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authordos-reis <gdr@axiomatics.org>2007-09-20 14:50:49 +0000
committerdos-reis <gdr@axiomatics.org>2007-09-20 14:50:49 +0000
commit0850ca5458cb09b2d04cec162558500e9a05cf4a (patch)
treeaa76b50f08c662dab9a49b6ee9f0dc7318139ea1 /src/interp/nag-c05.boot.pamphlet
parent6f8caa148526efc14239febdc12f91165389a8ea (diff)
downloadopen-axiom-0850ca5458cb09b2d04cec162558500e9a05cf4a.tar.gz
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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/interp nag-c05.boot}
+\author{The Axiom Team}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\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>>
+
+c05adf() ==
+ htInitPage('"C05ADF - Zero of continuous function in given interval, Bus and Dekker algorithm",nil)
+ htMakePage '(
+ (domainConditions
+ (isDomain EM $EmptyMode)
+ (isDomain F (Float)))
+ (text . "\windowlink{Manual Page}{manpageXXc05adf} for this routine ")
+ (text . "\newline ")
+ (text . "\lispwindowlink{Browser operation page}{(|oPageFrom| '|c05adf| '|NagRootFindingPackage|)} for this routine")
+ (text . "\newline \horizontalline ")
+ (text . "\newline ")
+ (text . "C05ADF locates a zero of a continuous function in a ")
+ (text . "interval by a combination of the methods of linear ")
+ (text . "interpolation, extrapolation and bisection. ")
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Enter the function whose zero is to be determined ")
+ (text . "as a function of X, {\it f}: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (55 "exp(-X)-X" expression EM))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "\newline Lower bound of the interval {\it a}:")
+ (text . "\tab{32} \menuitemstyle{}\tab{34}")
+ (text . "Upper bound {\it b}: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 "0.0" a F))
+ (text . "\tab{34} ")
+ (bcStrings (10 "1.0" b F))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "\newline Absolute tolerance {\it eps}:")
+ (text . "\tab{32} \menuitemstyle{}\tab{34}")
+ (text . "Value tolerance {\it eta}:")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 "1.0e-5" eps F))
+ (text . "\tab{34} ")
+ (bcStrings (10 "0.0" eta F))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "\newline Ifail value:")
+ (radioButtons ifail
+ ("" " -1, Print error messages" minusOne)
+ ("" " 1, Suppress error messages" one)))
+ htMakeDoneButton('"Continue", 'c05adfGen)
+ htShowPage()
+
+c05adfGen htPage ==
+ a := htpLabelInputString(htPage,'a)
+ b := htpLabelInputString(htPage,'b)
+ eps := htpLabelInputString(htPage,'eps)
+ eta := htpLabelInputString(htPage,'eta)
+ temp := READ_-FROM_-STRING(eps)
+ error := htpButtonValue(htPage,'ifail)
+ ifail :=
+ error = 'one => 1
+ -1
+ temp1 :=
+ temp > 0.0 => eps
+ '"1.0e-5"
+ expression := htpLabelInputString(htPage, 'expression)
+ prefix := STRCONC('"c05adf(",a,",",b,",",temp1,",",eta,",",STRINGIMAGE ifail)
+ linkGen STRCONC (prefix,",(",expression,")::ASP1(F))")
+
+
+c05nbf() ==
+ htInitPage('"C05NBF - Solution of system of nonlinear equations using function values only",nil)
+ htMakePage '(
+ (domainConditions
+ (isDomain PI (PositiveInteger)))
+ (text . "\windowlink{Manual Page}{manpageXXc05nbf} for this routine ")
+ (text . "\newline ")
+ (text . "\lispwindowlink{Browser operation page}{(|oPageFrom| '|c05nbf| '|NagRootFindingPackage|)} for this routine")
+ (text . "\newline \horizontalline ")
+ (text . "\newline ")
+ (text . "C05NBF finds a solution of a system of nonlinear equations ")
+ (text . "by a modification of the Powell hybrid method. ")
