octave-lyh: scripts/optimization/fsolve.m annotate

annotate scripts/optimization/fsolve.m @ 8596:8833c0b18eb2

enable default settings queries in optim funcs

author	Jaroslav Hajek <highegg@gmail.com>
date	Tue, 27 Jan 2009 08:15:08 +0100
parents	dacfd030633a
children	43f831758d42

rev	line source
8590 c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	1 ## Copyright (C) 2008, 2009 VZLU Prague, a.s.
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	2 ##
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	3 ## This file is part of Octave.
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	4 ##
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	5 ## Octave is free software; you can redistribute it and/or modify it
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	6 ## under the terms of the GNU General Public License as published by
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	7 ## the Free Software Foundation; either version 3 of the License, or (at
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	8 ## your option) any later version.
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	9 ##
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	10 ## Octave is distributed in the hope that it will be useful, but
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	13 ## General Public License for more details.
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	14 ##
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	15 ## You should have received a copy of the GNU General Public License
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	16 ## along with Octave; see the file COPYING. If not, see
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	17 ## <http://www.gnu.org/licenses/>.
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	18 ##
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	19 ## Author: Jaroslav Hajek <highegg@gmail.com>
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	20
8466 4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	21 ## -- texinfo --
8513 352d3245d4c1 fsolve.m: doc fix John W. Eaton <jwe@octave.org> parents: 8507 diff changeset	22 ## @deftypefn{Function File} {} fsolve (@var{fcn}, @var{x0}, @var{options})
8466 4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	23 ## @deftypefnx{Function File} {[@var{x}, @var{fvec}, @var{info}, @var{output}, @var{fjac}]} = fsolve (@var{fcn}, @dots{})
8513 352d3245d4c1 fsolve.m: doc fix John W. Eaton <jwe@octave.org> parents: 8507 diff changeset	24 ## Solve a system of nonlinear equations defined by the function @var{fcn}.
8466 4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	25 ## @var{fcn} should accepts a vector (array) defining the unknown variables,
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	26 ## and return a vector of left-hand sides of the equations. Right-hand sides
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	27 ## are defined to be zeros.
8514 39867b4aca52 fsolve.m: additional doc fix John W. Eaton <jwe@octave.org> parents: 8513 diff changeset	28 ## In other words, this function attempts to determine a vector @var{x} such
39867b4aca52 fsolve.m: additional doc fix John W. Eaton <jwe@octave.org> parents: 8513 diff changeset	29 ## that @code{@var{fcn} (@var{x})} gives (approximately) all zeros.
8466 4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	30 ## @var{x0} determines a starting guess. The shape of @var{x0} is preserved
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	31 ## in all calls to @var{fcn}, but otherwise it is treated as a column vector.
8515 ec2715c76039 fzero.m, fsolve.m: additional doc fixes John W. Eaton <jwe@octave.org> parents: 8514 diff changeset	32 ## @var{options} is a structure specifying additional options.
ec2715c76039 fzero.m, fsolve.m: additional doc fixes John W. Eaton <jwe@octave.org> parents: 8514 diff changeset	33 ## Currently, @code{fsolve} recognizes these options:
ec2715c76039 fzero.m, fsolve.m: additional doc fixes John W. Eaton <jwe@octave.org> parents: 8514 diff changeset	34 ## @code{"FunValCheck"}, @code{"OutputFcn"}, @code{"TolX"},
8590 c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	35 ## @code{"TolFun"}, @code{"MaxIter"}, @code{"MaxFunEvals"},
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	36 ## @code{"Jacobian"} and @code{"Updating"}.
8466 4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	37 ##
8513 352d3245d4c1 fsolve.m: doc fix John W. Eaton <jwe@octave.org> parents: 8507 diff changeset	38 ## If @code{"Jacobian"} is @code{"on"}, it specifies that @var{fcn},
352d3245d4c1 fsolve.m: doc fix John W. Eaton <jwe@octave.org> parents: 8507 diff changeset	39 ## called with 2 output arguments, also returns the Jacobian matrix
352d3245d4c1 fsolve.m: doc fix John W. Eaton <jwe@octave.org> parents: 8507 diff changeset	40 ## of right-hand sides at the requested point. @code{"TolX"} specifies
352d3245d4c1 fsolve.m: doc fix John W. Eaton <jwe@octave.org> parents: 8507 diff changeset	41 ## the termination tolerance in the unknown variables, while
8596 8833c0b18eb2 enable default settings queries in optim funcs Jaroslav Hajek <highegg@gmail.com> parents: 8592 diff changeset	42 ## @code{"TolFun"} is a tolerance for equations. Default is @code{1e-7}
8833c0b18eb2 enable default settings queries in optim funcs Jaroslav Hajek <highegg@gmail.com> parents: 8592 diff changeset	43 ## for both @code{"TolX"} and @code{"TolFun"}.
