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diff --git a/src/algebra/d02Package.spad.pamphlet b/src/algebra/d02Package.spad.pamphlet new file mode 100644 index 00000000..35d581e9 --- /dev/null +++ b/src/algebra/d02Package.spad.pamphlet @@ -0,0 +1,457 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/algebra d02Package.spad} +\author{Brian Dupee} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\section{package ODEPACK AnnaOrdinaryDifferentialEquationPackage} +<<package ODEPACK AnnaOrdinaryDifferentialEquationPackage>>= +)abbrev package ODEPACK AnnaOrdinaryDifferentialEquationPackage +++ Author: Brian Dupee +++ Date Created: February 1995 +++ Date Last Updated: December 1997 +++ Basic Operations: solve, measure +++ Description: +++ \axiomType{AnnaOrdinaryDifferentialEquationPackage} is a \axiom{package} +++ of functions for the \axiom{category} \axiomType{OrdinaryDifferentialEquationsSolverCategory} +++ with \axiom{measure}, and \axiom{solve}. +++ +EDF ==> Expression DoubleFloat +LDF ==> List DoubleFloat +MDF ==> Matrix DoubleFloat +DF ==> DoubleFloat +FI ==> Fraction Integer +EFI ==> Expression Fraction Integer +SOCDF ==> Segment OrderedCompletion DoubleFloat +VEDF ==> Vector Expression DoubleFloat +VEF ==> Vector Expression Float +EF ==> Expression Float +LF ==> List Float +F ==> Float +VDF ==> Vector DoubleFloat +VMF ==> Vector MachineFloat +MF ==> MachineFloat +LS ==> List Symbol +ST ==> String +LST ==> List String +INT ==> Integer +RT ==> RoutinesTable +ODEA ==> Record(xinit:DF,xend:DF,fn:VEDF,yinit:LDF,intvals:LDF,_ + g:EDF,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:LST) +Measure ==> Record(measure:F,name:String, explanations:List String) + +AnnaOrdinaryDifferentialEquationPackage(): with + solve:(NumericalODEProblem) -> Result + ++ solve(odeProblem) is a top level ANNA function to solve numerically a + ++ system of ordinary differential equations i.e. equations for the + ++ derivatives Y[1]'..Y[n]' defined in terms of X,Y[1]..Y[n], together + ++ with starting values for X and Y[1]..Y[n] (called the initial + ++ conditions), a final value of X, an accuracy requirement and any + ++ intermediate points at which the result is required. + ++ + ++ It iterates over the \axiom{domains} of + ++ \axiomType{OrdinaryDifferentialEquationsSolverCategory} + ++ 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}. + ++ + ++ The method used to perform the numerical + ++ process will be one of the routines contained in the NAG numerical + ++ Library. The function predicts the likely most effective routine + ++ by checking various attributes of the system of ODE's and calculating + ++ a measure of compatibility of each routine to these attributes. + ++ + ++ It then calls the resulting `best' routine. + solve:(NumericalODEProblem,RT) -> Result + ++ solve(odeProblem,R) is a top level ANNA function to solve numerically a + ++ system of ordinary differential equations i.e. equations for the + ++ derivatives Y[1]'..Y[n]' defined in terms of X,Y[1]..Y[n], together + ++ with starting values for X and Y[1]..Y[n] (called the initial + ++ conditions), a final value of X, an accuracy requirement and any + ++ intermediate points at which the result is required. + ++ + ++ It iterates over the \axiom{domains} of + ++ \axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in + ++ the table of routines \axiom{R} 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}. + ++ + ++ The method used to perform the numerical + ++ process will be one of the routines contained in the NAG numerical + ++ Library. The function predicts the likely most effective routine + ++ by checking various attributes of the system of ODE's and calculating + ++ a measure of compatibility of each routine to these attributes. + ++ + ++ It then calls the resulting `best' routine. + solve:(VEF,F,F,LF) -> Result + ++ solve(f,xStart,xEnd,yInitial) is a top level ANNA function to solve numerically a + ++ system of ordinary differential equations i.e. equations for the + ++ derivatives Y[1]'..Y[n]' defined in terms of X,Y[1]..Y[n], together + ++ with a starting value for X and Y[1]..Y[n] (called the initial + ++ conditions) and a final value of X. A default value + ++ is used for the accuracy requirement. + ++ + ++ It iterates over the \axiom{domains} of + ++ \axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in + ++ the table of routines \axiom{R} 