a default absolute accuracy is used.
-
- integrate: (EF,SOCF) -> Result
- ++ integrate(exp, a..b) is a top
- ++ level ANNA function to integrate an expression, {\tt exp},
- ++ over a given range {\tt a} to {\tt b}.
- ++
- ++ It iterates over the \axiom{domains} of
- ++ \axiomType{NumericalIntegrationCategory} to get the name and other
- ++ relevant information of the the (domain of the) numerical
- ++ routine likely to be the most appropriate,
- ++ i.e. have the best \axiom{measure}.
- ++
- ++ It then performs the integration of the given expression
- ++ on that \axiom{domain}.
- ++
- ++ Default values for the absolute and relative error are used.
-
- integrate:(EF,LSOCF) -> Result
- ++ integrate(exp, [a..b,c..d,...]) is a top
- ++ level ANNA function to integrate a multivariate expression, {\tt exp},
- ++ over a given set of ranges.
- ++
- ++ It iterates over the \axiom{domains} of
- ++ \axiomType{NumericalIntegrationCategory} to get the name and other
- ++ relevant information of the the (domain of the) numerical
- ++ routine likely to be the most appropriate,
- ++ i.e. have the best \axiom{measure}.
- ++
- ++ It then performs the integration of the given expression
- ++ on that \axiom{domain}.
- ++
- ++ Default values for the absolute and relative error are used.
-
- integrate:(EF,LSOCF,F) -> Result
- ++ integrate(exp, [a..b,c..d,...], epsrel) is a top
- ++ level ANNA function to integrate a multivariate expression, {\tt exp},
- ++ over a given set of ranges to the required relative
- ++ accuracy.
- ++
- ++ It iterates over the \axiom{domains} of
- ++ \axiomType{NumericalIntegrationCategory} to get the name and other
- ++ relevant information of the the (domain of the) numerical
- ++ routine likely to be the most appropriate,
- ++ i.e. have the best \axiom{measure}.
- ++
- ++ It then performs the integration of the given expression
- ++ on that \axiom{domain}.
- ++
- ++ If epsrel = 0, a default absolute accuracy is used.
-
- integrate:(EF,LSOCF,F,F) -> Result
- ++ integrate(exp, [a..b,c..d,...], epsabs, epsrel) is a top
- ++ level ANNA function to integrate a multivariate expression, {\tt exp},
- ++ over a given set of ranges to the required absolute and relative
- ++ accuracy.
- ++
- ++ It iterates over the \axiom{domains} of
- ++ \axiomType{NumericalIntegrationCategory} to get the name and other
- ++ relevant information of the the (domain of the) numerical
- ++ routine likely to be the most appropriate,
- ++ i.e. have the best \axiom{measure}.
- ++
- ++ It then performs the integration of the given expression
- ++ on that \axiom{domain}.
-
- integrate:(EF,LSOCF,F,F,RT) -> Result
- ++ integrate(exp, [a..b,c..d,...], epsabs, epsrel, routines) is a top
- ++ level ANNA function to integrate a multivariate expression, {\tt exp},
- ++ over a given set of ranges to the required absolute and relative
- ++ accuracy, using the routines available in the RoutinesTable provided.
- ++
- ++ It iterates over the \axiom{domains} of
- ++ \axiomType{NumericalIntegrationCategory} to get the name and other
- ++ relevant information of the the (domain of the) numerical
- ++ routine likely to be the most appropriate,
- ++ i.e. have the best \axiom{measure}.
- ++
- ++ It then performs the integration of the given expression
- ++ on that \axiom{domain}.
-
- measure:NumericalIntegrationProblem -> Measure
- ++ measure(prob) is a top level ANNA function for identifying the most
- ++ appropriate numerical routine for solving the numerical integration
- ++ problem defined by \axiom{prob}.
- ++
- ++ It calls each \axiom{domain} of \axiom{category}
- ++ \axiomType{NumericalIntegrationCategory} in turn to calculate all measures
- ++ and returns the best
- ++ i.e. the name of the most appropriate domain and any other relevant
- ++ information.
- measure:(NumericalIntegrationProblem,RT) -> Measure
- ++ measure(prob,R) is a top level ANNA function for identifying the most
- ++ appropriate numerical routine from those in the routines table
- ++ provided for solving the numerical integration
- ++ problem defined by \axiom{prob}.
