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authordos-reis <gdr@axiomatics.org>2007-08-14 05:14:52 +0000
committerdos-reis <gdr@axiomatics.org>2007-08-14 05:14:52 +0000
commitab8cc85adde879fb963c94d15675783f2cf4b183 (patch)
treec202482327f474583b750b2c45dedfc4e4312b1d /src/interp/nag-d03.boot.pamphlet
downloadopen-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz
Initial population.
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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/interp nag-d03.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>>
+
+d03edf() ==
+ htInitPage('"D03EDF - Elliptic PDE, solution of finite difference equations by a multigrid technique ",nil)
+ htMakePage '(
+ (domainConditions
+ (isDomain EM $EmptyMode)
+ (isDomain F (Float)))
+ (text . "\windowlink{Manual Page}{manpageXXd03edf} for this routine ")
+ (text . "\newline ")
+ (text . "\lispwindowlink{Browser operation page}{(|oPageFrom| '|d03edf| '|NagPartialDifferentialEquationsPackage|)} for this routine")
+ (text . "\newline \horizontalline ")
+ (text . "\newline ")
+ (text . "D03EDF solves, by multigrid iteration, the seven point scheme ")
+ (text . "\newline \htbitmap{d03edf} \newline which arises from the ")
+ (text . "discretization of an elliptic partial differential equation of ")
+ (text . "the form \center{\htbitmap{d03edf1}} and its boundary conditions")
+ (text . ", defined on a rectangular region. This we can write in matrix ")
+ (text . "form as \newline \center{{\it Au =f}}")
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "Read the input file to see the example program. ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "\spadcommand{)read d03edf \bound{s0}} ")
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "If you would like to enter a problem, ")
+ (text . "how would you like to input the matrices? ")
+ (radioButtons matrix
+ ("" " By entering individual entries" long)
+ ("" " By entering matrix names already defined on the command line" short)))
+ htMakeDoneButton('"Continue", 'd03edfControl)
+ htShowPage()
+
+d03edfControl(htPage) ==
+ type := htpButtonValue(htPage,'matrix)
+ if (type = 'long) then
+ d03edfLong()
+ else
+ d03edfShort()
+
+d03edfLong() ==
+ htInitPage('"D03EDF - Elliptic PDE, solution of finite difference equations by a multigrid technique ",nil)
+ htMakePage '(
+ (domainConditions
+ (isDomain EM $EmptyMode)
+ (isDomain F (Float)))
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Number of interior grid points in the {\it x}-direction ")
+ (text . "{\it ngx}: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 3 ngx PI))
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Number of interior grid points in the {\it y}-direction ")
+ (text . "{\it ngy}: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 3 ngy PI))
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "First dimension of A, {\it lda}: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 22 lda PI))
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Maximum permitted number of multigrid iterations, {\it maxit}: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 1 maxit PI))
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Tolerance required, {\it acc}: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 "1.0e-4" acc F))
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "\newline Output of printed information for routine {\it iout}:")
+ (radioButtons iout
+ ("" " 0 - no output" zero)
+ ("" " 1 - the solution \htbitmap{uij} {\it i} = 1,2,...,NGX; {\it j} = 1,2,...,NGY" one)