8833c0b18eb2 enable default settings queries in optim funcs Jaroslav Hajek <highegg@gmail.com> parents: 8592 diff changeset	44 ## If @code{"Updating"} is "on", the function will attempt to use Broyden
8590 c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	45 ## updates to update the Jacobian, in order to reduce the amount of jacobian
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	46 ## calculations.
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	47 ## If your user function always calculates the Jacobian (regardless of number
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	48 ## of output arguments), this option provides no advantage and should be set to
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	49 ## false.
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	50 ##
8466 4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	51 ## For description of the other options, see @code{optimset}.
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	52 ##
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	53 ## On return, @var{fval} contains the value of the function @var{fcn}
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	54 ## evaluated at @var{x}, and @var{info} may be one of the following values:
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	55 ##
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	56 ## @table @asis
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	57 ## @item 1
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	58 ## Converged to a solution point. Relative residual error is less than specified
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	59 ## by TolFun.
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	60 ## @item 2
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	61 ## Last relative step size was less that TolX.
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	62 ## @item 3
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	63 ## Last relative decrease in residual was less than TolF.
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	64 ## @item 0
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	65 ## Iteration limit exceeded.
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	66 ## @item -3
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	67 ## The trust region radius became excessively small.
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	68 ## @end table
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	69 ##
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	70 ## Note: If you only have a single nonlinear equation of one variable, using
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	71 ## @code{fzero} is usually a much better idea.
8513 352d3245d4c1 fsolve.m: doc fix John W. Eaton <jwe@octave.org> parents: 8507 diff changeset	72 ## @seealso{fzero, optimset}
8466 4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	73 ## @end deftypefn
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	74
8596 8833c0b18eb2 enable default settings queries in optim funcs Jaroslav Hajek <highegg@gmail.com> parents: 8592 diff changeset	75 function [x, fvec, info, output, fjac] = fsolve (fcn, x0, options = struct ())
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	76
8596 8833c0b18eb2 enable default settings queries in optim funcs Jaroslav Hajek <highegg@gmail.com> parents: 8592 diff changeset	77 ## Get default options if requested.
8833c0b18eb2 enable default settings queries in optim funcs Jaroslav Hajek <highegg@gmail.com> parents: 8592 diff changeset	78 if (nargin == 1 && ischar (fcn) && strcmp (fcn, 'defaults'))
8833c0b18eb2 enable default settings queries in optim funcs Jaroslav Hajek <highegg@gmail.com> parents: 8592 diff changeset	79 x = optimset ("MaxIter", 400, "MaxFunEvals", Inf, \
8833c0b18eb2 enable default settings queries in optim funcs Jaroslav Hajek <highegg@gmail.com> parents: 8592 diff changeset	80 "Jacobian", "off", "TolX", 1e-7, "TolF", 1e-7,
8833c0b18eb2 enable default settings queries in optim funcs Jaroslav Hajek <highegg@gmail.com> parents: 8592 diff changeset	81 "OutputFcn", [], "Updating", "on", "FunValCheck", "off");
8833c0b18eb2 enable default settings queries in optim funcs Jaroslav Hajek <highegg@gmail.com> parents: 8592 diff changeset	82 return;
8833c0b18eb2 enable default settings queries in optim funcs Jaroslav Hajek <highegg@gmail.com> parents: 8592 diff changeset	83 endif
8833c0b18eb2 enable default settings queries in optim funcs Jaroslav Hajek <highegg@gmail.com> parents: 8592 diff changeset	84
8833c0b18eb2 enable default settings queries in optim funcs Jaroslav Hajek <highegg@gmail.com> parents: 8592 diff changeset	85 if (nargin < 2 \|\| nargin > 3 \|\| ! ismatrix (x0))