- ++
- ++ It calls each \axiom{domain} listed in \axiom{R} of \axiom{category}
- ++ \axiomType{NumericalIntegrationCategory} in turn to calculate all measures
- ++ and returns the best
- ++ i.e. the name of the most appropriate domain and any other relevant
- ++ information.
- integrate:(EF,SBOCF,ST) -> Union(Result,"failed")
- ++ integrate(exp, x = a..b, "numerical") is a top level ANNA function to
- ++ integrate an expression, {\tt exp}, over a given range, {\tt a}
- ++ to {\tt b}.
- ++
- ++ It iterates over the \axiom{domains} of
- ++ \axiomType{NumericalIntegrationCategory} to get the name and other
- ++ relevant information of the the (domain of the) numerical
- ++ routine likely to be the most appropriate,
- ++ i.e. have the best \axiom{measure}.
- ++
- ++ It then performs the integration of the given expression
- ++ on that \axiom{domain}.\newline
- ++
- ++ Default values for the absolute and relative error are used.
- ++
- ++ It is an error of the last argument is not {\tt "numerical"}.
- integrate:(EF,SBOCF,S) -> Union(Result,"failed")
- ++ integrate(exp, x = a..b, numerical) is a top level ANNA function to
- ++ integrate an expression, {\tt exp}, over a given range, {\tt a}
- ++ to {\tt b}.
- ++
- ++ It iterates over the \axiom{domains} of
- ++ \axiomType{NumericalIntegrationCategory} to get the name and other
- ++ relevant information of the the (domain of the) numerical
- ++ routine likely to be the most appropriate,
- ++ i.e. have the best \axiom{measure}.
- ++
- ++ It then performs the integration of the given expression
- ++ on that \axiom{domain}.\newline
- ++
- ++ Default values for the absolute and relative error are used.
- ++
- ++ It is an error if the last argument is not {\tt numerical}.
-
- == add
-
- zeroMeasure: Measure -> Result
- scriptedVariables?: MDNIA -> Boolean
- preAnalysis:(Union(nia:NIA,mdnia:MDNIA),RT) -> RT
- measureSpecific:(ST,RT,Union(nia:NIA,mdnia:MDNIA)) -> Record(measure:F,explanations:LST,extra:Result)
- changeName:(Result,ST) -> Result
- recoverAfterFail:(Union(nia:NIA,mdnia:MDNIA),RT,Measure,INT,Result) -> Record(a:Result,b:Measure)
- better?:(Result,Result) -> Boolean
- integrateConstant:(EF,SOCF) -> Result
- integrateConstantList: (EF,LSOCF) -> Result
- integrateArgs:(NumericalIntegrationProblem,RT) -> Result
- integrateSpecific:(Union(nia:NIA,mdnia:MDNIA),ST,Result) -> Result
-
- import ExpertSystemToolsPackage
-
- integrateConstantList(exp:EF,ras:LSOCF):Result ==
- c:OCF := ((retract(exp)@F)$EF)::OCF
- b := [hi(j)-lo(j) for j in ras]
- c := c*reduce((#1)*(#2),b)
- a := coerce(c)$AnyFunctions1(OCF)
- text := coerce("Constant Function")$AnyFunctions1(ST)
- construct([[result@S,a],[method@S,text]])$Result
-
- integrateConstant(exp:EF,ra:SOCF):Result ==
- c := (retract(exp)@F)$EF
- r:OCF := (c::OCF)*(hi(ra)-lo(ra))
- a := coerce(r)$AnyFunctions1(OCF)
- text := coerce("Constant Function")$AnyFunctions1(ST)
- construct([[result@S,a],[method@S,text]])$Result
-
- zeroMeasure(m:Measure):Result ==
- a := coerce(0$DF)$AnyFunctions1(DF)
- text := coerce("Constant Function")$AnyFunctions1(String)
- r := construct([[result@Symbol,a],[method@Symbol,text]])$Result
- concat(measure2Result m,r)$ExpertSystemToolsPackage
-
- scriptedVariables?(mdnia:MDNIA):Boolean ==
- vars:List Symbol := variables(mdnia.fn)$EDF
- var1 := first(vars)$(List Symbol)
- not scripted?(var1) => false
- name1 := name(var1)$Symbol
