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diff --git a/src/algebra/d03Package.spad.pamphlet b/src/algebra/d03Package.spad.pamphlet deleted file mode 100644 index 3cb2a692..00000000 --- a/src/algebra/d03Package.spad.pamphlet +++ /dev/null @@ -1,307 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{\$SPAD/src/algebra d03Package.spad} -\author{Brian Dupee} -\maketitle -\begin{abstract} -\end{abstract} -\eject -\tableofcontents -\eject -\section{package PDEPACK AnnaPartialDifferentialEquationPackage} -<<package PDEPACK AnnaPartialDifferentialEquationPackage>>= -)abbrev package PDEPACK AnnaPartialDifferentialEquationPackage -++ Author: Brian Dupee -++ Date Created: June 1996 -++ Date Last Updated: December 1997 -++ Basic Operations: -++ Description: AnnaPartialDifferentialEquationPackage is an uncompleted -++ package for the interface to NAG PDE routines. It has been realised that -++ a new approach to solving PDEs will need to be created. -++ -LEDF ==> List Expression DoubleFloat -EDF ==> Expression DoubleFloat -LDF ==> List DoubleFloat -MDF ==> Matrix DoubleFloat -DF ==> DoubleFloat -LEF ==> List Expression Float -EF ==> Expression Float -MEF ==> Matrix Expression Float -LF ==> List Float -F ==> Float -LS ==> List Symbol -ST ==> String -LST ==> List String -INT ==> Integer -NNI ==> NonNegativeInteger -RT ==> RoutinesTable -PDEC ==> Record(start:DF, finish:DF, grid:NNI, boundaryType:INT, - dStart:MDF, dFinish:MDF) -PDEB ==> Record(pde:LEDF, constraints:List PDEC, - f:List LEDF, st:ST, tol:DF) -IFL ==> List(Record(ifail:INT,instruction:ST)) -Entry ==> Record(chapter:ST, type:ST, domainName: ST, - defaultMin:F, measure:F, failList:IFL, explList:LST) -Measure ==> Record(measure:F,name:ST, explanations:LST) - -AnnaPartialDifferentialEquationPackage(): with - solve:(NumericalPDEProblem) -> Result - ++ solve(PDEProblem) is a top level ANNA function to solve numerically a system - ++ of partial differential equations. - ++ - ++ 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 PDE's and calculating - ++ a measure of compatibility of each routine to these attributes. - ++ - ++ It then calls the resulting `best' routine. - ++ - ++ ** At the moment, only Second Order Elliptic Partial Differential - ++ Equations are solved ** - solve:(NumericalPDEProblem,RT) -> Result - ++ solve(PDEProblem,routines) is a top level ANNA function to solve numerically a system - ++ of partial differential equations. - ++ - ++ 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 PDE's and calculating - ++ a measure of compatibility of each routine to these attributes. - ++ - ++ It then calls the resulting `best' routine. - ++ - ++ ** At the moment, only Second Order Elliptic Partial Differential - ++ Equations are solved ** - solve:(F,F,F,F,NNI,NNI,LEF,List LEF,ST,DF) -> Result - ++ solve(xmin,ymin,xmax,ymax,ngx,ngy,pde,bounds,st,tol) is a top level - ++ ANNA function to solve numerically a system of partial differential - ++ equations. This is defined as a list of coefficients (\axiom{pde}), - ++ a grid (\axiom{xmin}, \axiom{ymin}, \axiom{xmax}, \axiom{ymax}, - ++ \axiom{ngx}, \axiom{ngy}), the boundary values (\axiom{bounds}) and a - ++ tolerance requirement (\axiom{tol}). There is also a parameter - ++ (\axiom{st}) which should contain the value "elliptic" if the PDE is - ++ known to be elliptic, or "unknown" if it is uncertain. This causes the - ++ routine to check whether the PDE is elliptic. - ++ - ++ 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 PDE's and calculating - ++ a measure of compatibility of each routine to these attributes. - ++ - ++ It then calls the resulting `best' routine. - ++ - ++ ** At the moment, only Second Order Elliptic Partial Differential - ++ Equations are solved ** - solve:(F,F,F,F,NNI,NNI,LEF,List LEF,ST) -> Result - ++ solve(xmin,ymin,xmax,ymax,ngx,ngy,pde,bounds,st) is a top level - ++ ANNA function to solve numerically a system of partial differential - ++ equations. This is defined as a list of coefficients (\axiom{pde}), - ++ a grid (\axiom{xmin}, \axiom{ymin}, \axiom{xmax}, \axiom{ymax}, - ++ \axiom{ngx}, \axiom{ngy}) and the boundary values (\axiom{bounds}). - ++ A default value for tolerance is used. There is also a parameter - ++ (\axiom{st}) which should contain the value "elliptic" if the PDE is - ++ known to be elliptic, or "unknown" if it is uncertain. This causes the - ++ routine to check whether the PDE is elliptic. - ++ - ++ 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 PDE's and calculating - ++ a measure of compatibility of each routine to these attributes. - ++ - ++ It then calls