8833c0b18eb2 enable default settings queries in optim funcs Jaroslav Hajek <highegg@gmail.com> parents: 8592 diff changeset	86 print_usage ();
8833c0b18eb2 enable default settings queries in optim funcs Jaroslav Hajek <highegg@gmail.com> parents: 8592 diff changeset	87 endif
8833c0b18eb2 enable default settings queries in optim funcs Jaroslav Hajek <highegg@gmail.com> parents: 8592 diff changeset	88
8833c0b18eb2 enable default settings queries in optim funcs Jaroslav Hajek <highegg@gmail.com> parents: 8592 diff changeset	89 if (ischar (fcn))
8833c0b18eb2 enable default settings queries in optim funcs Jaroslav Hajek <highegg@gmail.com> parents: 8592 diff changeset	90 fcn = str2func (fcn);
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	91 endif
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	92
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	93 xsiz = size (x0);
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	94 n = numel (x0);
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	95
8467 77b8d4aa2743 fsolve.m, fzero.m: style fixes; use strcmpi to compare options John W. Eaton <jwe@octave.org> parents: 8466 diff changeset	96 has_jac = strcmpi (optimget (options, "Jacobian", "off"), "on");
8596 8833c0b18eb2 enable default settings queries in optim funcs Jaroslav Hajek <highegg@gmail.com> parents: 8592 diff changeset	97 maxiter = optimget (options, "MaxIter", 400);
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	98 maxfev = optimget (options, "MaxFunEvals", Inf);
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	99 outfcn = optimget (options, "OutputFcn");
8596 8833c0b18eb2 enable default settings queries in optim funcs Jaroslav Hajek <highegg@gmail.com> parents: 8592 diff changeset	100 updating = strcmpi (optimget (options, "Updating", "on"), "on");
8590 c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	101
8467 77b8d4aa2743 fsolve.m, fzero.m: style fixes; use strcmpi to compare options John W. Eaton <jwe@octave.org> parents: 8466 diff changeset	102 funvalchk = strcmpi (optimget (options, "FunValCheck", "off"), "on");
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	103
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	104 if (funvalchk)
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8468 diff changeset	105 ## Replace fun with a guarded version.
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	106 fun = @(x) guarded_eval (fun, x);
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	107 endif
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	108
8466 4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	109 ## These defaults are rather stringent. I think that normally, user
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	110 ## prefers accuracy to performance.
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	111
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	112 macheps = eps (class (x0));
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	113
8596 8833c0b18eb2 enable default settings queries in optim funcs Jaroslav Hajek <highegg@gmail.com> parents: 8592 diff changeset	114 tolx = optimget (options, "TolX", 1e-7);
8833c0b18eb2 enable default settings queries in optim funcs Jaroslav Hajek <highegg@gmail.com> parents: 8592 diff changeset	115 tolf = optimget (options, "TolFun", 1e-7);
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	116
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	117 factor = 100;
8466 4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	118 ## FIXME: TypicalX corresponds to user scaling (???)
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	119 autodg = true;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	120
8467 77b8d4aa2743 fsolve.m, fzero.m: style fixes; use strcmpi to compare options John W. Eaton <jwe@octave.org> parents: 8466 diff changeset	121 niter = 1;
77b8d4aa2743 fsolve.m, fzero.m: style fixes; use strcmpi to compare options John W. Eaton <jwe@octave.org> parents: 8466 diff changeset	122 nfev = 0;
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	123
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	124 x = x0(:);
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	125 info = 0;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	126
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8468 diff changeset	127 ## Outer loop.
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	128 while (niter < maxiter && nfev < maxfev && ! info)
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	129
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8468 diff changeset	130 ## Calculate function value and Jacobian (possibly via FD).
cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8468 diff changeset	131 ## Handle arbitrary shapes of x and f and remember them.
