aboutsummaryrefslogtreecommitdiff
path: root/src/interp/anna.boot
diff options
context:
space:
mode:
Diffstat (limited to 'src/interp/anna.boot')
-rw-r--r--src/interp/anna.boot1910
1 files changed, 0 insertions, 1910 deletions
diff --git a/src/interp/anna.boot b/src/interp/anna.boot
deleted file mode 100644
index 8d501810..00000000
--- a/src/interp/anna.boot
+++ /dev/null
@@ -1,1910 +0,0 @@
--- 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
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-03 16:52:37 +0000