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diff --git a/src/algebra/annacat.spad.pamphlet b/src/algebra/annacat.spad.pamphlet new file mode 100644 index 00000000..70d5af6c --- /dev/null +++ b/src/algebra/annacat.spad.pamphlet @@ -0,0 +1,504 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/algebra annacat.spad} +\author{Brian Dupee} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\section{domain NIPROB NumericalIntegrationProblem} +<<domain NIPROB NumericalIntegrationProblem>>= +)abbrev domain NIPROB NumericalIntegrationProblem +++ Author: Brian Dupee +++ Date Created: December 1997 +++ Date Last Updated: December 1997 +++ Basic Operations: coerce, retract +++ Related Constructors: Union +++ Description: +++ \axiomType{NumericalIntegrationProblem} is a \axiom{domain} +++ for the representation of Numerical Integration problems for use +++ by ANNA. +++ +++ The representation is a Union of two record types - one for integration of +++ a function of one variable: +++ +++ \axiomType{Record}(var:\axiomType{Symbol}, +++ fn:\axiomType{Expression DoubleFloat}, +++ range:\axiomType{Segment OrderedCompletion DoubleFloat}, +++ abserr:\axiomType{DoubleFloat}, +++ relerr:\axiomType{DoubleFloat},) +++ +++ and one for multivariate integration: +++ +++ \axiomType{Record}(fn:\axiomType{Expression DoubleFloat}, +++ range:\axiomType{List Segment OrderedCompletion DoubleFloat}, +++ abserr:\axiomType{DoubleFloat}, +++ relerr:\axiomType{DoubleFloat},). +++ + +EDFA ==> Expression DoubleFloat +SOCDFA ==> Segment OrderedCompletion DoubleFloat +DFA ==> DoubleFloat +NIAA ==> Record(var:Symbol,fn:EDFA,range:SOCDFA,abserr:DFA,relerr:DFA) +MDNIAA ==> Record(fn:EDFA,range:List SOCDFA,abserr:DFA,relerr:DFA) + +NumericalIntegrationProblem():SetCategory with + coerce: NIAA -> % + ++ coerce(x) \undocumented{} + coerce: MDNIAA -> % + ++ coerce(x) \undocumented{} + coerce: Union(nia:NIAA,mdnia:MDNIAA) -> % + ++ coerce(x) \undocumented{} + coerce: % -> OutputForm + ++ coerce(x) \undocumented{} + retract: % -> Union(nia:NIAA,mdnia:MDNIAA) + ++ retract(x) \undocumented{} + + == + + add + Rep := Union(nia:NIAA,mdnia:MDNIAA) + + coerce(s:NIAA) == [s] + coerce(s:MDNIAA) == [s] + coerce(s:Union(nia:NIAA,mdnia:MDNIAA)) == s + coerce(x:%):OutputForm == + (x) case nia => (x.nia)::OutputForm + (x.mdnia)::OutputForm + retract(x:%):Union(nia:NIAA,mdnia:MDNIAA) == + (x) case nia => [x.nia] + [x.mdnia] + +@ +\section{domain ODEPROB NumericalODEProblem} +<<domain ODEPROB NumericalODEProblem>>= +)abbrev domain ODEPROB NumericalODEProblem +++ Author: Brian Dupee +++ Date Created: December 1997 +++ Date Last Updated: December 1997 +++ Basic Operations: coerce, retract +++ Related Constructors: Union +++ Description: +++ \axiomType{NumericalODEProblem} is a \axiom{domain} +++ for the representation of Numerical ODE problems for use +++ by ANNA. +++ +++ The representation is of type: +++ +++ \axiomType{Record}(xinit:\axiomType{DoubleFloat}, +++ xend:\axiomType{DoubleFloat}, +++ fn:\axiomType{Vector Expression DoubleFloat}, +++ yinit:\axiomType{List DoubleFloat},intvals:\axiomType{List DoubleFloat}, +++ g:\axiomType{Expression DoubleFloat},abserr:\axiomType{DoubleFloat}, +++ relerr:\axiomType{DoubleFloat}) +++ + +DFB ==> DoubleFloat +VEDFB ==> Vector Expression DoubleFloat +LDFB ==> List DoubleFloat +EDFB ==> Expression DoubleFloat +ODEAB ==> Record(xinit:DFB,xend:DFB,fn:VEDFB,yinit:LDFB,intvals:LDFB,g:EDFB,abserr:DFB,relerr:DFB) +NumericalODEProblem():SetCategory with + + coerce: ODEAB -> % + ++ coerce(x) \undocumented{} + coerce: % -> OutputForm + ++ coerce(x) \undocumented{} + retract: % -> ODEAB + ++ retract(x) \undocumented{} + + == + + add + Rep := ODEAB + + coerce(s:ODEAB) == s + coerce(x:%):OutputForm == + (retract(x))::OutputForm + retract(x:%):ODEAB == x :: Rep + +@ +\section{domain PDEPROB NumericalPDEProblem} +<<domain PDEPROB NumericalPDEProblem>>= +)abbrev domain PDEPROB NumericalPDEProblem +++ Author: Brian Dupee +++ Date Created: December 1997 +++ Date Last Updated: December 1997 +++ Basic Operations: coerce, retract +++ Related Constructors: Union +++ Description: +++ \axiomType{NumericalPDEProblem} is a \axiom{domain} +++ for the representation of Numerical PDE problems for use +++ by ANNA. +++ +++ The representation is of type: +++ +++ \axiomType{Record}(pde:\axiomType{List Expression DoubleFloat}, +++ constraints:\axiomType{List PDEC}, +++ f:\axiomType{List List Expression DoubleFloat}, +++ st:\axiomType{String}, +++ tol:\axiomType{DoubleFloat}) +++ +++ where \axiomType{PDEC} is of type: +++ +++ \axiomType{Record}(start:\axiomType{DoubleFloat}, +++ finish:\axiomType{DoubleFloat}, +++ grid:\axiomType{NonNegativeInteger}, +++ boundaryType:\axiomType{Integer}, +++ dStart:\axiomType{Matrix DoubleFloat}, +++ dFinish:\axiomType{Matrix DoubleFloat}) +++ + +DFC ==> DoubleFloat +NNIC ==> NonNegativeInteger +INTC ==> Integer +MDFC ==> Matrix DoubleFloat +PDECC ==> Record(start:DFC, finish:DFC, grid:NNIC, boundaryType:INTC, + dStart:MDFC, dFinish:MDFC) +LEDFC ==> List Expression DoubleFloat +PDEBC ==> Record(pde:LEDFC, constraints:List PDECC, f:List LEDFC, + st:String, tol:DFC) +NumericalPDEProblem():SetCategory with + + coerce: PDEBC -> % + ++ coerce(x) \undocumented{} + coerce: % -> OutputForm + ++ coerce(x) \undocumented{} + retract: % -> PDEBC + ++ retract(x) \undocumented{} + + == + + add + Rep := PDEBC + + coerce(s:PDEBC) == s + coerce(x:%):OutputForm == + (retract(x))::OutputForm + retract(x:%):PDEBC == x :: Rep + +@ +\section{domain OPTPROB NumericalOptimizationProblem} +<<domain OPTPROB NumericalOptimizationProblem>>= +)abbrev domain OPTPROB NumericalOptimizationProblem +++ Author: Brian Dupee +++ Date Created: December 1997 +++ Date Last Updated: December 1997 +++ Basic Operations: coerce, retract +++ Related Constructors: Union +++ Description: +++ \axiomType{NumericalOptimizationProblem} is a \axiom{domain} +++ for the representation of Numerical Optimization problems for use +++ by ANNA. +++ +++ The representation is a Union of two record types - one for otimization of +++ a single function of one or more variables: +++ +++ \axiomType{Record}( +++ fn:\axiomType{Expression DoubleFloat}, +++ init:\axiomType{List DoubleFloat}, +++ lb:\axiomType{List OrderedCompletion DoubleFloat}, +++ cf:\axiomType{List Expression DoubleFloat}, +++ ub:\axiomType{List OrderedCompletion DoubleFloat}) +++ +++ and one for least-squares problems i.e. optimization of a set of +++ observations of a data set: +++ +++ \axiomType{Record}(lfn:\axiomType{List Expression DoubleFloat}, +++ init:\axiomType{List DoubleFloat}). +++ + +LDFD ==> List DoubleFloat +LEDFD ==> List Expression DoubleFloat +LSAD ==> Record(lfn:LEDFD, init:LDFD) +UNOALSAD ==> Union(noa:NOAD,lsa:LSAD) +EDFD ==> Expression DoubleFloat +LOCDFD ==> List