fssv.m

包含大量遗传算法程序

function [mu,dd,nsteps,fails,grad] = fssv(w,f,k,d,max,tol,verbose)
%FSSV Structured singular value (from MIMO frequency response).
% [mu,dd,nsteps,fails,grad] = fssv(w,f,k,d,max,tol,verbose)
%                        mu = fssv(w,f,k)
% Calculates the Structured Singular Value (mu) of an MVFR matrix.
% Block perturbations are allowed, but not correlated.
% Input arguments:
%       w  frequency vector
%       f  square MVFR matrix whose SSV is to be computed, n x n.
%       k  vector of m block sizes,such that sum(k) == n
%                                               (Default: ones(1,n))
%       d  vector of m initial scaling numbers. (Default: ones(1,m))
%     max  maximum number of hill-climbing steps at each frequency
%                                               (Default: 100)
%     tol  convergence criterion at each frequency (Default: 1e-6)
% verbose  1 if diagnostic information to be output, 0 otherwise.
%                                               (Default: 1)
% Output arguments:
%      mu  column vector holding upper bounds for the SSV
%      dd  MVFR matrix, each row holding optimal scaling at one frequency
%  nsteps  column vector holding number of steps taken at each frequency
%   fails  row vector holding indices of frequencies at which
%          convergence was not obtained.
%    grad  MVFR matrix, each row holding final gradient at each frequency

% Copyright (C) 1989 by Cambridge Control Ltd. 
% Written by J.M.Maciejowski, 10.8.1989. Corrected 7.9.89.

%%%%% Check input arguments and assign defaults:
nargchk(nargin,2,7);
[nout,nin] = fsize(w,f);
if nout ~= nin, 
  error('Input MVFR matrix must have equal numbers of inputs and outputs')
end;
if nargin < 7, verbose = 1; end;
if nargin < 6, tol = 1e-6; end;
if nargin < 5, max = 100; end;
if nargin < 4,
  if nargin < 3, k = ones(1,nin); end;
  d = ones(1,length(k));
end;
if any(k<1), error('Block sizes must be positive integers'); end;
if sum(k)~=nin, error('Sum of block sizes must equal number of inputs'); end;
if length(d)~=length(k),
  error('Vectors k and d must have the same length');
end;
if any(d==0), error('Zero elements not allowed in d vector'); end;
%%%%% End of input argument checks
%
if verbose,
  disp('FSSV: Freq      Mu      Nsteps     To do');
end;
%   
%%%%% Find good initial scaling for first frequency:
k = k(:)'; d = d(:)'; % Ensure k and d are row vectors
if size(d)==[1,length(k)],
  if d == ones(1,length(k)),  % Only if default initial scalings
    if size(k) == [1,nin],
      if k == ones(1,nin), % Scalar blocks only
	[vp,lp,rp] = fperron(w(1),fgetf(w,f,1));
	d = lp;  % Initial scaling
      end;
    end;
  end;
end;
%%%%% End of initial scaling
%
mu=[]; dd=[]; nsteps=[]; grad=[];
%
%%%%% Find mu for each frequency:
lw = length(w);
for i = 1:lw,
  fi = fgetf(w,f,i);
  [mui,d,nsi,gradi] = ssv(fi,k,d,max,tol,0);
  mu=[mu;mui]; dd=[dd;d']; nsteps=[nsteps;nsi]; grad=[grad;gradi'];
  if verbose,
    fprintf(' %-10.3e  %-10.3e  %3.0f',w(i),mui,nsi);
    fprintf('        %3.0f\n',lw-i);
    if nsi==max,
      disp('***** Not converged at this frequency *****');
    end;
  end;
end;
%%%%% End of looping through frequencies
%
%%%%% Find failures:
fails = find(nsteps==max)';