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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-d01.boot.pamphlet
parent6f8caa148526efc14239febdc12f91165389a8ea (diff)
downloadopen-axiom-0850ca5458cb09b2d04cec162558500e9a05cf4a.tar.gz
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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/interp nag-d01.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>>
+
+d01ajf() ==
+ htInitPage('"D01AJF - 1-D quadrature, adaptive, finite interval, allowing for badly-behaved integrands", nil)
+ htMakePage '(
+ (domainConditions
+ (isDomain EM $EmptyMode)
+ (isDomain PI (PositiveInteger))
+ (isDomain F (Float)))
+ (text . "\windowlink{Manual Page}{manpageXXd01ajf} for this routine ")
+ (text . "\newline ")
+ (text . "\lispwindowlink{Browser operation page}{(|oPageFrom| '|d01ajf| '|NagIntegrationPackage|)} for this routine")
+ (text . "\newline \horizontalline ")
+ (text . "Evaluates the integral ")
+ (text . "\inputbitmap{\htbmdir{}/integral.bitmap} f(x) dx ")
+ (text . "using an adaptive method. ")
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Enter the {\em function} f to be integrated in terms of X: ")
+ (text . "\newline \tab{2} ")
+ (bcStrings (55 "X*sin(30*X)/(sqrt(1-(X/(2*\%pi))**2))" expression EM))
+ (text . "\blankline ")
+ (text . "\newline \menuitemstyle{}\tab{2} ")
+ (text . "\newline {\em Lower} bound of the interval: ")
+ (text . "\tab{32} \menuitemstyle{}\tab{34} ")
+ (text . "{\em Upper} bound:")
+ (text . "\newline\tab{2} ")
+ (bcStrings (20 "0.0" a F))
+ (text . "\tab{34} ")
+ (bcStrings (20 "\%pi*2" b EM))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "\newline Absolute accuracy required:")
+ (text . "\tab{32} \menuitemstyle{}\tab{34}")
+ (text . "Relative accuracy:")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 "0.0" epsabs F))
+ (text . "\tab{34} ")
+ (bcStrings (10 "1.0e-4" epsrel F))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "Dimension of workspace array: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 800 lw PI))
+ (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", 'd01ajfGen)
+ htShowPage()
+
+d01ajfGen htPage ==
+ lw :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'lw)
+ objValUnwrap htpLabelSpadValue(htPage, 'lw)
+ a := htpLabelInputString(htPage,'a)
+ b := htpLabelInputString(htPage,'b)
+ epsabs := htpLabelInputString(htPage,'epsabs)
+ epsrel := htpLabelInputString(htPage,'epsrel)
+ error := htpButtonValue(htPage,'ifail)
+ ifail :=
+ error = 'one => 1
+ -1
+ express := htpLabelInputString(htPage,'expression)
+ liw := lw/4
+ prefix := STRCONC("d01ajf(",a," ,",b," ,",epsabs," ,",epsrel," ,",STRINGIMAGE lw)
+ middle := STRCONC(" ,",STRINGIMAGE liw," ,",STRINGIMAGE ifail," ,")
+ end := STRCONC("(",express,"::Expression Float) :: ASP1(F))")
+ linkGen STRCONC(prefix,middle,end)
+
+d01akf() ==
+ htInitPage('"D01AKF - 1-D quadrature, adaptive, finite interval, method suitable for oscillating functions", nil)
+ htMakePage '(
+ (domainConditions
+ (isDomain EM $EmptyMode)
+ (isDomain PI (PositiveInteger))
+ (isDomain F (Float)))
+ (text . "\windowlink{Manual Page}{manpageXXd01akf} for this routine ")
+ (text . "\newline ")
+ (text . "\lispwindowlink{Browser operation page}{(|oPageFrom| '|d01akf| '|NagIntegrationPackage|)} for this routine")
+ (text . "\newline \horizontalline ")
+ (text . "Computes \space{1} \inputbitmap{\htbmdir{}/integral.bitmap} ")
+ (text . "f(x) dx using an adaptive method, ")
+ (text . "especially suited to oscillating, non-singular integrands. ")
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Enter the {\em function} f to be integrated in terms of X: ")
+ (text . "\newline \tab{2} ")
+ (bcStrings (55 "X*sin(30*X)*cos(X)" expression EM))
+ (text . "\blankline ")
+ (text . "\newline \menuitemstyle{}\tab{2} ")
+ (text . "\newline {\em Lower} bound of the interval: ")
+ (text . "\tab{32} \menuitemstyle{}\tab{34} ")
+ (text . "{\em Upper} bound:")
+ (text . "\newline\tab{2} ")
+ (bcStrings (20 "0.0" a F))
+ (text . "\tab{34} ")
+ (bcStrings (20 "\%pi*2" b EM))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "\newline Absolute accuracy required:")
+ (text . "\tab{32} \menuitemstyle{}\tab{34}")
+ (text . "Relative accuracy:")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 "0.0" epsabs F))
+ (text . "\tab{34} ")
+ (bcStrings (10 "1.0e-4" epsrel F))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "Dimension of workspace array: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 800 lw PI))
+ (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", 'd01akfGen)
+ htShowPage()
+
+d01akfGen htPage ==
+ lw :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'lw)
+ objValUnwrap htpLabelSpadValue(htPage, 'lw)
+ a := htpLabelInputString(htPage,'a)
+ b := htpLabelInputString(htPage,'b)
+ epsabs := htpLabelInputString(htPage,'epsabs)
+ epsrel := htpLabelInputString(htPage,'epsrel)
+ error := htpButtonValue(htPage,'ifail)
+ ifail :=
+ error = 'one => 1
+ -1
+ express := htpLabelInputString(htPage,'expression)
+ liw := lw/4
+ prefix := STRCONC("d01akf(",a," ,",b," ,",epsabs," ,",epsrel," ,",STRINGIMAGE lw)
+ middle := STRCONC(" ,",STRINGIMAGE liw," ,",STRINGIMAGE ifail," ,")
+ end := STRCONC("(",express,"::Expression Float) :: ASP1(F))")
+ linkGen STRCONC(prefix,middle,end)
+
+d01alf() ==
+ htInitPage('"D01ALF - 1-D quadrature, adaptive, finite interval, allowing for singularities at user-specified break-points ", nil)
+ htMakePage '(
+ (domainConditions
+ (isDomain EM $EmptyMode)
+ (isDomain PI (PositiveInteger))
+ (isDomain F (Float)))
+ (text . "\windowlink{Manual Page}{manpageXXd01alf} for this routine ")
+ (text . "\newline ")
+ (text . "\lispwindowlink{Browser operation page}{(|oPageFrom| '|d01alf| '|NagIntegrationPackage|)} for this routine")
+ (text . "\newline \horizontalline ")
+ (text . "Evaluates the integral \space{1} ")
+ (text . "\inputbitmap{\htbmdir{}/integral.bitmap} f(x) dx; ")
+ (text . "the integrand may have local singular behaviour at a ")
+ (text . "finite number of points within [a,b]. ")