- for i in 2..# vars repeat
- not ((scripted?(vars.i)$Symbol) and (name1 = name(vars.i)$Symbol)) =>
- return false
- true
-
- preAnalysis(args:Union(nia:NIA,mdnia:MDNIA),t:RT):RT ==
- import RT
- r:RT := selectIntegrationRoutines t
- args case nia =>
- arg:NIA := args.nia
- rangeIsFinite(arg)$d01AgentsPackage case finite =>
- selectFiniteRoutines r
- selectNonFiniteRoutines r
- selectMultiDimensionalRoutines r
-
- changeName(ans:Result,name:ST):Result ==
- sy:S := coerce(name "Answer")$S
- anyAns:Any := coerce(ans)$AnyFunctions1(Result)
- construct([[sy,anyAns]])$Result
-
- measureSpecific(name:ST,R:RT,args:Union(nia:NIA,mdnia:MDNIA)):
- Record(measure:F,explanations:ST,extra:Result) ==
- args case nia =>
- arg:NIA := args.nia
- name = "d01ajfAnnaType" => measure(R,arg)$d01ajfAnnaType
- name = "d01akfAnnaType" => measure(R,arg)$d01akfAnnaType
- name = "d01alfAnnaType" => measure(R,arg)$d01alfAnnaType
- name = "d01amfAnnaType" => measure(R,arg)$d01amfAnnaType
- name = "d01anfAnnaType" => measure(R,arg)$d01anfAnnaType
- name = "d01apfAnnaType" => measure(R,arg)$d01apfAnnaType
- name = "d01aqfAnnaType" => measure(R,arg)$d01aqfAnnaType
- name = "d01asfAnnaType" => measure(R,arg)$d01asfAnnaType
- name = "d01TransformFunctionType" =>
- measure(R,arg)$d01TransformFunctionType
- error("measureSpecific","invalid type name: " name)$ErrorFunctions
- args case mdnia =>
- arg2:MDNIA := args.mdnia
- name = "d01gbfAnnaType" => measure(R,arg2)$d01gbfAnnaType
- name = "d01fcfAnnaType" => measure(R,arg2)$d01fcfAnnaType
- error("measureSpecific","invalid type name: " name)$ErrorFunctions
- error("measureSpecific","invalid type name")$ErrorFunctions
-
- measure(a:NumericalIntegrationProblem,R:RT):Measure ==
- args:Union(nia:NIA,mdnia:MDNIA) := retract(a)$NumericalIntegrationProblem
- sofar := 0$F
- best := "none" :: ST
- routs := copy R
- routs := preAnalysis(args,routs)
- empty?(routs)$RT =>
- error("measure", "no routines found")$ErrorFunctions
- rout := inspect(routs)$RT
- e := retract(rout.entry)$AnyFunctions1(Entry)
- meth:LST := ["Trying " e.type " integration routines"]
- ext := empty()$Result
- for i in 1..# routs repeat
- rout := extract!(routs)$RT
- e := retract(rout.entry)$AnyFunctions1(Entry)
- n := e.domainName
- if e.defaultMin > sofar then
- m := measureSpecific(n,R,args)
- if m.measure > sofar then
- sofar := m.measure
- best := n
- ext := concat(m.extra,ext)$ExpertSystemToolsPackage
- str:LST := [string(rout.key)$S "measure: " outputMeasure(m.measure)
- " - " m.explanations]
- else
- str:LST := [string(rout.key)$S " is no better than other routines"]
- meth := append(meth,str)$LST
- [sofar,best,meth,ext]
-
- measure(a:NumericalIntegrationProblem):Measure ==
- measure(a,routines()$RT)
-
- integrateSpecific(args:Union(nia:NIA,mdnia:MDNIA),n:ST,ex:Result):Result ==
- args case nia =>
- arg:NIA := args.nia
- n = "d01ajfAnnaType" => numericalIntegration(arg,ex)$d01ajfAnnaType
- n = "d01TransformFunctionType" =>
- numericalIntegration(arg,ex)$d01TransformFunctionType
- n = "d01amfAnnaType" => numericalIntegration(arg,ex)$d01amfAnnaType
- n = "d01apfAnnaType" => numericalIntegration(arg,ex)$d01apfAnnaType
- n = "d01aqfAnnaType" => numericalIntegration(arg,ex)$d01aqfAnnaType
- n = "d01alfAnnaType" => numericalIntegration(arg,ex)$d01alfAnnaType
- n = "d01akfAnnaType" => numericalIntegration(arg,ex)$d01akfAnnaType
- n = "d01anfAnnaType" => numericalIntegration(arg,ex)$d01anfAnnaType