+ ("" " 2 - residual 2-norm after each iteration " two)
+ ("" " 3 - as for iout = 1 & iout = 2" three)
+ ("" " 4 - as for iout = 3, plus the final residual" four)
+ ("" " 5 - as for iout = 4, plus initial elements of A & RHS" five)
+ ("" " 6 - as for iout = 5, plus Galerkin coarse grid approximations" six)
+ ("" " 7 - as for iout = 6, plus the incomplete Crout decompositions" seven)
+ ("" " 8 - as for iout = 7, plus the residual after each iteration" eight))
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "\newline Ifail value:")
+ (radioButtons ifail
+ ("" " -1, Print error messages" ifail_minusOne)
+ ("" " 1, Suppress error messages" ifail_one)))
+ htMakeDoneButton('"Continue", 'd03edfSolve)
+ htShowPage()
+
+
+d03edfSolve htPage ==
+ ngx :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'ngx)
+ objValUnwrap htpLabelSpadValue(htPage, 'ngx)
+ ngy :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'ngy)
+ objValUnwrap htpLabelSpadValue(htPage, 'ngy)
+ lda :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'lda)
+ objValUnwrap htpLabelSpadValue(htPage, 'lda)
+ maxit :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'maxit)
+ objValUnwrap htpLabelSpadValue(htPage, 'maxit)
+ acc := htpLabelInputString(htPage,'acc)
+ control := htpButtonValue(htPage,'iout)
+ iout :=
+ control = 'zero => '0
+ control = 'one => '1
+ control = 'two => '2
+ control = 'three => '3
+ control = 'four => '4
+ control = 'five => '5
+ control = 'six => '6
+ control = 'seven => '7
+ '8
+ error := htpButtonValue(htPage,'ifail)
+ ifail :=
+ error = 'ifail_one => '1
+ '-1
+ aList :=
+ "append"/[fa(i) for i in 1..lda] where fa(i) ==
+ labelList :=
+ "append"/[fb(i,j) for j in 1..7] where fb(i,j) ==
+ anam := INTERN STRCONC ('"a",STRINGIMAGE i,STRINGIMAGE j)
+ [['bcStrings,[5, 0, anam, 'F]]]
+ prefix := ('"\newline ")
+ labelList := [['text,:prefix],:labelList]
+ middle := ('"\blankline \menuitemstyle{} \tab{2} Enter the matrix ")
+ middle := STRCONC(middle,'"{\it rhs(lda)}: \newline ")
+ rList :=
+ "append"/[fc(i) for i in 1..lda] where fc(i) ==
+ rnam := INTERN STRCONC ('"r",STRINGIMAGE i)
+ [['bcStrings,[6, "0.0", rnam, 'F]]]
+ rList := [['text,:middle],:rList]
+ mid:= ('"\blankline \menuitemstyle{} \tab{2} Enter the matrix ")
+ mid := STRCONC(mid,'" {\it ub(ngx*ngy)}: \newline ")
+ uList :=
+ "append"/[fd(i) for i in 1..(ngx*ngy)] where fd(i) ==
+ unam := INTERN STRCONC ('"u",STRINGIMAGE i)
+ [['bcStrings,[6, 0, unam, 'F]]]
+ uList := [['text,:mid],:uList]
+ equationPart := [
+ '(domainConditions
+ (isDomain EM $EmptyMode)
+ (isDomain S (String))
+ (isDomain F (Float))
+ (isDomain I (Integer))),
+ :aList,:rList,:uList]
+ page := htInitPage('"D03EDF - Elliptic PDE, solution of finite difference equations by a multigrid technique ",nil)
+ htSay '"\menuitemstyle{}\tab{2} "
+ htSay '"Enter the matrix {\it a(lda,7)}: "
+ htSay '"\newline "
+ htMakePage equationPart
+ htMakeDoneButton('"Continue",'d03edfLongGen)
+ htpSetProperty(page,'ngx,ngx)
+ htpSetProperty(page,'ngy,ngy)
+ htpSetProperty(page,'lda,lda)
+ htpSetProperty(page,'maxit,maxit)
+ htpSetProperty(page,'acc,acc)
+ htpSetProperty(page,'iout,iout)
+ htpSetProperty(page,'ifail,ifail)
+ htpSetProperty(page,'inputArea, htpInputAreaAlist htPage)
+ htShowPage()
+
+d03edfLongGen htPage ==
+ ngx := htpProperty(htPage, 'ngx)
+ ngy := htpProperty(htPage, 'ngy)
+ lda := htpProperty(htPage, 'lda)
+ maxit := htpProperty(htPage, 'maxit)
+ acc := htpProperty(htPage, 'acc)
+ iout := htpProperty(htPage, 'iout)
+ ifail := htpProperty(htPage, 'ifail)
+ alist := htpInputAreaAlist htPage
+ y := alist