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Enter the {\em function} f to be integrated in terms of X: ")
+ (text . "\newline \tab{2} ")
+ (bcStrings (55 "1/sqrt(abs(X-1/7))" expression EM))
+ (text . "\blankline ")
+ (text . "\newline \menuitemstyle{}\tab{2} ")
+ (text . "\newline {\em Lower} bound of the interval: ")
+ (text . "\tab{32} \menuitemstyle{}\tab{34} ")
+ (text . "{\em Upper} bound:")
+ (text . "\newline\tab{2} ")
+ (bcStrings (20 "0.0" a F))
+ (text . "\tab{34} ")
+ (bcStrings (20 "1.0" b EM))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "\newline Number of user supplied break-points: \tab{38}")
+ (bcStrings (10 "1" npts PI))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "\newline User supplied break-points (separated by commas): ")
+ (text . "\newline \tab{2} ")
+ (bcStrings (40 "1/7" points EM))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "\newline Absolute accuracy required:")
+ (text . "\tab{32} \menuitemstyle{}\tab{34}")
+ (text . "Relative accuracy:")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 "0.0" epsabs F))
+ (text . "\tab{34} ")
+ (bcStrings (10 "1.0e-4" epsrel F))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "Dimension of workspace array: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 800 lw PI))
+ (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", 'd01alfGen)
+ htShowPage()
+
+d01alfGen htPage ==
+ lw :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'lw)
+ objValUnwrap htpLabelSpadValue(htPage, 'lw)
+ a := htpLabelInputString(htPage,'a)
+ b := htpLabelInputString(htPage,'b)
+ npts :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'npts)
+ objValUnwrap htpLabelSpadValue(htPage, 'npts)
+ points := htpLabelInputString(htPage, 'points)
+ points := STRCONC ('"[[",points,"]]")
+ epsabs := htpLabelInputString(htPage,'epsabs)
+ epsrel := htpLabelInputString(htPage,'epsrel)
+ error := htpButtonValue(htPage,'ifail)
+ ifail :=
+ error = 'one => 1
+ -1
+ express := htpLabelInputString(htPage,'expression)
+ liw := lw/2
+ prefix := STRCONC('"d01alf(",a," ,",b," ,",STRINGIMAGE npts,",",points,",")
+ prefix := STRCONC(prefix,epsabs," ,",epsrel," ,",STRINGIMAGE lw)
+ middle := STRCONC('" ,",STRINGIMAGE liw," ,",STRINGIMAGE ifail," ,")
+ end := STRCONC('"(",express,"::Expression Float) :: ASP1(F))")
+ linkGen STRCONC(prefix,middle,end)
+
+d01amf() ==
+ htInitPage('"D01AMF 1-D quadrature, adaptive, infinite or semi-infinite interval",nil)
+ htMakePage '(
+ (domainConditions
+ (isDomain EM $EmptyMode)
+ (isDomain PI (PositiveInteger))
+ (isDomain F (Float)))
+ (text . "\windowlink{Manual Page}{manpageXXd01amf} for this routine ")
+ (text . "\newline ")
+ (text . "\lispwindowlink{Browser operation page}{(|oPageFrom| '|d01amf| '|NagIntegrationPackage|)} for this routine")
+ (text . "\newline \horizontalline ")
+ (text . "\newline ")
+ (text . "Evaluates the integral \space{1} ")
+ (text . "\inputbitmap{\htbmdir{}/integral.bitmap} f(x) dx, ")
+ (text . "where (a,b) can be an infinite or semi-infinite interval.")
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Enter the {\em function} f to be integrated in terms of X: ")
+ (text . "\newline \tab{2} ")
+ (bcStrings (55 "1/((X+1)*sqrt(X))" expression EM))
+ (text . "\blankline ")
+ (text . "\newline \menuitemstyle{}\tab{2} ")
+ (text . "\newline {\em Bound} the finite limit of the integration range: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 "0.0" a F))
+ (text . "\blankline ")
+ (text . "\newline \menuitemstyle{}\tab{2} ")
+ (text . "\newline Choose the kind of integration range: ")
+ (radioButtons inf
+ (" 1" "\tab{2} Range is [Bound, +infinity] " plus)
+ ("-1" "\tab{2} Range is [-infinity, Bound] " minus)
+ ("2" "\tab{2} Range is [-infinity, +infinity] (Bound is not used) " minusPlus))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "\newline Absolute accuracy required:")
+ (text . "\tab{32} \menuitemstyle{}\tab{34}")
+ (text . "Relative accuracy:")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 "0.0" epsabs F))
+ (text . "\tab{34} ")
+ (bcStrings (10 "1.0e-4" epsrel F))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "Dimension of workspace array: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 800 lw PI))
+ (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", 'd01amfGen)
+ htShowPage()
+
+d01amfGen htPage ==
+ lw :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'lw)
+ objValUnwrap htpLabelSpadValue(htPage, 'lw)
+ a := htpLabelInputString(htPage,'a)
+ b := htpLabelInputString(htPage,'b)
+ infinity := htpButtonValue(htPage,'inf)
+ inf :=
+ infinity = 'plus => 1
+ infinity = 'minus => -1
+ 2
+ epsabs := htpLabelInputString(htPage,'epsabs)
+ epsrel := htpLabelInputString(htPage,'epsrel)
+ error := htpButtonValue(htPage,'ifail)
+ ifail :=
+ error = 'one => 1
+ -1
+ express := htpLabelInputString(htPage,'expression)
+ liw := lw/4
+ prefix := STRCONC('"d01amf(",a," ,",STRINGIMAGE inf," ,")
+ prefix := STRCONC(prefix,epsabs," ,",epsrel," ,",STRINGIMAGE lw)
+ middle := STRCONC('" ,",STRINGIMAGE liw," ,",STRINGIMAGE ifail," ,")
+ end := STRCONC('"(",express,"::Expression Float) :: ASP1(F))")
+ linkGen STRCONC(prefix,middle,end)
+
+d01anf() ==
+ htInitPage('"D01ANF - 1-D quadrature, adaptive, finite interval, weight function cos(\omega x) or sin(\omega x)", nil)
+ htMakePage '(
+ (domainConditions
+ (isDomain EM $EmptyMode)
+ (isDomain PI (PositiveInteger))
+ (isDomain F (Float)))
+ (text . "\windowlink{Manual Page}{manpageXXd01anf} for this routine ")
+ (text . "\newline ")
+ (text . "\lispwindowlink{Browser operation page}{(|oPageFrom| '|d01anf| '|NagIntegrationPackage|)} for this routine")
+ (text . "\newline \horizontalline ")
+ (text . "Evaluates \inputbitmap{\htbmdir{}/integral.bitmap} g(x)sin(\omega x) dx ")
+ (text . "or \inputbitmap{\htbmdir{}/integral.bitmap} g(x)cos(\omega x) dx, ")
+ (text . "the sine and cosine transform respectively. ")
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Enter the {\em function} f to be integrated in terms of X: ")
+ (text . "\newline \tab{2} ")
+ (bcStrings (55 "log(X)" expression EM))
+ (text . "\blankline ")
