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\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}
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