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From: Robert Dodier <robert_dodier@us...>  20051020 02:14:57

Update of /cvsroot/maxima/maxima/share In directory sc8prcvs1.sourceforge.net:/tmp/cvsserv32503 Modified Files: Makefile.am Log Message: Put new share files on list. Index: Makefile.am =================================================================== RCS file: /cvsroot/maxima/maxima/share/Makefile.am,v retrieving revision 1.58 retrieving revision 1.59 diff u d r1.58 r1.59  Makefile.am 2 Oct 2005 09:33:44 0000 1.58 +++ Makefile.am 20 Oct 2005 02:14:49 0000 1.59 @@ 110,6 +110,7 @@ contrib/Zeilberger/testGosper.mac\ contrib/Zeilberger/testZeilberger.mac\ contrib/Zeilberger/whatsnew.txt\ +contrib/augmented_lagrangian.mac\ contrib/defstruct.lisp\ contrib/descriptive/README\ contrib/descriptive/biomed.data\ @@ 130,6 +131,7 @@ contrib/descriptive/doc/histogram2.eps\ contrib/descriptive/pidigits.data\ contrib/descriptive/wind.data\ +contrib/devine.mac\ contrib/diag.dem\ contrib/diag.mac\ contrib/diag.usg\ @@ 246,6 +248,7 @@ contrib/gentran/test/type.output\ contrib/gentran/vaxinit.lisp\ contrib/gentran/vaxlsp.lisp\ +contrib/ggf.mac\ contrib/impdiff.mac\ contrib/lindstedt.mac\ contrib/lsquares.dem\ 
From: Robert Dodier <robert_dodier@us...>  20051020 02:10:52

Update of /cvsroot/maxima/maxima/share/contrib In directory sc8prcvs1.sourceforge.net:/tmp/cvsserv31928 Added Files: devine.mac Log Message: A package to guess closed form for a sequence of numbers. Written by Martin Rubey; committed verbatim by Robert Dodier.  NEW FILE: devine.mac  /* devine.usg * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Copyright (C) 2002 Martin Rubey <Martin.Rubey@...> * * * * This file is part of GNU Maxima. * * * * This program is free software; you can redistribute it and/or * * modify it under the terms of the GNU General Public License as * * published by the Free Software Foundation; either version 2 of * * the License, or (at your option) any later version. * * * * This program is distributed in the hope that it will be * * useful, but WITHOUT ANY WARRANTY; without even the implied * * warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR * * PURPOSE. See the GNU General Public License for more details. * * * * History: * * This is a translation of the Mathematica package Rate.m * * by Christian Krattenthaler <Kratt@...>. * * The translation to Maple was done by JeanFrancois Beraud * * <JeanFrancois.Beraud@...> and Bruno Gauthier * * <Bruno.Gauthier@...> * * * * All features of this package are due to C. Krattenthaler * * The help text is due to JeanFrancois Beraud and Bruno Gauthier * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * A package to guess closed form for a sequence of numbers. CALLING SEQUENCE: guess(l, optional_args); SYNOPSIS:  This package provides functions to find a closed form for a sequence, of numbers within the hierarchy of expressions of the form, <rational function>, <product of rational function>, <product of product, of rational function>, etc. EXAMPLES: guess([1,2,3]); [i0] guess([1,4,9,16]); 2 [i0 ] guess([1,2,6,24,120]); i0  1 /===\ ! ! [ ! ! (i1 + 1)] ! ! i1 = 1 guess(makelist(product(product(GAMMA(i)*i^2,i,1,j),j,1,k),k,1,8)); i0  1 i1  1 i2  1 /===\ /===\ /===\ 2 ! ! ! ! ! ! (i3 + 3) [ ! ! 4 ! ! 18 ! ! ] ! ! ! ! ! ! i3 + 2 i1 = 1 i2 = 1 i3 = 1 guess([1,2,7,42,429,7436,218348,10850216]); i0  1 i1  1 /===\ /===\ ! ! ! ! 3 (3 i2 + 2) (3 i2 + 4) [ ! ! 2 ! ! ] ! ! ! ! 4 (2 i2 + 1) (2 i2 + 3) i1 = 1 i2 = 1 guess(makelist(k^3+k^2,k,1,7)); Dependent equations eliminated: (6) i0  1 /===\ 2 ! ! 5040 [i0 (i0 + 1), 2 ! ! ( ), ! ! 4 3 2 i1 = 1 i1  24 i1 + 245 i1  1422 i1 + 360 i0  1 /===\ ! ! (i1 + 1) (i1 + 2) 2 ! ! ] ! ! 2 i1 = 1 i1 Note that the last example produces three solutions. The first and the last are equivalent, but the second is different! In this case, guess(makelist(k^3+k^2,k,1,7),1); or guess(makelist(k^3+k^2,k,1,7),"one"); 2 find only the solution i0 (i0 + 1), which is a rational function, and is also the first function guess finds. PARAMETERS: l  a list of numbers, level  an integer (optional), "one"  the string "one" (optional), "nogamma"  the string "nogamma" (optional), SYNOPSIS:,  guess(l) tries to find a closed form for a sequence within the hierarchy, of expressions of the form <rational function>, <product of rational, function>, <product of product of rational function>, etc.  guess(l,level) does the same thing as guess(l) but it searches only within the first 'level' levels  guess(l,"one") does the same thing as guess(l) but it returns the first solution it finds.  