+ (text . "\newline \menuitemstyle{}\tab{2} ")
+ (text . "\newline {\em Lower} bound of the interval: ")
+ (text . "\tab{32} \menuitemstyle{}\tab{34} ")
+ (text . "{\em Upper} bound:")
+ (text . "\newline\tab{2} ")
+ (bcStrings (20 "1.0e-6" a F))
+ (text . "\tab{34} ")
+ (bcStrings (20 "1.0" b EM))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "\newline Absolute accuracy required:")
+ (text . "\tab{32} \menuitemstyle{}\tab{34}")
+ (text . "Relative accuracy:")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 "0.0" epsabs F))
+ (text . "\tab{34} ")
+ (bcStrings (10 "1.0e-4" epsrel F))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "Dimension of workspace: ")
+ (text . "\tab{32} \menuitemstyle{}\tab{34}")
+ (text . "\omega the weight function:")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 800 lw PI))
+ (text . "\tab{34} ")
+ (bcStrings (20 "10*\%pi" omega F))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "Key value, indicates which integral is to be computed:")
+ (radioButtons key
+ ("" " sin" sin)
+ ("" " cos" cos))
+ (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", 'd01anfGen)
+ htShowPage()
+
+d01anfGen htPage ==
+ lw :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'lw)
+ objValUnwrap htpLabelSpadValue(htPage, 'lw)
+ a := htpLabelInputString(htPage,'a)
+ b := htpLabelInputString(htPage,'b)
+ epsabs := htpLabelInputString(htPage,'epsabs)
+ epsrel := htpLabelInputString(htPage,'epsrel)
+ omega := htpLabelInputString(htPage,'omega)
+ type := htpButtonValue(htPage,'key)
+ key :=
+ type = 'cos => 1
+ 2
+ error := htpButtonValue(htPage,'ifail)
+ ifail :=
+ error = 'one => 1
+ -1
+ express := htpLabelInputString(htPage,'expression)
+ liw := lw/4
+ prefix := STRCONC("d01anf(",a," ,",b," ,",omega," ,",STRINGIMAGE key," ,",epsabs," ,",epsrel," ,",STRINGIMAGE lw)
+ middle := STRCONC(" ,",STRINGIMAGE liw," ,",STRINGIMAGE ifail," ,")
+ end := STRCONC("(",express,"::Expression Float) :: ASP1(G))")
+ linkGen STRCONC(prefix,middle,end)
+
+d01apf() ==
+ htInitPage('"D01APF - 1-D quadrature, adaptive, finite interval, weight function with end point singularities of algebraico-logarithmic type", nil)
+ htMakePage '(
+ (domainConditions
+ (isDomain EM $EmptyMode)
+ (isDomain PI (PositiveInteger))
+ (isDomain F (Float)))
+ (text . "\windowlink{Manual Page}{manpageXXd01apf} for this routine ")
+ (text . "\newline ")
+ (text . "\lispwindowlink{Browser operation page}{(|oPageFrom| '|d01apf| '|NagIntegrationPackage|)} for this routine")
+ (text . "\newline \horizontalline ")
+ (text . "Evaluates \inputbitmap{\htbmdir{}/integral.bitmap} g(x)w(x) dx, where w(x) ")
+ (text . "has end-point singularities of algebraico-logarithmic type. ")
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Enter the {\em function} g(x) in terms of X: ")
+ (text . "\newline \tab{2} ")
+ (bcStrings (55 "sin(10*X)" expression EM))
+ (text . "\blankline ")
+ (text . "\newline \menuitemstyle{}\tab{2} ")
+ (text . "\newline {\em Lower} bound of the interval: ")
+ (text . "\tab{32} \menuitemstyle{}\tab{34} ")
+ (text . "{\em Upper} bound:")
+ (text . "\newline\tab{2} ")
+ (bcStrings (20 "1.0e-6" a F))
+ (text . "\tab{34} ")
+ (bcStrings (20 "1.0" b EM))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "\newline \alpha in the weight function:")
+ (text . "\tab{32} \menuitemstyle{}\tab{34}")
+ (text . "\beta in the weight function:")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 "-0.5" alpha F))
+ (text . "\tab{34} ")
+ (bcStrings (10 "-0.5" beta F))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "\newline Absolute accuracy required:")
+ (text . "\tab{32} \menuitemstyle{}\tab{34}")
+ (text . "Relative accuracy:")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 "0.0" epsabs F))
+ (text . "\tab{34} ")
+ (bcStrings (10 "1.0e-4" epsrel F))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "Dimension of workspace: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 800 lw PI))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "Key value, indicates which weight function is to be used: ")
+ (radioButtons key
+ ("" "\space{1}w(x) = (x-a)**\alpha\space{1}* (b-x)**\beta" kone)
+ ("" "\space{1}w(x) = (x-a)**\alpha\space{1}* (b-x)**\beta * ln(x-a)" ktwo)
+ ("" "\space{1}w(x) = (x-a)**\alpha\space{1}* (b-x)**\beta * ln(b-x)" kthree)
+ ("" "\space{1}w(x) = (x-a)**\alpha\space{1}* (b-x)**\beta * ln(x-a) * ln(b-x) " kfour))
+ (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", 'd01apfGen)
+ htShowPage()
+
+d01apfGen htPage ==
+ express := htpLabelInputString(htPage,'expression)
+ lw :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'lw)
+ objValUnwrap htpLabelSpadValue(htPage, 'lw)
+ a := htpLabelInputString(htPage,'a)
+ b := htpLabelInputString(htPage,'b)
+ alpha := htpLabelInputString(htPage,'alpha)
+ beta := htpLabelInputString(htPage,'beta)
+ epsabs := htpLabelInputString(htPage,'epsabs)
+ epsrel := htpLabelInputString(htPage,'epsrel)
+ type := htpButtonValue(htPage,'key)
+ key :=
+ type = 'kone => 1
+ type = 'ktwo => 2
+ type = 'kthree => 3
+ 4
+ error := htpButtonValue(htPage,'ifail)
+ ifail :=
+ error = 'one => 1
+ -1
+ liw := lw/4
+ prefix := STRCONC("d01apf(",a," ,",b," ,",alpha," ,",beta," ,")
+ prefix := STRCONC(prefix,STRINGIMAGE key," ,",epsabs," ,",epsrel," ,")
+ prefix := STRCONC(prefix,STRINGIMAGE lw," ,",STRINGIMAGE liw," ,")
+ end := STRCONC("(",express,"::Expression Float) :: ASP1(G))")
+ linkGen STRCONC(prefix,STRINGIMAGE ifail," ,",end)
+
+d01aqf() ==
+ htInitPage('"D01AQF - 1-D quadrature, adaptive, finite interval, weight function 1/(x-c), Cauchy principal value (Hilbert transform)",nil)
+ htMakePage '(
+ (domainConditions
+ (isDomain EM $EmptyMode)
+ (isDomain PI (PositiveInteger))
+ (isDomain F (Float)))
+ (text . "\windowlink{Manual Page}{manpageXXd01aqf} for this routine ")
+ (text . "\newline ")
+ (text . "\lispwindowlink{Browser operation page}{(|oPageFrom| '|d01aqf| '|NagIntegrationPackage|)} for this routine")
+ (text . "\newline \horizontalline ")
+ (text . "Evaluates the Hilbert transform \inputbitmap{\htbmdir{}/integral.bitmap}")
+ (text . "g(x)/(x-c) dx.")