+ (text . "\blankline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "Enter the number of equations in the system {\it n}:")
+ (text . "\newline\tab{2} ")
+ (bcStrings (5 9 n PI))
+ (text . "\newline ")
+ (text . "\blankline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "Accuracy required {\it xtol}:")
+ (text . "\newline\tab{2} ")
+ -- should be sqrt(machine precision)
+ (bcStrings (10 "1.0e-9" xtol F))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "Ifail value:")
+ (radioButtons ifail
+ ("" " -1, Print error messages" minusOne)
+ ("" " 1, Suppress error messages" one)))
+ htMakeDoneButton('"Continue", 'c05nbfSolve)
+ htShowPage()
+
+c05nbfSolve htPage ==
+ n :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'n)
+ objValUnwrap htpLabelSpadValue(htPage, 'n)
+ xtol := htpLabelInputString(htPage,'xtol)
+ error := htpButtonValue(htPage,'ifail)
+ ifail :=
+ error = 'one => '1
+ '-1
+ n = '9 => c05nbfDefaultSolve(htPage,ifail,xtol)
+ funcList :=
+ "append"/[fa(i) for i in 1..n] where fa(i) ==
+ prefix := ('"\newline {\em Function ")
+ prefix := STRCONC(prefix,STRINGIMAGE i,'":} \space{1}")
+ funct := STRCONC ('"X[",STRINGIMAGE i ,"] + 1")
+ nam := INTERN STRCONC ('"n",STRINGIMAGE i)
+ [['text,:prefix],['bcStrings,[42, funct, nam, 'EM]]]
+ middle := ('"\blankline \menuitemstyle{}\tab{2} Enter initial guess ")
+ middle := STRCONC(middle,'"of the solution vector {\it x}: \newline ")
+ middle := cons('text,middle)
+ vecList :=
+ [fb(i) for i in 1..n] where fb(i) ==
+ xnam := INTERN STRCONC ('"x",STRINGIMAGE i)
+ ['bcStrings,[4, -1.0, xnam, 'F]]
+ funcList := [:funcList,middle,:vecList]
+ equationPart := [
+ '(domainConditions
+ (isDomain EM $EmptyMode)
+ (isDomain F (Float))
+ (isDomain I (Integer))),
+ :funcList]
+ page := htInitPage("C05NBF - Solution of system of nonlinear equations using function values only", htpPropertyList htPage)
+ htSay '"\menuitemstyle{}\tab{2} "
+ htSay '"Enter the functions \htbitmap{fi} below in terms of X[1]...X[n]: "
+ htSay '"\newline "
+ htMakePage equationPart
+ htMakeDoneButton('"Continue",'c05nbfGen)
+ htpSetProperty(page,'n,n)
+ htpSetProperty(page,'ifail,ifail)
+ htpSetProperty(page,'xtol,xtol)
+ htpSetProperty(page,'inputArea, htpInputAreaAlist htPage)
+ htShowPage()
+
+
+c05nbfDefaultSolve (htPage,ifail,xtol) ==
+ n := '9
+ page := htInitPage("C05NBF - Solution of system of nonlinear equations using function values only", nil)
+ htMakePage '(
+ (domainConditions
+ (isDomain EM $EmptyMode)
+ (isDomain F (Float))
+ (isDomain I (Integer)))
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "Enter the functions \htbitmap{fi} below in terms of X[1]...X[n]; ")
+ (text . " \newline ")
+ (text . "\newline {\em Function 1:} \space{1}")
+ (bcStrings (42 "3*X[1] - 2*X[1]**2 - 2*X[2] + 1" n1 EM))
+ (text . "\newline {\em Function 2:} \space{1}")
+ (bcStrings (42 "-X[1] + 3*X[2] - 2*X[2]**2 - 2*X[3] + 1" n2 EM))
+ (text . "\newline {\em Function 3:} \space{1}")
+ (bcStrings (42 "-X[2] + 3*X[3] - 2*X[3]**2 - 2*X[4] + 1" n3 EM))
+ (text . "\newline {\em Function 4:} \space{1}")
+ (bcStrings (42 "-X[3] + 3*X[4] - 2*X[4]**2 - 2*X[5] + 1" n4 EM))
+ (text . "\newline {\em Function 5:} \space{1}")
+ (bcStrings (42 "-X[4] + 3*X[5] - 2*X[5]**2 - 2*X[6] + 1" n5 EM))
+ (text . "\newline {\em Function 6:} \space{1}")
+ (bcStrings (42 "-X[5] + 3*X[6] - 2*X[6]**2 - 2*X[7] + 1" n6 EM))
+ (text . "\newline {\em Function 7:} \space{1}")
+ (bcStrings (42 "-X[6] + 3*X[7] - 2*X[7]**2 - 2*X[8] + 1" n7 EM))
+ (text . "\newline {\em Function 8:} \space{1}")
+ (bcStrings (42 "-X[7] + 3*X[8] - 2*X[8]**2 - 2*X[9] + 1" n8 EM))