guess(l,"nogamma") does the same thing as guess(l) but it returns expressions without GAMMA functions. In fact, there is not much difference just at the moment, because Maxima doesn't simplify products yet... */ /* devine.mac * mode: Maxima; * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Copyright (C) 2002 Martin Rubey <Martin.Rubey@...> * * * * This file is part of GNU Maxima. * * * * This program is free software; you can redistribute it and/or * * modify it under the terms of the GNU General Public License as * * published by the Free Software Foundation; either version 2 of * * the License, or (at your option) any later version. * * * * This program is distributed in the hope that it will be * * useful, but WITHOUT ANY WARRANTY; without even the implied * * warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR * * PURPOSE. See the GNU General Public License for more details. * * * * History: * * This is a translation of the Mathematica package Rate.m * * by Christian Krattenthaler <Kratt@...>. * * The translation to Maple was done by JeanFrancois Beraud * * <JeanFrancois.Beraud@...> and Bruno Gauthier * * <Bruno.Gauthier@...> * * * * All features of this package are due to C. Krattenthaler * * The help text is due to JeanFrancois Beraud and Bruno Gauthier * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */ /* * Rational Interpolation * Gives the rational interpolant to the set of points defined by xlist and * ylist, where m and k are respectively the degrees of the numerator and * denominator, and xlist is a list of m+k+1 abscissas of the interpolation * points, x is the variable the result is supposed to be a function of. */ rationalinterpolation(xlist, ylist, x, m, k) := block([tempvec : makelist(1, i, 1, m+k+1), /* contains the new row of mat */ rowlist, /* first set of rows of mat */ mat, /* matrix that describes the interpolation problem */ varlist : makelist('x[i], i, 1, m+k+2)], mode_declare([tempvec,rowlist,varlist,mat],list,[m,k],fixnum), if max(m, k) > 0 then rowlist : cons(tempvec, makelist(tempvec : tempvec * xlist, i, 1, max(m, k))) else rowlist : [tempvec], mat : transpose(apply(matrix, append(rest(rowlist, (max(m, k)  m) ), 1 * makelist(rowlist[i] * ylist, i, 1, k + 1)))), mat : ev(mat . varlist, SCALARMATRIXP : false), /* not sure whether it is save to modify xlist... */ xlist : linsolve(makelist(mat[i, 1], i, 1, (m+k)+1), varlist), if length(xlist) = 0 /* something went wrong */ then NULL /* use the solution to define the interpolating rational function */ else factor(subst(xlist, sum('x[i+1]*x^i, i, 0, m) /sum('x[(i+m)+2]*x^i, i, 0, k)))); /* Intermediate function */ guesscons(l, t) := block([lsize : length(l), res : [], x, ri], mode_declare(lsize, fixnum, res, list, ri, any), for i : 0 thru lsize2 do (ri : rationalinterpolation(makelist(k, k, 1, lsize1), rest(l,1), x, (lsize2)i, i), if ri # NULL then if (subst(x=lsize, denom(ri)) # 0) and (subst(x=lsize, ri)last(l) = 0) and not member(subst(x=t, ri), res) then res : cons(subst(x=t, ri), res)), res); /* * Main function of the package * it tries to find a closed form for a sequence * within the hierarchy of expressions of the * form <rational function>, <product of rational functions>, * <product of product of rational functions>, etc. It may * give several answers */ guess(l, [optargs]) := block([lsize : length(l), tempres, maxlevel, maxlevellist : sublist(optargs, numberp), res : [], onep : member("one", optargs), unevp : member("nogamma", optargs), g], mode_declare([lsize, maxlevel], fixnum, [tempres, maxlevellist, res], list, [onep, unevp], boolean, g, any), optargs : delete("nogamma", delete("one", optargs, 1), 1), if length(maxlevellist) > 1 or length(optargs)length(maxlevellist) > 0 then error("Wrong number of optional arguments: ", optargs) else maxlevel : mode_identity(fixnum, apply(min, cons(lsize1, maxlevellist))  1), g : make_array('ANY, maxlevel + 1), for k : 0 thru maxlevel do (g[k] : l, l : makelist(l[i+1]/l[i], i, 1, (lsizek)1), tempres : guesscons(g[k], concat('i, k)), if tempres # [] then (if k > 0 then for i : 1 thru k do if unevp then tempres : subst('j = concat('i, (ki)+1), map(lambda([expr], g[ki][1] * 'product(expr, j, 1, concat('i, ki)1)), tempres)) else tempres : subst('j = concat('i, (ki)+1), map(lambda([expr], g[ki][1] * product(expr, j, 1, concat('i, ki)1)), tempres)), res : append(res, tempres), if onep then return())), res); 
