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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}
generated by cgit v1.2.3 (git 2.39.1) at 2024-12-26 15:05:28 +0000