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diff --git a/src/algebra/d02routine.spad.pamphlet b/src/algebra/d02routine.spad.pamphlet new file mode 100644 index 00000000..106f29bc --- /dev/null +++ b/src/algebra/d02routine.spad.pamphlet @@ -0,0 +1,424 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/algebra d02routine.spad} +\author{Brian Dupee} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\section{domain D02BBFA d02bbfAnnaType} +<<domain D02BBFA d02bbfAnnaType>>= +)abbrev domain D02BBFA d02bbfAnnaType +++ Author: Brian Dupee +++ Date Created: February 1995 +++ Date Last Updated: January 1996 +++ Basic Operations: +++ Description: +++ \axiomType{d02bbfAnnaType} is a domain of +++ \axiomType{OrdinaryDifferentialEquationsInitialValueProblemSolverCategory} +++ for the NAG routine D02BBF, a ODE routine which uses an +++ Runge-Kutta method to solve a system of differential +++ equations. The function \axiomFun{measure} measures the +++ usefulness of the routine D02BBF for the given problem. The +++ function \axiomFun{ODESolve} performs the integration by using +++ \axiomType{NagOrdinaryDifferentialEquationsPackage}. + + +d02bbfAnnaType():OrdinaryDifferentialEquationsSolverCategory == Result add -- Runge Kutta + + EDF ==> Expression DoubleFloat + LDF ==> List DoubleFloat + MDF ==> Matrix DoubleFloat + DF ==> DoubleFloat + F ==> Float + FI ==> Fraction Integer + EFI ==> Expression Fraction Integer + SOCDF ==> Segment OrderedCompletion DoubleFloat + VEDF ==> Vector Expression DoubleFloat + VEF ==> Vector Expression Float + EF ==> Expression Float + VDF ==> Vector DoubleFloat + VMF ==> Vector MachineFloat + MF ==> MachineFloat + ODEA ==> Record(xinit:DF,xend:DF,fn:VEDF,yinit:LDF,intvals:LDF,_ + g:EDF,abserr:DF,relerr:DF) + RSS ==> Record(stiffnessFactor:F,stabilityFactor:F) + INT ==> Integer + EF2 ==> ExpressionFunctions2 + + import d02AgentsPackage, NagOrdinaryDifferentialEquationsPackage + import AttributeButtons + + accuracyCF(ode:ODEA):F == + b := getButtonValue("d02bbf","accuracy")$AttributeButtons + accuracyIntensityValue := combineFeatureCompatibility(b,accuracyIF(ode)) + accuracyIntensityValue > 0.999 => 0$F + 0.8*exp(-((10*accuracyIntensityValue)**3)$F/266)$F + + stiffnessCF(stiffnessIntensityValue:F):F == + b := getButtonValue("d02bbf","stiffness")$AttributeButtons + 0.5*exp(-(2*combineFeatureCompatibility(b,stiffnessIntensityValue))**2)$F + + stabilityCF(stabilityIntensityValue:F):F == + b := getButtonValue("d02bbf","stability")$AttributeButtons + 0.5 * cos(combineFeatureCompatibility(b,stabilityIntensityValue))$F + + expenseOfEvaluationCF(ode:ODEA):F == + b := getButtonValue("d02bbf","expense")$AttributeButtons + expenseOfEvaluationIntensityValue := + combineFeatureCompatibility(b,expenseOfEvaluationIF(ode)) + 0.35+0.2*exp(-(2.0*expenseOfEvaluationIntensityValue)**3)$F + + measure(R:RoutinesTable,args:ODEA) == + m := getMeasure(R,d02bbf :: Symbol)$RoutinesTable + ssf := stiffnessAndStabilityOfODEIF args + m := combineFeatureCompatibility(m,[accuracyCF(args), + stiffnessCF(ssf.stiffnessFactor), + expenseOfEvaluationCF(args), + stabilityCF(ssf.stabilityFactor)]) + [m,"Runge-Kutta Merson method"] + + ODESolve(ode:ODEA) == + i:LDF := ode.intvals + M := inc(# i)$INT + irelab := 0$INT + if positive?(a := ode.abserr) then + inc(irelab)$INT + if positive?(r := ode.relerr) then + inc(irelab)$INT + if positive?