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Enter the function {\it g(x)} in terms of X: ")
+ (text . "\newline \tab{2} ")
+ (bcStrings (55 "(X**2+0.01**2)**-1" expression EM))
+ (text . "\blankline ")
+ (text . "\newline \menuitemstyle{}\tab{2} ")
+ (text . "\newline {\em Lower} bound of the interval {\it a}: ")
+ (text . "\tab{32} \menuitemstyle{}\tab{34} ")
+ (text . "{\em Upper} bound {\it b}:")
+ (text . "\newline\tab{2} ")
+ (bcStrings (20 "-1.0" a F))
+ (text . "\tab{34} ")
+ (bcStrings (20 "1.0" b F))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} \newline ")
+ (text . "Parameter {\it c} \notequal {\it a} or {\it b}: ")
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "0.5" c F))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "\newline Absolute accuracy required:")
+ (text . "\tab{32} \menuitemstyle{}\tab{34}")
+ (text . "Relative accuracy:")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 "0.0" epsabs F))
+ (text . "\tab{34} ")
+ (bcStrings (10 "1.0e-4" epsrel F))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "Dimension of workspace: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 800 lw PI))
+ (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", 'd01aqfGen)
+ htShowPage()
+
+d01aqfGen htPage ==
+ express := htpLabelInputString(htPage,'expression)
+ lw :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'lw)
+ objValUnwrap htpLabelSpadValue(htPage, 'lw)
+ a := htpLabelInputString(htPage,'a)
+ b := htpLabelInputString(htPage,'b)
+ c := htpLabelInputString(htPage,'c)
+ epsabs := htpLabelInputString(htPage,'epsabs)
+ epsrel := htpLabelInputString(htPage,'epsrel)
+ error := htpButtonValue(htPage,'ifail)
+ ifail :=
+ error = 'one => 1
+ -1
+ liw := lw/4
+ prefix := STRCONC("d01aqf(",a," ,",b," ,",c," ,",epsabs," ,",epsrel," ,")
+ prefix := STRCONC(prefix,STRINGIMAGE lw," ,",STRINGIMAGE liw," ,")
+ end := STRCONC("((",express,")::Expression Float) :: ASP1(G))")
+ linkGen STRCONC(prefix,STRINGIMAGE ifail," ,",end)
+
+d01asf() ==
+ htInitPage('"D01ASF - 1-D quadrature, adaptive, semi-infinite interval, weight function cos(\omega x) or sin(\omega x)", nil)
+ htMakePage '(
+ (domainConditions
+ (isDomain EM $EmptyMode)
+ (isDomain PI (PositiveInteger))
+ (isDomain F (Float)))
+ (text . "\windowlink{Manual Page}{manpageXXd01asf} for this routine ")
+ (text . "\newline ")
+ (text . "\lispwindowlink{Browser operation page}{(|oPageFrom| '|d01asf| '|NagIntegrationPackage|)} for this routine")
+ (text . "\newline \horizontalline ")
+ (text . "Evaluates \inputbitmap{\htbmdir{}/si-integral.bitmap} ")
+ (text . "g(x)sin(\omega x) dx ")
+ (text . "or \inputbitmap{\htbmdir{}/si-integral.bitmap} ")
+ (text . "g(x)cos(\omega x) dx, ")
+ (text . "the sine and cosine transform respectively. ")
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Enter the function {\it g(x)} in terms of X: ")
+ (text . "\newline \tab{2} ")
+ (bcStrings (45 "1/sqrt(X)" expression EM))
+ (text . "\blankline ")
+ (text . "\newline \menuitemstyle{}\tab{2} ")
+ (text . "\newline {\em Lower} bound of the interval: ")
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "1.0e-12" a F))
+ (text . "\blankline ")
+ (text . "\newline \menuitemstyle{}\tab{2} ")
+ (text . "Parameter \omega in the weight function of the transform: ")
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "\%pi/2" omega F))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "\newline Absolute accuracy required:")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 "1.0e-3" epsabs F))
+ (text . "\newline \menuitemstyle{}\tab{2}")
+ (text . "Dimension of workspace array: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 800 lw PI))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "{\it LIMLST} upper bound on number of intervals:")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 50 limlst PI))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "Key value, indicates which integral is to be computed:")
+ (radioButtons key
+ ("" " cos(\omega x)" cos)
+ ("" " sin(\omega x)" sin))
+ (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", 'd01asfGen)
+ htShowPage()
+
+d01asfGen htPage ==
+ lw :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'lw)
+ objValUnwrap htpLabelSpadValue(htPage, 'lw)
+ limlst :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'limlst)
+ objValUnwrap htpLabelSpadValue(htPage, 'limlst)
+ a := htpLabelInputString(htPage,'a)
+ epsabs := htpLabelInputString(htPage,'epsabs)
+ omega := htpLabelInputString(htPage,'omega)
+ type := htpButtonValue(htPage,'key)
+ key :=
+ type = 'cos => 1
+ 2
+ error := htpButtonValue(htPage,'ifail)
+ ifail :=
+ error = 'one => 1
+ -1
+ express := htpLabelInputString(htPage,'expression)
+ liw := lw/2
+ prefix := STRCONC("d01asf(",a," ,",omega," ,",STRINGIMAGE key," ,",epsabs)
+ prefix := STRCONC(prefix," ,",STRINGIMAGE limlst," ,",STRINGIMAGE lw)
+ middle := STRCONC(" ,",STRINGIMAGE liw," ,",STRINGIMAGE ifail," ,")
+ end := STRCONC("(",express,"::Expression Float) :: ASP1(G))")
+ linkGen STRCONC(prefix,middle,end)
+
+
+
+d01gaf() ==
+ htInitPage('"D01GAF - \space{1} 1-D quadrature, integration of function defined by data values, Gill-Miller method", nil)