+ for i in 1..(ngx*ngy) repeat
+ utemp := STRCONC((first y).1," ")
+ uList := [utemp,:uList]
+ y := rest y
+ ustring := bcwords2liststring uList
+ for i in 1..lda repeat
+ rtemp := STRCONC((first y).1," ")
+ rList := [rtemp,:rList]
+ y := rest y
+ rstring := bcwords2liststring rList
+ for i in 1..lda repeat
+ for j in 1..7 repeat
+ v := STRCONC((first y).1," ")
+ rowList := [v,:rowList]
+ y := rest y
+ vList := [:vList,rowList]
+ rowList := []
+ vList := reverse vList
+ astring := bcwords2liststring [bcwords2liststring x for x in vList]
+ prefix := STRCONC("d03edf(", STRINGIMAGE ngx,", ",STRINGIMAGE ngy,", ")
+ prefix := STRCONC(prefix,STRINGIMAGE lda,", ",STRINGIMAGE maxit,", ",acc)
+ mid := STRCONC(", ",STRINGIMAGE iout,", ",astring,"::Matrix DoubleFloat,[")
+ mid := STRCONC(mid,rstring,"],[",ustring,"],",STRINGIMAGE ifail,")")
+ linkGen STRCONC(prefix,mid)
+
+d03edfShort() ==
+ htInitPage('"D03EDF - Elliptic PDE, solution of finite difference equations by a multigrid technique ",nil)
+ htMakePage '(
+ (domainConditions
+ (isDomain EM $EmptyMode)
+ (isDomain F (Float)))
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Number of interior grid points in the {\it x}-direction ")
+ (text . "\htbitmap{nx}: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 0 ngx PI))
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Number of interior grid points in the {\it y}-direction ")
+ (text . "\htbitmap{ny}: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 0 ngy PI))
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "First dimension of A, {\it lda}: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 0 lda PI))
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Name of the array {\it a(lda,7)} defined on the command line: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 "a" a EM))
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Name of the array {\it rhs(lda)} defined on the command line: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 "rhs" rhs EM))
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Name of the array {\it ub(ngx*ngy)} defined on the command line:")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 "ub" ub EM))
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Maximum permitted number of multigrid iterations, {\it maxit}: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 0 maxit PI))
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Tolerance required, {\it acc}: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 "1.0e-4" acc F))
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "\newline Output of printed information for routine {\it iout}:")
+ (radioButtons iout
+ ("" " 0 - no output" zero)
+ ("" " 1 - the solution \htbitmap{uij} {\it i} = 1,2,...,NGX; {\it j} = 1,2,...,NGY" one)
+ ("" " 2 - residual 2-norm after each iteration " two)
+ ("" " 3 - as for iout = 1 & iout = 2" three)
+ ("" " 4 - as for iout = 3, plus the final residual" four)
+ ("" " 5 - as for iout = 4, plus initial elements of A & RHS" five)
+ ("" " 6 - as for iout = 5, plus Galerkin coarse grid approximations" six)
+ ("" " 7 - as for iout = 6, plus the incomplete Crout decompositions" seven)
+ ("" " 8 - as for iout = 7, plus the residual after each iteration" eight))
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "\newline Ifail value:")
+ (radioButtons ifail
+ ("" " -1, Print error messages" ifail_minusOne)
+ ("" " 1, Suppress error messages" ifail_one)))
+ htMakeDoneButton('"Continue", 'd03edfShortGen)
+ htShowPage()
+
+
+d03edfShortGen htPage ==
+ ngx :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'ngx)