(a+r) then + tol:DF := a + r + else + tol := float(1,-4,10)$DF + asp7:Union(fn:FileName,fp:Asp7(FCN)) := + [retract(vedf2vef(ode.fn)$ExpertSystemToolsPackage)$Asp7(FCN)] + asp8:Union(fn:FileName,fp:Asp8(OUTPUT)) := + [coerce(ldf2vmf(i)$ExpertSystemToolsPackage)$Asp8(OUTPUT)] + d02bbf(ode.xend,M,# ode.fn,irelab,ode.xinit,matrix([ode.yinit])$MDF, + tol,-1,asp7,asp8) + +@ +\section{domain D02BHFA d02bhfAnnaType} +<<domain D02BHFA d02bhfAnnaType>>= +)abbrev domain D02BHFA d02bhfAnnaType +++ Author: Brian Dupee +++ Date Created: February 1995 +++ Date Last Updated: January 1996 +++ Basic Operations: +++ Description: +++ \axiomType{d02bhfAnnaType} is a domain of +++ \axiomType{OrdinaryDifferentialEquationsInitialValueProblemSolverCategory} +++ for the NAG routine D02BHF, a ODE routine which uses an +++ Runge-Kutta method to solve a system of differential +++ equations. The function \axiomFun{measure} measures the +++ usefulness of the routine D02BHF for the given problem. The +++ function \axiomFun{ODESolve} performs the integration by using +++ \axiomType{NagOrdinaryDifferentialEquationsPackage}. + +d02bhfAnnaType():OrdinaryDifferentialEquationsSolverCategory == Result add -- Runge Kutta + EDF ==> Expression DoubleFloat + LDF ==> List DoubleFloat + MDF ==> Matrix DoubleFloat + DF ==> DoubleFloat + F ==> Float + FI ==> Fraction Integer + EFI ==> Expression Fraction Integer + SOCDF ==> Segment OrderedCompletion DoubleFloat + VEDF ==> Vector Expression DoubleFloat + VEF ==> Vector Expression Float + EF ==> Expression Float + VDF ==> Vector DoubleFloat + VMF ==> Vector MachineFloat + MF ==> MachineFloat + ODEA ==> Record(xinit:DF,xend:DF,fn:VEDF,yinit:LDF,intvals:LDF,_ + g:EDF,abserr:DF,relerr:DF) + RSS ==> Record(stiffnessFactor:F,stabilityFactor:F) + INT ==> Integer + EF2 ==> ExpressionFunctions2 + + import d02AgentsPackage, NagOrdinaryDifferentialEquationsPackage + import AttributeButtons + + accuracyCF(ode:ODEA):F == + b := getButtonValue("d02bhf","accuracy")$AttributeButtons + accuracyIntensityValue := combineFeatureCompatibility(b,accuracyIF(ode)) + accuracyIntensityValue > 0.999 => 0$F + 0.8*exp(-((10*accuracyIntensityValue)**3)$F/266)$F + + stiffnessCF(stiffnessIntensityValue:F):F == + b := getButtonValue("d02bhf","stiffness")$AttributeButtons + 0.5*exp(-(2*combineFeatureCompatibility(b,stiffnessIntensityValue))**2)$F + + stabilityCF(stabilityIntensityValue:F):F == + b := getButtonValue("d02bhf","stability")$AttributeButtons + 0.5 * cos(combineFeatureCompatibility(b,stabilityIntensityValue))$F + + expenseOfEvaluationCF(ode:ODEA):F == + b := getButtonValue("d02bhf","expense")$AttributeButtons + expenseOfEvaluationIntensityValue := + combineFeatureCompatibility(b,expenseOfEvaluationIF(ode)) + 0.35+0.2*exp(-(2.0*expenseOfEvaluationIntensityValue)**3)$F + + measure(R:RoutinesTable,args:ODEA) == + m := getMeasure(R,d02bhf :: Symbol)$RoutinesTable + ssf := stiffnessAndStabilityOfODEIF args + m := combineFeatureCompatibility(m,[accuracyCF(args), + stiffnessCF(ssf.stiffnessFactor), + expenseOfEvaluationCF(args), + stabilityCF(ssf.stabilityFactor)]) + [m,"Runge-Kutta Merson method"] + + ODESolve(ode:ODEA) == + irelab := 0$INT + if positive?(a := ode.abserr) then + inc(irelab)$INT + if positive?(r := ode.relerr) then + inc(irelab)$INT + if positive?