+ htMakePage '(
+ (domainConditions
+ (isDomain PI (PositiveInteger)))
+ (text . "\windowlink{Manual Page}{manpageXXd01gaf} for this routine ")
+ (text . "\newline ")
+ (text . "\lispwindowlink{Browser operation page}{(|oPageFrom| '|d01gaf| '|NagIntegrationPackage|)} for this routine")
+ (text . "\newline \horizontalline ")
+ (text . "Evaluates the integral ")
+ (text . "\inputbitmap{\htbmdir{}/d01gaf1.bitmap} y(x)dx ")
+ (text . "where the numerical value of the function {\em y} is ")
+ (text . "specified at the n distinct points \vspace{-26} ")
+ (text . "\inputbitmap{\htbmdir{}/d01gaf2.bitmap} ")
+ (text . "\blankline ")
+ (text . "Enter the number of points:")
+ (text . "\newline\tab{2} ")
+ (bcStrings (5 21 n PI))
+ (text . "\blankline ")
+ (text . "\newline Ifail value:")
+ (radioButtons ifail
+ ("" " -1, Print error messages" minusOne)
+ ("" " 1, Suppress error messages" one)))
+ htMakeDoneButton('"Continue", 'd01gafSolve)
+ htShowPage()
+
+d01gafSolve htPage ==
+ n :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'n)
+ objValUnwrap htpLabelSpadValue(htPage, 'n)
+ error := htpButtonValue(htPage,'ifail)
+ ifail :=
+ error = 'one => '1
+ '-1
+ n = '21 => d01gafDefaultSolve(htPage,ifail)
+ labelList :=
+ "append"/[f(i) for i in 1..n] where f(i) ==
+ prefix := ('"\newline \tab{2} ")
+ post := ('"\tab{40} ")
+ xnam := INTERN STRCONC ('"x",STRINGIMAGE i)
+ ynam := INTERN STRCONC ('"y",STRINGIMAGE i)
+ [['text,:prefix],['bcStrings,[10, 0.0, xnam, 'F]],
+ ['text,:post],['bcStrings,[10, 0.0, ynam, 'F]]]
+ equationPart := [
+ '(domainConditions
+ (isDomain P (Polynomial $EmptyMode))
+ (isDomain S (String))
+ (isDomain F (Float))
+ (isDomain PI (PositiveInteger))),
+ :labelList]
+ page := htInitPage("D01GAF - 1-D quadrature, integration of function defined by data values", htpPropertyList htPage)
+ htSay '"\menuitemstyle{}\tab{2} Enter values for {\em x}: \tab{38} "
+ htSay '"\menuitemstyle{}\tab{40} Enter values for {\em y}: "
+ htMakePage equationPart
+ htSay '"\blankline "
+ htSay '"Note:\space{1}{\em x} values in ascending or descending order only "
+ htMakeDoneButton('"Continue",'d01gafGen)
+ htpSetProperty(page,'n,n)
+ htpSetProperty(page,'ifail,ifail)
+ htpSetProperty(page,'inputArea, htpInputAreaAlist htPage)
+ htShowPage()
+
+d01gafDefaultSolve (htPage, ifail) ==
+ n := '21
+ page := htInitPage('"D01GAF - 1-D quadrature, integration of function defined by data values",htpPropertyList htPage)
+ htMakePage '(
+ (domainConditions
+ (isDomain F (Float)))
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} Enter values for {\em x}: \tab{38} ")
+ (text . "\menuitemstyle{}\tab{40} Enter values for {\em y}: ")
+ (text . "\newline \tab{2}")
+ (bcStrings (10 "0.00" x1 F))
+ (text . "\tab{40} ")
+ (bcStrings (10 "4.0000" y1 F))
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "0.04" x2 F))
+ (text . "\tab{40} ")
+ (bcStrings (10 "3.9936" y2 F))
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "0.08" x3 F))
+ (text . "\tab{40} ")
+ (bcStrings (10 "3.9746" y3 F))
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "0.12" x4 F))
+ (text . "\tab{40} ")
+ (bcStrings (10 "3.9432" y4 F))
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "0.22" x5 F))
+ (text . "\tab{40} ")
+ (bcStrings (10 "3.8153" y5 F))
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "0.26" x6 F))
+ (text . "\tab{40} ")
+ (bcStrings (10 "3.7467" y6 F))
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "0.30" x7 F))
+ (text . "\tab{40} ")
+ (bcStrings (10 "3.6697" y7 F))
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "0.38" x8 F))
+ (text . "\tab{40} ")
+ (bcStrings (10 "3.4943" y8 F))
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "0.39" x9 F))
+ (text . "\tab{40} ")
+ (bcStrings (10 "3.4719" y9 F))
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "0.42" x10 F))
+ (text . "\tab{40} ")
+ (bcStrings (10 "3.4002" y10 F))
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "0.45" x11 F))
+ (text . "\tab{40} ")
+ (bcStrings (10 "3.3264" y11 F))
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "0.46" x12 F))
+ (text . "\tab{40} ")
+ (bcStrings (10 "3.3014" y12 F))
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "0.60" x13 F))
+ (text . "\tab{40} ")
+ (bcStrings (10 "2.9412" y13 F))
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "0.68" x14 F))
+ (text . "\tab{40} ")
+ (bcStrings (10 "2.7352" y14 F))
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "0.72" x15 F))
+ (text . "\tab{40} ")
+ (bcStrings (10 "2.6344" y15 F))
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "0.73" x16 F))
+ (text . "\tab{40} ")
+ (bcStrings (10 "2.6094" y16 F))
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "0.83" x17 F))
+ (text . "\tab{40} ")
+ (bcStrings (10 "2.3684" y17 F))
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "0.85" x18 F))
+ (text . "\tab{40} ")
+ (bcStrings (10 "2.3222" y18 F))
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "0.88" x19 F))
+ (text . "\tab{40} ")
+ (bcStrings (10 "2.2543" y19 F))
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "0.90" x20 F))
+ (text . "\tab{40} ")
+ (bcStrings (10 "2.2099" y20 F))
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "1.00" x21 F))
