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Diffstat (limited to 'src/interp/anna.boot')
| -rw-r--r-- | src/interp/anna.boot | 1910 |
1 files changed, 1910 insertions, 0 deletions
diff --git a/src/interp/anna.boot b/src/interp/anna.boot new file mode 100644 index 00000000..8d501810 --- /dev/null +++ b/src/interp/anna.boot @@ -0,0 +1,1910 @@ +-- 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. + + +annaGen command == + htInitPage('"AXIOM/NAG Expert System Command",nil) + string := + #command < 50 => STRCONC('"{\centerline{\tt ",command,'" }}") + STRCONC('"{\tt ",command,'" }") + htMakePage [ + '(text + "\center{{\em Here is the AXIOM command}}" + "\center{{\em you could have issued to compute this result:}}" + "\vspace{2}\newline "), + ['text,: string]] + htMakeDoitButton('"Do It", command) + htShowPage() + +annaInt() == + htInitPage('"Integration using AXIOM/NAG Expert System",nil) + htMakePage '( + (domainConditions + (isDomain F (Float)) + (isDomain PI (PositiveInteger)) + (isDomain EM $EmptyMode)) + (text . "\blankline ") + (text . "Analyses the function for various attributes, chooses and ") + (text . "then uses a suitable integration routine to ") + (text . "evaluate the finite, semi-infinite or infinite integral ") + (text . "\blankline ") + (text . "\tab{22} \space{1} \vspace{-32} ") + (text . "\inputbitmap{\htbmdir{}/ing.bitmap} \vspace{-34} f(x) dx ") + (text . "\blankline ") + (text . "\newline") + (text . "\newline \menuitemstyle{} \tab{2} {\em Lower} bound of the interval {\em a}: ") + (radioButtons lower + ("" " Finite" lowerFinite) + ("" " Minus Infinity" lowerInfinite)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{} \tab{2} {\em Upper} bound of the interval {\em b}: ") + (radioButtons upper + ("" " Finite" upperFinite) + ("" " Plus Infinity" upperInfinite))) + htMakeDoneButton('"Continue",'annaIntSolve) + htShowPage() + +annaDan() == + + page := htInitPage('"Integration using AXIOM/NAG Expert System",nil) + htMakePage '( + (domainConditions + (isDomain F (Float)) + (isDomain PI (PositiveInteger)) + (isDomain EM $EmptyMode)) + (text . "\menuitemstyle{}\tab{2} ") + (text . "Enter the {\em function} f to be integrated: \newline \tab{2} ") + (bcStrings (50 "(log(2-x)*log(x))/((2-x)^(2/3)*sqrt(x))" expression EM)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline {\em Lower} bound of the interval {\em a}: ") + (text . "\tab{30} \menuitemstyle{}\tab{32} ") + (text . "{\em Upper} bound of the interval {\em b}:") + (text . "\newline\tab{2} ") + (bcStrings (15 "0.0" lower EM)) + (text . "\tab{32} ") + (bcStrings (15 "2.0" upper EM)) + (text . "\blankline ") + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "\newline Absolute accuracy required:") + (text . "\tab{30} \menuitemstyle{}\tab{32}") + (text . "Relative accuracy required:") + (text . "\newline\tab{2} ") + (bcStrings (10 "0.0" epsabs F)) + (text . "\tab{32} ") + (bcStrings (10 "1.0e-6" epsrel F)) + (text . "\blankline")) + htMakeDoneButton('"Continue",'annaIntGen) + htShowPage() + +annaBar() == + + page := htInitPage('"Integration using AXIOM/NAG Expert System",nil) + htMakePage '( + (domainConditions + (isDomain F (Float)) + (isDomain PI (PositiveInteger)) + (isDomain EM $EmptyMode)) + (text . "\menuitemstyle{}\tab{2} ") + (text . "Enter the {\em function} f to be integrated: \newline \tab{2} ") + (bcStrings (50 "exp(-y)/sqrt(y)" expression EM)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline {\em Lower} bound of the interval {\em a}: ") + (text . "\tab{30} \menuitemstyle{}\tab{32} ") + (text . "{\em Upper} bound of the interval {\em b}:") + (text . "\newline\tab{2} ") + (bcStrings (15 "0.0" lower EM)) + (text . "\tab{32} ") + (bcStrings (15 "%plusInfinity" upper EM)) + (text . "\blankline ") + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "\newline Absolute accuracy required:") + (text . "\tab{30} \menuitemstyle{}\tab{32}") + (text . "Relative accuracy required:") + (text . "\newline\tab{2} ") + (bcStrings (10 "0.0" epsabs F)) + (text . "\tab{32} ") + (bcStrings (10 "1.0e-6" epsrel F)) + (text . "\blankline")) + htMakeDoneButton('"Continue",'annaIntGen) + htShowPage() + +annaFoo() == + + page := htInitPage('"Integration using AXIOM/NAG Expert System",nil) + htMakePage '( + (domainConditions + (isDomain F (Float)) + (isDomain PI (PositiveInteger)) + (isDomain EM $EmptyMode)) + (text . "\menuitemstyle{}\tab{2} ") + (text . "Enter the {\em function} f to be integrated: \newline \tab{2} ") + (bcStrings (50 "(exp(-x^3)+exp(-3*x^2))/sqrt(x)" expression EM)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline {\em Lower} bound of the interval {\em a}: ") + (text . "\tab{30} \menuitemstyle{}\tab{32} ") + (text . "{\em Upper} bound of the interval {\em b}:") + (text . "\newline\tab{2} ") + (bcStrings (15 "0.0" lower EM)) + (text . "\tab{32} ") + (bcStrings (15 "%plusInfinity" upper EM)) + (text . "\blankline ") + (text . "\newline ") + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "\newline Absolute accuracy required:") + (text . "\tab{30} \menuitemstyle{}\tab{32}") + (text . "Relative accuracy required:") + (text . "\newline\tab{2} ") + (bcStrings (10 "0.0" epsabs F)) + (text . "\tab{32} ") + (bcStrings (10 "1.0e-6" epsrel F)) + (text . "\blankline")) + htMakeDoneButton('"Continue",'annaIntGen) + htShowPage() + +annaBlah() == + + page := htInitPage('"Integration using AXIOM/NAG Expert System",nil) + htMakePage '( + (domainConditions + (isDomain F (Float)) + (isDomain PI (PositiveInteger)) + (isDomain EM $EmptyMode)) + (text . "\menuitemstyle{}\tab{2} ") + (text . "Enter the {\em function} f to be integrated: \newline \tab{2} ") + (bcStrings (50 "exp(-omega)/((omega-5)*(omega-1/2))" expression EM)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline {\em Lower} bound of the interval {\em a}: ") + (text . "\tab{30} \menuitemstyle{}\tab{32} ") + (text . "{\em Upper} bound of the interval {\em b}:") + (text . "\newline\tab{2} ") + (bcStrings (15 "0.0" lower EM)) + (text . "\tab{32} ") + (bcStrings (15 "%plusInfinity" upper EM)) + (text . "\blankline ") + (text . "\newline ") + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "\newline Absolute accuracy required:") + (text . "\tab{30} \menuitemstyle{}\tab{32}") + (text . "Relative accuracy required:") + (text . "\newline\tab{2} ") + (bcStrings (10 "0.0" epsabs F)) + (text . "\tab{32} ") + (bcStrings (10 "1.0e-6" epsrel F)) + (text . "\blankline")) + htMakeDoneButton('"Continue",'annaIntGen) + htShowPage() + +annaJoe() == + + page := htInitPage('"Integration using AXIOM/NAG Expert System",nil) + htMakePage '( + (domainConditions + (isDomain F (Float)) + (isDomain PI (PositiveInteger)) + (isDomain EM $EmptyMode)) + (text . "\menuitemstyle{}\tab{2} ") + (text . "Enter the {\em function} f to be integrated: \newline \tab{2} ") + (bcStrings (50 "(exp(-x^3)+exp(-3*x^2))/(x^2-2)" expression EM)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline {\em Lower} bound of the interval {\em a}: ") + (text . "\tab{30} \menuitemstyle{}\tab{32} ") + (text . "{\em Upper} bound of the interval {\em b}:") + (text . "\newline\tab{2} ") + (bcStrings (15 "0.0" lower EM)) + (text . "\tab{32} ") + (bcStrings (15 "2.0" upper EM)) + (text . "\blankline ") + (text . "\newline ") + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "\newline Absolute accuracy required:") + (text . "\tab{30} \menuitemstyle{}\tab{32}") + (text . "Relative accuracy required:") + (text . "\newline\tab{2} ") + (bcStrings (10 "0.0" epsabs F)) + (text . "\tab{32} ") + (bcStrings (10 "1.0e-6" epsrel F)) + (text . "\blankline")) + htMakeDoneButton('"Continue",'annaIntGen) + htShowPage() + +annaSue() == + + page := htInitPage('"Integration using AXIOM/NAG Expert System",nil) + htMakePage '( + (domainConditions + (isDomain F (Float)) + (isDomain PI (PositiveInteger)) + (isDomain EM $EmptyMode)) + (text . "\menuitemstyle{}\tab{2} ") + (text . "Enter the {\em function} f to be integrated: \newline \tab{2} ") + (bcStrings (50 "1/(x^6-1)" expression EM)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline {\em Lower} bound of the interval {\em a}: ") + (text . "\tab{30} \menuitemstyle{}\tab{32} ") + (text . "{\em Upper} bound of the interval {\em b}:") + (text . "\newline\tab{2} ") + (bcStrings (15 "0.0" lower EM)) + (text . "\tab{32} ") + (bcStrings (15 "2.0" upper EM)) + (text . "\blankline ") + (text . "\newline ") + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "\newline Absolute accuracy required:") + (text . "\tab{30} \menuitemstyle{}\tab{32}") + (text . "Relative accuracy required:") + (text . "\newline\tab{2} ") + (bcStrings (10 "0.0" epsabs F)) + (text . "\tab{32} ") + (bcStrings (10 "1.0e-6" epsrel F)) + (text . "\blankline")) + htMakeDoneButton('"Continue",'annaIntGen) + htShowPage() + +annaAnn() == + + page := htInitPage('"Integration using AXIOM/NAG Expert System",nil) + htMakePage '( + (domainConditions + (isDomain F (Float)) + (isDomain PI (PositiveInteger)) + (isDomain EM $EmptyMode)) + (text . "\menuitemstyle{}\tab{2} ") + (text . "Enter the {\em function} f to be integrated: \newline \tab{2} ") + (bcStrings (50 "cos(t^2)+sin(t)+cos(sin(t^3))" expression EM)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline {\em Lower} bound of the interval {\em a}: ") + (text . "\tab{30} \menuitemstyle{}\tab{32} ") + (text . "{\em Upper} bound of the interval {\em b}:") + (text . "\newline\tab{2} ") + (bcStrings (15 "-%pi" lower EM)) + (text . "\tab{32} ") + (bcStrings (15 "%pi" upper EM)) + (text . "\blankline ") + (text . "\newline ") + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "\newline Absolute accuracy required:") + (text . "\tab{30} \menuitemstyle{}\tab{32}") + (text . "Relative accuracy required:") + (text . "\newline\tab{2} ") + (bcStrings (10 "0.0" epsabs F)) + (text . "\tab{32} ") + (bcStrings (10 "1.0e-6" epsrel F)) + (text . "\blankline")) + htMakeDoneButton('"Continue",'annaIntGen) + htShowPage() + +annaBab() == + + page := htInitPage('"Integration using AXIOM/NAG Expert System",nil) + htMakePage '( + (domainConditions + (isDomain F (Float)) + (isDomain PI (PositiveInteger)) + (isDomain EM $EmptyMode)) + (text . "\menuitemstyle{}\tab{2} ") + (text . "Enter the {\em function} f to be integrated: \newline \tab{2} ") + (bcStrings (50 "x*product(x-i/10,i=-4..4)" expression EM)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline {\em Lower} bound of the interval {\em a}: ") + (text . "\tab{30} \menuitemstyle{}\tab{32} ") + (text . "{\em Upper} bound of the interval {\em b}:") + (text . "\newline\tab{2} ") + (bcStrings (15 "-1" lower EM)) + (text . "\tab{32} ") + (bcStrings (15 "1" upper EM)) + (text . "\blankline ") + (text . "\newline ") + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "\newline Absolute accuracy required:") + (text . "\tab{30} \menuitemstyle{}\tab{32}") + (text . "Relative accuracy required:") + (text . "\newline\tab{2} ") + (bcStrings (10 "0.0" epsabs F)) + (text . "\tab{32} ") + (bcStrings (10 "1.0e-6" epsrel F)) + (text . "\blankline")) + htMakeDoneButton('"Continue",'annaIntGen) + htShowPage() + +annaFnar() == + + page := htInitPage('"Integration using AXIOM/NAG Expert System",nil) + htMakePage '( + (domainConditions + (isDomain F (Float)) + (isDomain PI (PositiveInteger)) + (isDomain EM $EmptyMode)) + (text . "\menuitemstyle{}\tab{2} ") + (text . "Enter the {\em function} f to be integrated: \newline \tab{2} ") + (bcStrings (50 "cos(20*rho)*(sin(rho^2) + cos(rho^2))" expression EM)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline {\em Lower} bound of the interval {\em a}: ") + (text . "\tab{30} \menuitemstyle{}\tab{32} ") + (text . "{\em Upper} bound of the interval {\em b}:") + (text . "\newline\tab{2} ") + (bcStrings (15 "0" lower EM)) + (text . "\tab{32} ") + (bcStrings (15 "1" upper EM)) + (text . "\blankline ") + (text . "\newline ") + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "\newline Absolute accuracy required:") + (text . "\tab{30} \menuitemstyle{}\tab{32}") + (text . "Relative accuracy required:") + (text . "\newline\tab{2} ") + (bcStrings (10 "0.0" epsabs F)) + (text . "\tab{32} ") + (bcStrings (10 "1.0e-6" epsrel F)) + (text . "\blankline")) + htMakeDoneButton('"Continue",'annaIntGen) + htShowPage() + +annaTub() == + + page := htInitPage('"Integration using AXIOM/NAG Expert System",nil) + htMakePage '( + (domainConditions + (isDomain F (Float)) + (isDomain PI (PositiveInteger)) + (isDomain EM $EmptyMode)) + (text . "\menuitemstyle{}\tab{2} ") + (text . "Enter the {\em function} f to be integrated: \newline \tab{2} ") + (bcStrings (50 "exp(-z^2/2)/sqrt(2*%pi)" expression EM)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline {\em Lower} bound of the interval {\em a}: ") + (text . "\tab{30} \menuitemstyle{}\tab{32} ") + (text . "{\em Upper} bound of the interval {\em b}:") + (text . "\newline\tab{2} ") + (bcStrings (15 "%minusInfinity" lower EM)) + (text . "\tab{32} ") + (bcStrings (15 "%plusInfinity" upper EM)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "\newline Absolute accuracy required:") + (text . "\tab{30} \menuitemstyle{}\tab{32}") + (text . "Relative accuracy required:") + (text . "\newline\tab{2} ") + (bcStrings (10 "0.0" epsabs F)) + (text . "\tab{32} ") + (bcStrings (10 "1.0e-6" epsrel F)) + (text . "\blankline")) + htMakeDoneButton('"Continue",'annaIntGen) + htShowPage() + +annaRats() == + + page := htInitPage('"Integration using AXIOM/NAG Expert System",nil) + htMakePage '( + (domainConditions + (isDomain F (Float)) + (isDomain PI (PositiveInteger)) + (isDomain EM $EmptyMode)) + (text . "\menuitemstyle{}\tab{2} ") + (text . "Enter the {\em function} f to be integrated: \newline \tab{2} ") + (bcStrings (50 "log(u*u)" expression EM)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline {\em Lower} bound of the interval {\em a}: ") + (text . "\tab{30} \menuitemstyle{}\tab{32} ") + (text . "{\em Upper} bound of the interval {\em b}:") + (text . "\newline\tab{2} ") + (bcStrings (15 "-1" lower EM)) + (text . "\tab{32} ") + (bcStrings (15 "1" upper EM)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "\newline Absolute accuracy required:") + (text . "\tab{30} \menuitemstyle{}\tab{32}") + (text . "Relative accuracy required:") + (text . "\newline\tab{2} ") + (bcStrings (10 "0.0" epsabs F)) + (text . "\tab{32} ") + (bcStrings (10 "1.0e-6" epsrel F)) + (text . "\blankline")) + htMakeDoneButton('"Continue",'annaIntGen) + htShowPage() + +annaIntSolve htPage == + + l := htpButtonValue(htPage,'lower) + u := htpButtonValue(htPage,'upper) + a := + l = 'lowerFinite => '"finite" + '"%minusInfinity" + b := + u = 'upperFinite => '"finite" + '"%plusInfinity" + (a = b) => annaDan() + a = '"finite" => annaFoo() + b = '"%plusInfinity" => annaTub() + page := htInitPage('"Integration using AXIOM/NAG Expert System",htPage) + htMakePage '( + (domainConditions + (isDomain F (Float)) + (isDomain PI (PositiveInteger)) + (isDomain EM $EmptyMode)) + (text . "\menuitemstyle{}\tab{2} ") + (text . "Enter the {\em function} f to be integrated: \newline \tab{2} ") + (bcStrings (45 "exp(-x^2/2)/sqrt(2*%pi)" expression EM)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline {\em Lower} bound of the interval {\em a}: ") + (text . "\tab{30} \menuitemstyle{}\tab{32} ") + (text . "{\em Upper} bound of the interval {\em b}:") + (text . "\newline\tab{2} ") + (bcStrings (15 "%minusInfinity" lower EM)) + (text . "\tab{32} ") + (bcStrings (15 "0.0" upper EM)) + (text . "\blankline ") + (text . "\newline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "\newline Absolute accuracy required:") + (text . "\tab{30} \menuitemstyle{}\tab{32}") + (text . "Relative accuracy required:") + (text . "\newline\tab{2} ") + (bcStrings (10 "0.0" epsabs F)) + (text . "\tab{32} ") + (bcStrings (10 "1.0e-6" epsrel F)) + (text . "\blankline")) + htMakeDoneButton('"Continue",'annaIntGen) + htpSetProperty(page,'inputArea, htpInputAreaAlist htPage) + htShowPage() + + +annaIntGen htPage == + lower := htpLabelInputString(htPage,'lower) + upper := htpLabelInputString(htPage,'upper) + expression := htpLabelInputString(htPage,'expression) + epsabs := htpLabelInputString(htPage,'epsabs) + epsrel := htpLabelInputString(htPage,'epsrel) + annaGen STRCONC('"integrate(",expression,", ",lower,"..",upper,", ",epsabs,", ",epsrel,")") + +annaMInt() == + htInitPage('"Integration using AXIOM/NAG Expert System",nil) + htMakePage '( + (domainConditions + (isDomain PI (PositiveInteger)) + (isDomain EM $EmptyMode)) + (text . "Analyses the function for various attributes, chooses and ") + (text . "then uses a suitable integration routine ") + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2} ") + (text . "Enter the {\em function} f of the form: ") + (text . "\center{\inputbitmap{\htbmdir{}/d01fcf.bitmap}} ") + (text . "\newline ") + (text . "to be integrated in terms of subscripted ") + (text . "variables e.g. X[1]...X[n]: \newline \tab{2} ") + (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 . "\menuitemstyle{}\tab{2} ") + (text . "Number of dimensions n in the integral, 2 \htbitmap{less=} ") + (text . "{\it N} \htbitmap{less=} 15: ") + (text . "\newline\tab{2} ") + (bcStrings (2 4 n PI)) + (text . "\blankline ") + (text . "\blankline ")) + htMakeDoneButton('"Continue", 