+ objValUnwrap htpLabelSpadValue(htPage, 'ngx)
+ ngy :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'ngy)
+ objValUnwrap htpLabelSpadValue(htPage, 'ngy)
+ lda :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'lda)
+ objValUnwrap htpLabelSpadValue(htPage, 'lda)
+ maxit :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'maxit)
+ objValUnwrap htpLabelSpadValue(htPage, 'maxit)
+ a := htpLabelInputString(htPage, 'a)
+ rhs := htpLabelInputString(htPage, 'rhs)
+ ub := htpLabelInputString(htPage, 'ub)
+ acc := htpLabelInputString(htPage,'acc)
+ control := htpButtonValue(htPage,'iout)
+ iout :=
+ control = 'zero => '0
+ control = 'one => '1
+ control = 'two => '2
+ control = 'three => '3
+ control = 'four => '4
+ control = 'five => '5
+ control = 'six => '6
+ control = 'seven => '7
+ '8
+ error := htpButtonValue(htPage,'ifail)
+ ifail :=
+ error = 'ifail_one => '1
+ '-1
+ prefix := STRCONC("d03edf(", STRINGIMAGE ngx,", ",STRINGIMAGE ngy,", ")
+ prefix := STRCONC(prefix,STRINGIMAGE lda,", ",STRINGIMAGE maxit,", ",acc)
+ mid := STRCONC(", ",STRINGIMAGE iout,", ",a,", ")
+ mid := STRCONC(mid,rhs,", ",ub,", ",STRINGIMAGE ifail,")")
+ linkGen STRCONC(prefix,mid)
+
+
+
+d03eef() ==
+ htInitPage('"D03EEF - Discretize a 2nd order elliptic PDE on a rectangle",nil)
+ htMakePage '(
+ (domainConditions
+ (isDomain EM $EmptyMode)
+ (isDomain F (Float)))
+ (text . "\windowlink{Manual Page}{manpageXXd03eef} for this routine ")
+ (text . "\newline ")
+ (text . "\lispwindowlink{Browser operation page}{(|oPageFrom| '|d03eef| '|NagPartialDifferentialEquationsPackage|)} for this routine")
+ (text . "\newline \horizontalline ")
+ (text . "\newline ")
+ (text . "D03EEF discretizes a second order linear elliptic partial ")
+ (text . "differential equation of the form \center{\htbitmap{d03eef}} ")
+ (text . "on a rectangular region \newline \tab{2} ")
+ (text . "{\it x}a \htbitmap{less=} {\it x} \htbitmap{less=} {\it x}b ")
+ (text . "\newline \tab{2} {\it y}a \htbitmap{less=} {\it y} ")
+ (text . "\htbitmap{less=} {\it y}b \newline subject to the boundary ")
+ (text . "conditions of the form \newline \htbitmap{d03eef1} \newline ")
+ (text . "where {\it \delta U/ \delta n} denotes the outward pointing ")
+ (text . "normal derivative on the boundary. The equation is said to be ")
+ (text . "elliptic if \center{\htbitmap{d03eef2}} \newline for all points ")
+ (text . "in the rectangular region. The seven-diagonal linear equations ")
+ (text . "produced are in a form suitable for passing directly to the ")
+ (text . "multigrid routine D03EDF. \blankline ")
+ (text . "The equation is discretized on a rectangular grid, with ")
+ (text . "\htbitmap{nx} grid points in the {\it x}-direction and ")
+ (text . "\htbitmap{ny} grid points in the {\it y}-direction. "))
+ htMakeDoneButton('"Continue", 'd03eefInput)
+ htShowPage()
+
+d03eefInput() ==
+ htInitPage('"D03EEF - Discretize a 2nd order elliptic PDE on a rectangle",nil)
+ htMakePage '(
+ (domainConditions
+ (isDomain EM $EmptyMode)
+ (isDomain F (Float)))
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Enter the value {\it x}a, {\it xmin}: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 "0.0" xmin F))
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Enter the value {\it x}b, {\it xmax}: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 "1.0" xmax F))
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Enter the value {\it y}a, {\it ymin}: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 "0.0" ymin F))