(a+r) then + tol := max(a,r)$DF + else + tol:DF := float(1,-4,10)$DF + asp7:Union(fn:FileName,fp:Asp7(FCN)) := + [retract(e:VEF := vedf2vef(ode.fn)$ExpertSystemToolsPackage)$Asp7(FCN)] + asp9:Union(fn:FileName,fp:Asp9(G)) := + [retract(edf2ef(ode.g)$ExpertSystemToolsPackage)$Asp9(G)] + d02bhf(ode.xend,# e,irelab,0$DF,ode.xinit,matrix([ode.yinit])$MDF, + tol,-1,asp9,asp7) + +@ +\section{domain D02CJFA d02cjfAnnaType} +<<domain D02CJFA d02cjfAnnaType>>= +)abbrev domain D02CJFA d02cjfAnnaType +++ Author: Brian Dupee +++ Date Created: February 1995 +++ Date Last Updated: January 1996 +++ Basic Operations: +++ Description: +++ \axiomType{d02cjfAnnaType} is a domain of +++ \axiomType{OrdinaryDifferentialEquationsInitialValueProblemSolverCategory} +++ for the NAG routine D02CJF, a ODE routine which uses an +++ Adams-Moulton-Bashworth method to solve a system of differential +++ equations. The function \axiomFun{measure} measures the +++ usefulness of the routine D02CJF for the given problem. The +++ function \axiomFun{ODESolve} performs the integration by using +++ \axiomType{NagOrdinaryDifferentialEquationsPackage}. + +d02cjfAnnaType():OrdinaryDifferentialEquationsSolverCategory == Result add -- Adams + EDF ==> Expression DoubleFloat + LDF ==> List DoubleFloat + MDF ==> Matrix DoubleFloat + DF ==> DoubleFloat + F ==> Float + FI ==> Fraction Integer + EFI ==> Expression Fraction Integer + SOCDF ==> Segment OrderedCompletion DoubleFloat + VEDF ==> Vector Expression DoubleFloat + VEF ==> Vector Expression Float + EF ==> Expression Float + VDF ==> Vector DoubleFloat + VMF ==> Vector MachineFloat + MF ==> MachineFloat + ODEA ==> Record(xinit:DF,xend:DF,fn:VEDF,yinit:LDF,intvals:LDF,_ + g:EDF,abserr:DF,relerr:DF) + RSS ==> Record(stiffnessFactor:F,stabilityFactor:F) + INT ==> Integer + EF2 ==> ExpressionFunctions2 + + import d02AgentsPackage, NagOrdinaryDifferentialEquationsPackage + + accuracyCF(ode:ODEA):F == + b := getButtonValue("d02cjf","accuracy")$AttributeButtons + accuracyIntensityValue := combineFeatureCompatibility(b,accuracyIF(ode)) + accuracyIntensityValue > 0.9999 => 0$F + 0.6*(cos(accuracyIntensityValue*(pi()$F)/2)$F)**0.755 + + stiffnessCF(ode:ODEA):F == + b := getButtonValue("d02cjf","stiffness")$AttributeButtons + ssf := stiffnessAndStabilityOfODEIF ode + stiffnessIntensityValue := + combineFeatureCompatibility(b,ssf.stiffnessFactor) + 0.5*exp(-(1.1*stiffnessIntensityValue)**3)$F + + measure(R:RoutinesTable,args:ODEA) == + m := getMeasure(R,d02cjf :: Symbol)$RoutinesTable + m := combineFeatureCompatibility(m,[accuracyCF(args), stiffnessCF(args)]) + [m,"Adams method"] + + ODESolve(ode:ODEA) == + i:LDF := ode.intvals + if empty?(i) then + i := [ode.xend] + M := inc(# i)$INT + if positive?((a := ode.abserr)*(r := ode.relerr))$DF then + ire:String := "D" + else + if positive?(a) then + ire:String := "A" + else + ire:String := "R" + tol := max(a,r)$DF + asp7:Union(fn:FileName,fp:Asp7(FCN)) := + [retract(e:VEF := vedf2vef(ode.fn)$ExpertSystemToolsPackage)$Asp7(FCN)] + asp8:Union(fn:FileName,fp:Asp8(OUTPUT)) := + [coerce(ldf2vmf(i)$ExpertSystemToolsPackage)$Asp8(OUTPUT)] + asp9:Union(fn:FileName,fp:Asp9(G)) := + [retract(edf2ef(ode.g)$ExpertSystemToolsPackage)$Asp9(G)] + d02cjf(ode.xend,M,# e,tol,ire,ode.xinit,matrix([ode.yinit])$MDF, + -1,asp9,asp7,asp8) + +@ +\section{domain D02EJFA d02ejfAnnaType} +<<domain D02EJFA d02ejfAnnaType>>= +)abbrev domain D02EJFA d02ejfAnnaType +++ Author: Brian Dupee +++ Date Created: February 1995 +++ Date Last Updated: January 1996 +++ Basic Operations: +++ Description: +++ \axiomType{d02ejfAnnaType} is a domain of +++ \axiomType{OrdinaryDifferentialEquationsInitialValueProblemSolverCategory} +++ for the NAG routine D02EJF, a ODE routine which uses a backward +++ differentiation formulae method to handle a stiff system +++ of differential