Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / tsa-4.2.4 / mvfilter.m

diff --git a/octave_packages/tsa-4.2.4/mvfilter.m b/octave_packages/tsa-4.2.4/mvfilter.m
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+
+function [x,z]=mvfilter(B,A,x,z)
+% Multi-variate filter function
+%
+% Y = MVFILTER(B,A,X)
+% [Y,Z] = MVFILTER(B,A,X,Z)
+%
+%  Y = MVFILTER(B,A,X) filters the data in matrix X with the
+%    filter described by cell arrays A and B to create the filtered
+%    data Y.  The filter is a 'Direct Form II Transposed'
+%    implementation of the standard difference equation:
+% 
+%    a0*Y(n) = b0*X(:,n) + b1*X(:,n-1) + ... + bq*X(:,n-q)
+%                        - a1*Y(:,n-1) - ... - ap*Y(:,n-p)
+%
+%  A=[a0,a1,a2,...,ap] and B=[b0,b1,b2,...,bq] must be matrices of
+%  size  Mx((p+1)*M) and Mx((q+1)*M), respectively. 
+%  a0,a1,...,ap, b0,b1,...,bq are matrices of size MxM
+%  a0 is usually the identity matrix I or must be invertible 
+%  X should be of size MxN, if X has size NxM a warning 
+%  is raised, and the output Y is also transposed. 
+%
+% A simulated MV-AR process can be generiated with 
+%      Y = mvfilter(eye(M), [eye(M),-AR],randn(M,N));
+%
+% A multivariate inverse filter can be realized with 
+%       [AR,RC,PE] = mvar(Y,P);
+%      E = mvfilter([eye(M),-AR],eye(M),Y);
+%
+% see also: MVAR, FILTER
+
+%      $Id: mvfilter.m 6981 2010-03-02 23:38:34Z schloegl $
+%      Copyright (C) 1996-2003 by Alois Schloegl <a.schloegl@ieee.org> 
+%
+%    This program is free software: you can redistribute it and/or modify
+%    it under the terms of the GNU General Public License as published by
+%    the Free Software Foundation, either version 3 of the License, or
+%    (at your option) any later version.
+%
+%    This program is distributed in the hope that it will be useful,
+%    but WITHOUT ANY WARRANTY; without even the implied warranty of
+%    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+%    GNU General Public License for more details.
+%
+%    You should have received a copy of the GNU General Public License
+%    along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+
+[ra, ca] = size(A);
+[rb, cb] = size(B);
+[M,  N ] = size(x);
+
+if (ra~=rb),
+        fprintf(2,'ERROR MVFILTER: number of rows of A and B do not fit\n');
+       return;
+end;
+if nargin<4,
+        z = []; %zeros(M,oo);
+end;
+
+if (M~=ra),
+       if (N==ra),
+               fprintf(2,'Warning MVFILTER: dimensions fit only to transposed data. X has been transposed.\n');
+               x = x.';
+               %[x,z] = mvfilter(B,A,x,z); x = x.'; return;
+       else
+               fprintf(2,'ERROR MVFILTER: dimensions do not fit\n');
+               return;
+       end;
+end;        
+
+p  = ca/M-1;
+q  = cb/M-1;
+oo = max(p,q);
+
+if isempty(z)
+        z = zeros(M,oo);
+else
+        if  any(size(z)~=[M,oo])
+                fprintf('Error MVFILTER: size of z does not fit\n');
+                [size(z),oo,M]
+                return;
+       end;    
+end;
+
+%%%%% normalization to A{1}=I;
+if p<=q, 
+        for k=1:p,
+                %A{k}=A{k}/A{1};
+                A(:,k*M+(1:M)) = A(:,k*M+(1:M)) / A(:,1:M);
+        end;
+       A(:,1:M) = eye(M);
+else
+        for k=0:q,
+                %B{k}=B{k}/A{1};
+                B(:,k*M+(1:M)) = B(:,k*M+(1:M)) / A(:,1:M);
+        end;
+end; 
+
+for k = 1:N,
+        acc = B(:,1:M) * x(:,k) + z(:,1);  % / A{1};
+       z   = [z(:,2:oo), zeros(M,1)];
+        for l = 1:q,
+               z(:,l) = z(:,l) + B(:,l*M+(1:M)) * x(:,k);
+        end;
+        for l = 1:p,
+               z(:,l) = z(:,l) - A(:,l*M+(1:M)) * acc;
+        end;
+        x(:,k) = acc;
+end;
+