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diff --git a/src/algebra/noptip.as.pamphlet b/src/algebra/noptip.as.pamphlet new file mode 100644 index 00000000..150087bb --- /dev/null +++ b/src/algebra/noptip.as.pamphlet @@ -0,0 +1,241 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/algebra noptip.as} +\author{Michael Richardson} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\section{NagOptimisationInterfacePackage} +<<NagOptimisationInterfacePackage>>= ++++ Author: M.G. Richardson ++++ Date Created: 1996 Feb. 01 ++++ Date Last Updated: ++++ Basic Functions: ++++ Related Constructors: ++++ Also See: ++++ AMS Classifications: ++++ Keywords: ++++ References: ++++ Description: ++++ This package provides Axiom-like interfaces to some of the NAG ++++ optimisation routines in the NAGlink. + +NagOptimisationInterfacePackage: with { + + nagMin : (EDF,LEQPDF) -> LEQPDF ; + +} == add { + + import from MINT ; + import from BOOL ; + import from LLDF ; + import from VDF ; + import from PDF ; + import from LEQEDF ; + import from MDF ; + import from EDF ; + import from FL ; + import from SMBL ; + import from A49 ; + import from A55 ; + import from U49 ; + import from U55 ; + import from NagOptimisationPackage ; + import from OF ; + import from LOF ; + import from LLOF ; + import from ListFunctions2(INT,OF) ; + import from NagResultChecks ; + import from EF2DFFL ; + + local (..)(a:INT,b:INT):Generator INT == { + generate { + t := a ; + while (t <= b) repeat { + yield t ; + t := t + 1 ; + } + } + } + + -- to avoid unrecognised versions of U49 type for e04dgf: + e04dgflocal := e04dgf$NagOptimisationPackage pretend + ((INT,DF,DF,INT,DF,BOOL, DF,DF,INT,INT,INT,INT,MDF,INT, U49)->RSLT) ; + + nagMin(objective:EDF,startList:LEQPDF) : LEQPDF == { + + -- Note that, as objective is an EDF, subst and eval + -- for this have as 2nd parameters LEQEDFs. + + local nv : INT ; + local substList : LEQEDF ; + local indxOb : EF ; + local startVals : LDF ; + local startListXDF : LEQEDF ; + local startFVal : DF ; + local e04dgfResult : RSLT ; + local location : LDF ; + + + nv := ((# startList)@NNI pretend INT) ; -- @ avoids SI + + substList := [lhs(startList.i)::EDF + = (script("x"::SMBL,[[i::OF]]@LLOF))::EDF + for i in 1..nv] ; + -- [x=x[1], y=x[2], etc.] + + indxOb := map(convert$Float,subst(objective,substList)) ; + -- objective function as an EF with x[i]'s, as required by A49 + + startVals := [retract(rhs(startList.i))@DF for i in 1..nv] ; + + startListXDF := [lhs(startList.i)::EDF = rhs(startList.i)::EDF + for i in 1..nv] ; + startFVal := ground(eval(objective,startListXDF))::DF ; + startFVal := startFVal * 1.015625 ; + +-- Note that there appears to be a problem running the standard NAG +-- example on Suns with an exact value for startFVal. It looks as if +-- this causes too large a stepsize, perhaps due to exception code +-- being obeyed in the Fortran. Until this is fixed, using the above +-- slightly perturbed value (adding 1/64) seems to avoid the problem. + + e04dgfResult := e04dgflocal( + nv, -- No.vbls. + -- + -- "optional" params next: + -- + startFVal, -- es(timated obj've fn val) + -1.0, -- fun: + -1, -- it: + -1.0, -- lin: + false, -- list: + -1.0, -- ma: + -2.0, -- opt: made < fun for safety + 0, -- pr: + -1, -- sta: + -1, -- sto: + -1, -- ve: + -- + matrix [startVals], -- initial position estimate + -1, -- IFAIL + [retract(indxOb)@A49]@U49 -- objective function + ) ; + + location := entries(row(checkMxDF(e04dgfResult,"x","E04DGF"),1)) ; + + [ ((retract(lhs(startList.i))@SMBL)::PDF + = (location.i)::PDF)@EQPDF for i in 1..nv ] + + } + +} + +#if NeverAssertThis + +-- Note that the conversions of results from DoubleFloat to Float +-- will become unnecessary if outputGeneral is extended to apply to +-- DoubleFloat quantities. + +)lib nrc + +outputGeneral 5 + +f := %e^x*(4*x^2 + 2*y^2 + 4*x*y + 2*y + 1); +start := [x=-1.0, y=1.0]; +nagMin(f,start) :: List Equation Polynomial Float + +-- [x= 0.5,y= - 1.0] + +outputGeneral() + +output "End of tests" + +#endif + +@ +\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>> + +-- To test: +-- sed '1,/^#if NeverAssertThis/d;/#endif/d' < noptip.as > noptip.input +-- axiom +-- )set nag host <some machine running nagd> +-- )r noptip.input + +#unassert saturn + +#include "axiom.as" + +INT ==> Integer ; +NNI ==> NonNegativeInteger ; +MINT ==> Matrix INT ; +DF ==> DoubleFloat ; +EDF ==> Expression DF ; +EQEDF ==> Equation EDF ; +LEQEDF ==> List EQEDF ; +LDF ==> List DF ; +LLDF ==> List LDF ; +VDF ==> Vector DF ; +MDF ==> Matrix DF ; +PDF ==> Polynomial DF ; +EQPDF ==> Equation PDF ; +LEQPDF ==> List EQPDF ; +FL ==> Float ; +EF ==> Expression FL ; +BOOL ==> Boolean ; +A49 ==> Asp49("OBJFUN") ; +A55 ==> Asp55("CONFUN") ; +U49 ==> Union(fn: FileName, fp: A49) ; +U55 ==> Union(fn: FileName, fp: A55) ; +SMBL ==> Symbol ; +RSLT ==> Result ; +OF ==> OutputForm ; +LOF ==> List OF ; +LLOF ==> List LOF ; +EF2DFFL ==> ExpressionFunctions2(DF,FL) ; + +<<NagOptimisationInterfacePackage>> +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} |