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}. + ++ + ++ The method used to perform the numerical + ++ process will be one of the routines contained in the NAG numerical + ++ Library. The function predicts the likely most effective routine + ++ by checking various attributes of the system of ODE's and calculating + ++ a measure of compatibility of each routine to these attributes. + ++ + ++ It then calls the resulting `best' routine. + solve:(VEF,F,F,LF,F) -> Result + ++ solve(f,xStart,xEnd,yInitial,tol) is a top level ANNA function to solve + ++ numerically a system of ordinary differential equations, \axiom{f}, i.e. + ++ equations for the derivatives Y[1]'..Y[n]' defined in terms + ++ of X,Y[1]..Y[n] from \axiom{xStart} to \axiom{xEnd} with the initial + ++ values for Y[1]..Y[n] (\axiom{yInitial}) to a tolerance \axiom{tol}. + ++ + ++ It iterates over the \axiom{domains} of + ++ \axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in + ++ the table of routines \axiom{R} 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}. + ++ + ++ The method used to perform the numerical + ++ process will be one of the routines contained in the NAG numerical + ++ Library. The function predicts the likely most effective routine + ++ by checking various attributes of the system of ODE's and calculating + ++ a measure of compatibility of each routine to these attributes. + ++ + ++ It then calls the resulting `best' routine. + solve:(VEF,F,F,LF,EF,F) -> Result + ++ solve(f,xStart,xEnd,yInitial,G,tol) is a top level ANNA function to solve + ++ numerically a system of ordinary differential equations, \axiom{f}, i.e. + ++ equations for the derivatives Y[1]'..Y[n]' defined in terms + ++ of X,Y[1]..Y[n] from \axiom{xStart} to \axiom{xEnd} with the initial + ++ values for Y[1]..Y[n] (\axiom{yInitial}) to a tolerance \axiom{tol}. + ++ The calculation will stop if the function G(X,Y[1],..,Y[n]) evaluates to zero before + ++ X = xEnd. + ++ + ++ It iterates over the \axiom{domains} of + ++ \axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in + ++ the table of routines \axiom{R} 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}. + ++ + ++ The method used to perform the numerical + ++ process will be one of the routines contained in the NAG numerical + ++ Library. The function predicts the likely most effective routine + ++ by checking various attributes of the system of ODE's and calculating + ++ a measure of compatibility of each routine to these attributes. + ++ + ++ It then calls the resulting `best' routine. + solve:(VEF,F,F,LF,LF,F) -> Result + ++ solve(f,xStart,xEnd,yInitial,intVals,tol) is a top level ANNA function to solve + ++ numerically a system of ordinary differential equations, \axiom{f}, i.e. + ++ equations for the derivatives Y[1]'..Y[n]' defined in terms + ++ of X,Y[1]..Y[n] from \axiom{xStart} to \axiom{xEnd} with the initial + ++ values for Y[1]..Y[n] (\axiom{yInitial}) to a tolerance \axiom{tol}. + ++ The values of Y[1]..Y[n] will be output for the values of X in + ++ \axiom{intVals}. + ++ + ++ It iterates over the \axiom{domains} of + ++ \axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in + ++ the table of routines \axiom{R} 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}. + ++ + ++ The method used to perform the numerical + ++ process will be one of the routines contained in the NAG numerical + ++ Library. The function predicts the likely most effective routine + ++ by checking various attributes of the system of ODE's and calculating + ++ a measure of compatibility of each routine to these attributes. + ++ + ++ It then calls the resulting `best' routine. + solve:(VEF,F,F,LF,EF,LF,F) -> Result + ++ solve(f,xStart,xEnd,yInitial,G,intVals,tol) is a top level ANNA function to solve + ++ numerically a system of ordinary differential equations, \axiom{f}, i.e. + ++ equations for the derivatives Y[1]'..Y[n]' defined in terms + ++ of X,Y[1]..Y[n] from \axiom{xStart} to \axiom{xEnd} with the initial + ++ values for Y[1]..Y[n] (\axiom{yInitial}) to a tolerance \axiom{tol}. + ++ The values of Y[1]..Y[n] will be output for the values of X in + ++ \axiom{intVals}. The calculation will stop if the function + ++ G(X,Y[1],..,Y[n]) evaluates to zero before X = xEnd. + ++ + ++ It iterates over the \axiom{domains} of + ++ \axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in + ++ the table of routines \axiom{R} 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}. + ++ + ++ The method used to perform the numerical + ++ process will be one of the routines contained in the NAG numerical + ++ Library. The function predicts the likely most effective routine + ++ by checking various attributes of the system of ODE's and calculating + ++ a measure of compatibility of each routine to these attributes. + ++ + ++ It then calls the resulting `best' routine. + solve:(VEF,F,F,LF,EF,LF,F,F) -> Result + ++ solve(f,xStart,xEnd,yInitial,G,intVals,epsabs,epsrel) is a top level ANNA function to solve + ++ numerically a system of ordinary differential equations, \axiom{f}, i.e. + ++ equations for the derivatives Y[1]'..Y[n]' defined in terms + ++ of X,Y[1]..Y[n] from \axiom{xStart} to \axiom{xEnd} with the initial + ++ values for Y[1]..Y[n] (\axiom{yInitial}) to an absolute error + ++ requirement \axiom{epsabs} and relative error \axiom{epsrel}. + ++ The values of Y[1]..Y[n] will be output for the values of X in + ++ \axiom{intVals}. The calculation will stop if the function + ++ G(X,Y[1],..,Y[n]) evaluates to zero before X = xEnd. + ++ + ++ It iterates over the \axiom{domains} of + ++ \axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in + ++ the table of routines \axiom{R} 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}. + ++ + ++ The method used to perform the numerical + ++ process will be one of the routines contained in the NAG numerical + ++ Library. The function predicts the likely most effective routine + ++ by checking various attributes of the system of ODE's and calculating + ++ a measure of compatibility of each routine to these attributes. + ++ + ++ It then calls the resulting `best' routine. + measure:(NumericalODEProblem) -> Measure + ++ measure(prob) is a top level ANNA function for identifying the most + ++ appropriate numerical routine from those in the routines table + ++ provided for solving the numerical ODE + ++ problem defined by \axiom{prob}. + ++ + ++ It calls each \axiom{domain} of \axiom{category} + ++ \axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to + ++ calculate all measures and returns the best i.e. the name of + ++ the most appropriate domain and any other relevant information. + ++ It predicts the likely most effective NAG numerical + ++ Library routine to solve the input set of ODEs + ++ by checking various attributes of the system of ODEs and calculating + ++ a measure of compatibility of each routine to these attributes. + measure:(NumericalODEProblem,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 ODE + ++ problem defined by \axiom{prob}. + ++ + ++ It calls each \axiom{domain} listed in \axiom{R} of \axiom{category} + ++ \axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to + ++ calculate all measures and returns the best i.e. the name of + ++ the most appropriate domain and any other relevant information. + ++ It predicts the likely most effective NAG numerical + ++ Library routine to solve the input set of ODEs + ++ by checking various attributes of the system of ODEs and calculating + ++ a measure of compatibility of each routine to these attributes. + + == add + + import ODEA,NumericalODEProblem + + f2df:F -> DF + ef2edf:EF -> EDF + preAnalysis:(ODEA,RT) -> RT + zeroMeasure:Measure -> Result + measureSpecific:(ST,RT,ODEA) -> Record(measure:F,explanations:ST) + solveSpecific:(ODEA,ST) -> Result + changeName:(Result,ST) -> Result + recoverAfterFail:(ODEA,RT,Measure,Integer,Result) -> Record(a:Result,b:Measure) + + f2df(f:F):DF == (convert(f)@DF)$F + + ef2edf(f:EF):EDF == map(f2df,f)$ExpressionFunctions2(F,DF) + + preAnalysis(args:ODEA,t:RT):RT == + rt := selectODEIVPRoutines(t)$RT + if positive?(# variables(args.g)) then + changeMeasure(rt,d02bbf@Symbol,getMeasure(rt,d02bbf@Symbol)*0.8) + if positive?(# args.intvals) then + changeMeasure(rt,d02bhf@Symbol,getMeasure(rt,d02bhf@Symbol)*0.8) + rt + + zeroMeasure(m:Measure):Result == + a := coerce(0$F)$AnyFunctions1(F) + text := coerce("Zero Measure")$AnyFunctions1(ST) + r := construct([[result@Symbol,a],[method@Symbol,text]])$Result + concat(measure2Result m,r)$ExpertSystemToolsPackage + + measureSpecific(name:ST,R:RT,ode:ODEA):Record(measure:F,explanations:ST) == + name = "d02bbfAnnaType" => measure(R,ode)$d02bbfAnnaType + name = "d02bhfAnnaType" => measure(R,ode)$d02bhfAnnaType + name = "d02cjfAnnaType" => measure(R,ode)$d02cjfAnnaType + name = "d02ejfAnnaType" => measure(R,ode)$d02ejfAnnaType + error("measureSpecific","invalid type name: " name)$ErrorFunctions + + measure(Ode:NumericalODEProblem,R:RT):Measure == + ode:ODEA := retract(Ode)$NumericalODEProblem + sofar := 0$F + best := "none" :: ST + routs := copy R + routs := preAnalysis(ode,routs) + empty?