+ (text . "\tab{40} ")
+ (bcStrings (10 "2.0000" y21 F))
+ (text . "\newline \tab{2} ")
+ (text . "\blankline ")
+ (text . "Note:\space{1}{\em x} values in ascending or descending order only ")
+ (text . "\blankline"))
+ htMakeDoneButton('"Continue",'d01gafGen)
+ htpSetProperty(page,'n,n)
+ htpSetProperty(page,'ifail,ifail)
+ htpSetProperty(page,'inputArea, htpInputAreaAlist htPage)
+ htShowPage()
+
+
+d01gafGen htPage ==
+ n := htpProperty(htPage,'n)
+ ifail := htpProperty(htPage,'ifail)
+ alist := htpInputAreaAlist htPage
+ y := alist
+ while y repeat
+ right := STRCONC ((first y).1," ")
+ y := rest y
+ left := STRCONC ((first y).1," ")
+ y := rest y
+ reallist := [left,:reallist]
+ imaglist := [right,:imaglist]
+ realstring := bcwords2liststring reallist
+ imagstring := bcwords2liststring imaglist
+ linkGen STRCONC ('"d01gaf([",realstring,"],[",imagstring,"],",STRINGIMAGE n,",", STRINGIMAGE ifail,")")
+
+d01fcf() ==
+ htInitPage('"D01FCF - Multi-dimensional adaptive quadrature over hyper-rectangle",nil)
+ htMakePage '(
+ (domainConditions
+ (isDomain EM $EmptyMode)
+ (isDomain PI (PositiveInteger))
+ (isDomain F (Float)))
+ (text . "\windowlink{Manual Page}{manpageXXd01fcf} for this routine ")
+ (text . "\newline ")
+ (text . "\lispwindowlink{Browser operation page}{(|oPageFrom| '|d01fcf| '|NagIntegrationPackage|)} for this routine")
+ (text . "\newline \horizontalline ")
+ (text . "Evaluates the multi-dimensional integral ")
+ (text . "\center{\htbitmap{d01fcf}}")
+ (text . "with constant finite limits, using an adaptive subdivision ")
+ (text . "strategy.")
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Number of dimensions n in the integral, 2 \htbitmap{less=} ")
+ (text . "{\it NDIM} \htbitmap{less=} 15: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (6 4 ndim F))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Enter the integrand {\it f} in terms of X[1]...X[n]: ")
+ (text . "\newline ")
+ (bcStrings (58 "4.0*X[1]*X[3]*X[3]*exp(2.0*X[1]*X[3])/((1.0+X[2]+X[4])**2)" expression EM))
+ (text . "\blankline ")
+ (text . "\newline \menuitemstyle{}\tab{2} ")
+ (text . "\newline Minimum number of evaluations: ")
+ (text . "\tab{32} \menuitemstyle{}\tab{34} ")
+ (text . "Maximum number of evaluations: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 1000 minpts PI))
+ (text . "\tab{34} ")
+ (bcStrings (10 5700 maxpts PI))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "Relative accuracy required:")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 "0.0001" eps F))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "Dimension of workspace array: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 606 lenwrk PI))
+ (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", 'd01fcfSolve)
+ htShowPage()
+
+
+d01fcfSolve htPage ==
+ ndim :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'ndim)
+ objValUnwrap htpLabelSpadValue(htPage, 'ndim)
+ expression := htpLabelInputString(htPage,'expression)
+ minpts :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'minpts)
+ objValUnwrap htpLabelSpadValue(htPage, 'minpts)
+ maxpts :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'maxpts)
+ objValUnwrap htpLabelSpadValue(htPage, 'maxpts)
+ eps := htpLabelInputString(htPage,'eps)
+ lenwrk :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'lenwrk)
+ objValUnwrap htpLabelSpadValue(htPage, 'lenwrk)
+ error := htpButtonValue(htPage,'ifail)
+ ifail :=
+ error = 'one => '1
+ '-1
+ ndim = '4 => d01fcfDefaultSolve(htPage,minpts,maxpts,eps,lenwrk,expression,ifail)
+ labelList :=
+ "append"/[f(i) for i in 1..ndim] where f(i) ==
+ prefix := ('"\newline \tab{2} ")
+ post := ('"\tab{32} ")
+ rnam := INTERN STRCONC ('"a",STRINGIMAGE i)
+ inam := INTERN STRCONC ('"b",STRINGIMAGE i)
+ [['text,:prefix],['bcStrings,[10, 0.0, rnam, 'P]],
+ ['text,:post],['bcStrings,[10, 1.0, inam, 'P]]]
+ equationPart := [
+ '(domainConditions
+ (isDomain P (Polynomial $EmptyMode))
+ (isDomain S (String))
+ (isDomain PI (PositiveInteger))),
+ :labelList]
+ page := htInitPage('"D01FCF - Multi-dimensional adaptive quadrature over hyper-rectangle",nil)
+ htSay '"Please enter the limits of integration:- "
+ htSay '"\blankline "
+ htSay '"\menuitemstyle{}\tab{2} Lower limits: \tab{30} "
+ htSay '"\menuitemstyle{}\tab{32} Upper limits: "
+ htMakePage equationPart
+ htMakeDoneButton('"Continue",'d01fcfGen)
+ htpSetProperty(page,'ndim,ndim)
+ htpSetProperty(page,'expression,expression)
+ htpSetProperty(page,'minpts,minpts)
+ htpSetProperty(page,'maxpts,maxpts)
+ htpSetProperty(page,'eps,eps)
+ htpSetProperty(page,'lenwrk,lenwrk)
+ htpSetProperty(page,'ifail,ifail)
+ htpSetProperty(page,'inputArea, htpInputAreaAlist htPage)
+ htShowPage()
+
+d01fcfDefaultSolve(htPage,minpts,maxpts,eps,lenwrk,expression,ifail) ==
+ ndim := '4
+ page := htInitPage('"D01FCF - Multi-dimensional adaptive quadrature over hyper-rectangle",nil)
+ htMakePage '(
+ (domainConditions
+ (isDomain F (Float)))
+ (text . "\newline ")
+ (text . "Please enter the limits of integration:- ")
+ (text . "\blankline ")
+ (text . "\newline \menuitemstyle{} \tab{2} ")
+ (text . "Lower limits: \tab{30} ")
+ (text . "\menuitemstyle{} \tab{32} Upper limits: ")
