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diff --git a/src/algebra/d03Package.spad.pamphlet b/src/algebra/d03Package.spad.pamphlet new file mode 100644 index 00000000..7a0a146f --- /dev/null +++ b/src/algebra/d03Package.spad.pamphlet @@ -0,0 +1,307 @@ +\documentclass{article} +\usepackage{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} |