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Enter the value {\it y}b, {\it ymax}: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 "1.0" ymax F))
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Number of interior grid points in the {\it x}-direction ")
+ (text . "{\it ngx}: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 9 ngx PI))
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Number of interior grid points in the {\it y}-direction ")
+ (text . "{\it ngy}: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 9 ngy PI))
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "First dimension of A, {\it lda}: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 133 lda PI))
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "\newline Which {\it scheme} would you like to use: ")
+ (radioButtons scheme
+ (" C" " central differences" cent)
+ (" U" " upwind differences" up))
+ (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", 'd03eefSolve)
+ htShowPage()
+
+
+
+d03eefSolve htPage ==
+ xmin := htpLabelInputString(htPage,'xmin)
+ xmax := htpLabelInputString(htPage,'xmax)
+ ymin := htpLabelInputString(htPage,'ymin)
+ ymax := htpLabelInputString(htPage,'ymax)
+ ngx :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'ngx)
+ objValUnwrap htpLabelSpadValue(htPage, 'ngx)
+ ngy :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'ngy)
+ objValUnwrap htpLabelSpadValue(htPage, 'ngy)
+ lda :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'lda)
+ objValUnwrap htpLabelSpadValue(htPage, 'lda)
+ diff := htpButtonValue(htPage,'scheme)
+ scheme :=
+ diff = 'cent => '"C"
+ '"U"
+ error := htpButtonValue(htPage,'ifail)
+ ifail :=
+ error = 'one => '1
+ '-1
+ d03eefDefaultSolve(htPage,xmin,xmax,ymin,ymax,ngx,ngy,lda,scheme,ifail)
+
+d03eefDefaultSolve(htPage,xmin,xmax,ymin,ymax,ngx,ngy,lda,scheme,ifail) ==
+ page := htInitPage('"D03EEF - Discretize a 2nd order elliptic PDE on a rectangle",nil)
+ htMakePage '(
+ (domainConditions
+ (isDomain EM $EmptyMode)
+ (isDomain F (Float)))
+ (text . "Please enter the values of \alpha to \psi to construct PDEF.")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "\alpha (x,y): \tab{10} ")
+ (bcStrings (46 1 alpha F))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "\beta (x,y): \tab{10} ")
+ (bcStrings (46 0 beta F))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "\gamma (x,y): \tab{10} ")
+ (bcStrings (46 1 gamma F))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "\delta (x,y): \tab{10} ")
+ (bcStrings (46 50 delta F))
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "\epsilon (x,y): \tab{10} ")
+ (bcStrings (46 50 eps F))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "\phi (x,y): \tab{10} ")
+ (bcStrings (46 0 phi F))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "\psi (x,y): \tab{10} ")
+ (bcStrings (55 "-2*sin(X)*sin(Y) + 50*cos(X)*sin(Y) +50*sin(X)*cos(Y)" psi EM))
+ (text . "\blankline ")
+ (text . "Please enter the boundary conditions a(x,y), b(x,y), and c(x,y) ")
+ (text . "for the top, bottom, left and right hand sides, to construct ")
+ (text . "BNDY. \blankline")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Bottom boundary conditions: ")
+ (text . "\newline a(x,y): \tab{10} ")
+ (bcStrings (46 0 a11 F))
+ (text . "\newline b(x,y): \tab{10} ")
+ (bcStrings (46 1 a12 F))
+ (text . "\newline c(x,y): \tab{10} ")
+ (bcStrings (46 "-sin(X)" a13 EM))
+ (text . "\blankline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Right boundary conditions: ")
+ (text . "\newline a(x,y): \tab{10} ")
+ (bcStrings (46 1 a21 F))
+ (text . "\newline b(x,y): \tab{10} ")
