|
|
Subject:Why do I receive a warning message when using FZERO in MATLAB 5.3 (R11) or higher?
Problem Description:The code I'm using works fine in MATLAB 5.2 (R10). Here's the warning I received:
Warning: Cannot determine from calling sequence whether to use new or
grandfathered FZERO function. Using new; if call was grandfathered
FZERO syntax, this may give unexpected results.
Solution:This enhancement has been made for Release 14 (R14). For previousproduct releases, please read below for any possible workarounds:
Thesyntax for FZERO has changed in MATLAB 5.3 (R11) to make this functionmore consistent with other optimization/minimization functions. Westrongly suggest using the newer version and syntax of FZERO, but youcan still use the older version of FZERO if you wish. When in MATLAB,type:
to see more details on the new usage. Basically, instead ofsupplying two empty arguments, if you want to use the default settingsyou can use the following:
By leaving the third input empty, you're requesting that thedefault options be used. With FZERO, this will produce a warningindicating that the calling syntax is ambiguous, but will usuallyproduce the answer you're expecting.
In MATLAB 5.3 (R11), thetolerance and trace are specified inside the options structure, whichis the third input parameter. To choose the defaults, use the followingsyntax:
fzero('fun',x0,optimset('fzero'),p1)
or in two separate lines:
options=optimset('fzero');
fzero('fun',x0,options,p1);
If you must use the older version, you'll need to use the old FZEROcode from MATLAB 5.2 (R10). You may want to rename the old "fzero.m"file to "fzero_old.m" and then use the "Search and Replace" feature inyour M-file editor to change calls to "fzero" to calls to "fzero_old".Though this isn't necessary and you can use the name FZERO, if you givethe older version a different name you are less likely to affect otherM-files which rely on the newer FZERO. The older FZERO code is listedbelow at the end of this solution.
You should also be aware thatwe've stablized the older FZERO code and are no longer making changesto it. If you run into problems with it you may want to try using thenewer version to see if they have been corrected there.
Below is the FZERO code used with MATLAB 5.2 (R10):
function b = fzero(FunFcn,x,tol,trace,varargin)
%FZERO Find zero of function of one variable.
% FZERO(F,X) tries to find a zero of F. F is a string containing
% the name of a real-valued function of a single real variable.
% The value returned is near a point where F changes sign, or NaN
% if the search fails.
%
% FZERO(F,X), where X is a vector of length 2, assumes X is an
% interval where the sign of F(X(1)) differs from the sign of F(X(2)).
% An error occurs if this is not true. Calling FZERO with an interval
% guarantees FZERO will return a value near a point where F changes
% sign.
%
% FZERO(F,X), where X is a scalar value, uses X as a starting guess.
% FZERO looks for an interval containing a sign change for F and
% containing X. If no such interval is found, NaN is returned.
% In this case, the search terminates when the search interval
% is expanded until an Inf, NaN, or complex value is found.
%
% FZERO(F,X,TOL) sets the relative tolerance for the convergence test.
% FZERO(F,X,TOL,TRACE) displays information at each iteration when
% TRACE is nonzero.
% FZERO(F,X,TOL,TRACE,P1,P2,...) allows for additional arguments
% which are passed to the function, F(X,P1,P2,...). Pass an empty
% matrix for TOL or TRACE to use the default value.
%
% Examples
% fzero('sin', 3) returns pi. Note the quotes around sin.
% Ordinarily, functions are defined in M-files.
% fzero('abs(x)+1', 1) returns NaN since this function does
% not change sign anywhere on the real axis (and does not have
% a zero as well).
% fzero('sin', 3, [], 1) returns pi, uses the default tolerance,
% and displays iteration information.
%
% See also ROOTS.
% Copyright (c) 1984-98 by The MathWorks, Inc.
% $Revision: 5.12 $ $Date: 1997/11/21 23:30:46 $
% This algorithm was originated by T. Dekker. An Algol 60 version,
% with some improvements, is given by Richard Brent in "Algorithms for
% Minimization Without Derivatives", Prentice-Hall, 1973. A Fortran
% version is in Forsythe, Malcolm and Moler, "Computer Methods
% for Mathematical Computations", Prentice-Hall, 1976.
% Initialization
if nargin < 3 | isempty(tol), tol = eps; end
if nargin < 4 | isempty(trace), trace = 0; end
if trace
header = ' Func evals x f(x) Procedure';
step=' ';
count = 0;
end
if (~isfinite(x))
error('Second argument must be finite.')
end
% Convert to inline function as needed.
