mpoly.m

几个关于多小波的程序

function P = mpoly(varargin)

% MPOLY -- create matrix polynomial
% 
%         P = mpoly(C,kmin,'type',m,r)
%         P = mpoly(P)
% 
% FIRST FORM: P = mpoly(C,kmin,'type',m,r)
%
%    This is the constructor method. C represents the matrix polynomial 
%    in one of the following forms:
%
%        1. A three-dimensional matrix, where C(:,:,k) represents
%           the kth coefficient matrix.
%        2. A cell vector of two-dimensional matrices, where
%           C{k} represents the kth coefficient matrix.
%
%    KMIN is the starting exponent. 'TYPE' is '', 'symbol' or 'polyphase'.
%    M is the dilation factor, R is the multiplicity. If 'TYPE' is set, 
%    M and R must also be given.
%
%    Default input arguments are C=0, KMIN=0, 'TYPE' = '', M = R = 0.
%
%    For example, the matrix polynomial
%
%                  (1 2)       (5 6)  2
%           P(z) = (3 4) z  +  (7 8) z
%
%    could be created in one of the following two ways:
%
%           P = mpoly({[1,2;3,4],[5,6;7,8]},1)
%
%    or
%
%           C = [1,2;3,4];
%           C(:,:,2) = [5,6;7,8];
%           P = mpoly(C,1);
%
% SECOND FORM: P = mpoly(P)
%
%    This is the conversion routine.
%
%    If P is of type ''           do nothing
%                    'polyphase'  convert it to a matrix polynomial 
%                                 of type '' by rearranging the coefficients.
%                    'symbol'     convert it to a matrix polynomial 
%                                 of type '' by scaling by sqrt(m).

% 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

% The following statement insures that operations between 
% symbolic constants and matrix polynomials work properly
superiorto('sym');

switch class(varargin{1})
 
 case 'mpoly'
% First form: P = mpoly(P)
  P = varargin{1};
  switch P.type
      
   case ''
% nothing to do
    
   case 'polyphase'
    P.type = '';
    [n1,n2] = size(P);
    P = reshape(P,n1,P.r);
    
   case 'symbol'
    P.type = '';
    P = P * sqrt(m);
    
   otherwise
    disp('this should not happen');
    keyboard;
  end
  
 otherwise
% Second form: P = mpoly(C,kmin,'type',m,r)
  if (nargin < 1)
      C = 0;
  else
      C = varargin{1};
  end
  if (nargin < 2)
      kmin = 0;
  else
      kmin = varargin{2};
  end
  if (nargin == 3 | nargin == 4)
      error('MPOLY must have 1, 2, or 5 arguments');
  end
  if (nargin >= 5)
      type = varargin{3};
      m = varargin{4};
      r = varargin{5};
  else
      type = '';
      m = 0;
      r = 0;
  end
  
% check type of C, do appropriate conversion
  switch class(C)
      
   case {'double','sym'}
% check that a third dimension is provided
    if (size(C,3) == 0)
	C = zeros(size(C,1),size(C,2));
    end
    
   case 'cell'
% convert cell array to 3d matrix
    if (length(C) == 0)
	C = 0;
    else
	C = cat(3,C{:});
    end
    
   otherwise
    error(['I don''t know how to convert ''',class(C),''' to ''mpoly''']);
  end
  
% build P  
  P = struct('coef',{C},'min',{kmin},'type',{type},'m',{m},'r',{r});
  P = class(P,'mpoly');
end

% don't do any trimming here
% sometimes we need to create an empty matrix polynomial
% with a known number of zero entries