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	132 if (has_jac)
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	133 [fvec, fjac] = fcn (reshape (x, xsiz));
8592 dacfd030633a handle sparse jacobians in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8590 diff changeset	134 ## If the jacobian is sparse, disable Broyden updating.
dacfd030633a handle sparse jacobians in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8590 diff changeset	135 if (issparse (fjac))
dacfd030633a handle sparse jacobians in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8590 diff changeset	136 updating = false;
dacfd030633a handle sparse jacobians in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8590 diff changeset	137 endif
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	138 nfev ++;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	139 else
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	140 [fvec, fjac] = __fdjac__ (fcn, reshape (x, xsiz));
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	141 nfev += 1 + length (x);
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	142 endif
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	143 fsiz = size (fvec);
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	144 fvec = fvec(:);
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	145 fn = norm (fvec);
8383 a762d9daa700 allow overdetermined systems in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8306 diff changeset	146 m = length (fvec);
a762d9daa700 allow overdetermined systems in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8306 diff changeset	147 n = length (x);
8590 c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	148
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	149 ## For square and overdetermined systems, we update a (pivoted) QR
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	150 ## factorization of the jacobian to avoid solving a full system in each
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	151 ## step. In this case, we pass a triangular matrix to __dogleg__.
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	152 ## Pivoted QR is used for slightly better robustness and invariance
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	153 ## w.r.t. permutations of variables.
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	154 useqr = updating && m >= n && n > 10;
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	155
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	156 if (useqr)
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	157 ## Get QR factorization of the jacobian, optionally with column pivoting.
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	158 ## TODO: pivoting is only done in the first step, to get invariance
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	159 ## w.r.t. permutations of variables. Maybe it could be beneficial to
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	160 ## repivot occassionally?
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	161 if (niter == 1)
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	162 [q, r, p] = qr (fjac, 0);
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	163 ## p is a column vector. Blame Matlab for the inconsistency.
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	164 ## Octave can handle permutation matrices gracefully.
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	165 p = eye (n)(:, p);
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	166 else
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	167 [q, r] = qr (fjac*p, 0);
8383 a762d9daa700 allow overdetermined systems in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8306 diff changeset	168 endif
a762d9daa700 allow overdetermined systems in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8306 diff changeset	169 endif
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	170
8590 c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	171 ## Get column norms, use them as scaling factors.
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	172 jcn = norm (fjac, 'columns').';
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	173 if (niter == 1)
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	174 if (autodg)
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	175 dg = jcn;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	176 dg(dg == 0) = 1;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	177 endif
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	178 xn = norm (dg .* x);
8590 c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	179 ## FIXME: something better?
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	180 delta = max (factor * xn, 1);
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	181 endif
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	182
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8468 diff changeset	183 ## Rescale if necessary.
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	184 if (autodg)
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	185 dg = max (dg, jcn);
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	186 endif
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	187
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	188 nfail = 0;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	189 nsuc = 0;
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8468 diff changeset	190 ## Inner loop.
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	191 while (niter <= maxiter && nfev < maxfev && ! info)
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	192
8590 c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	193 if (useqr)
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	194 tr_mat = r;
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	195 tr_vec = q'*fvec;
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	196 else
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	197 tr_mat = fjac;
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	198 tr_vec = fvec;
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	199 endif
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	200
8590 c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	201 ## Get trust-region model (dogleg) minimizer.
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	202 if (useqr)
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	203 qtf = q'*fvec;
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	204 s = - __dogleg__ (r, qtf, dg, delta);
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	205 w = qtf + r * s;
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	206 s = p * s;
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	207 else
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	208 s = - __dogleg__ (fjac, fvec, dg, delta);
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	209 w = fvec + fjac * s;
8395 88fd356b0d95 optionally allow pivoting in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8383 diff changeset	210 endif
8590 c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	211
8395 88fd356b0d95 optionally allow pivoting in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8383 diff changeset	212 sn = norm (dg .* s);
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	213 if (niter == 1)
8395 88fd356b0d95 optionally allow pivoting in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8383 diff changeset	214 delta = min (delta, sn);
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	215 endif
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	216
8395 88fd356b0d95 optionally allow pivoting in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8383 diff changeset	217 fvec1 = fcn (reshape (x + s, xsiz)) (:);
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	218 fn1 = norm (fvec1);
8590 c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	219 nfev ++;
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	220
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	221 if (fn1 < fn)
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8468 diff changeset	222 ## Scaled actual reduction.
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	223 actred = 1 - (fn1/fn)^2;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	224 else
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	225 actred = -1;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	226 endif
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	227
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8468 diff changeset	228 ## Scaled predicted reduction, and ratio.