FunFcn = fcnchk(FunFcn,length(varargin));
% Interval input
if (length(x) == 2)
a = x(1);
b = x(2);
fa = feval(FunFcn,a,varargin{:});
fb = feval(FunFcn,b,varargin{:});
if any(~isfinite([fa fb])) | any(~isreal([fa fb]))
error('Function values at interval endpoints must be finite and real.')
end
if trace
disp(header)
data = [a fa]; step=' initial';
count = count + 1;
disp([sprintf('%5.0f %13.6g %13.6g ',count, data), step])
data = [b fb]; step = ' initial';
count = count + 1;
disp([sprintf('%5.0f %13.6g %13.6g ',count, data), step])
end
if (fa > 0) == (fb > 0)
error('The function values at the interval endpoints must differ in sign.')
end
% Starting guess scalar input
elseif (length(x) == 1)
fx = feval(FunFcn,x,varargin{:});
if fx == 0
b = x;
return
elseif ~isfinite(fx) | ~isreal(fx)
error('Function value at starting guess must be finite and real.');
end
if trace
disp(header)
data = [x fx]; step=' initial';
count = count + 1;
disp([sprintf('%5.0f %13.6g %13.6g ',count, data), step])
end
if x ~= 0,
dx = x/50;
else,
dx = 1/50;
end
% Find change of sign.
twosqrt = sqrt(2);
a = x; fa = fx; b = x; fb = fx;
while (fa > 0) == (fb > 0)
dx = twosqrt*dx;
a = x - dx; fa = feval(FunFcn,a,varargin{:});
if ~isfinite(fa) | ~isreal(fa)
disperr(a,fa);
b = NaN;
return
end
if trace
data = [a fa]; step=' search';
count = count + 1;
disp([sprintf('%5.0f %13.6g %13.6g ',count, data), step])
end
if (fa > 0) ~= (fb > 0)
break
end
b = x + dx; fb = feval(FunFcn,b,varargin{:});
if ~isfinite(fb) | ~isreal(fb)
disperr(b,fb);
b = NaN;
return
end
if trace
data = [b fb]; step=' search';
count = count + 1;
disp([sprintf('%5.0f %13.6g %13.6g ',count, data), step])
end
end % while
if trace
disp(' ')
disp([' Looking for a zero in the interval [', ...
num2str(a) , ', ', num2str(b), ']']);
disp(' ')
end
else
error('Second argument must be of length 1 or 2.');
end % if (length(x) == 2
fc = fb;
% Main loop, exit from middle of the loop
while fb ~= 0
% Insure that b is the best result so far, a is the previous
% value of b, and c is on the opposite of the zero from b.
if (fb > 0) == (fc > 0)
c = a; fc = fa;
d = b - a; e = d;
end
if abs(fc) < abs(fb)
a = b; b = c; c = a;
fa = fb; fb = fc; fc = fa;
end
% Convergence test and possible exit
m = 0.5*(c - b);
toler = 2.0*tol*max(abs(b),1.0);
if (abs(m) <= toler) + (fb == 0.0), break, end
% Choose bisection or interpolation
if (abs(e) < toler) + (abs(fa) <= abs(fb))
% Bisection
d = m; e = m;
step=' bisection';
else
% Interpolation
s = fb/fa;
if (a == c)
% Linear interpolation
p = 2.0*m*s;
q = 1.0 - s;
else
% Inverse quadratic interpolation
q = fa/fc;
r = fb/fc;
p = s*(2.0*m*q*(q - r) - (b - a)*(r - 1.0));
q = (q - 1.0)*(r - 1.0)*(s - 1.0);
end;
if p > 0, q = -q; else p = -p; end;
% Is interpolated point acceptable
if (2.0*p < 3.0*m*q - abs(toler*q)) * (p < abs(0.5*e*q))
e = d; d = p/q;
step=' interpolation';
else
d = m; e = m;
step=' bisection';
end;
end % Interpolation
% Next point
a = b;
fa = fb;
if abs(d) > toler, b = b + d;
else if b > c, b = b - toler;
else b = b + toler;
end
end
fb = feval(FunFcn,b,varargin{:});
if trace
data = [b fb];
count = count + 1;
disp([sprintf('%5.0f %13.6g %13.6g ',count, data), step])
end
end % Main loop
%------------------------------------------------------------------
function disperr(y, fy)
%DISPERR Display an appropriate error message when FY is Inf,
% NaN, or complex. Assumes Y is the value and FY is the function
% value at Y. If FY is neither Inf, NaN, or complex, it generates
% an error message.
if ~isfinite(fy) % NaN or Inf detected
disp('NaN or Inf function value encountered during ');
disp(' search for an interval containing a sign change.');
disp(['Function value at ', num2str(y),' is ',num2str(fy)]);
disp('Aborting since no such interval was found.')
disp('Check function or try again with a different starting value.')
elseif ~isreal(fy) % Complex value detected
disp('Complex function value encountered during ');
disp(' search for an interval containing a sign change.');
disp(['Function value at ', num2str(y),' is ',num2str(fy)]);
disp('Aborting since no such interval was found.')
disp('Check function or try again with a different starting value.')
else
error('Disperr called with invalid argument.')
end
http://www.mathworks.com/support/solutions/data/1-179SF.html?product=OP&solution=1-179SF |
评分
-
1
查看全部评分
-
|
发表于 2007-3-12 18:50
提升卡
变色卡
显身卡
发表于 2007-3-12 21:11