(routs)$RT => + error("measure", "no routines found")$ErrorFunctions + rout := inspect(routs)$RT + e := retract(rout.entry)$AnyFunctions1(Entry) + meth := empty()$LST + 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,ode) + if m.measure > sofar then + sofar := m.measure + best := n + str:LST := [string(rout.key)$Symbol "measure: " + outputMeasure(m.measure)$ExpertSystemToolsPackage " - " + m.explanations] + else + str := [string(rout.key)$Symbol " is no better than other routines"] + meth := append(meth,str)$LST + [sofar,best,meth] + + measure(ode:NumericalODEProblem):Measure == measure(ode,routines()$RT) + + solveSpecific(ode:ODEA,n:ST):Result == + n = "d02bbfAnnaType" => ODESolve(ode)$d02bbfAnnaType + n = "d02bhfAnnaType" => ODESolve(ode)$d02bhfAnnaType + n = "d02cjfAnnaType" => ODESolve(ode)$d02cjfAnnaType + n = "d02ejfAnnaType" => ODESolve(ode)$d02ejfAnnaType + error("solveSpecific","invalid type name: " n)$ErrorFunctions + + changeName(ans:Result,name:ST):Result == + sy:Symbol := coerce(name "Answer")$Symbol + anyAns:Any := coerce(ans)$AnyFunctions1(Result) + construct([[sy,anyAns]])$Result + + recoverAfterFail(ode:ODEA,routs:RT,m:Measure,iint:Integer,r:Result): + Record(a:Result,b:Measure) == + while positive?(iint) repeat + routineName := m.name + s := recoverAfterFail(routs,routineName(1..6),iint)$RT + s case "failed" => iint := 0 + if s = "increase tolerance" then + ode.relerr := ode.relerr*(10.0::DF) + ode.abserr := ode.abserr*(10.0::DF) + if s = "decrease tolerance" then + ode.relerr := ode.relerr/(10.0::DF) + ode.abserr := ode.abserr/(10.0::DF) + (s = "no action")@Boolean => iint := 0 + fl := coerce(s)$AnyFunctions1(ST) + flrec:Record(key:Symbol,entry:Any):=[failure@Symbol,fl] + m2 := measure(ode::NumericalODEProblem,routs) + zero?(m2.measure) => iint := 0 + r2:Result := solveSpecific(ode,m2.name) + m := m2 + insert!(flrec,r2)$Result + r := concat(r2,changeName(r,routineName))$ExpertSystemToolsPackage + iany := search(ifail@Symbol,r2)$Result + iany case "failed" => iint := 0 + iint := retract(iany)$AnyFunctions1(Integer) + [r,m] + + solve(Ode:NumericalODEProblem,t:RT):Result == + ode:ODEA := retract(Ode)$NumericalODEProblem + routs := copy(t)$RT + m := measure(Ode,routs) + zero?(m.measure) => zeroMeasure m + r := solveSpecific(ode,n := m.name) + iany := search(ifail@Symbol,r)$Result + iint := 0$Integer + if (iany case Any) then + iint := retract(iany)$AnyFunctions1(Integer) + if positive?(iint) then + tu:Record(a:Result,b:Measure) := recoverAfterFail(ode,routs,m,iint,r) + r := tu.a + m := tu.b + r := concat(measure2Result m,r)$ExpertSystemToolsPackage + expl := getExplanations(routs,n(1..6))$RoutinesTable + expla := coerce(expl)$AnyFunctions1(LST) + explaa:Record(key:Symbol,entry:Any) := ["explanations"::Symbol,expla] + r := concat(construct([explaa]),r) + iflist := showIntensityFunctions(ode)$ODEIntensityFunctionsTable + iflist case "failed" => r + concat(iflist2Result iflist, r)$ExpertSystemToolsPackage + + solve(ode:NumericalODEProblem):Result == solve(ode,routines()$RT) + + solve(f:VEF,xStart:F,xEnd:F,yInitial:LF,G:EF,intVals:LF,epsabs:F,epsrel:F):Result == + d:ODEA := [f2df xStart,f2df xEnd,vector([ef2edf e for e in members f])$VEDF, + [f2df i for i in yInitial], [f2df j for j in intVals], + ef2edf G,f2df epsabs,f2df epsrel] + solve(d::NumericalODEProblem,routines()$RT) + + solve(f:VEF,xStart:F,xEnd:F,yInitial:LF,G:EF,intVals:LF,tol:F):Result == + solve(f,xStart,xEnd,yInitial,G,intVals,tol,tol) + + solve(f:VEF,xStart:F,xEnd:F,yInitial:LF,intVals:LF,tol:F):Result == + solve(f,xStart,xEnd,yInitial,1$EF,intVals,tol) + + solve(f:VEF,xStart:F,xEnd:F,y:LF,G:EF,tol:F):Result == + solve(f,xStart,xEnd,y,G,empty()$LF,tol) + + solve(f:VEF,xStart:F,xEnd:F,yInitial:LF,tol:F):Result == + solve(f,xStart,xEnd,yInitial,1$EF,empty()$LF,tol) + + solve(f:VEF,xStart:F,xEnd:F,yInitial:LF):Result == solve(f,xStart,xEnd,yInitial,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 ODEPACK AnnaOrdinaryDifferentialEquationPackage>> +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} |