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	229 t = norm (w);
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	230 if (t < fn)
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	231 prered = 1 - (t/fn)^2;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	232 ratio = actred / prered;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	233 else
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	234 prered = 0;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	235 ratio = 0;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	236 endif
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	237
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8468 diff changeset	238 ## Update delta.
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	239 if (ratio < 0.1)
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	240 nsuc = 0;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	241 nfail ++;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	242 delta *= 0.5;
8590 c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	243 if (delta <= 1e1machepsxn)
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8468 diff changeset	244 ## Trust region became uselessly small.
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	245 info = -3;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	246 break;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	247 endif
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	248 else
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	249 nfail = 0;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	250 nsuc ++;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	251 if (abs (1-ratio) <= 0.1)
8395 88fd356b0d95 optionally allow pivoting in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8383 diff changeset	252 delta = 2*sn;
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	253 elseif (ratio >= 0.5 \|\| nsuc > 1)
8395 88fd356b0d95 optionally allow pivoting in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8383 diff changeset	254 delta = max (delta, 2*sn);
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	255 endif
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	256 endif
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	257
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	258 if (ratio >= 1e-4)
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8468 diff changeset	259 ## Successful iteration.
8395 88fd356b0d95 optionally allow pivoting in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8383 diff changeset	260 x += s;
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	261 xn = norm (dg .* x);
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	262 fvec = fvec1;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	263 fn = fn1;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	264 niter ++;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	265 endif
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	266
8590 c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	267 ## FIXME: should outputfcn be only called after a successful iteration?
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	268 if (outfcn)
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	269 optimvalues.iter = niter;
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	270 optimvalues.funccount = nfev;
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	271 optimvalues.fval = fn;
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	272 optimvalues.searchdirection = s;
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	273 state = 'iter';
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	274 stop = outfcn (x, optimvalues, state);
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	275 if (stop)
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	276 info = -1;
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	277 break;
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	278 endif
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	279 endif
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	280
8466 4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	281 ## Tests for termination conditions. A mysterious place, anything
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	282 ## can happen if you change something here...
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	283
8466 4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	284 ## The rule of thumb (which I'm not sure M*b is quite following)
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	285 ## is that for a tolerance that depends on scaling, only 0 makes
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	286 ## sense as a default value. But 0 usually means uselessly long
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	287 ## iterations, so we need scaling-independent tolerances wherever
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	288 ## possible.
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	289
8466 4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	290 ## FIXME -- why tolfnxn? If abs (e) ~ abs(x) * eps is a vector
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	291 ## of perturbations of x, then norm (fjace) <= epsn*xn, i.e. by
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	292 ## tolf ~ eps we demand as much accuracy as we can expect.
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	293 if (fn <= tolfnxn)
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	294 info = 1;
8466 4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	295 ## The following tests done only after successful step.
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	296 elseif (actred > 0)
8466 4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	297 ## This one is classic. Note that we use scaled variables again,
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	298 ## but compare to scaled step, so nothing bad.
8395 88fd356b0d95 optionally allow pivoting in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8383 diff changeset	299 if (sn <= tolx*xn)
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	300 info = 2;
8466 4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	301 ## Again a classic one. It seems weird to use the same tolf
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	302 ## for two different tests, but that's what M*b manual appears
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	303 ## to say.
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	304 elseif (actred < tolf)
8383 a762d9daa700 allow overdetermined systems in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8306 diff changeset	305 info = 3;
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	306 endif
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	307 endif
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	308
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8468 diff changeset	309 ## Criterion for recalculating jacobian.
8590 c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	310 if (! updating \|\| nfail == 2)
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	311 break;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	312 endif
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	313
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8468 diff changeset	314 ## Compute the scaled Broyden update.
8590 c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	315 if (useqr)
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	316 u = (fvec1 - q*w) / sn;
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	317 v = dg .* ((dg .* s) / sn);
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	318 v = p' * v;
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	319
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	320 ## Update the QR factorization.
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	321 [q, r] = qrupdate (q, r, u, v);
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	322 else
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	323 u = (fvec1 - w);
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	324 v = dg .* ((dg .* s) / sn);
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	325
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	326 ## update the jacobian
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	327 fjac += u * v';
8395 88fd356b0d95 optionally allow pivoting in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8383 diff changeset	328 endif
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	329 endwhile
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	330 endwhile
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	331
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 8468 diff changeset	332 ## Restore original shapes.