'annaMIntSolve) + htShowPage() + +annaMIntSolve htPage == + n := + $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'n) + objValUnwrap htpLabelSpadValue(htPage, 'n) + n = '4 => annaMIntDefaultSolve(htPage) + expression := htpLabelInputString(htPage,'expression) + rangeList := + "append"/[f(i,n) for i in 1..n] where f(i,n) == + prefix := ('"\newline a") + prefix := STRCONC(prefix,STRINGIMAGE i,'"\space{1}") + post := ('"\tab{30} b") + post := STRCONC(post,STRINGIMAGE i,'"\space{1}") + rnam := INTERN STRCONC ('"x",STRINGIMAGE i) + inam := INTERN STRCONC ('"y",STRINGIMAGE i) + [['text,:prefix],['bcStrings,[5, 0.0, rnam, 'EM]], + ['text,:post],['bcStrings,[5, 1.0, inam, 'EM]]] + errList := + errtext := ('"\newline \blankline \menuitemstyle{}\tab{2}") + errtext := STRCONC(errtext,'"Absolute accuracy required:") + errtext := STRCONC(errtext,'"\tab{30} \menuitemstyle{}\tab{32}") + errtext := STRCONC(errtext,'"Relative accuracy required: \newline\tab{2} ") + [['text,:errtext],['bcStrings,[10, 0.0, 'abserr, 'F]], + ['text,"\tab{32} "],['bcStrings,[10, 1.0e-4, 'relerr, 'F]]] + equationPart := [ + '(domainConditions + (isDomain EM ($EmptyMode)) + (isDomain F (Float)) + (isDomain S (String)) + (isDomain PI (PositiveInteger))), + :rangeList,:errList] + page := htInitPage("AXIOM/NAG Multiple Integration", htpPropertyList htPage) + htSay '"Please enter the limits of integration:- " + htSay '"\blankline \menuitemstyle{} \tab{2} " + htSay '"Lower Limits: \tab{30} \menuitemstyle{} \tab{32} " + htSay '"Upper Limits: \newline " + htMakePage equationPart + htMakeDoneButton('"Continue",'annaMIntGen) + htpSetProperty(page,'expression,expression) + htpSetProperty(page,'inputArea, htpInputAreaAlist htPage) + htShowPage() + +annaMIntDefaultSolve (htPage) == + + page := htInitPage('"AXIOM/NAG Multiple Integration",nil) + expression := htpLabelInputString(htPage,'expression) + htMakePage '( + (domainConditions + (isDomain F (Float)) + (isDomain EM $EmptyMode)) + (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 a1 ") + (bcStrings (10 "0.0" a1 F)) + (text . "\tab{30} b1 ") + (bcStrings (10 "1.0" b1 F)) + (text . "\newline a2 ") + (bcStrings (10 "0.0" a2 F)) + (text . "\tab{30} b2 ") + (bcStrings (10 "1.0" b2 F)) + (text . "\newline a3 ") + (bcStrings (10 "0.0" a3 F)) + (text . "\tab{30} b3 ") + (bcStrings (10 "1.0" b3 F)) + (text . "\newline a4 ") + (bcStrings (10 "0.0" a4 F)) + (text . "\tab{30} b4 ") + (bcStrings (10 "1.0" b4 F)) + (text . "\newline ") + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "\newline Absolute accuracy required:") + (text . "\tab{30} \menuitemstyle{}\tab{32}") + (text . "Relative accuracy required:") + (text . "\newline\tab{2} ") + (bcStrings (10 "0.0" epsabs F)) + (text . "\tab{32} ") + (bcStrings (10 "1.0e-4" epsrel F)) + (text . "\blankline")) + htMakeDoneButton('"Continue",'annaMIntGen) + htpSetProperty(page,'expression,expression) + htpSetProperty(page,'inputArea, htpInputAreaAlist htPage) + htShowPage() + + +annaMIntGen htPage == + expression := htpProperty(htPage,'expression) + alist := htpInputAreaAlist htPage + y := alist + epsrel := STRCONC((first y).1,'"") + y := rest y + epsabs := STRCONC((first y).1,'"") + y := rest y + while y repeat + right := STRCONC((first y).1,'"") + y := rest y + left := STRCONC((first y).1,"..") + y := rest y + rangelist := [STRCONC(left,right),:rangelist] + rangestring := bcwords2liststring rangelist + annaGen STRCONC ('"integrate( ",expression,", ",rangestring,", ",epsabs,", ",epsrel,")") + +annaOde() == + htInitPage('"Solution of Initial Value Problems of Ordinary Differential Equations using AXIOM/NAG Expert System",nil) + htMakePage '( + (domainConditions + (isDomain F (Float)) + (isDomain PI (PositiveInteger)) + (isDomain EM $EmptyMode)) + (text . "Analyses the function for various attributes, chooses and ") + (text . "then uses a suitable ODE solver to provide a ") + (text . "solution to the system of n ODEs \center{\htbitmap{d02gaf},}" ) + (text . "for i = 1,2,...,n.") + (text . "\blankline ") + (text . "\newline \menuitemstyle{} \tab{2} Is there any stopping criteria (i.e. some function ") + (text . "G(X,Y) such that the algorithm should stop when G(X,Y) = 0)? ") + (radioButtons stoppingCriteria + ("" " No \space{1} If No, G(X,Y) is set to 1.0" nostop) + ("" " Yes" stop)) + (text . "\blankline") + (text . "\newline \menuitemstyle{} \tab{2} Are intermediate values required? ") + (radioButtons intermediateValues + ("" " No" noint) + ("" " Yes" int)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2} ") + (text . "\newline Size of the system of equations:\space{1}") + (bcStrings (3 3 n PI)) + (text . "\newline")) + htMakeDoneButton('"Continue",'annaOdeSolve) + htShowPage() + +annaOdeSolve htPage == + + s := htpButtonValue(htPage,'stoppingCriteria) + i := htpButtonValue(htPage,'intermediateValues) + stoppingCriteria := + s = 'nostop => '"no" + '"stopping" + intermediateValues := + i = 'noint => '"no" + '"intervals" + n := + $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'n) + objValUnwrap htpLabelSpadValue(htPage, 'n) + (n = '3) => + (stoppingCriteria = intermediateValues) => annaOdeDefaultSolve() + (stoppingCriteria = '"stopping") => + (intermediateValues = '"intervals") => annaOdeDefaultSolve1() + annaOdeDefaultSolve2() + annaOdeDefaultSolve3() + expressionList := + "append"/[fe(i,n) for i in 1..n] where fe(i,n) == + prefix := ('"\blankline \newline Y") + prefix := STRCONC(prefix,STRINGIMAGE i,'"'\space{1}") + expression := INTERN STRCONC ('"Y",STRINGIMAGE i) + [['text,:prefix], + ['bcStrings,[45, STRCONC ('"Y[",STRINGIMAGE i,'"]"), expression, 'EM]]] + xList := + prefix := ('"\blankline \newline \menuitemstyle{} \tab{2} Initial Value for X: ") + middle := ('"\tab{24} \menuitemstyle{} \tab{26} Final Value for X: ") + [['text,:prefix],['bcStrings,[5, "0.0", "xinit", 'EM]], + ['text,:middle],['bcStrings,[5, "10.0", "xend", 'EM]]] + middle := ('"\blankline \menuitemstyle{} \tab{2} Initial Value for Y[i]: ") + middle := STRCONC(middle,"\newline ") + yinitList := + "append"/[fy(i,n) for i in 1..n] where fy(i,n) == + prefix := ('"\newline Y") + prefix := STRCONC(prefix,STRINGIMAGE i,'"\space{1}") + yinit := INTERN STRCONC ('"y",STRINGIMAGE i) + [['text,:prefix],['bcStrings,[10, '"0.0", yinit, 'EM]]] + yinitList := [['text,:middle],:yinitList] + if stoppingCriteria = '"no" then + sExpression := [] + else + sText := '"\blankline \newline \menuitemstyle{} \tab{2}" + sText := STRCONC(sText,'"\newline Enter the function G(x,y) (The Stopping Criteria): ") + sText := STRCONC(sText,'"\newline \tab{2}") + sExpression := [['bcStrings,[15, '"Y[1]", "stop", 'EM]]] + sExpression := [['text,sText],:sExpression] + if intermediateValues = '"no" then + ilist := [] + else + iText := '"\blankline \newline \menuitemstyle{} \tab{2}" + iText := STRCONC(iText,'"Enter the list of Intermediate Values required: ") + iText := STRCONC(iText,"\newline \tab{2}") + iList := [['bcStrings,[15, '"[2,4,6,8]", "ivals", 'EM]]] + iList := [['text,iText],:iList] + tolList := + tolText := '"\blankline \newline \menuitemstyle{} \tab{2}" + tolText := STRCONC(tolText,'"Relative accuracy required:\space{1}") + [['text,tolText],['bcStrings,[10, '"1.0e-4", "relerr", 'F]]] + expressionPart := [ + '(domainConditions + (isDomain EM ($EmptyMode)) + (isDomain F (Float)) + (isDomain S (String)) + (isDomain PI (PositiveInteger))), + :expressionList,:xList,:yinitList,:sExpression,:iList,:tolList] + page := htInitPage("AXIOM/NAG ODE Solvers", htpPropertyList htPage) + htSay '"\menuitemstyle{} \tab{2} Enter the list of ODE's (i.e.