OrderedCompletion DoubleFloat +NOAD ==> Record(fn:EDFD, init:LDFD, lb:LOCDFD, cf:LEDFD, ub:LOCDFD) +NumericalOptimizationProblem():SetCategory with + + coerce: NOAD -> % + ++ coerce(x) \undocumented{} + coerce: LSAD -> % + ++ coerce(x) \undocumented{} + coerce: UNOALSAD -> % + ++ coerce(x) \undocumented{} + coerce: % -> OutputForm + ++ coerce(x) \undocumented{} + retract: % -> UNOALSAD + ++ retract(x) \undocumented{} + + == + + add + Rep := UNOALSAD + + coerce(s:NOAD) == [s] + coerce(s:LSAD) == [s] + coerce(x:UNOALSAD) == x + coerce(x:%):OutputForm == + (x) case noa => (x.noa)::OutputForm + (x.lsa)::OutputForm + retract(x:%):UNOALSAD == + (x) case noa => [x.noa] + [x.lsa] + +@ +\section{category NUMINT NumericalIntegrationCategory} +<<category NUMINT NumericalIntegrationCategory>>= +)abbrev category NUMINT NumericalIntegrationCategory +++ Author: Brian Dupee +++ Date Created: February 1994 +++ Date Last Updated: March 1996 +++ Description: +++ \axiomType{NumericalIntegrationCategory} is the \axiom{category} for +++ describing the set of Numerical Integration \axiom{domains} with +++ \axiomFun{measure} and \axiomFun{numericalIntegration}. + +EDFE ==> Expression DoubleFloat +SOCDFE ==> Segment OrderedCompletion DoubleFloat +DFE ==> DoubleFloat +NIAE ==> Record(var:Symbol,fn:EDFE,range:SOCDFE,abserr:DFE,relerr:DFE) +MDNIAE ==> Record(fn:EDFE,range:List SOCDFE,abserr:DFE,relerr:DFE) +NumericalIntegrationCategory(): Category == SetCategory with + + measure:(RoutinesTable,NIAE)->Record(measure:Float,explanations:String,extra:Result) + ++ measure(R,args) calculates an estimate of the ability of a particular + ++ method to solve a problem. + ++ + ++ This method may be either a specific NAG routine or a strategy (such + ++ as transforming the function from one which is difficult to one which + ++ is easier to solve). + ++ + ++ It will call whichever agents are needed to perform analysis on the + ++ problem in order to calculate the measure. There is a parameter, + ++ labelled \axiom{sofar}, which would contain the best compatibility + ++ found so far. + + numericalIntegration: (NIAE, Result) -> Result + ++ numericalIntegration(args,hints) performs the integration of the + ++ function given the strategy or method returned by \axiomFun{measure}. + + measure:(RoutinesTable,MDNIAE)->Record(measure:Float,explanations:String,extra:Result) + ++ measure(R,args) calculates an estimate of the ability of a particular + ++ method to solve a problem. + ++ + ++ This method may be either a specific NAG routine or a strategy (such + ++ as transforming the function from one which is difficult to one which + ++ is easier to solve). + ++ + ++ It will call whichever agents are needed to perform analysis on the + ++ problem in order to calculate the measure. There is a parameter, + ++ labelled \axiom{sofar}, which would contain the best compatibility + ++ found so far. + + numericalIntegration: (MDNIAE, Result) -> Result + ++ numericalIntegration(args,hints) performs the integration of the + ++ function given the strategy or method returned by \axiomFun{measure}. + +@ +\section{category ODECAT OrdinaryDifferentialEquationsSolverCategory} +<<category ODECAT OrdinaryDifferentialEquationsSolverCategory>>= +)abbrev category ODECAT OrdinaryDifferentialEquationsSolverCategory +++ Author: Brian Dupee +++ Date Created: February 1995 +++ Date Last Updated: June 1995 +++ Basic Operations: +++ Description: +++ \axiomType{OrdinaryDifferentialEquationsSolverCategory} is the +++ \axiom{category} for describing the set of ODE solver \axiom{domains} +++ with \axiomFun{measure} and \axiomFun{ODEsolve}. + +DFF ==> DoubleFloat +VEDFF ==> Vector Expression DoubleFloat +LDFF ==> List DoubleFloat +EDFF ==> Expression DoubleFloat +ODEAF ==> Record(xinit:DFF,xend:DFF,fn:VEDFF,yinit:LDFF,intvals:LDFF,g:EDFF,abserr:DFF,relerr:DFF) +OrdinaryDifferentialEquationsSolverCategory(): Category == SetCategory with + + measure:(RoutinesTable,ODEAF) -> Record(measure:Float,explanations:String) + ++ measure(R,args) calculates an estimate of the ability of a particular + ++ method to solve a problem. + ++ + ++ This method may be either a specific NAG routine or a strategy (such + ++ as transforming the function from one which is difficult to one which + ++ is easier to solve). + ++ + ++ It will call whichever agents are needed to perform analysis on the + ++ problem in order to calculate the measure. There is a parameter, + ++ labelled \axiom{sofar}, which would contain the best compatibility + ++ found so far. + + ODESolve: ODEAF -> Result + ++ ODESolve(args) performs the integration of the + ++ function given the strategy or method returned by \axiomFun{measure}. + +@ +\section{category PDECAT PartialDifferentialEquationsSolverCategory} +<<category PDECAT PartialDifferentialEquationsSolverCategory>>= +)abbrev category PDECAT PartialDifferentialEquationsSolverCategory +++ Author: Brian Dupee +++ Date Created: February 1995 +++ Date Last Updated: June 1995 +++ Basic Operations: +++ Description: +++ \axiomType{PartialDifferentialEquationsSolverCategory} is the +++ \axiom{category} for describing the set of PDE solver \axiom{domains} +++ with \axiomFun{measure} and \axiomFun{PDEsolve}. + +-- PDEA ==> Record(xmin:F,xmax:F,ymin:F,ymax:F,ngx:NNI,ngy:NNI,_ +-- pde:List Expression Float, bounds:List List Expression Float,_ +-- st:String, tol:DF) + +-- measure:(RoutinesTable,PDEA) -> Record(measure:F,explanations:String) +-- ++ measure(R,args) calculates an estimate of the ability of a particular +-- ++ method to solve a problem. +-- ++ +-- ++ This method may be either a specific NAG routine or a strategy (such +-- ++ as transforming the function from one which is difficult to one which +-- ++ is easier to solve). +-- ++ +-- ++ It will call whichever agents are needed to perform analysis on the +-- ++ problem in order to calculate the measure. There is a parameter, +-- ++ labelled \axiom{sofar}, which would contain the best compatibility +-- ++ found so far. + +-- PDESolve: PDEA -> Result +-- ++ PDESolve(args) performs the integration of the +-- ++ function given the strategy or method returned by \axiomFun{measure}. + +DFG ==> DoubleFloat +NNIG ==> NonNegativeInteger +INTG ==> Integer +MDFG ==> Matrix DoubleFloat +PDECG ==> Record(start:DFG, finish:DFG, grid:NNIG, boundaryType:INTG, + dStart:MDFG, dFinish:MDFG) +LEDFG ==> List Expression DoubleFloat +PDEBG ==> Record(pde:LEDFG, constraints:List PDECG, f:List LEDFG, + st:String, tol:DFG) +PartialDifferentialEquationsSolverCategory(): Category == SetCategory with + + measure:(RoutinesTable,PDEBG) -> Record(measure:Float,explanations:String) + ++ measure(R,args) calculates an estimate of the ability of a particular + ++ method to solve a problem. + ++ + ++ This method may be either a specific NAG routine or a