range.m

几个关于多小波的程序

function Q = range(A)

% RANGE --  find range of a matrix
%
%         Q = range(A)
%
% This does essentially the same thing as the Matlab system
% routine ORTH, except it uses the tolerance parameter MPOLY_TOLERANCE
% instead of the Matlab default tolerance.
%
% Also, this routine will accept symbolic matrices, so checking for that
% is not required in other places. Symbolic matrices are converted to 
% DOUBLE, since there is no symbolic version of ORTH.

% 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

global MPOLY_TOLERANCE

if isempty(MPOLY_TOLERANCE)
    tol = 1.e-12;
else
    tol = MPOLY_TOLERANCE;
end

[m,n] = size(A);

if (isnumeric(A))
% this is essentially the built-in routine ORTH, except with different tolerance    
    [U,S,V] = svd(A,0);
    if m > 1
	s = diag(S);
    elseif m == 1
	s = S(1);
    else 
	s = 0;
    end
    
    r = sum(s > tol);
    Q = U(:,1:r);
    return
end

% if we get to this point, A is symbolic

if (issymbolic(A))
% matrix contains symbolic variables
    error('range is not defined for matrices containing symbolic variables');
end

% If we get here, the matrix contains symbolic constants
% We do a Gram-Schmid orthonormalization (without pivoting, 
% since the values are exact).
% Zero vectors get tossed out.
Q = sym(zeros(m,0));
for i = 1:n
    u = A(:,i);
    for j = 1:size(Q,2)
	u = u - (u'*Q(:,j))*Q(:,j);
    end
    if iszero(u)
	continue
    end
    u = u / norm(u);
    Q = [Q,u];
end