the resulting `best' routine. - ++ - ++ ** At the moment, only Second Order Elliptic Partial Differential - ++ Equations are solved ** - measure:(NumericalPDEProblem) -> 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 PDE - ++ problem defined by \axiom{prob}. - ++ - ++ It calls each \axiom{domain} of \axiom{category} - ++ \axiomType{PartialDifferentialEquationsSolverCategory} 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 PDEs - ++ by checking various attributes of the system of PDEs and calculating - ++ a measure of compatibility of each routine to these attributes. - measure:(NumericalPDEProblem,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 PDE - ++ problem defined by \axiom{prob}. - ++ - ++ It calls each \axiom{domain} listed in \axiom{R} of \axiom{category} - ++ \axiomType{PartialDifferentialEquationsSolverCategory} 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 PDEs - ++ by checking various attributes of the system of PDEs and calculating - ++ a measure of compatibility of each routine to these attributes. - - - == add - - import PDEB, d03AgentsPackage, ExpertSystemToolsPackage, NumericalPDEProblem - - zeroMeasure:Measure -> Result - measureSpecific:(ST,RT,PDEB) -> Record(measure:F,explanations:ST) - solveSpecific:(PDEB,ST) -> Result - changeName:(Result,ST) -> Result - recoverAfterFail:(PDEB,RT,Measure,Integer,Result) -> Record(a:Result,b:Measure) - - zeroMeasure(m:Measure):Result == - a := coerce(0$F)$AnyFunctions1(F) - text := coerce("No available routine appears appropriate")$AnyFunctions1(ST) - r := construct([[result@Symbol,a],[method@Symbol,text]])$Result - concat(measure2Result m,r)$ExpertSystemToolsPackage - - measureSpecific(name:ST,R:RT,p:PDEB):Record(measure:F,explanations:ST) == - name = "d03eefAnnaType" => measure(R,p)$d03eefAnnaType - --name = "d03fafAnnaType" => measure(R,p)$d03fafAnnaType - error("measureSpecific","invalid type name: " name)$ErrorFunctions - - measure(P:NumericalPDEProblem,R:RT):Measure == - p:PDEB := retract(P)$NumericalPDEProblem - sofar := 0$F - best := "none" :: ST - routs := copy R - routs := selectPDERoutines(routs)$RT - empty?(routs)$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,p) - 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(P:NumericalPDEProblem):Measure == measure(P,routines()$RT) - - solveSpecific(p:PDEB,n:ST):Result == - n = "d03eefAnnaType" => PDESolve(p)$d03eefAnnaType - --n = "d03fafAnnaType" => PDESolve(p)$d03fafAnnaType - error("solveSpecific","invalid type name: " n)$ErrorFunctions - - changeName(ans:Result,name:ST):Result == - sy:Symbol := coerce(name "Answer")$Symbol - anyAns:Any := coerce(ans)$AnyFunctions1(Result) - construct([[sy,anyAns]])$Result - - recoverAfterFail(p:PDEB,routs:RT,m:Measure,iint:Integer,r:Result): - Record(a:Result,b:Measure) == - while positive?(iint) repeat - routineName := m.name - s := recoverAfterFail(routs,routineName(1..6),iint)$RT - s case "failed" => iint := 0 - (s = "no action")@Boolean => iint := 0 - fl := coerce(s)$AnyFunctions1(ST) - flrec:Record(key:Symbol,entry:Any):=[failure@Symbol,fl] - m2 := measure(p::NumericalPDEProblem,routs) - zero?(m2.measure) => iint := 0 - r2:Result := solveSpecific(p,m2.name) - m := m2 - insert!(flrec,r2)$Result - r := concat(r2,changeName(r,routineName))$ExpertSystemToolsPackage - iany := search(ifail@Symbol,r2)$Result - iany case "failed" => iint := 0 - iint := retract(iany)$AnyFunctions1(Integer) - [r,m] - - solve(P:NumericalPDEProblem,t:RT):Result == - routs := copy(t)$RT - m := measure(P,routs) - p:PDEB := retract(P)$NumericalPDEProblem - zero?(m.measure) => zeroMeasure m - r := solveSpecific(p,n := m.name) - iany := search(ifail@Symbol,r)$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(p,routs,m,iint,r) - r := tu.a - m := tu.b - 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) - concat(measure2Result m,r)$ExpertSystemToolsPackage - - solve(P:NumericalPDEProblem):Result == solve(P,routines()$RT) - - solve(xmi:F,xma:F,ymi:F,yma:F,nx:NNI,ny:NNI,pe:LEF,bo:List - LEF,s:ST,to:DF):Result == - cx:PDEC := [f2df xmi, f2df xma, nx, 1, empty()$MDF, empty()$MDF] - cy:PDEC := [f2df ymi, f2df yma, ny, 1, empty()$MDF, empty()$MDF] - p:PDEB := [[ef2edf e for e in pe],[cx,cy], - [[ef2edf u for u in w] for w in bo],s,to] - solve(p::NumericalPDEProblem,routines()$RT) - - solve(xmi:F,xma:F,ymi:F,yma:F,nx:NNI,ny:NNI,pe:LEF,bo:List - LEF,s:ST):Result == - solve(xmi,xma,ymi,yma,nx,ny,pe,bo,s,0.0001::DF) - -@ -\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 PDEPACK AnnaPartialDifferentialEquationPackage>> -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} |