+ (bcStrings (46 0 a22 F))
+ (text . "\newline c(x,y): \tab{10} ")
+ (bcStrings (46 "sin(X)*sin(Y)" a23 EM))
+ (text . "\blankline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Top boundary conditions: ")
+ (text . "\newline a(x,y): \tab{10} ")
+ (bcStrings (46 1 a31 F))
+ (text . "\newline b(x,y): \tab{10} ")
+ (bcStrings (46 0 a32 F))
+ (text . "\newline c(x,y): \tab{10} ")
+ (bcStrings (46 "sin(X)*sin(Y)" a33 EM))
+ (text . "\blankline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Left boundary conditions: ")
+ (text . "\newline a(x,y): \tab{10} ")
+ (bcStrings (46 0 a41 F))
+ (text . "\newline b(x,y): \tab{10} ")
+ (bcStrings (46 1 a42 F))
+ (text . "\newline c(x,y): \tab{10} ")
+ (bcStrings (46 "-sin(Y)" a43 EM)))
+ htMakeDoneButton('"Continue",'d03eefGen)
+ htpSetProperty(page,'xmin,xmin)
+ htpSetProperty(page,'xmax,xmax)
+ htpSetProperty(page,'ymin,ymin)
+ htpSetProperty(page,'ymax,ymax)
+ htpSetProperty(page,'ngx,ngx)
+ htpSetProperty(page,'ngy,ngy)
+ htpSetProperty(page,'lda,lda)
+ htpSetProperty(page,'scheme,scheme)
+ htpSetProperty(page,'ifail,ifail)
+ htpSetProperty(page,'inputArea, htpInputAreaAlist htPage)
+ htShowPage()
+
+d03eefGen htPage ==
+ xmin := htpProperty(htPage, 'xmin)
+ xmax := htpProperty(htPage, 'xmax)
+ ymin := htpProperty(htPage, 'ymin)
+ ymax := htpProperty(htPage, 'ymax)
+ ngx := htpProperty(htPage, 'ngx)
+ ngy := htpProperty(htPage, 'ngy)
+ lda := htpProperty(htPage, 'lda)
+ scheme := htpProperty(htPage, 'scheme)
+ ifail := htpProperty(htPage, 'ifail)
+ alist := htpInputAreaAlist htPage
+ y := alist
+ for i in 1..4 repeat
+ for j in 1..3 repeat
+ v := STRCONC((first y).1," ")
+ rowList := [v,:rowList]
+ y := rest y
+ vList := [:vList,rowList]
+ rowList := []
+ vList := reverse vList
+ astring := bcwords2liststring [bcwords2liststring x for x in vList]
+ for i in 1..7 repeat
+ utemp := STRCONC((first y).1," ")
+ uList := [utemp,:uList]
+ y := rest y
+ ustring := bcwords2liststring uList
+ prefix := STRCONC("d03eef(",xmin,", ",xmax,", ",ymin,", ",ymax,", ")
+ prefix := STRCONC(prefix,STRINGIMAGE ngx,", ",STRINGIMAGE ngy,", ")
+ prefix := STRCONC(prefix,STRINGIMAGE lda,",_"",scheme,"_", ")
+ prefix := STRCONC(prefix,STRINGIMAGE ifail,", (",ustring)
+ prefix := STRCONC(prefix,"::Vector Expression Float)::ASP73('PDEF),(")
+ prefix := STRCONC(prefix,astring,"::Matrix Expression Float)::ASP74('BNDY))")
+ linkGen prefix
+
+d03faf() ==
+ htInitPage('"D03FAF - Elliptic PDE, Helmholtz equation, 3-D Cartesian co-ordinates",nil)
+ htMakePage '(
+ (domainConditions
+ (isDomain EM $EmptyMode)
+ (isDomain F (Float)))
+ (text . "\windowlink{Manual Page}{manpageXXd03faf} for this routine ")
+ (text . "\newline ")
+ (text . "\lispwindowlink{Browser operation page}{(|oPageFrom| '|d03faf| '|NagPartialDifferentialEquationsPackage|)} for this routine")
+ (text . "\newline \horizontalline ")
+ (text . "\newline ")
+ (text . "D03FAF solves the three-dimensional Helmholtz equation ")
+ (text . "in cartesian co-ordinates: \center{\htbitmap{d03faf}} \newline ")
+ (text . "This subroutine forms the system of linear equations resulting ")
+ (text . "fom the standard seven-point finite difference equations, ")
+ (text . "and then solves the system using a method based on the fast ")
+ (text . "Fourier transform (FFT) described by Swartztrauber. ")
+ (text . "\blankline")
+ (text . "\newline ")
+ (text . "Read the input file to see the example program. ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "\spadcommand{)read d03faf \bound{s0}} "))
+ htShowPage()
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}