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diff --git a/src/algebra/d02Package.spad.pamphlet b/src/algebra/d02Package.spad.pamphlet deleted file mode 100644 index d346bab9..00000000 --- a/src/algebra/d02Package.spad.pamphlet +++ /dev/null @@ -1,457 +0,0 @@ -\documentclass{article} -\usepackage{open-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} |