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "0.0" a1 F))
+ (text . "\tab{32} ")
+ (bcStrings (10 "1.0" b1 F))
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "0.0" a2 F))
+ (text . "\tab{32} ")
+ (bcStrings (10 "1.0" b2 F))
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "0.0" a3 F))
+ (text . "\tab{32} ")
+ (bcStrings (10 "1.0" b3 F))
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "0.0" a4 F))
+ (text . "\tab{32} ")
+ (bcStrings (10 "1.0" b4 F))
+ (text . "\newline ")
+ (text . "\blankline"))
+ htMakeDoneButton('"Continue",'d01fcfGen)
+ htpSetProperty(page,'ndim,ndim)
+ htpSetProperty(page,'expression,expression)
+ htpSetProperty(page,'minpts,minpts)
+ htpSetProperty(page,'maxpts,maxpts)
+ htpSetProperty(page,'eps,eps)
+ htpSetProperty(page,'lenwrk,lenwrk)
+ htpSetProperty(page,'ifail,ifail)
+ htpSetProperty(page,'inputArea, htpInputAreaAlist htPage)
+ htShowPage()
+
+d01fcfGen htPage ==
+ ndim := htpProperty(htPage,'ndim)
+ minpts := htpProperty(htPage,'minpts)
+ maxpts := htpProperty(htPage,'maxpts)
+ eps := htpProperty(htPage,'eps)
+ lenwrk := htpProperty(htPage,'lenwrk)
+ expression := htpProperty(htPage,'expression)
+ ifail := htpProperty(htPage,'ifail)
+ alist := htpInputAreaAlist htPage
+ y := alist
+ while y repeat
+ right := (first y).1
+ y := rest y
+ left := (first y).1
+ y := rest y
+ reallist := [left,:reallist]
+ imaglist := [right,:imaglist]
+ astring := bcwords2liststring reallist
+ bstring := bcwords2liststring imaglist
+ prefix := STRCONC("d01fcf(",STRINGIMAGE ndim,", [",astring,"],[",bstring,"], ")
+ middle := STRCONC(STRINGIMAGE maxpts,", ",eps," ,",STRINGIMAGE lenwrk," ,")
+ middle := STRCONC(middle,STRINGIMAGE minpts," ,",STRINGIMAGE ifail," ,")
+ end := STRCONC("(",expression,"::Expression Float) :: ASP4(FUNCTN))")
+ linkGen STRCONC(prefix,middle,end)
+
+
+d01gbf() ==
+ htInitPage('"D01GBF - Multi-dimensional quadrature over hyper-rectangle, Monte Carlo method",nil)
+ htMakePage '(
+ (domainConditions
+ (isDomain EM $EmptyMode)
+ (isDomain PI (PositiveInteger))
+ (isDomain F (Float)))
+ (text . "\windowlink{Manual Page}{manpageXXd01gbf} for this routine ")
+ (text . "\newline ")
+ (text . "\lispwindowlink{Browser operation page}{(|oPageFrom| '|d01gbf| '|NagIntegrationPackage|)} for this routine")
+ (text . "\newline \horizontalline ")
+ (text . "Evaluates the multidimensional integral ")
+ (text . "\center{\htbitmap{d01fcf}} with constant finite limits, ")
+ (text . "using an adaptive Monte-Carlo method;")
+ (text . " the routine is suitable for low accuracy work. ")
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Number of dimensions n in the integral, {\it NDIM}:")
+ (text . "\newline\tab{2} ")
+ (bcStrings (6 4 ndim F))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Enter the integrand {\it f} in terms of X[1]...X[n]: ")
+ (text . "\newline ")
+ (bcStrings (60 "4.0*X[1]*X[3]*X[3]*exp(2.0*X[1]*X[3])/((1.0+X[2]+X[4])**2)" expression EM))
+ (text . "\blankline ")
+ (text . "\newline \menuitemstyle{}\tab{2} ")
+ (text . "\newline Minimum number of FUNCTN calls: ")
+ (text . "\tab{32} \menuitemstyle{}\tab{34} ")
+ (text . "Maximum number of FUNCTN calls: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 1000 mincls PI))
+ (text . "\tab{34} ")
+ (bcStrings (10 20000 maxcls PI))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "Relative accuracy required:")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 "0.01" eps F))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "Dimension of workspace array: ")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 500 lenwrk PI))
+ (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", 'd01gbfSolve)
+ htShowPage()
+
+
+d01gbfSolve htPage ==
+ ndim :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'ndim)
+ objValUnwrap htpLabelSpadValue(htPage, 'ndim)
+ expression := htpLabelInputString(htPage,'expression)
+ mincls :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'mincls)
+ objValUnwrap htpLabelSpadValue(htPage, 'mincls)
+ maxcls :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'maxcls)
+ objValUnwrap htpLabelSpadValue(htPage, 'maxcls)
+ eps := htpLabelInputString(htPage,'eps)
+ lenwrk :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'lenwrk)
+ objValUnwrap htpLabelSpadValue(htPage, 'lenwrk)
+ error := htpButtonValue(htPage,'ifail)
+ ifail :=
+ error = 'one => '1
+ '-1
+ ndim = '4 => d01gbfDefaultSolve(htPage,mincls,maxcls,eps,lenwrk,expression,ifail)
+ labelList :=
+ "append"/[f(i) for i in 1..ndim] where f(i) ==
+ prefix := ('"\newline \tab{2} ")
+ post := ('"\tab{32} ")
+ rnam := INTERN STRCONC ('"a",STRINGIMAGE i)
+ inam := INTERN STRCONC ('"b",STRINGIMAGE i)
+ [['text,:prefix],['bcStrings,[10, 0.0, rnam, 'P]],
+ ['text,:post],['bcStrings,[10, 1.0, inam, 'P]]]
+ equationPart := [
+ '(domainConditions
+ (isDomain P (Polynomial $EmptyMode))
+ (isDomain S (String))
+ (isDomain PI (PositiveInteger))),
+ :labelList]
+ page := htInitPage('"D01GBF - Multi-dimensional quadrature over hyper-rectangle, Monte Carlo method",nil)
+ htSay '"Please enter the limits of integration:- "
+ htSay '"\blankline "
+ htSay '"\menuitemstyle{}\tab{2} Lower limits: \tab{30} "
+ htSay '"\menuitemstyle{}\tab{32} Upper limits: "