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	333 x = reshape (x, xsiz);
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	334 fvec = reshape (fvec, fsiz);
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	335
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	336 output.iterations = niter;
8590 c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	337 output.funcCount = nfev;
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	338
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	339 endfunction
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	340
8466 4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	341 ## An assistant function that evaluates a function handle and checks for
4d008d9f0ccf fsolve.m: style fixes John W. Eaton <jwe@octave.org> parents: 8395 diff changeset	342 ## bad results.
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	343 function fx = guarded_eval (fun, x)
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	344 fx = fun (x);
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	345 if (! all (isreal (fx)))
8468 866492035ecf fsolve.m, fzero.m: undo part of previous change John W. Eaton <jwe@octave.org> parents: 8467 diff changeset	346 error ("fsolve:notreal", "fsolve: non-real value encountered");
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	347 elseif (any (isnan (fx)))
8468 866492035ecf fsolve.m, fzero.m: undo part of previous change John W. Eaton <jwe@octave.org> parents: 8467 diff changeset	348 error ("fsolve:isnan", "fsolve: NaN value encountered");
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	349 endif
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	350 endfunction
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	351
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	352 %!function retval = f (p)
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	353 %! x = p(1);
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	354 %! y = p(2);
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	355 %! z = p(3);
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	356 %! retval = zeros (3, 1);
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	357 %! retval(1) = sin(x) + y**2 + log(z) - 7;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	358 %! retval(2) = 3x + 2y -z*3 + 1;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	359 %! retval(3) = x + y + z - 5;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	360 %!test
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	361 %! x_opt = [ 0.599054;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	362 %! 2.395931;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	363 %! 2.005014 ];
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	364 %! tol = 1.0e-5;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	365 %! [x, fval, info] = fsolve (@f, [ 0.5; 2.0; 2.5 ]);
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	366 %! assert (info > 0);
8383 a762d9daa700 allow overdetermined systems in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8306 diff changeset	367 %! assert (norm (x - x_opt, Inf) < tol);
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	368 %! assert (norm (fval) < tol);
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	369
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	370 %!function retval = f (p)
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	371 %! x = p(1);
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	372 %! y = p(2);
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	373 %! z = p(3);
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	374 %! w = p(4);
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	375 %! retval = zeros (4, 1);
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	376 %! retval(1) = 3x + 4y + exp (z + w) - 1.007;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	377 %! retval(2) = 6x - 4y + exp (3*z + w) - 11;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	378 %! retval(3) = x^4 - 4y^2 + 6z - 8*w - 20;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	379 %! retval(4) = x^2 + 2*y^3 + z - w - 4;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	380 %!test
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	381 %! x_opt = [ -0.767297326653401, 0.590671081117440, 1.47190018629642, -1.52719341133957 ];
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	382 %! tol = 1.0e-5;
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	383 %! [x, fval, info] = fsolve (@f, [-1, 1, 2, -1]);
43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	384 %! assert (info > 0);
8383 a762d9daa700 allow overdetermined systems in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8306 diff changeset	385 %! assert (norm (x - x_opt, Inf) < tol);
8306 43795cf108d0 initial implementation of fsolve Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	386 %! assert (norm (fval) < tol);
8383 a762d9daa700 allow overdetermined systems in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8306 diff changeset	387
a762d9daa700 allow overdetermined systems in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8306 diff changeset	388 %!function retval = f (p)
a762d9daa700 allow overdetermined systems in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8306 diff changeset	389 %! x = p(1);
a762d9daa700 allow overdetermined systems in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8306 diff changeset	390 %! y = p(2);
a762d9daa700 allow overdetermined systems in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8306 diff changeset	391 %! z = p(3);
a762d9daa700 allow overdetermined systems in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8306 diff changeset	392 %! retval = zeros (3, 1);
a762d9daa700 allow overdetermined systems in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8306 diff changeset	393 %! retval(1) = sin(x) + y**2 + log(z) - 7;
