norm.m

几个关于多小波的程序

function n = norm(S,varargin)

% NORM -- norm function for symbolic variables
%
%        n = norm(x,type)
%
% This is the same as the usual NORM function, but for vectors
% or matrices of symbolic constants (not symbolic variables).
%
% There should be no problem for vectors and for the 1-,
% infinity-, or Frobenius-norm of matrices. However, it is likely 
% to be VERY slow and result in a VERY messy expression for 
% 2-norms of matrices larger than 2x2.

% Copyright (c) 2004 by Fritz Keinert ([e-mail]),
% Dept. of Mathematics, Iowa State University, Ames, IA 50011.
% This software may be freely used and distributed for non-commercial
% purposes, provided this copyright statement is preserved, and
% appropriate credit for its use is given.
%
% Last update: Feb 20, 2004

m = size(S);
S = reshape(simplify(S(:)),m);

if issymbolic(S)
    error('NORM is not defined for symbolic variables');
end

if (length(m) > 2)
    error('NORM is only defined for vectors and two-dimensional matrices');
end

if (nargin < 2)
    p = 2;
else
    p = varargin{1};
end
if (m(1) == 1 | m(2) == 1)
% S is a vector
    switch p
     case {inf,'inf'}
      n = simplify(max(abs(S)));
     case {-inf,'-inf'}
      n = simplify(min(abs(S)));
     case 1
      n = simplify(sum(abs(S)));
     otherwise
      if ~isnumeric(p)
	  error('P must be a number, ''inf'', or ''-inf''');
      end
      if (p < 1)
	  error('P must be between >= 1');
      end
      n = simplify((sum(abs(S).^p))^(1/p));
    end
else
% S is a matrix
    switch p
     case {inf,'inf'}
      n = max(sum(abs(S.')));
     case 1
      n = max(sum(abs(S)));
     case 'fro'
      n = sqrt(sum(diag(S'*S)));
     case 2
      n = max(svd(S));
     otherwise
      error('P must be 1, 2, ''inf'' or ''fro''');
    end
end