- n = "d01asfAnnaType" => numericalIntegration(arg,ex)$d01asfAnnaType
- error("integrateSpecific","invalid type name: " n)$ErrorFunctions
- args case mdnia =>
- arg2:MDNIA := args.mdnia
- n = "d01gbfAnnaType" => numericalIntegration(arg2,ex)$d01gbfAnnaType
- n = "d01fcfAnnaType" => numericalIntegration(arg2,ex)$d01fcfAnnaType
- error("integrateSpecific","invalid type name: " n)$ErrorFunctions
- error("integrateSpecific","invalid type name: " n)$ErrorFunctions
-
- better?(r:Result,s:Result):Boolean ==
- a1 := search("abserr"::S,r)$Result
- a1 case "failed" => false
- abserr1 := retract(a1)$AnyFunctions1(DF)
- negative?(abserr1) => false
- a2 := search("abserr"::S,s)$Result
- a2 case "failed" => true
- abserr2 := retract(a2)$AnyFunctions1(DF)
- negative?(abserr2) => true
- (abserr1 < abserr2) -- true if r.abserr better than s.abserr
-
- recoverAfterFail(n:Union(nia:NIA,mdnia:MDNIA),routs:RT,m:Measure,iint:INT,
- r:Result):Record(a:Result,b:Measure) ==
- bestName := m.name
- while positive?(iint) repeat
- routineName := m.name
- s := recoverAfterFail(routs,routineName(1..6),iint)$RoutinesTable
- s case "failed" => iint := 0
- if s = "changeEps" then
- nn := n.nia
- zero?(nn.abserr) =>
- nn.abserr := 1.0e-8 :: DF
- m := measure(n::NumericalIntegrationProblem,routs)
- zero?(m.measure) => iint := 0
- r := integrateSpecific(n,m.name,m.extra)
- iint := 0
- rn := routineName(1..6)
- buttVal := getButtonValue(rn,"functionEvaluations")$AttributeButtons
- if (s = "incrFunEvals") and (buttVal < 0.8) then
- increase(rn,"functionEvaluations")$AttributeButtons
- if s = "increase tolerance" then
- (n.nia).relerr := (n.nia).relerr*(10.0::DF)
- if s = "decrease tolerance" then
- (n.nia).relerr := (n.nia).relerr/(10.0::DF)
- fl := coerce(s)$AnyFunctions1(ST)
- flrec:Record(key:S,entry:Any):=[failure@S,fl]
- m2 := measure(n::NumericalIntegrationProblem,routs)
- zero?(m2.measure) => iint := 0
- r2:Result := integrateSpecific(n,m2.name,m2.extra)
- better?(r,r2) =>
- m.name := m2.name
- insert!(flrec,r)$Result
- bestName := m2.name
- m := m2
- insert!(flrec,r2)$Result
- r := concat(r2,changeName(r,routineName))$ExpertSystemToolsPackage
- iany := search(ifail@S,r2)$Result
- iany case "failed" => iint := 0
- iint := retract(iany)$AnyFunctions1(INT)
- m.name := bestName
- [r,m]
-
- integrateArgs(prob:NumericalIntegrationProblem,t:RT):Result ==
- args:Union(nia:NIA,mdnia:MDNIA) := retract(prob)$NumericalIntegrationProblem
- routs := copy(t)$RT
- if args case mdnia then
- arg := args.mdnia
- v := (# variables(arg.fn))
- not scriptedVariables?(arg) =>
- error("MultiDimensionalNumericalIntegrationPackage",
- "invalid variable names")$ErrorFunctions
- (v ~= # arg.range)@Boolean =>
- error("MultiDimensionalNumericalIntegrationPackage",
- "number of variables do not match number of ranges")$ErrorFunctions
- m := measure(prob,routs)
- zero?(m.measure) => zeroMeasure m
- r := integrateSpecific(args,m.name,m.extra)
- iany := search(ifail@S,r)$Result
- iint := 0$INT
- if (iany case Any) then
- iint := retract(iany)$AnyFunctions1(INT)
- if positive?(iint) then
- tu:Record(a:Result,b:Measure) := recoverAfterFail(args,routs,m,iint,r)
- r := tu.a
- m := tu.b
- r := concat(measure2Result m,r)$ExpertSystemToolsPackage
- n := m.name
- nn:ST :=
- (# n > 14) => "d01transform"
- n(1..6)
- expl := getExplanations(routs,nn)$RoutinesTable
- expla := coerce(expl)$AnyFunctions1(LST)