+ (text . "\newline {\em Function 9:} \space{1}")
+ (bcStrings (42 "-X[8] + 3*X[9] - 2*X[9]**2 + 1" n9 EM))
+ (text . "\blankline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "Enter initial guess of the solution vector {\it x}: \newline ")
+ (bcStrings (4 "-1.0" x1 F))
+ (bcStrings (4 "-1.0" x2 F))
+ (bcStrings (4 "-1.0" x3 F))
+ (bcStrings (4 "-1.0" x4 F))
+ (bcStrings (4 "-1.0" x5 F))
+ (bcStrings (4 "-1.0" x6 F))
+ (bcStrings (4 "-1.0" x7 F))
+ (bcStrings (4 "-1.0" x8 F))
+ (bcStrings (4 "-1.0" x9 F)))
+ htMakeDoneButton('"Continue",'c05nbfGen)
+ htpSetProperty(page,'n,n)
+ htpSetProperty(page,'ifail,ifail)
+ htpSetProperty(page,'xtol,xtol)
+ htpSetProperty(page,'inputArea, htpInputAreaAlist htPage)
+ htShowPage()
+
+c05nbfGen htPage ==
+ n := htpProperty(htPage, 'n)
+ ifail := htpProperty(htPage,'ifail)
+ xtol := htpProperty(htPage,'xtol)
+ alist := htpInputAreaAlist htPage
+ y := alist
+ i := 1
+ while y repeat
+ if i < (n+1) then
+ temp1 := STRCONC ((first y).1," ")
+ temp1list := [temp1,:temp1list]
+ else
+ temp2 := (first y).1
+ temp2list := [temp2,:temp2list]
+ y := rest y
+ i := i + 1
+ string1 := bcwords2liststring temp1list
+ string2 := bcwords2liststring temp2list
+ lwa := n*(3*n+13)/2
+ prefix := STRCONC ("c05nbf(",STRINGIMAGE n,",",STRINGIMAGE lwa,",[",string1,"],")
+ middle := STRCONC (xtol,",",STRINGIMAGE ifail,",")
+ linkGen STRCONC (prefix,middle,"(",string2,"::Vector Expression(Float))::ASP6(FCN))")
+
+c05pbf() ==
+ htInitPage('"C05PBF - Solution of system of nonlinear equations using first derivatives",nil)
+ htMakePage '(
+ (domainConditions
+ (isDomain PI (PositiveInteger)))
+ (text . "\windowlink{Manual Page}{manpageXXc05pbf} for this routine ")
+ (text . "\newline ")
+ (text . "\lispwindowlink{Browser operation page}{(|oPageFrom| '|c05pbf| '|NagRootFindingPackage|)} for this routine")
+ (text . "\newline \horizontalline ")
+ (text . "\newline ")
+ (text . "C05PBF finds a solution of a system of nonlinear equations ")
+ (text . "by a modification of the Powell hybrid method. ")
+ (text . "\blankline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "Enter the number of equations in the system {\it n}:")
+ (text . "\newline\tab{2} ")
+ (bcStrings (5 9 n PI))
+ (text . "\newline ")
+ (text . "\blankline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "Accuracy required {\it xtol}:")
+ (text . "\newline\tab{2} ")
+ -- should be sqrt(machine precision)
+ (bcStrings (10 "1.0e-9" xtol F))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "Ifail value:")
+ (radioButtons ifail
+ ("" " -1, Print error messages" minusOne)
+ ("" " 1, Suppress error messages" one)))
+ htMakeDoneButton('"Continue", 'c05pbfSolve)
+ htShowPage()
+
+c05pbfSolve htPage ==
+ n :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'n)
+ objValUnwrap htpLabelSpadValue(htPage, 'n)
+ xtol := htpLabelInputString(htPage,'xtol)
+ error := htpButtonValue(htPage,'ifail)
+ ifail :=
+ error = 'one => '1
+ '-1
+ n = '9 => c05pbfDefaultSolve(htPage,ifail,xtol)
+ funcList :=
+ "append"/[fa(i) for i in 1..n] where fa(i) ==
+ prefix := ('"\newline {\em Function ")
+ prefix := STRCONC(prefix,STRINGIMAGE i,'":} \space{1}")
+ funct := STRCONC ('"X[",STRINGIMAGE i ,"] + 1")
+ nam := INTERN STRCONC ('"n",STRINGIMAGE i)
+ [['text,:prefix],['bcStrings,[42, funct, nam, 'EM]]]
+ middle := ('"\blankline \menuitemstyle{}\tab{2} Enter initial guess ")
+ middle := STRCONC(middle,'"of the solution vector {\it x}: \newline ")
+ middle := cons('text,middle)
+ vecList :=
+ [fb(i) for i in 1..n] where fb(i) ==
+ xnam := INTERN STRCONC ('"x",STRINGIMAGE i)