a762d9daa700 allow overdetermined systems in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8306 diff changeset	394 %! retval(2) = 3x + 2y -z*3 + 1;
a762d9daa700 allow overdetermined systems in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8306 diff changeset	395 %! retval(3) = x + y + z - 5;
a762d9daa700 allow overdetermined systems in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8306 diff changeset	396 %! retval(4) = xx + y - zlog(z) - 1.36;
a762d9daa700 allow overdetermined systems in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8306 diff changeset	397 %!test
a762d9daa700 allow overdetermined systems in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8306 diff changeset	398 %! x_opt = [ 0.599054;
a762d9daa700 allow overdetermined systems in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8306 diff changeset	399 %! 2.395931;
a762d9daa700 allow overdetermined systems in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8306 diff changeset	400 %! 2.005014 ];
a762d9daa700 allow overdetermined systems in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8306 diff changeset	401 %! tol = 1.0e-5;
8590 c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	402 %! [x, fval, info] = fsolve (@f, [ 0.5; 2.0; 2.5 ]);
8383 a762d9daa700 allow overdetermined systems in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8306 diff changeset	403 %! assert (info > 0);
a762d9daa700 allow overdetermined systems in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8306 diff changeset	404 %! assert (norm (x - x_opt, Inf) < tol);
a762d9daa700 allow overdetermined systems in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8306 diff changeset	405 %! assert (norm (fval) < tol);
a762d9daa700 allow overdetermined systems in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8306 diff changeset	406
8395 88fd356b0d95 optionally allow pivoting in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8383 diff changeset	407 %!function retval = f (p)
88fd356b0d95 optionally allow pivoting in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8383 diff changeset	408 %! x = p(1);
88fd356b0d95 optionally allow pivoting in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8383 diff changeset	409 %! y = p(2);
88fd356b0d95 optionally allow pivoting in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8383 diff changeset	410 %! z = p(3);
88fd356b0d95 optionally allow pivoting in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8383 diff changeset	411 %! retval = zeros (3, 1);
88fd356b0d95 optionally allow pivoting in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8383 diff changeset	412 %! retval(1) = sin(x) + y**2 + log(z) - 7;
88fd356b0d95 optionally allow pivoting in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8383 diff changeset	413 %! retval(2) = 3x + 2y -z*3 + 1;
88fd356b0d95 optionally allow pivoting in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8383 diff changeset	414 %! retval(3) = x + y + z - 5;
88fd356b0d95 optionally allow pivoting in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8383 diff changeset	415 %!test
88fd356b0d95 optionally allow pivoting in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8383 diff changeset	416 %! x_opt = [ 0.599054;
88fd356b0d95 optionally allow pivoting in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8383 diff changeset	417 %! 2.395931;
88fd356b0d95 optionally allow pivoting in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8383 diff changeset	418 %! 2.005014 ];
88fd356b0d95 optionally allow pivoting in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8383 diff changeset	419 %! tol = 1.0e-5;
8590 c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	420 %! opt = optimset ("Updating", "qrp");
8395 88fd356b0d95 optionally allow pivoting in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8383 diff changeset	421 %! [x, fval, info] = fsolve (@f, [ 0.5; 2.0; 2.5 ], opt);
88fd356b0d95 optionally allow pivoting in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8383 diff changeset	422 %! assert (info > 0);
88fd356b0d95 optionally allow pivoting in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8383 diff changeset	423 %! assert (norm (x - x_opt, Inf) < tol);
88fd356b0d95 optionally allow pivoting in fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8383 diff changeset	424 %! assert (norm (fval) < tol);
8590 c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	425
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	426 %!test
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	427 %! b0 = 3;
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	428 %! a0 = 0.2;
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	429 %! x = 0:.5:5;
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	430 %! noise = 1e-5 * sin (100*x);
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	431 %! y = exp (-a0*x) + b0 + noise;
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	432 %! c_opt = [a0, b0];
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	433 %! tol = 1e-5;
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	434 %!
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	435 %! [c, fval, info, output] = fsolve (@(c) (exp(-c(1)*x) + c(2) - y), [0, 0]);
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	436 %! assert (info > 0);
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	437 %! assert (norm (c - c_opt, Inf) < tol);
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	438 %! assert (norm (fval) < norm (noise));
c136d313206a improvements to fsolve Jaroslav Hajek <highegg@gmail.com> parents: 8562 diff changeset	439

Mercurial > hg > octave-lyh

annotate scripts/optimization/fsolve.m @ 8596:8833c0b18eb2