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diff --git a/src/algebra/annacat.spad.pamphlet b/src/algebra/annacat.spad.pamphlet deleted file mode 100644 index 1c92b907..00000000 --- a/src/algebra/annacat.spad.pamphlet +++ /dev/null @@ -1,496 +0,0 @@ -\documentclass{article} -\usepackage{open-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{} - 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{} - 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{} - 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{} - 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} |