~the derivatives " + htSay '"Y[1]'..Y[n]') in terms of Y[1]..Y[n]: " + htSay '"\newline " + htMakePage expressionPart + htMakeDoneButton('"Continue",'annaOdeGen) + htpSetProperty(page,'n,n) + htpSetProperty(page,'stoppingCriteria,stoppingCriteria) + htpSetProperty(page,'intermediateValues,intermediateValues) + htShowPage() + + +annaOdeDefaultSolve() == + + n := '3 + stoppingCriteria := '"no" + intermediateValues := '"no" + page := htInitPage('"Solution of Initial Value Problems of Ordinary Differential Equations using AXIOM/NAG Expert System",nil) + htMakePage '( + (domainConditions + (isDomain F (Float)) + (isDomain PI (PositiveInteger)) + (isDomain EM $EmptyMode)) + (text . "\menuitemstyle{} \tab{2} Enter the list of ODE's (i.e. the derivatives Y[1]'..Y[n]') ") + (text . "in terms of Y[1]..Y[n]: ") + (text . "\blankline ") + (text . "\newline \tab{2} {\em Y[1]':} \space{1}") + (bcStrings (42 "tan(Y[3])" Y1 EM)) + (text . "\blankline ") + (text . "\newline \tab{2} {\em Y[2]':} \space{1}") + (bcStrings (42 "-0.032*tan(Y[3])/Y[2]-0.02*Y[2]/cos(Y[3])" Y2 EM)) + (text . "\blankline ") + (text . "\newline \tab{2} {\em Y[3]':} \space{1}") + (bcStrings (42 "-0.032/(Y[2]**2)" Y3 EM)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline Initial Value for X: ") + (text . "\tab{24} \menuitemstyle{}\tab{26} ") + (text . "Final Value for X:") + (text . "\newline\tab{2} ") + (bcStrings (10 "0.0" xinit EM)) + (text . "\tab{26} ") + (bcStrings (10 "10.0" xend EM)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline Initial Value for Y[i]: ") + (text . "\newline \tab{2} {\em Y[1]:} \space{1}") + (bcStrings (10 "0.5" y1 EM)) + (text . "\newline \tab{2} {\em Y[2]:} \space{1}") + (bcStrings (10 "0.5" y2 EM)) + (text . "\newline \tab{2} {\em Y[3]:} \space{1}") + (bcStrings (10 "%pi*0.2" y3 EM)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "Relative accuracy required:\space{1}") + (bcStrings (10 "1.0e-4" tol F)) + (text . "\blankline ")) + htMakeDoneButton('"Continue",'annaOdeGen) + htpSetProperty(page,'stoppingCriteria,stoppingCriteria) + htpSetProperty(page,'intermediateValues,intermediateValues) + htpSetProperty(page,'n,n) + htShowPage() + +annaOdeDefaultSolve3() == + + n := '3 + stoppingCriteria := '"no" + intermediateValues := '"intervals" + page := htInitPage('"Solution of Initial Value Problems of Ordinary Differential Equations using AXIOM/NAG Expert System",nil) + htMakePage '( + (domainConditions + (isDomain F (Float)) + (isDomain PI (PositiveInteger)) + (isDomain EM $EmptyMode)) + (text . "\menuitemstyle{} \tab{2} Enter the list of ODE's (i.e. the derivatives Y[1]'..Y[n]') ") + (text . "in terms of Y[1]..Y[n]: ") + (text . "\blankline ") + (text . "\newline \tab{2} {\em Y[1]':} \space{1}") + (bcStrings (42 "-0.04*Y[1]+1.0e4*Y[2]*Y[3]" Y1 EM)) + (text . "\blankline ") + (text . "\newline \tab{2} {\em Y[2]':} \space{1}") + (bcStrings (42 "0.04*Y[1]-1.0e4*Y[2]*Y[3]-3.0e7*Y[2]*Y[2]" Y2 EM)) + (text . "\blankline ") + (text . "\newline \tab{2} {\em Y[3]':} \space{1}") + (bcStrings (42 "3.0e7*Y[2]*Y[2]" Y3 EM)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline Initial Value for X: ") + (text . "\tab{24} \menuitemstyle{}\tab{26} ") + (text . "Final Value for X:") + (text . "\newline\tab{2} ") + (bcStrings (10 "0.0" xinit EM)) + (text . "\tab{26} ") + (bcStrings (10 "10.0" xend EM)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline Initial Value for Y[i]: ") + (text . "\newline \tab{2} {\em Y[1]:} \space{1}") + (bcStrings (10 "1.0" y1 EM)) + (text . "\newline \tab{2} {\em Y[2]:} \space{1}") + (bcStrings (10 "0.0" y2 EM)) + (text . "\newline \tab{2} {\em Y[3]:} \space{1}") + (bcStrings (10 "0.0" y3 EM)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline Enter the list of Intermediate Values required: ") + (bcStrings (10 "[2,4,6,8]" intvals EM)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "Relative accuracy required:\space{1}") + (bcStrings (10 "1.0e-4" tol F)) + (text . "\blankline ")) + htMakeDoneButton('"Continue",'annaOdeGen) + htpSetProperty(page,'stoppingCriteria,stoppingCriteria) + htpSetProperty(page,'intermediateValues,intermediateValues) + htpSetProperty(page,'n,n) + htShowPage() + +annaOdeDefaultSolve2() == + + n := '3 + stoppingCriteria := '"stopping" + intermediateValues := '"no" + page := htInitPage('"Solution of Initial Value Problems of Ordinary Differential Equations using AXIOM/NAG Expert System",nil) + htMakePage '( + (domainConditions + (isDomain F (Float)) + (isDomain PI (PositiveInteger)) + (isDomain EM $EmptyMode)) + (text . "\menuitemstyle{} \tab{2} Enter the list of ODE's (i.e. the derivatives Y[1]'..Y[n]') ") + (text . "in terms of Y[1]..Y[n]: ") + (text . "\blankline ") + (text . "\newline \tab{2} {\em Y[1]':} \space{1}") + (bcStrings (42 "tan(Y[3])" Y1 EM)) + (text . "\blankline ") + (text . "\newline \tab{2} {\em Y[2]':} \space{1}") + (bcStrings (42 "-0.032*tan(Y[3])/Y[2]-0.02*Y[2]/cos(Y[3])" Y2 EM)) + (text . "\blankline ") + (text . "\newline \tab{2} {\em Y[3]':} \space{1}") + (bcStrings (42 "-0.032/(Y[2]**2)" Y3 EM)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline Initial Value for X: ") + (text . "\tab{24} \menuitemstyle{}\tab{26} ") + (text . "Final Value for X:") + (text . "\newline\tab{2} ") + (bcStrings (10 "0.0" xinit EM)) + (text . "\tab{26} ") + (bcStrings (10 "10.0" xend EM)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline Initial Value for Y[i]: ") + (text . "\newline \tab{2} {\em Y[1]:} \space{1}") + (bcStrings (10 "0.5" y1 EM)) + (text . "\newline \tab{2} {\em Y[2]:} \space{1}") + (bcStrings (10 "0.5" y2 EM)) + (text . "\newline \tab{2} {\em Y[3]:} \space{1}") + (bcStrings (10 "%pi*0.2" y3 EM)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline Enter the function G(x,y) (The Stopping Criteria): ") + (bcStrings (10 "Y[1]" g EM)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "Relative accuracy required:\space{1}") + (bcStrings (10 "1.0e-4" tol F)) + (text . "\blankline ")) + htMakeDoneButton('"Continue",'annaOdeGen) + htpSetProperty(page,'stoppingCriteria,stoppingCriteria) + htpSetProperty(page,'intermediateValues,intermediateValues) + htpSetProperty(page,'n,n) + htShowPage() + +annaOdeDefaultSolve1() == + + n := '3 + stoppingCriteria := '"stopping" + intermediateValues := '"intervals" + page := htInitPage('"Solution of Initial Value Problems of Ordinary Differential Equations using AXIOM/NAG Expert System",nil) + htMakePage '( + (domainConditions + (isDomain F (Float)) + (isDomain PI (PositiveInteger)) + (isDomain EM $EmptyMode)) + (text . "\menuitemstyle{} \tab{2} Enter the list of ODE's (i.e. the derivatives Y[1]'..Y[n]') ") + (text . "in terms of Y[1]..Y[n]: ") + (text . "\blankline ") + (text . "\newline \tab{2} {\em Y[1]':} \space{1}") + (bcStrings (42 "-0.04*Y[1]+1.0e4*Y[2]*Y[3]" Y1 EM)) + (text . "\blankline ") + (text . "\newline \tab{2} {\em Y[2]':} \space{1}") + (bcStrings (42 "0.04*Y[1]-1.0e4*Y[2]*Y[3]-3.0e7*Y[2]*Y[2]" Y2 EM)) + (text . "\blankline ") + (text . "\newline \tab{2} {\em Y[3]':} \space{1}") + (bcStrings (42 "3.0e7*Y[2]*Y[2]" Y3 EM)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline Initial Value for X: ") + (text . "\tab{24} \menuitemstyle{}\tab{26} ") + (text . "Final Value for X:") + (text . "\newline\tab{2} ") + (bcStrings (10 "0.0" xinit EM)) + (text . "\tab{26} ") + (bcStrings (10 "10.0" xend EM)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline Initial Value for Y[i]: ") + (text . "\newline \tab{2} {\em Y[1]:} \space{1}") + (bcStrings (10 "1.0" y1 EM)) + (text . "\newline \tab{2} {\em Y[2]:} \space{1}") + (bcStrings (10 "0.0" y2 EM)) + (text . "\newline \tab{2} {\em Y[3]:} \space{1}") + (bcStrings (10 "0.0" y3 EM)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline Enter the function G(x,y) (The Stopping Criteria): ") + (bcStrings (10 "Y[1]-0.9" g EM)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "\newline Enter the list of Intermediate Values required: ") + (bcStrings (10 "[2,4,6,8]" intvals EM)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{}\tab{2} ") + (text . "Relative accuracy required:\space{1}") + (bcStrings (10 "1.0e-4" tol F)) + (text . "\blankline ")) + htMakeDoneButton('"Continue",'annaOdeGen) + htpSetProperty(page,'stoppingCriteria,stoppingCriteria) + htpSetProperty(page,'intermediateValues,intermediateValues) + htpSetProperty(page,'n,n) + htShowPage() + +annaOdeGen htPage == + + n := htpProperty(htPage,'n) + stoppingCriteria := htpProperty(htPage,'stoppingCriteria) + intermediateValues := htpProperty(htPage,'intermediateValues) + alist := htpInputAreaAlist htPage + y := alist + epsrel := STRCONC((first y).1,'"") + epsrelString := STRCONC(", ",epsrel) + y := rest y + if intermediateValues = '"no" then + intvalsString := '"" + else + intvals := STRCONC((first y).1,'"") + intvalsString := STRCONC(", ",intvals) + y := rest y + if stoppingCriteria = '"no" then + gString := '"" + else + g := STRCONC((first y).1,'"") + gString := STRCONC(", ",g) + y := rest y + for i in 1..n repeat + yi := STRCONC((first y).1,'"") + yiList := [yi,:yiList] + y := rest y + yiString := bcwords2liststring yiList + xend := STRCONC((first y).1,'"") + y := rest y + xinit := STRCONC((first y).1,'"") + y := rest y + for i in 1..n repeat + fi := STRCONC((first y).1,'"") + fiList := [fi,:fiList] + y := rest y + fiString := bcwords2liststring fiList + prefix := STRCONC('"solve(",fiString,", ", xinit,", ", xend,", ") + prefix := STRCONC(prefix,yiString,gString,intvalsString,epsrelString) + prefix := STRCONC(prefix,")") + annaGen prefix + +--d03fafVariables() == +-- htInitPage('"Helmholtz Equation in 3-D, Cartesian Coordinates",nil) +-- htMakePage '( +-- (domainConditions +-- (isDomain F (Float)) +-- (isDomain S (String))) +-- (text . "Descretizing the PDE:") +-- (text . "\newline\centerline{\inputbitmap{\htbmdir{}/d03faf.xbm}}") +-- (text . "\newline and solving the resulting seven-diagonal finite ") +-- (text . "difference equations using a method based on the Fast ") +-- (text . "Fourier Transform.