strategy (such + ++ as transforming the function from one which is difficult to one which + ++ is easier to solve). + ++ + ++ It will call whichever agents are needed to perform analysis on the + ++ problem in order to calculate the measure. There is a parameter, + ++ labelled \axiom{sofar}, which would contain the best compatibility + ++ found so far. + + PDESolve: PDEBG -> Result + ++ PDESolve(args) performs the integration of the + ++ function given the strategy or method returned by \axiomFun{measure}. + +@ +\section{category OPTCAT NumericalOptimizationCategory} +<<category OPTCAT NumericalOptimizationCategory>>= +)abbrev category OPTCAT NumericalOptimizationCategory +++ Author: Brian Dupee +++ Date Created: January 1996 +++ Date Last Updated: March 1996 +++ Description: +++ \axiomType{NumericalOptimizationCategory} is the \axiom{category} for +++ describing the set of Numerical Optimization \axiom{domains} with +++ \axiomFun{measure} and \axiomFun{optimize}. + +LDFH ==> List DoubleFloat +LEDFH ==> List Expression DoubleFloat +LSAH ==> Record(lfn:LEDFH, init:LDFH) +EDFH ==> Expression DoubleFloat +LOCDFH ==> List OrderedCompletion DoubleFloat +NOAH ==> Record(fn:EDFH, init:LDFH, lb:LOCDFH, cf:LEDFH, ub:LOCDFH) +NumericalOptimizationCategory(): Category == SetCategory with + measure:(RoutinesTable,NOAH)->Record(measure:Float,explanations:String) + ++ measure(R,args) calculates an estimate of the ability of a particular + ++ method to solve an optimization problem. + ++ + ++ This method may be either a specific NAG routine or a strategy (such + ++ as transforming the function from one which is difficult to one which + ++ is easier to solve). + ++ + ++ It will call whichever agents are needed to perform analysis on the + ++ problem in order to calculate the measure. There is a parameter, + ++ labelled \axiom{sofar}, which would contain the best compatibility + ++ found so far. + + measure:(RoutinesTable,LSAH)->Record(measure:Float,explanations:String) + ++ measure(R,args) calculates an estimate of the ability of a particular + ++ method to solve an optimization problem. + ++ + ++ This method may be either a specific NAG routine or a strategy (such + ++ as transforming the function from one which is difficult to one which + ++ is easier to solve). + ++ + ++ It will call whichever agents are needed to perform analysis on the + ++ problem in order to calculate the measure. There is a parameter, + ++ labelled \axiom{sofar}, which would contain the best compatibility + ++ found so far. + + numericalOptimization:LSAH -> Result + ++ numericalOptimization(args) performs the optimization of the + ++ function given the strategy or method returned by \axiomFun{measure}. + + numericalOptimization:NOAH -> Result + ++ numericalOptimization(args) performs the optimization of the + ++ function given the strategy or method returned by \axiomFun{measure}. + +@ +\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 NIPROB NumericalIntegrationProblem>> +<<domain ODEPROB NumericalODEProblem>> +<<domain PDEPROB NumericalPDEProblem>> +<<domain OPTPROB NumericalOptimizationProblem>> +<<category NUMINT NumericalIntegrationCategory>> +<<category ODECAT OrdinaryDifferentialEquationsSolverCategory>> +<<category PDECAT PartialDifferentialEquationsSolverCategory>> +<<category OPTCAT NumericalOptimizationCategory>> +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} |