+ ['bcStrings,[4, -1.0, xnam, 'F]]
+ funcList := [:funcList,middle,:vecList]
+ equationPart := [
+ '(domainConditions
+ (isDomain EM $EmptyMode)
+ (isDomain F (Float))
+ (isDomain I (Integer))),
+ :funcList]
+ page := htInitPage('"C05PBF - Solution of system of nonlinear equations using first derivatives",htpPropertyList htPage)
+ htSay '"\menuitemstyle{}\tab{2} "
+ htSay '"Enter the functions \htbitmap{fi} below in terms of X[1]...X[n]: "
+ htSay '"\newline "
+ htMakePage equationPart
+ htMakeDoneButton('"Continue",'c05pbfGen)
+ htpSetProperty(page,'n,n)
+ htpSetProperty(page,'ifail,ifail)
+ htpSetProperty(page,'xtol,xtol)
+ htpSetProperty(page,'inputArea, htpInputAreaAlist htPage)
+ htShowPage()
+
+
+c05pbfDefaultSolve (htPage,ifail,xtol) ==
+ n := '9
+ page := htInitPage('"C05PBF - Solution of system of nonlinear equations using first derivatives",nil)
+ htMakePage '(
+ (domainConditions
+ (isDomain EM $EmptyMode)
+ (isDomain F (Float))
+ (isDomain I (Integer)))
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "Enter the functions \htbitmap{fi} below in terms of X[1]...X[n]: ")
+ (text . "\newline ")
+ (text . "\newline {\em Function 1:} \space{1}")
+ (bcStrings (42 "3*X[1] - 2*X[1]**2 - 2*X[2] + 1" n1 EM))
+ (text . "\newline {\em Function 2:} \space{1}")
+ (bcStrings (42 "-X[1] + 3*X[2] - 2*X[2]**2 - 2*X[3] + 1" n2 EM))
+ (text . "\newline {\em Function 3:} \space{1}")
+ (bcStrings (42 "-X[2] + 3*X[3] - 2*X[3]**2 - 2*X[4] + 1" n3 EM))
+ (text . "\newline {\em Function 4:} \space{1}")
+ (bcStrings (42 "-X[3] + 3*X[4] - 2*X[4]**2 - 2*X[5] + 1" n4 EM))
+ (text . "\newline {\em Function 5:} \space{1}")
+ (bcStrings (42 "-X[4] + 3*X[5] - 2*X[5]**2 - 2*X[6] + 1" n5 EM))
+ (text . "\newline {\em Function 6:} \space{1}")
+ (bcStrings (42 "-X[5] + 3*X[6] - 2*X[6]**2 - 2*X[7] + 1" n6 EM))
+ (text . "\newline {\em Function 7:} \space{1}")
+ (bcStrings (42 "-X[6] + 3*X[7] - 2*X[7]**2 - 2*X[8] + 1" n7 EM))
+ (text . "\newline {\em Function 8:} \space{1}")
+ (bcStrings (42 "-X[7] + 3*X[8] - 2*X[8]**2 - 2*X[9] + 1" n8 EM))
+ (text . "\newline {\em Function 9:} \space{1}")
+ (bcStrings (42 "-X[8] + 3*X[9] - 2*X[9]**2 + 1" n9 EM))
+ (text . "\blankline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "Enter initial guess of the solution vector {\it x}: \newline ")
+ (bcStrings (4 "-1.0" x1 F))
+ (bcStrings (4 "-1.0" x2 F))
+ (bcStrings (4 "-1.0" x3 F))
+ (bcStrings (4 "-1.0" x4 F))
+ (bcStrings (4 "-1.0" x5 F))
+ (bcStrings (4 "-1.0" x6 F))
+ (bcStrings (4 "-1.0" x7 F))
+ (bcStrings (4 "-1.0" x8 F))
+ (bcStrings (4 "-1.0" x9 F)))
+ htMakeDoneButton('"Continue",'c05pbfGen)
+ htpSetProperty(page,'n,n)
+ htpSetProperty(page,'ifail,ifail)
+ htpSetProperty(page,'xtol,xtol)
+ htpSetProperty(page,'inputArea, htpInputAreaAlist htPage)
+ htShowPage()
+
+c05pbfGen htPage ==
+ n := htpProperty(htPage, 'n)
+ ifail := htpProperty(htPage,'ifail)
+ xtol := htpProperty(htPage,'xtol)
+ alist := htpInputAreaAlist htPage
+ y := alist
+ i := 1
+ while y repeat
+ if i < (n+1) then
+ temp1 := STRCONC ((first y).1," ")
+ temp1list := [temp1,:temp1list]
+ else
+ temp2 := (first y).1
+ temp2list := [temp2,:temp2list]
+ y := rest y
+ i := i + 1
+ string1 := bcwords2liststring temp1list
+ string2 := bcwords2liststring temp2list
+ lwa := n*(n+13)/2
+ prefix := STRCONC("c05pbf(",STRINGIMAGE n,",",STRINGIMAGE n)
+ middle := STRCONC(",",STRINGIMAGE lwa,",[",string1,"],")
+ middle := STRCONC (middle,xtol,",",STRINGIMAGE ifail,",")
+ linkGen STRCONC (prefix,middle,"(",string2,"::Vector Expression(Float))::ASP35(FCN))")
+
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}