Mercurial > forge
view main/symbolic/inst/symfsolve.m @ 5679:2b962ee1530a octave-forge
Use cell() instead of the deprecated list()
The list() function has been deprecated in Octave. The patch below
replaces all calls to list() in the scripts poly2sym.m, sym2poly.m,
and symfsolve.m by calls to cell().
Also, add a new test using cell in function sym2poly.
author | rlaboiss |
---|---|
date | Sat, 23 May 2009 13:32:29 +0000 |
parents | 51728d4bcdd4 |
children | 414bba9f010d |
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## Copyright (C) 2003 Willem J. Atsma ## ## 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. ## ## You should have received a copy of the GNU General Public License ## along with this program; If not, see <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Function File} {[ @var{x},@var{inf},@var{msg} ] =} symfsolve (...) ## Solve a set of symbolic equations using fsolve(). There are a number of ## ways in which this function can be called. ## ## This solves for all free variables, initial values set to 0: ## ## @example ## symbols ## x=sym("x"); y=sym("y"); ## f=x^2+3*x-1; g=x*y-y^2+3; ## a = symfsolve(f,g); ## @end example ## ## This solves for x and y and sets the initial values to 1 and 5 respectively: ## ## @example ## a = symfsolve(f,g,x,1,y,5); ## a = symfsolve(f,g,@{x==1,y==5@}); ## a = symfsolve(f,g,[1 5]); ## @end example ## ## In all the previous examples vector a holds the results: x=a(1), y=a(2). ## If initial conditions are specified with variables, the latter determine ## output order: ## ## @example ## a = symfsolve(f,g,@{y==1,x==2@}); # here y=a(1), x=a(2) ## @end example ## ## The system of equations to solve for can be given as separate arguments or ## as a single cell-array: ## ## @example ## a = symfsolve(@{f,g@},@{y==1,x==2@}); # here y=a(1), x=a(2) ## @end example ## ## If the variables are not specified explicitly with the initial conditions, ## they are placed in alphabetic order. The system of equations can be comma- ## separated or given in a cell-array. The return-values are those of ## fsolve; @var{x} holds the found roots. ## @end deftypefn ## @seealso{fsolve} ## Author: Willem J. Atsma <watsma(at)users.sf.net> ## ## 2003-04-22 Willem J. Atsma <watsma(at)users.sf.net> ## * Initial revision function [ x,inf,msg ] = symfsolve (varargin) #separate variables and equations eqns = cell(); vars = cell(); if iscell(varargin{1}) if !strcmp(typeinfo(varargin{1}{1}),"ex") error("First argument must be (a cell-array of) symbolic expressions.") endif eqns = varargin{1}; arg_count = 1; else arg_count = 0; for i=1:nargin tmp = disp(varargin{i}); if( iscell(varargin{i}) | ... all(isalnum(tmp) | tmp=="_" | tmp==",") | ... !strcmp(typeinfo(varargin{i}),"ex") ) break; endif eqns=append(eqns,varargin{i}); arg_count = arg_count+1; endfor endif neqns = length(eqns); if neqns==0 error("No equations specified.") endif # make a list with all variables from equations tmp=eqns{1}; for i=2:neqns tmp = tmp+eqns{i}; endfor evars = findsymbols(tmp); nevars=length(evars); # After the equations may follow initial values. The formats are: # [0 0.3 -3 ...] # x,0,y,0.3,z,-3,... # {x==0, y==0.3, z==-3 ...} # none - default of al zero initial values if arg_count==nargin vars = evars; nvars = nevars; X0 = zeros(nvars,1); elseif (nargin-arg_count)>1 if mod(nargin-arg_count,2) error("Initial value symbol-value pairs don't match up.") endif for i=(arg_count+1):2:nargin tmp = disp(varargin{i}); if all(isalnum(tmp) | tmp=="_" | tmp==",") vars=append(vars,varargin{i}); X0((i-arg_count+1)/2)=varargin{i+1}; else error("Error in symbol-value pair arguments.") endif endfor nvars = length(vars); else nvars = length(varargin{arg_count+1}); if nvars!=nevars error("The number of initial conditions does not match the number of free variables.") endif if iscell(varargin{arg_count+1}) # cell-array of relations - this should work for a list of strings ("x==3") too. for i=1:nvars tmp = disp(varargin{arg_count+1}{i}); vars = append(vars,sym(strtok(tmp,"=="))); X0(i) = str2num(tmp((findstr(tmp,"==")+2):length(tmp))); endfor else # straight numbers, match up with symbols in alphabetic order vars = evars; X0 = varargin{arg_count+1}; endif endif # X0 is now a vector, vars a list of variables. # create temporary function: symfn = sprintf("function Y=symfn(X) "); for i=1:nvars symfn = [symfn sprintf("%s=X(%d); ",disp(vars{i}),i)]; endfor for i=1:neqns symfn = [symfn sprintf("Y(%d)=%s; ",i,disp(eqns{i}))]; endfor symfn = [symfn sprintf("endfunction")]; eval(symfn); [x,inf,msg] = fsolve("symfn",X0); endfunction %!shared % x = sym ("x"); % y = sym ("y"); % f = x ^ 2 + 3 * x - 1; % g = x * y - y ^ 2 + 3; %!test % assert (symfsolve (f, g), [0.30278; -1.58727]', 1e-5); %!test % assert (symfsolve (f, g, x, 1, y, 5), [0.30278; 1.89004]', 1e-5); %!test % assert (symfsolve (f, g, {x==1,y==5}), [0.30278; 1.89004]', 1e-5); %!test % assert (symfsolve (f, g, [1 5]), [0.30278; 1.89004]', 1e-5); %!test % assert (symfsolve ({f, g}, {y==1,x==2}), [1.89004; 0.30278]', 1e-5);