equations. The function \axiomFun{measure} measures +++ the usefulness of the routine D02EJF for the given problem. The +++ function \axiomFun{ODESolve} performs the integration by using +++ \axiomType{NagOrdinaryDifferentialEquationsPackage}. + +d02ejfAnnaType():OrdinaryDifferentialEquationsSolverCategory == Result add -- BDF "Stiff" + EDF ==> Expression DoubleFloat + LDF ==> List DoubleFloat + MDF ==> Matrix DoubleFloat + DF ==> DoubleFloat + F ==> Float + FI ==> Fraction Integer + EFI ==> Expression Fraction Integer + SOCDF ==> Segment OrderedCompletion DoubleFloat + VEDF ==> Vector Expression DoubleFloat + VEF ==> Vector Expression Float + EF ==> Expression Float + VDF ==> Vector DoubleFloat + VMF ==> Vector MachineFloat + MF ==> MachineFloat + ODEA ==> Record(xinit:DF,xend:DF,fn:VEDF,yinit:LDF,intvals:LDF,_ + g:EDF,abserr:DF,relerr:DF) + RSS ==> Record(stiffnessFactor:F,stabilityFactor:F) + INT ==> Integer + EF2 ==> ExpressionFunctions2 + + import d02AgentsPackage, NagOrdinaryDifferentialEquationsPackage + + accuracyCF(ode:ODEA):F == + b := getButtonValue("d02ejf","accuracy")$AttributeButtons + accuracyIntensityValue := combineFeatureCompatibility(b,accuracyIF(ode)) + accuracyIntensityValue > 0.999 => 0$F + 0.5*exp(-((10*accuracyIntensityValue)**3)$F/250)$F + + intermediateResultsCF(ode:ODEA):F == + intermediateResultsIntensityValue := intermediateResultsIF(ode) + i := 0.5 * exp(-(intermediateResultsIntensityValue/1.649)**3)$F + a := accuracyCF(ode) + i+(0.5-i)*(0.5-a) + + stabilityCF(ode:ODEA):F == + b := getButtonValue("d02ejf","stability")$AttributeButtons + ssf := stiffnessAndStabilityOfODEIF ode + stabilityIntensityValue := + combineFeatureCompatibility(b,ssf.stabilityFactor) + 0.68 - 0.5 * exp(-(stabilityIntensityValue)**3)$F + + expenseOfEvaluationCF(ode:ODEA):F == + b := getButtonValue("d02ejf","expense")$AttributeButtons + expenseOfEvaluationIntensityValue := + combineFeatureCompatibility(b,expenseOfEvaluationIF(ode)) + 0.5 * exp(-(1.7*expenseOfEvaluationIntensityValue)**3)$F + + systemSizeCF(args:ODEA):F == + (1$F - systemSizeIF(args))/2.0 + + measure(R:RoutinesTable,args:ODEA) == + arg := copy args + m := getMeasure(R,d02ejf :: Symbol)$RoutinesTable + m := combineFeatureCompatibility(m,[intermediateResultsCF(arg), + accuracyCF(arg), + systemSizeCF(arg), + expenseOfEvaluationCF(arg), + stabilityCF(arg)]) + [m,"BDF method for Stiff Systems"] + + ODESolve(ode:ODEA) == + i:LDF := ode.intvals + m := inc(# i)$INT + if positive?((a := ode.abserr)*(r := ode.relerr))$DF then + ire:String := "D" + else + if positive?(a) then + ire:String := "A" + else + ire:String := "R" + if positive?(a+r)$DF then + tol := max(a,r)$DF + else + tol := float(1,-4,10)$DF + asp7:Union(fn:FileName,fp:Asp7(FCN)) := + [retract(e:VEF := vedf2vef(ode.fn)$ExpertSystemToolsPackage)$Asp7(FCN)] + asp31:Union(fn:FileName,fp:Asp31(PEDERV)) := + [retract(e)$Asp31(PEDERV)] + asp8:Union(fn:FileName,fp:Asp8(OUTPUT)) := + [coerce(ldf2vmf(i)$ExpertSystemToolsPackage)$Asp8(OUTPUT)] + asp9:Union(fn:FileName,fp:Asp9(G)) := + [retract(edf2ef(ode.g)$ExpertSystemToolsPackage)$Asp9(G)] + n:INT := # ode.yinit + iw:INT := (12+n)*n+50 + ans := d02ejf(ode.xend,m,n,ire,iw,ode.xinit,matrix([ode.yinit])$MDF, + tol,-1,asp9,asp7,asp31,asp8) + +@ +\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>> + +<<domain D02BBFA d02bbfAnnaType>> +<<domain D02BHFA d02bhfAnnaType>> +<<domain D02CJFA d02cjfAnnaType>> +<<domain D02EJFA d02ejfAnnaType>> +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} |