+ htMakePage equationPart
+ htMakeDoneButton('"Continue",'d01gbfGen)
+ htpSetProperty(page,'ndim,ndim)
+ htpSetProperty(page,'expression,expression)
+ htpSetProperty(page,'mincls,mincls)
+ htpSetProperty(page,'maxcls,maxcls)
+ htpSetProperty(page,'eps,eps)
+ htpSetProperty(page,'lenwrk,lenwrk)
+ htpSetProperty(page,'ifail,ifail)
+ htpSetProperty(page,'inputArea, htpInputAreaAlist htPage)
+ htShowPage()
+
+d01gbfDefaultSolve(htPage,mincls,maxcls,eps,lenwrk,expression,ifail) ==
+ ndim := '4
+ page := htInitPage('"D01GBF - Multi-dimensional quadrature over hyper-rectangle, Monte Carlo method",nil)
+ htMakePage '(
+ (domainConditions
+ (isDomain F (Float)))
+ (text . "\newline ")
+ (text . "Please enter the limits of integration:- ")
+ (text . "\blankline ")
+ (text . "\newline \menuitemstyle{} \tab{2} ")
+ (text . "Lower limits: \tab{30} ")
+ (text . "\menuitemstyle{} \tab{32} Upper limits: ")
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "0.0" a1 F))
+ (text . "\tab{32} ")
+ (bcStrings (10 "1.0" b1 F))
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "0.0" a2 F))
+ (text . "\tab{32} ")
+ (bcStrings (10 "1.0" b2 F))
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "0.0" a3 F))
+ (text . "\tab{32} ")
+ (bcStrings (10 "1.0" b3 F))
+ (text . "\newline \tab{2} ")
+ (bcStrings (10 "0.0" a4 F))
+ (text . "\tab{32} ")
+ (bcStrings (10 "1.0" b4 F))
+ (text . "\newline ")
+ (text . "\blankline"))
+ htMakeDoneButton('"Continue",'d01gbfGen)
+ htpSetProperty(page,'ndim,ndim)
+ htpSetProperty(page,'expression,expression)
+ htpSetProperty(page,'mincls,mincls)
+ htpSetProperty(page,'maxcls,maxcls)
+ htpSetProperty(page,'eps,eps)
+ htpSetProperty(page,'lenwrk,lenwrk)
+ htpSetProperty(page,'ifail,ifail)
+ htpSetProperty(page,'inputArea, htpInputAreaAlist htPage)
+ htShowPage()
+
+
+
+
+d01gbfGen htPage ==
+ ndim := htpProperty(htPage,'ndim)
+ mincls := htpProperty(htPage,'mincls)
+ maxcls := htpProperty(htPage,'maxcls)
+ eps := htpProperty(htPage,'eps)
+ lenwrk := htpProperty(htPage,'lenwrk)
+ expression := htpProperty(htPage,'expression)
+ ifail := htpProperty(htPage,'ifail)
+ alist := htpInputAreaAlist htPage
+ y := alist
+ while y repeat
+ right := (first y).1
+ y := rest y
+ left := (first y).1
+ y := rest y
+ reallist := [left,:reallist]
+ imaglist := [right,:imaglist]
+ astring := bcwords2liststring reallist
+ bstring := bcwords2liststring imaglist
+ prefix := STRCONC("d01gbf(",STRINGIMAGE ndim,", [",astring,"],[",bstring,"], ")
+ middle := STRCONC(STRINGIMAGE maxcls,", ",eps," ,",STRINGIMAGE lenwrk," ,")
+ middle := STRCONC(middle,STRINGIMAGE mincls," ,[[0.0 for i in 1..")
+ middle := STRCONC(middle,STRINGIMAGE lenwrk,"]],",STRINGIMAGE ifail," ,")
+ end := STRCONC("(",expression,"::Expression Float) :: ASP4(FUNCTN))")
+ linkGen STRCONC(prefix,middle,end)
+
+d01bbf() ==
+ htInitPage('"D01BBF - Weights and abscissae for Gaussian quadrature rules",nil)
+ htMakePage '(
+ (domainConditions
+ (isDomain EM $EmptyMode)
+ (isDomain PI (PositiveInteger))
+ (isDomain F (Float)))
+ (text . "\windowlink{Manual Page}{manpageXXd01bbf} for this routine ")
+ (text . "\newline ")
+ (text . "\lispwindowlink{Browser operation page}{(|oPageFrom| '|d01bbf| '|NagIntegrationPackage|)} for this routine")
+ (text . "\newline \horizontalline ")
+ (text . "Returns the weights and abscissae appropriate to a Gaussian ")
+ (text . "quadrature formula with a specified number of abscissae. ")
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Enter the D01XXX subroutine: ")
+ (radioButtons gtype
+ ("" " D01BAZ" gZero)
+ ("" " D01BAY" gOne)
+ ("" " D01BAX" gTwo)
+ ("" " D01BAW" gThree))
+ (text . "\blankline ")
+ (text . "\newline \menuitemstyle{}\tab{2} ")
+ (text . "\newline {\em Lower} bound of the interval: ")
+ (text . "\tab{32} \menuitemstyle{}\tab{34} ")
+ (text . "{\em Upper} bound:")
+ (text . "\newline\tab{2} ")
+ (bcStrings (20 "0.0" a F))
+ (text . "\tab{34} ")
+ (bcStrings (20 "1.0" b EM))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2} ")
+ (text . "Type of weights for Gauss-Laguerre or Gauss-Hermite quadrature:")
+ (radioButtons itype
+ ("" " adjusted weights" iOne)
+ ("" " normal weights" iZero))
+ (text . "\blankline ")
+ (text . "\newline ")
+ (text . "\menuitemstyle{}\tab{2}")
+ (text . "\newline Number of weights & abscissae to be used {\em n}:")
+ (text . "\newline\tab{2} ")
+ (bcStrings (10 "6" n PI))
+ (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", 'd01bbfGen)
+ htShowPage()
+
+d01bbfGen htPage ==
+ sub := htpButtonValue(htPage,'gtype)
+ gtype :=
+ sub = 'gZero => 0
+ sub = 'gOne => 1
+ sub = 'gTwo => 2
+ 3
+ a := htpLabelInputString(htPage,'a)
+ b := htpLabelInputString(htPage,'b)
+ n :=
+ $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'n)
+ objValUnwrap htpLabelSpadValue(htPage, 'n)
+ wgts := htpButtonValue(htPage,'itype)
+ itype :=
+ wgts = 'iOne => 1
+ 0
+ error := htpButtonValue(htPage,'ifail)
+ ifail :=
+ error = 'one => 1
+ -1
+ prefix := STRCONC("d01bbf(",a," ,",b," ,",STRINGIMAGE itype," ,")
+ end := STRCONC(STRINGIMAGE n," ,",STRINGIMAGE gtype," ,",STRINGIMAGE ifail,")")
+ linkGen STRCONC(prefix,end)
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}