\blankline Entering the names of pre-prepared ") +-- (text . "variables for xCond, yCond, zCond and f(x,y,z)") +-- (text . "\blankline Please enter the names of the condition variables") +-- (text . "\blankline \menuitemstyle{}\tab{2} xCond:\space{1} ") +-- (bcStrings (10 "xCond" x S)) +-- (text . "\newline \menuitemstyle{}\tab{2} yCond:\space{1} ") +-- (bcStrings (10 "yCond" y S)) +-- (text . "\newline \menuitemstyle{}\tab{2} zCond:\space{1} ") +-- (bcStrings (10 "zCond" z S)) +-- (text . "\blankline \menuitemstyle{}\tab{2} Please enter the value of lambda:\space{1} ") +-- (bcStrings (8 "-1.0" lambda F)) +-- (text . "\blankline \menuitemstyle{}\tab{2} Please enter the name of the variable for f(x,y,z):") +-- (text . "\space{1} ") +-- (bcStrings (10 "foo" f S)) +-- (text . "\blankline ")) +-- htMakeDoneButton('"Continue",'annaOptSolve) +-- htShowPage() + +annaPDESolve() == + htInitPage('"Second Order Elliptic Partial Differential Equation",nil) + htMakePage '( + (domainConditions + (isDomain F (Float)) + (isDomain S (String)) + (isDomain EM $EmptyMode)) + (text . "Descretizing the PDE:") + (text . "\newline\centerline{\inputbitmap{\htbmdir{}/d03eef.xbm}}") + (text . "\newline defined on a rectangular region with boundary conditions of the form ") + (text . "\centerline{\inputbitmap{\htbmdir{}/d03eef1.bitmap}} ") + (text . " and solving the resulting seven-diagonal finite ") + (text . "difference equations using a multigrid technique. \blankline ") + (text . "\menuitemstyle{} \tab{2} Enter the rectangle on which to discretize the PDE : \newline ") + (text . "\tab{11} Start \tab{20} Number of grid lines \tab{41} End ") + (text . " \newline \tab{6} X : \space{1} " ) + (bcStrings(7 "0.0" xmin F)) + (text . "\space{7} ") + (bcStrings(3 "9" ngx I)) + (text . "\space{7} ") + (bcStrings(7 "1.0" xmax F)) + (text . "\newline \tab{6} Y : \space{1} " ) + (bcStrings(7 "0.0" ymin F)) + (text . "\space{7} ") + (bcStrings(3 "9" ngy I)) + (text . "\space{7} ") + (bcStrings(7 "1.0" ymax F)) + (text . "\blankline \menuitemstyle{} Enter the values of the expressions\space{1}") + (text . " \inputbitmap{\htbmdir{}/alpha.xbm}(X,Y) to\space{1}") + (text . " \inputbitmap{\htbmdir{}/psi.xbm}(X,Y) : ") + (text . "\blankline \tab{3} \inputbitmap{\htbmdir{}/alpha.xbm}(X,Y) : ") + (bcStrings (36 "1" alpha EM)) + (text . "\newline \tab{3} \inputbitmap{\htbmdir{}/beta.xbm}(X,Y) : ") + (bcStrings (36 "0" beta EM)) + (text . "\newline \tab{3} \inputbitmap{\htbmdir{}/gamma.xbm}(X,Y) : ") + (bcStrings (36 "1" gamma EM)) + (text . "\newline \tab{3} \inputbitmap{\htbmdir{}/delta.xbm}(X,Y) : ") + (bcStrings (36 "50" delta EM)) + (text . "\newline \tab{3} \inputbitmap{\htbmdir{}/epsilon.xbm}(X,Y) : ") + (bcStrings (36 "50" epsilon EM)) + (text . "\newline \tab{3} \inputbitmap{\htbmdir{}/phi.xbm}(X,Y) : ") + (bcStrings (36 "0" phi EM)) + (text . "\newline \tab{3} \inputbitmap{\htbmdir{}/psi.xbm}(X,Y) : ") + (bcStrings (36 "-2*sin(X)*sin(Y) + 50*cos(X)*sin(Y) + 50*sin(X)*cos(Y)" psi EM)) + (text . "\blankline \menuitemstyle{} Enter the values of the boundary ") + (text . " condition expressions for the bottom, top, left and right sides : ") + (text . " \blankline \tab{2} \menuitemstyle{} Bottom boundary conditions :") + (text . " (Y := \inputbitmap{\htbmdir{}/ys.xbm})") + (text . "\newline \tab{4} a(X,Y) : ") + (bcStrings (34 "0" ba EM)) + (text . "\newline \tab{4} b(X,Y) : ") + (bcStrings (34 "1" bb EM)) + (text . "\newline \tab{4} c(X,Y) : ") + (bcStrings (34 "-sin(X)" bc EM)) + (text . " \blankline \tab{2} \menuitemstyle{} Top boundary conditions :") + (text . " (Y := \inputbitmap{\htbmdir{}/ye.xbm})") + (text . "\newline \tab{4} a(X,Y) : ") + (bcStrings (34 "1" ta EM)) + (text . "\newline \tab{4} b(X,Y) : ") + (bcStrings (34 "0" tb EM)) + (text . "\newline \tab{4} c(X,Y) : ") + (bcStrings (34 "sin(X)*sin(Y)" tc EM)) + (text . " \blankline \tab{2} \menuitemstyle{} Left boundary conditions :") + (text . " (X := \inputbitmap{\htbmdir{}/xs.xbm})") + (text . "\newline \tab{4} a(X,Y) : ") + (bcStrings (34 "0" la EM)) + (text . "\newline \tab{4} b(X,Y) : ") + (bcStrings (34 "1" lb EM)) + (text . "\newline \tab{4} c(X,Y) : ") + (bcStrings (34 "-sin(Y)" lc EM)) + (text . " \blankline \tab{2} \menuitemstyle{} Right boundary conditions :") + (text . " (Y := \inputbitmap{\htbmdir{}/xe.xbm})") + (text . "\newline \tab{4} a(X,Y) : ") + (bcStrings (34 "1" ra EM)) + (text . "\newline \tab{4} b(X,Y) : ") + (bcStrings (34 "0" rb EM)) + (text . "\newline \tab{4} c(X,Y) : ") + (bcStrings (34 "sin(X)*sin(Y)" rc EM)) + (text . "\blankline \menuitemstyle{} Do you know that the PDE described is elliptic? \space{2}") + (text . "\newline \tab{6} ") + (bcRadioButtons ell + ("" " Yes \space{2} " yes) + ("" " Unknown" no)) + (text . "\blankline \menuitemstyle{} Required Tolerance : ") + (bcStrings (10 "1.0e-4" tol F)) + (text . " \newline ")) + htMakeDoneButton('"Continue",'annaPDESolve2) + htShowPage() + +annaPDESolve2 htPage == + e := htpButtonValue(htPage,'ell) + ell := + e = 'yes => '"elliptic" + '"unknown" + xmin := htpLabelInputString(htPage,'xmin) + ngx := htpLabelInputString(htPage,'ngx) + xmax := htpLabelInputString(htPage,'xmax) + ymin := htpLabelInputString(htPage,'ymin) + ngy := htpLabelInputString(htPage,'ngy) + ymax := htpLabelInputString(htPage,'ymax) + alpha := htpLabelInputString(htPage,'alpha) + beta := htpLabelInputString(htPage,'beta) + gamma := htpLabelInputString(htPage,'gamma) + delta := htpLabelInputString(htPage,'delta) + epsilon := htpLabelInputString(htPage,'epsilon) + phi := htpLabelInputString(htPage,'phi) + psi := htpLabelInputString(htPage,'psi) + ba := htpLabelInputString(htPage,'ba) + bb := htpLabelInputString(htPage,'bb) + bc := htpLabelInputString(htPage,'bc) + ta := htpLabelInputString(htPage,'ta) + tb := htpLabelInputString(htPage,'tb) + tc := htpLabelInputString(htPage,'tc) + la := htpLabelInputString(htPage,'la) + lb := htpLabelInputString(htPage,'lb) + lc := htpLabelInputString(htPage,'lc) + ra := htpLabelInputString(htPage,'ra) + rb := htpLabelInputString(htPage,'rb) + rc := htpLabelInputString(htPage,'rc) + tol := htpLabelInputString(htPage,'tol) + bCond := STRCONC('"[[ ", ba, '", ", bb, '", ", bc, '"],") + bCond := STRCONC(bCond, '"[ ", ra, '", ", rb, '", ", rc, '"],") + bCond := STRCONC(bCond, '"[ ", ta, '", ", tb, '", ", tc, '"],") + bCond := STRCONC(bCond, '"[ ", la, '", ", lb, '", ", lc, '"]]") + pde := STRCONC('"[", alpha, '", ", beta, '", ", gamma, '", ", delta) + pde := STRCONC( pde, '", ", epsilon, '", ", phi, '", ", psi, '"]") + outputString := STRCONC('"solve(", xmin, '", ", xmax, '", ", ymin, '", ", ymax, '", ") + outputString := STRCONC(outputString , ngx, '", ", ngy, '", ", pde, '", ") + outputString := STRCONC(outputString , bCond, '", _"", ell ,'"_", ", tol, " )") + annaGen outputString + +annaOpt() == + htInitPage('"Minimization of a Multivariate Function using AXIOM/NAG Expert System",nil) + htMakePage '( + (domainConditions + (isDomain F (Float)) + (isDomain NNI (NonNegativeInteger)) + (isDomain S (String)) + (isDomain PI (PositiveInteger)) + (isDomain I (Integer)) + (isDomain EM $EmptyMode)) + (text . "Analyses the function for various attributes, chooses and ") + (text . "then uses a suitable optimization routine for finding the ") + (text . "minimum of a nonlinear function {\it F(x)} of {\it n} variables.") + (text . "\newline {\bf Minimize F(x)} where \center{\htbitmap{e04fdf1}} possibly subject to linear or non-linear ") + (text . "constraints on the variables. ") + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Number of variables \htbitmap{xj}, {\it n}:") + (text . "\space{1} ") + (bcStrings (2 4 n PI)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{} \tab{2} Are there any constraints ") + (text . "on the function?") + (radioButtons constraints + (" " " No" nocons) + (" " " Yes" cFunctions)) + (text . "\blankline \menuitemstyle{}") + (text . "Number of linear and/or non-linear constraint functions:\space{1}") + (bcStrings (2 "0" cons NNI)) + (text . "\blankline ")) + htMakeDoneButton('"Continue",'annaOptSolve) + htShowPage() + +annaOptSolve htPage == + n := + $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'n) + objValUnwrap htpLabelSpadValue(htPage, 'n) + c := htpButtonValue(htPage,'constraints) + constraints := + c = 'nocons => '"none" + '"cf" + cons := + $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'cons) + objValUnwrap htpLabelSpadValue(htPage, 'cons) + constraints = '"none" => annaOptSolve1(n) + ((n = '4) and (cons = '0)) => annaOptDefaultSolve2() + ((n = '4) and (cons = '3)) => annaOptDefaultSolve3() + ((n = '7) and (cons = '7)) => annaOptDefaultSolve4() + cText := ('"\blankline \menuitemstyle{}\tab{2} Enter lower and upper ") + cText := STRCONC(cText,'"boundary conditions {\it bl(n)} and {\it bu(n)}: ") + cText := STRCONC(cText,'"\newline \tab{5} Lower \tab{25} Constraint ") + cText := STRCONC(cText,'"\tab{45} Upper ") + cList := + "append"/[fc(i) for i in 1..n] where fc(i) == + prefix := ('"\newline \tab{2}") + xn := INTERN STRCONC ("\tab{27}",'"X",STRINGIMAGE i,"\tab{42}") + blnam := INTERN STRCONC ('"bl",STRINGIMAGE i) + bunam := INTERN STRCONC ('"bu",STRINGIMAGE i) + [['text,:prefix],['bcStrings,[8, '"-1.0", blnam, 'F]],['text,:xn], + ['bcStrings,[8, '"1.0", bunam, 'F]]] + consList := + "append"/[fe(i) for i in n+1..n+cons] where fe(i) == + lineEnd := ('"\newline\tab{2}") + space := ('"\space{1}") + space2 := ('"\tab{42}") + cnam := INTERN STRCONC ('"c",STRINGIMAGE i) + blnam := INTERN STRCONC ('"bl",STRINGIMAGE i) + bunam := INTERN STRCONC ('"bu",STRINGIMAGE i) + [['text,:lineEnd],['bcStrings,[8, '"-1.0", blnam, 'F]],['text,:space], + ['bcStrings,[26, '"X[1]", cnam, 'EM]],['text,:space2], + ['bcStrings,[8, '"1.0", bunam, 'F]]] + cList := [['text,:cText],:cList,:consList] + funcList := [['bcStrings,[48, '"X[1]", 'f, 'EM]]] + xmiddle := ('"\blankline \menuitemstyle{}\tab{2} Enter initial guess of the") + xmiddle := STRCONC(xmiddle,'" solution vector {\it x(n)}: ") + xList := + "append"/[fg(i) for i in 1..n] where fg(i) == + xnam := INTERN STRCONC ('"x",STRINGIMAGE i) + [['text,'"\newline\tab{2}"],['bcStrings,[8, '"0.0", xnam, 'F]]] + xList := [['text,:xmiddle],:xList] + equationPart := [ + '(domainConditions + (isDomain EM $EmptyMode) + (isDomain F (Float))), + :funcList,:cList,:xList] + page := htInitPage('"Minimization of a Multivariate Function using AXIOM/NAG Expert System", nil) + htSay '"\menuitemstyle{}\tab{2} " + htSay '"Enter the objective function, {\it F(x)} in terms of X[1]...X[n]: " + htSay '"\newline \tab{2} " + htMakePage equationPart + htMakeDoneButton('"Continue",'annaOptGen) + htpSetProperty(page,'constraints,constraints) + htpSetProperty(page,'cons,cons) + htpSetProperty(page,'n,n) + htShowPage() + +annaOptSolve1(n) == + + n = '2 => annaOptDefaultSolve1() + constraints := '"none" + cons := '0 + funcList := [['bcStrings,[48, "X[1]", 'f, 'EM]]] + xmiddle := ('"\blankline \menuitemstyle{}\tab{2} Enter initial guess of the") + xmiddle := STRCONC(xmiddle,'" solution vector {\it x(n)}: ") + xList := + "append"/[fg(i) for i in 1..n] where fg(i) == + xnam := INTERN STRCONC ('"x",STRINGIMAGE i) + [['text,'"\newline\tab{2}"],['bcStrings,[8, '"0.0", xnam, 'F]]] + xList := [['text,:xmiddle],:xList] + equationPart := [ + '(domainConditions + (isDomain EM $EmptyMode) + (isDomain F (Float))), + :funcList,:xList] + page := htInitPage('"Minimization of a Multivariate Function using AXIOM/NAG Expert System", nil) + htSay '"\menuitemstyle{}\tab{2} " + htSay '"Enter the objective function, {\it F(x)} in terms of X[1]...X[n]: " + htSay '"\newline \tab{2} " + htMakePage equationPart + htMakeDoneButton('"Continue",'annaOptGen) + htpSetProperty(page,'constraints,constraints) + htpSetProperty(page,'cons,cons) + htpSetProperty(page,'n,n) + htShowPage() + +annaOptDefaultSolve5() == + n := '7 + constraints := '"cf" + cons := '7 + page := htInitPage('"Minimization of a Multivariate Function using AXIOM/NAG Expert System", nil) + htMakePage '( + (domainConditions + (isDomain F (Float)) + (isDomain EM $EmptyMode)) + (text . "\menuitemstyle{}\tab{2} ") + (text . "Enter the objective function, {\it F(x)} in terms of X[1]...X[n]: ") + (text . "\newline \tab{2} ") + (bcStrings (51 "(X[1]-0.02)*X[1]+(X[2]-0.2)*X[2]+(X[3]-0.2)*X[3]+(X[4]+2*X[3]-0.2)*X[4]+(X[5]-0.2)*X[5]+(0.04-X[6])*X[6]+(0.04-2*X[6]-X[7])*X[7]" f EM)) + (text . "\blankline \menuitemstyle{}\tab{2} Enter lower and upper ") + (text . "boundary conditions {\it bl(n)} and {\it bu(n)}: ") + (text . "\newline \tab{5} Lower \tab{25} Constraint \tab{45} Upper ") + (text . "\newline \tab{2}") + (bcStrings (8 "-0.01" bl1 F)) + (text . "\tab{27} X1 \tab{42}") + (bcStrings (8 "0.01" bu1 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-0.1" bl2 F)) + (text . "\tab{27} X2 \tab{42}") + (bcStrings (8 "0.15" bu2 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-0.01" bl3 F)) + (text . "\tab{27} X3 \tab{42}") + (bcStrings (8 "0.03" bu3 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-0.04" bl4 F)) + (text . "\tab{27} X4 \tab{42}") + (bcStrings (8 "0.04" bu4 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-0.1" bl5 F)) + (text . "\tab{27} X5 \tab{42}") + (bcStrings (8 "0.05" bu5 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-0.01" bl6 F)) + (text . "\tab{27} X6 \tab{42}") + (bcStrings (8 "1.0E21" bu6 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-0.01" bl7 F)) + (text . "\tab{27} X7 \tab{42}") + (bcStrings (8 "1.0E21" bu7 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-0.13" bl8 F)) + (text . "\space{1}") + (bcStrings (26 "X[1]+X[2]+X[3]+X[4]+X[5]+X[6]+X[7]" c8 EM)) + (text . "\tab{42}") + (bcStrings (8 "-0.13" bu8 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-1.0E21" bl9 F)) + (text . "\space{1}") + (bcStrings (26 "0.15*X[1]+0.04*X[2]+0.02*X[3]+0.04*X[4]+0.02*X[5]+0.01*X[6]+0.03*X[7]" c9 EM)) + (text . "\tab{42}") + (bcStrings (8 "-0.0049" bu9 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-1.0E21" bl10 F)) + (text . "\space{1}") + (bcStrings (26 "0.03*X[1]+0.05*X[2]+0.08*X[3]+0.02*X[4]+0.06*X[5]+0.01*X[6]" c10 EM)) + (text . "\tab{42}") + (bcStrings (8 "-0.0064" bu10 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-1.0E21" bl11 F)) + (text . "\space{1}") + (bcStrings (26 "0.02*X[1]+0.04*X[2]+0.01*X[3]+0.02*X[4]+0.02*X[5]" c11 EM)) + (text . "\tab{42}") + (bcStrings (8 "-0.0037" bu11 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-1.0E21" bl12 F)) + (text . "\space{1}") + (bcStrings (26 "0.02*X[1]+0.03*X[2]+0.01*X[5]" c12 EM)) + (text . "\tab{42}") + (bcStrings (8 "-0.0012" bu12 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-0.0992" bl13 F)) + (text . "\space{1}") + (bcStrings (26 "0.7*X[1]+0.75*X[2]+0.8*X[3]+0.75*X[4]+0.8*X[5]+0.97*X[6]" c13 EM)) + (text . "\tab{42}") + (bcStrings (8 "1.0E21" bu13 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-0.003" bl14 F)) + (text . "\space{1}") + (bcStrings (26 "0.02*X[1]+0.06*X[2]+0.08*X[3]+0.12*X[4]+0.02*X[5]+0.01*X[6]+0.97*X[7]" c14 EM)) + (text . "\tab{42}") + (bcStrings (8 "0.002" bu14 F)) + (text . "\blankline \menuitemstyle{}\tab{2} Enter initial guess of the") + (text . " solution vector {\it x(n)}: \newline \tab{2} ") + (bcStrings (8 "-0.01" x1 F)) + (text . "\newline\tab{2}") + (bcStrings (8 "-0.03" x2 F)) + (text . "\newline\tab{2}") + (bcStrings (8 "0.0" x3 F)) + (text . "\newline\tab{2}") + (bcStrings (8 "-0.01" x4 F)) + (text . "\newline\tab{2}") + (bcStrings (8 "-0.1" x5 F)) + (text . "\newline\tab{2}") + (bcStrings (8 "0.02" x6 F)) + (text . "\newline\tab{2}") + (bcStrings (8 "0.01" x7 F)) + (text . "\blankline")) + htMakeDoneButton('"Continue",'annaOptGen) + htpSetProperty(page,'constraints,constraints) + htpSetProperty(page,'cons,cons) + htpSetProperty(page,'n,n) + htShowPage() + +annaOptDefaultSolve4() == + n := '7 + constraints := '"cf" + cons := '7 + page := htInitPage('"Minimization of a Multivariate Function using AXIOM/NAG Expert System", nil) + htMakePage '( + (domainConditions + (isDomain F (Float)) + (isDomain EM $EmptyMode)) + (text . "\menuitemstyle{}\tab{2} ") + (text . "Enter the objective function, {\it F(x)} in terms of X[1]...X[n]: ") + (text . "\newline \tab{2} ") + (bcStrings (51 "-0.2*(0.1*X[1]+X[2]+X[3]+X[4]+X[5]-0.2*(X[6]+X[7]))" f EM)) + (text . "\blankline \menuitemstyle{}\tab{2} Enter lower and upper ") + (text . "boundary conditions {\it bl(n)} and {\it bu(n)}: ") + (text . "\newline \tab{5} Lower \tab{25} Constraint \tab{45} Upper ") + (text . "\newline \tab{2}") + (bcStrings (8 "-0.01" bl1 F)) + (text . "\tab{27} X1 \tab{42}") + (bcStrings (8 "0.01" bu1 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-0.1" bl2 F)) + (text . "\tab{27} X2 \tab{42}") + (bcStrings (8 "0.15" bu2 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-0.01" bl3 F)) + (text . "\tab{27} X3 \tab{42}") + (bcStrings (8 "0.03" bu3 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-0.04" bl4 F)) + (text . "\tab{27} X4 \tab{42}") + (bcStrings (8 "0.04" bu4 