From: Robert Dodier <robert_dodier@us...>  20051020 02:09:22

Update of /cvsroot/maxima/maxima/share/contrib In directory sc8prcvs1.sourceforge.net:/tmp/cvsserv31466 Added Files: augmented_lagrangian.mac Log Message: Implementation of the augmented Lagrangian method for constrained optimization.  NEW FILE: augmented_lagrangian.mac  /* augmented Lagrangian method for constrained optimization * * See http://wwwfp.mcs.anl.gov/otc/Guide/OptWeb/continuous/constrained/nonlinearcon/auglag.html * and http://www.cs.ubc.ca/spider/ascher/542/chap10.pdf * * At present this code minimizes the augmented Lagrangian by * solving for a stationary point of its gradient. * That's pretty weak, and the code could be improved by plugging in * a conjugate gradient or quasiNewton minimization algorithm. * * FOM = figure of merit expression * xx = list of variables over which to minimize * constraints = list of expressions to be held equal to zero * yy = list of initial guesses for xx * * mnewton (to solve grad L = 0) has to be loaded before calling augmented_lagrangian_method. * * Example: * * load (mnewton); * FOM: x^2 + 2*y^2; * xx: [x, y]; * C: [x + y  1]; * yy: [1, 1]; * augmented_lagrangian_method (FOM, xx, C, yy); * * => [0.6478349834, 0.3239174917] * * copyright Robert Dodier, October 2005 * Released under the terms of the GNU Public License */ niter: 10; augmented_lagrangian_method (FOM, xx, constraints, yy) := block ([n, augmented_lagrangian, augmented_lagrangian_gradient, %lambda, %nu], nc: length (constraints), augmented_lagrangian: FOM + apply ("+", makelist (%lambda[i] * constraints[i], i, 1, nc)) + apply ("+", makelist (%nu[i] * constraints[i]^2, i, 1, nc)), augmented_lagrangian_gradient: map (lambda ([a], diff (augmented_lagrangian, a)), xx), %lambda: makelist (1, i, 1, nc), %nu: makelist (1, i, 1, nc), for i:1 thru niter do (soln: mnewton (ev (augmented_lagrangian_gradient), xx, yy), yy: map (rhs, soln[1]), %lambda: %lambda + apply ("+", %nu * map (lambda ([c], subst (soln[1], c)), constraints))), yy); 
From: Robert Dodier <robert_dodier@us...>  20051020 02:08:11

Update of /cvsroot/maxima/maxima/share/contrib In directory sc8prcvs1.sourceforge.net:/tmp/cvsserv31141 Added Files: ggf.mac Log Message: Compute the generating function (if it is a fraction of two polynomials) of a sequence, its first terms being given. Written by Thomas Baruchel, committed verbatim by Robert Dodier.  NEW FILE: ggf.mac  /* ggf.mac v1.0 for Maxima (tested with Maxima 5.9.1). Compute the generating function (if it is a fraction of two polynomials) of a sequence, its first terms being given. Usage: ggf(Terms); Terms  list of first terms of the sequence (integer or rational) Examples: ggf(makelist(fib(n),n,0,40)); ggf(makelist(2*fib(n+1)fib(n),n,0,40)); Flags: GGFINFINITY default: 3  when computing the continued fraction of the generating function, a partial quotient having a degree (strictly) greater than GGFINFINITY will be discarded and the current convergent will be considered as the exact value of the generating function; most often the degree of all partial quotients will be 0 or 1; if you use a greater value, then you should give enough terms in order to make the computation accurate enough. GGFCFMAX default: 24  when computing the continued fraction of the generating function, if no good result has been found (see the GGFINFINITY flag) after having computed GGFCFMAX partial quotients, the generating function will be considered as not being a fraction of two polynomials and the function will exit. Put freely a greater value for more complicated generating functions. Results: The solution is returned as a fraction of two polynomials. If no solution has been found, it returns with DONE. History: 200509 Thomas Baruchel  version 1.0  Copyright (C) 2005 Thomas Baruchel This library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this library; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 021111307 USA */ GGFINFINITY: 3; GGFCFMAX: 24; ggf(l) := block([p0:0, q0:1, p1:1, q1:0, x, p, q:1, i], p : sum(l[i]*x^(i1),i,1,length(l)), for i:1 thru GGFCFMAX do if block([j:lopow(p,x),k:lopow(q,x),a,p2,q2], if abs(jk) > GGFINFINITY then return(true) else a : x^(jk) * coeff(p,x,j)/coeff(q,x,k), p2 : a*p1 + p0, q2 : a*q1 + q0, p0 : p1, q0 : q1, p1 : p2, q1 : q2, p : rat(p  a*q), if p = 0 then return(true), p2 : p, p : q, q : p2, false) then return(ratsimp(p1/q1))); 