- explaa:Record(key:Symbol,entry:Any) := ["explanations"::Symbol,expla]
- r := concat(construct([explaa]),r)
- args case nia =>
- att := showAttributes(args.nia)$IntegrationFunctionsTable
- att case "failed" => r
- concat(att2Result att,r)$ExpertSystemToolsPackage
- r
-
- integrate(args:NumericalIntegrationProblem):Result ==
- integrateArgs(args,routines()$RT)
-
- integrate(exp:EF,ra:SOCF,epsabs:F,epsrel:F,r:RT):Result ==
- Var:LS := variables(exp)$EF
- empty?(Var)$LS => integrateConstant(exp,ra)
- args:NIA := [first(Var)$LS,ef2edf exp,socf2socdf ra,f2df epsabs,f2df epsrel]
- integrateArgs(args::NumericalIntegrationProblem,r)
-
- integrate(exp:EF,ra:SOCF,epsabs:F,epsrel:F):Result ==
- integrate(exp,ra,epsabs,epsrel,routines()$RT)
-
- integrate(exp:EF,ra:SOCF,err:F):Result ==
- positive?(err)$F => integrate(exp,ra,0$F,err)
- integrate(exp,ra,1.0E-5,err)
-
- integrate(exp:EF,ra:SOCF):Result == integrate(exp,ra,0$F,1.0E-5)
-
- integrate(exp:EF,sb:SBOCF, st:ST) ==
- st = "numerical" => integrate(exp,segment sb)
- "failed"
-
- integrate(exp:EF,sb:SBOCF, s:S) ==
- s = (numerical::Symbol) => integrate(exp,segment sb)
- "failed"
-
- integrate(exp:EF,ra:LSOCF,epsabs:F,epsrel:F,r:RT):Result ==
- vars := variables(exp)$EF
- empty?(vars)$LS => integrateConstantList(exp,ra)
- args:MDNIA := [ef2edf exp,convert ra,f2df epsabs,f2df epsrel]
- integrateArgs(args::NumericalIntegrationProblem,r)
-
- integrate(exp:EF,ra:LSOCF,epsabs:F,epsrel:F):Result ==
- integrate(exp,ra,epsabs,epsrel,routines()$RT)
-
- integrate(exp:EF,ra:LSOCF,epsrel:F):Result ==
- zero? epsrel => integrate(exp,ra,1.0e-6,epsrel)
- integrate(exp,ra,0$F,epsrel)
-
- integrate(exp:EF,ra:LSOCF):Result == integrate(exp,ra,1.0e-4)
-
-@
-\section{License}
-<<license>>=
---Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
---All rights reserved.
---
---Redistribution and use in source and binary forms, with or without
---modification, are permitted provided that the following conditions are
---met:
---
--- - Redistributions of source code must retain the above copyright
--- notice, this list of conditions and the following disclaimer.
---
--- - Redistributions in binary form must reproduce the above copyright
--- notice, this list of conditions and the following disclaimer in
--- the documentation and/or other materials provided with the
--- distribution.
---
--- - Neither the name of The Numerical ALgorithms Group Ltd. nor the
--- names of its contributors may be used to endorse or promote products
--- derived from this software without specific prior written permission.
---
---THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
---IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
---TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
---PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
---OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
---EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
---PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
---PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
---LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
---NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
---SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-@
-<<*>>=
-<<license>>
-
-<<package INTPACK AnnaNumericalIntegrationPackage>>
-@
-\eject
-\begin{thebibliography}{99}
-\bibitem{1} nothing
-\end{thebibliography}
-\end{document}