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-0.1" bl5 F)) + (text . "\tab{27} X5 \tab{42}") + (bcStrings (8 "0.05" bu5 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-0.01" bl6 F)) + (text . "\tab{27} X6 \tab{42}") + (bcStrings (8 "1.0E21" bu6 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-0.01" bl7 F)) + (text . "\tab{27} X7 \tab{42}") + (bcStrings (8 "1.0E21" bu7 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-0.13" bl8 F)) + (text . "\space{1}") + (bcStrings (26 "X[1]+X[2]+X[3]+X[4]+X[5]+X[6]+X[7]" c8 EM)) + (text . "\tab{42}") + (bcStrings (8 "-0.13" bu8 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-1.0E21" bl9 F)) + (text . "\space{1}") + (bcStrings (26 "0.15*X[1]+0.04*X[2]+0.02*X[3]+0.04*X[4]+0.02*X[5]+0.01*X[6]+0.03*X[7]" c9 EM)) + (text . "\tab{42}") + (bcStrings (8 "-0.0049" bu9 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-1.0E21" bl10 F)) + (text . "\space{1}") + (bcStrings (26 "0.03*X[1]+0.05*X[2]+0.08*X[3]+0.02*X[4]+0.06*X[5]+0.01*X[6]" c10 EM)) + (text . "\tab{42}") + (bcStrings (8 "-0.0064" bu10 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-1.0E21" bl11 F)) + (text . "\space{1}") + (bcStrings (26 "0.02*X[1]+0.04*X[2]+0.01*X[3]+0.02*X[4]+0.02*X[5]" c11 EM)) + (text . "\tab{42}") + (bcStrings (8 "-0.0037" bu11 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-1.0E21" bl12 F)) + (text . "\space{1}") + (bcStrings (26 "0.02*X[1]+0.03*X[2]+0.01*X[5]" c12 EM)) + (text . "\tab{42}") + (bcStrings (8 "-0.0012" bu12 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-0.0992" bl13 F)) + (text . "\space{1}") + (bcStrings (26 "0.7*X[1]+0.75*X[2]+0.8*X[3]+0.75*X[4]+0.8*X[5]+0.97*X[6]" c13 EM)) + (text . "\tab{42}") + (bcStrings (8 "1.0E21" bu13 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-0.003" bl14 F)) + (text . "\space{1}") + (bcStrings (26 "0.02*X[1]+0.06*X[2]+0.08*X[3]+0.12*X[4]+0.02*X[5]+0.01*X[6]+0.97*X[7]" c14 EM)) + (text . "\tab{42}") + (bcStrings (8 "0.002" bu14 F)) + (text . "\blankline \menuitemstyle{}\tab{2} Enter initial guess of the") + (text . " solution vector {\it x(n)}: \newline \tab{2} ") + (bcStrings (8 "-0.01" x1 F)) + (text . "\newline\tab{2}") + (bcStrings (8 "-0.03" x2 F)) + (text . "\newline\tab{2}") + (bcStrings (8 "0.0" x3 F)) + (text . "\newline\tab{2}") + (bcStrings (8 "-0.01" x4 F)) + (text . "\newline\tab{2}") + (bcStrings (8 "-0.1" x5 F)) + (text . "\newline\tab{2}") + (bcStrings (8 "0.02" x6 F)) + (text . "\newline\tab{2}") + (bcStrings (8 "0.01" x7 F)) + (text . "\blankline")) + htMakeDoneButton('"Continue",'annaOptGen) + htpSetProperty(page,'constraints,constraints) + htpSetProperty(page,'cons,cons) + htpSetProperty(page,'n,n) + htShowPage() + +annaOptDefaultSolve3() == + n := '4 + constraints := '"cf" + cons := '3 + page := htInitPage('"Minimization of a Multivariate Function using AXIOM/NAG Expert System", nil) + htMakePage '( + (domainConditions + (isDomain F (Float)) + (isDomain EM $EmptyMode)) + (text . "\menuitemstyle{}\tab{2} ") + (text . "Enter the objective function, {\it F(x)} in terms of X[1]...X[n]: ") + (text . "\newline \tab{2} ") + (bcStrings (48 "X[1]*X[4]*(X[1]+X[2]+X[3])+X[3]" f EM)) + (text . "\blankline \menuitemstyle{}\tab{2} Enter lower and upper ") + (text . "boundary conditions {\it bl(n)} and {\it bu(n)}: ") + (text . "\newline \tab{5} Lower \tab{25} Constraint \tab{45} Upper ") + (text . "\newline \tab{2}") + (bcStrings (8 "1.0" bl1 F)) + (text . "\tab{27} X1 \tab{42}") + (bcStrings (8 "5.0" bu1 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "1.0" bl2 F)) + (text . "\tab{27} X2 \tab{42}") + (bcStrings (8 "5.0" bu2 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "1.0" bl3 F)) + (text . "\tab{27} X3 \tab{42}") + (bcStrings (8 "5.0" bu3 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "1.0" bl4 F)) + (text . "\tab{27} X4 \tab{42}") + (bcStrings (8 "5.0" bu4 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-1.E25" bl5 F)) + (text . "\space{1}") + (bcStrings (26 "X[1]+X[2]+X[3]+X[4]" c5 EM)) + (text . "\tab{42}") + (bcStrings (8 "20.0" bu5 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-1.E25" bl6 F)) + (text . "\space{1}") + (bcStrings (26 "X[1]**2+X[2]**2+X[3]**2+X[4]**2" c6 EM)) + (text . "\tab{42}") + (bcStrings (8 "40.0" bu6 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "25.0" bl7 F)) + (text . "\space{1}") + (bcStrings (26 "X[1]*X[2]*X[3]*X[4]" c7 EM)) + (text . "\tab{42}") + (bcStrings (8 "1.E25" bu7 F)) + (text . "\blankline \menuitemstyle{}\tab{2} Enter initial guess of the") + (text . " solution vector {\it x(n)}: \newline \tab{2} ") + (bcStrings (8 "1.0" x1 F)) + (text . "\newline\tab{2}") + (bcStrings (8 "5.0" x2 F)) + (text . "\newline\tab{2}") + (bcStrings (8 "5.0" x3 F)) + (text . "\newline\tab{2}") + (bcStrings (8 "1.0" x4 F)) + (text . "\blankline")) + htMakeDoneButton('"Continue",'annaOptGen) + htpSetProperty(page,'constraints,constraints) + htpSetProperty(page,'cons,cons) + htpSetProperty(page,'n,n) + htShowPage() + +annaOptDefaultSolve2() == + n := '4 + constraints := '"cf" + cons := '0 + page := htInitPage('"Minimization of a Multivariate Function using AXIOM/NAG Expert System", nil) + htMakePage '( + (domainConditions + (isDomain F (Float)) + (isDomain EM $EmptyMode)) + (text . "\menuitemstyle{}\tab{2} ") + (text . "Enter the objective function, {\it F(x)} in terms of X[1]...X[n]: ") + (text . "\newline \tab{2} ") + (bcStrings (70 "(X[1]+10*X[2])**2+5*(X[3]-X[4])**2+(X[2]-2*X[3])**4+10*(X[1]-X[4])**4" f EM)) + (text . "\blankline \menuitemstyle{}\tab{2} Enter lower and upper ") + (text . "boundary conditions {\it bl(n)} and {\it bu(n)}: ") + (text . "\newline \tab{5} Lower \tab{25} Constraint \tab{45} Upper ") + (text . "\newline \tab{2}") + (bcStrings (8 "1" bl1 F)) + (text . "\tab{27} X1 \tab{42}") + (bcStrings (8 "3" bu1 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-2" bl2 F)) + (text . "\tab{27} X2 \tab{42}") + (bcStrings (8 "0" bu2 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "-1.0E-6" bl3 F)) + (text . "\tab{27} X3 \tab{42}") + (bcStrings (8 "1.0E6" bu3 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "1" bl4 F)) + (text . "\tab{27} X4 \tab{42}") + (bcStrings (8 "3" bu4 F)) + (text . "\blankline \menuitemstyle{}\tab{2} Enter initial guess of the") + (text . " solution vector {\it x(n)}: \newline \tab{2} ") + (bcStrings (8 "3" x1 F)) + (text . "\newline\tab{2}") + (bcStrings (8 "-1" x2 F)) + (text . "\newline\tab{2}") + (bcStrings (8 "0" x3 F)) + (text . "\newline\tab{2}") + (bcStrings (8 "1" x4 F)) + (text . "\blankline")) + htMakeDoneButton('"Continue",'annaOptGen) + htpSetProperty(page,'constraints,constraints) + htpSetProperty(page,'cons,cons) + htpSetProperty(page,'n,n) + htShowPage() + +annaOptDefaultSolve1() == + + n := '2 + constraints := '"none" + cons := '0 + page := htInitPage('"Minimization of a Multivariate Function using AXIOM/NAG Expert System", nil) + htMakePage '( + (domainConditions + (isDomain F (Float)) + (isDomain EM $EmptyMode)) + (text . "\menuitemstyle{} \tab{2} Enter the objective function,") + (text . " {\it F(x)} in terms of X[1]...X[n]: \newline \tab{2} ") + (bcStrings (52 "exp(X[1])*(4*X[1]**2+2*X[2]**2+4*X[1]*X[2]+2*X[2]+1)" f EM)) + (text . "\blankline \menuitemstyle{} \tab{2} Enter initial guess of the ") + (text . "solution vector {\it x(n)}: \newline\tab{2}") + (bcStrings (8 "-1.0" x1 F)) + (text . "\newline\tab{2}") + (bcStrings (8 "1.0" x2 F)) + (text . "\blankline")) + htMakeDoneButton('"Continue",'annaOptGen) + htpSetProperty(page,'constraints,constraints) + htpSetProperty(page,'cons,cons) + htpSetProperty(page,'n,n) + htShowPage() + +annaOptGen htPage == + n := htpProperty(htPage,'n) + cons := htpProperty(htPage,'cons) + constraints := htpProperty(htPage,'constraints) + alist := htpInputAreaAlist htPage + y := alist + for i in 1..n repeat + init := STRCONC((first y).1,'"") + initList := [init,:initList] + y := rest y + initString := bcwords2liststring initList + if constraints = '"cf" then + for i in 1..cons repeat + upper := STRCONC((first y).1,'"") + uList := [upper,:uList] + y := rest y + con := STRCONC((first y).1," ") + cList := [con,:cList] + y := rest y + lower := STRCONC((first y).1,'"") + lList := [lower,:lList] + y := rest y + for i in 1..n repeat + upper := STRCONC((first y).1,'"") + uList := [upper,:uList] + y := rest y + lower := STRCONC((first y).1,'"") + lList := [lower,:lList] + y := rest y + uString := bcwords2liststring uList + cString := bcwords2liststring cList + lString := bcwords2liststring lList + f := STRCONC((first y).1,'"") + prefix := STRCONC('"optimize(",f,", ") + if constraints = '"none" then + midfix := initString + else + if cons = '0 then + midfix := STRCONC(initString,", ",lString,", ",uString) + else + midfix := STRCONC(initString,", ",lString,", ",cString,", ",uString) + suffix := STRCONC(prefix, midfix,")") + annaGen suffix + +annaOpt2() == + htInitPage('"Minimization of a Sum of Squares using AXIOM/NAG Expert System",nil) + htMakePage '( + (domainConditions + (isDomain PI (PositiveInteger))) + (text . "Analyses the functions for various attributes, chooses and ") + (text . "then uses a suitable optimization routine for finding the ") + (text . "minimum of a sum of squares of {\it m} nonlinear functions in ") + (text . "{\it n} variables ({\it m} \htbitmap{great=} {\it n}), i.e., it ") + (text . "is applicable to problems of the form ") + (text . "\center{\htbitmap{e04fdf}} where \center{\htbitmap{e04fdf1}}") + (text . "The routines are intended for ") + (text . "functions which have continous first and second derivatives, ") + (text . "though they will usually work if the derivatives have occasional ") + (text . "discontinuities. ") + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Number of functions {\it \htbitmap{fi}(x)}, {\it m}:") + (text . "\newline\tab{2} ") + (bcStrings (5 15 m PI)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Number of variables \htbitmap{xj}, {\it n}:") + (text . "\newline\tab{2} ") + (bcStrings (5 3 n PI)) + (text . "\blankline ") + (text . "\newline \menuitemstyle{} \tab{2} Do you wish for a check for ") + (text . "goodness of fit of the least squares model?") + (radioButtons goodness + (" " " No" nogood) + (" " " Yes" good)) + (text . "\blankline ")) + htMakeDoneButton('"Continue", 'annaOpt2Solve) + htShowPage() + +annaOpt2Solve htPage == + g := htpButtonValue(htPage,'goodness) + goodness := + g = 'nogood => '"nogood" + '"good" + n := + $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'n) + objValUnwrap htpLabelSpadValue(htPage, 'n) + m := + $bcParseOnly => PARSE_-INTEGER htpLabelInputString(htPage, 'm) + objValUnwrap htpLabelSpadValue(htPage, 'm) + m = '15 and n = '3 and goodness = '"nogood" => annaOpt2DefaultSolve() + m = '15 and n = '3 => annaOpt2DefaultSolve2() + fList := + "append"/[f(i) for i in 1..m] where f(i) == + lineEnd := ('"\newline\tab{2}") + fnam := INTERN STRCONC ('"f",STRINGIMAGE i) + [['text,:lineEnd], ['bcStrings,[42, '"X[1]", fnam, 'EM]]] + xmiddle := ('"\blankline \menuitemstyle{}\tab{2} Enter initial guess of the") + xmiddle := STRCONC(xmiddle,'" solution vector {\it x(n)}: ") + xList := + "append"/[fg(i) for i in 1..n] where fg(i) == + xnam := INTERN STRCONC ('"x",STRINGIMAGE i) + [['text,'"\newline\tab{2}"],['bcStrings,[8, '"0.0", xnam, 'F]]] + xList := [['text,:xmiddle],:xList] + equationPart := [ + '(domainConditions + (isDomain EM $EmptyMode) + (isDomain F (Float))), + :fList,:xList] + page := htInitPage('"Minimization of a Sum of Squares using AXIOM/NAG Expert System",nil) + htSay '"\menuitemstyle{}\tab{2} " + htSay '"Enter the objective functions, {\it F(x)} in terms of X[1]...X[n]: " + htSay '"\newline \tab{2} " + htMakePage equationPart + htMakeDoneButton('"Continue",'annaOpt2Gen) + htpSetProperty(page,'n,n) + htpSetProperty(page,'m,m) + htpSetProperty(page,'goodness,goodness) + htShowPage() + +annaOpt2DefaultSolve() == + goodness := '"nogood" + n := '3 + m := '15 + page := htInitPage('"Minimization of a Sum of Squares using AXIOM/NAG Expert System",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 ") + (text . "in terms of X[1]...X[n]: ") + (text . "\newline ") + (text . "\newline {\em Function 1:} \space{1}") + (bcStrings (42 "(X[3]+15*X[2])**(-1)+X[1]-0.14" f1 EM)) + (text . "\newline {\em Function 2:} \space{1}") + (bcStrings (42 "2*(2*X[3]+14*X[2])**(-1)+X[1]-0.18" f2 EM)) + (text . "\newline {\em Function 3:} \space{1}") + (bcStrings (42 "3*(3*X[3]+13*X[2])**(-1)+X[1]-0.22" f3 EM)) + (text . "\newline {\em Function 4:} \space{1}") + (bcStrings (42 "4*(4*X[3]+12*X[2])**(-1)+X[1]-0.25" f4 EM)) + (text . "\newline {\em Function 5:} \space{1}") + (bcStrings (42 "5*(5*X[3]+11*X[2])**(-1)+X[1]-0.29" f5 EM)) + (text . "\newline {\em Function 6:} \space{1}") + (bcStrings (42 "6*(6*X[3]+10*X[2])**(-1)+X[1]-0.32" f6 EM)) + (text . "\newline {\em Function 7:} \space{1}") + (bcStrings (42 "7*(7*X[3]+9*X[2])**(-1)+X[1]-0.35" f7 EM)) + (text . "\newline {\em Function 8:} \space{1}") + (bcStrings (42 "8*(8*X[3]+8*X[2])**(-1)+X[1]-0.39" f8 EM)) + (text . "\newline {\em Function 9:} \space{1}") + (bcStrings (42 "9*(7*X[3]+7*X[2])**(-1)+X[1]-0.37" f9 EM)) + (text . "\newline {\em Function 10:} \space{1}") + (bcStrings (42 "10*(6*X[3]+6*X[2])**(-1)+X[1]-0.58" f10 EM)) + (text . "\newline {\em Function 11:} \space{1}") + (bcStrings (42 "11*(5*X[3]+5*X[2])**(-1)+X[1]-0.73" f11 EM)) + (text . "\newline {\em Function 12:} \space{1}") + (bcStrings (42 "12*(4*X[3]+4*X[2])**(-1)+X[1]-0.96" f12 EM)) + (text . "\newline {\em Function 13:} \space{1}") + (bcStrings (42 "13*(3*X[3]+3*X[2])**(-1)+X[1]-1.34" f13 EM)) + (text . "\newline {\em Function 14:} \space{1}") + (bcStrings (42 "14*(2*X[3]+2*X[2])**(-1)+X[1]-2.1" f14 EM)) + (text . "\newline {\em Function 15:} \space{1}") + (bcStrings (42 "15*(X[3]+X[2])**(-1)+X[1]-4.39" f15 EM)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Enter initial guess of the solution vector {\it x(n)}: \newline \tab{2}") + (bcStrings (8 "0.5" x1 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "1.0" x2 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "1.5" x3 F))) + htMakeDoneButton('"Continue",'annaOpt2Gen) + htpSetProperty(page,'n,n) + htpSetProperty(page,'m,m) + htpSetProperty(page,'goodness,goodness) + htShowPage() + +annaOpt2DefaultSolve2() == + goodness := '"good" + n := '3 + m := '15 + page := htInitPage('"Minimization of a Sum of Squares using AXIOM/NAG Expert System",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 ") + (text . "in terms of X[1]...X[n]: ") + (text . "\newline ") + (text . "\newline {\em Function 1:} \space{1}") + (bcStrings (42 "(X[3]+15*X[2])**(-1)+X[1]-0.14" f1 EM)) + (text . "\newline {\em Function 2:} \space{1}") + (bcStrings (42 "2*(2*X[3]+14*X[2])**(-1)+X[1]-0.18" f2 EM)) + (text . "\newline {\em Function 3:} \space{1}") + (bcStrings (42 "3*(3*X[3]+13*X[2])**(-1)+X[1]-0.22" f3 EM)) + (text . "\newline {\em Function 4:} \space{1}") + (bcStrings (42 "4*(4*X[3]+12*X[2])**(-1)+X[1]-0.25" f4 EM)) + (text . "\newline {\em Function 5:} \space{1}") + (bcStrings (42 "5*(5*X[3]+11*X[2])**(-1)+X[1]-0.29" f5 EM)) + (text . "\newline {\em Function 6:} \space{1}") + (bcStrings (42 "6*(6*X[3]+10*X[2])**(-1)+X[1]-0.32" f6 EM)) + (text . "\newline {\em Function 7:} \space{1}") + (bcStrings (42 "7*(7*X[3]+9*X[2])**(-1)+X[1]-0.35" f7 EM)) + (text . "\newline {\em Function 8:} \space{1}") + (bcStrings (42 "8*(8*X[3]+8*X[2])**(-1)+X[1]-0.39" f8 EM)) + (text . "\newline {\em Function 9:} \space{1}") + (bcStrings (42 "9*(7*X[3]+7*X[2])**(-1)+X[1]-0.37" f9 EM)) + (text . "\newline {\em Function 10:} \space{1}") + (bcStrings (42 "10*(6*X[3]+6*X[2])**(-1)+X[1]-0.58" f10 EM)) + (text . "\newline {\em Function 11:} \space{1}") + (bcStrings (42 "11*(5*X[3]+5*X[2])**(-1)+X[1]-0.73" f11 EM)) + (text . "\newline {\em Function 12:} \space{1}") + (bcStrings (42 "12*(4*X[3]+4*X[2])**(-1)+X[1]-0.96" f12 EM)) + (text . "\newline {\em Function 13:} \space{1}") + (bcStrings (42 "13*(3*X[3]+3*X[2])**(-1)+X[1]-1.34" f13 EM)) + (text . "\newline {\em Function 14:} \space{1}") + (bcStrings (42 "14*(2*X[3]+2*X[2])**(-1)+X[1]-2.1" f14 EM)) + (text . "\newline {\em Function 15:} \space{1}") + (bcStrings (42 "15*(X[3]+X[2])**(-1)+X[1]-4.39" f15 EM)) + (text . "\blankline ") + (text . "\menuitemstyle{}\tab{2}") + (text . "Enter initial guess of the solution vector {\it x(n)}: \newline \tab{2}") + (bcStrings (8 "0.5" x1 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "1.0" x2 F)) + (text . "\newline \tab{2}") + (bcStrings (8 "1.5" x3 F))) + htMakeDoneButton('"Continue",'annaOpt2Gen) + htpSetProperty(page,'n,n) + htpSetProperty(page,'m,m) + htpSetProperty(page,'goodness,goodness) + htShowPage() + +annaOpt2Gen htPage == + + goodness := htpProperty(htPage,'goodness) + n := htpProperty(htPage,'n) + m := htpProperty(htPage,'m) + alist := htpInputAreaAlist htPage + y := alist + for i in 1..n repeat + init := STRCONC((first y).1,'"") + initList := [init,:initList] + y := rest y + initString := bcwords2liststring initList + for i in 1..m repeat + f := STRCONC((first y).1," ") + fList := [f,:fList] + y := rest y + fString := bcwords2liststring fList + prefix := + goodness = '"good" => '"goodnessOfFit( " + '"optimize( " + midfix := STRCONC(fString,", ",initString) + suffix := STRCONC(prefix, midfix,")") + annaGen suffix |