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 Sourcecode: octave-tsa version 3.10.63.10.6-24.0.04.0.0-24.0.14.0.1-14.0.1-24.1.0+svn20110501-1

# mvfilter.m

```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);
%

%     \$Revision: 4585 \$
%     \$Id: mvfilter.m 4585 2008-02-04 13:47:45Z adb014 \$
%     Copyright (C) 1996-2003 by Alois Schloegl <a.schloegl@ieee.org>

% This library is free software; you can redistribute it and/or
% modify it under the terms of the GNU Library General Public
% Version 2 of the License, or (at your option) any later version.
%
% This library 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
% Library General Public License for more details.
%
% You should have received a copy of the GNU Library General Public

[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   = ;
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;
```

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