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function [x0,B,D,V,rcnd]=findx0BD(A,C,y,u,withx0,withd,tol,printw)
x0=[];B=[];D=[];V=[];rcnd=[];
[nargout,nargin] = argn(0)
//FINDX0BD Estimates the initial state and/or the matrices B and D of a
// discrete-time linear system, given the (estimated) system
// matrices A, C, and a set of input/output data.
//
// [X0,B,D] = FINDX0BD(A,C,Y,U,WITHX0,WITHD,TOL,PRINTW) estimates the
// initial state X0 and the matrices B and D of a discrete-time
// system using the system matrices A, C, output data Y and the input
// data U. The model structure is :
//
// x(k+1) = Ax(k) + Bu(k), k >= 1,
// y(k) = Cx(k) + Du(k),
//
// The vectors y(k) and u(k) are transposes of the k-th rows of Y and U,
// respectively.
//
// WITHX0 is a select for estimating the initial state x0.
// WITHX0 = 1: estimate x0;
// = 0: do not estimate x0.
// Default: WITHX0 = 1.
//
// WITHD is a select for estimating the matrix D.
// WITHD = 1: estimate the matrix D;
// = 0: do not estimate the matrix D.
// Default: WITHD = 1.
//
// TOL is the tolerance used for estimating the rank of matrices.
// If TOL > 0, then the given value of TOL is used as a lower bound
// for the reciprocal condition number.
// Default: prod(size(matrix))*epsilon_machine where epsilon_machine
// is the relative machine precision.
//
// PRINTW is a select for printing the warning messages.
// PRINTW = 1: print warning messages;
// = 0: do not print warning messages.
// Default: PRINTW = 0.
//
// [x0,B,D,V,rcnd] = FINDX0BD(A,C,Y,U) also returns the orthogonal
// matrix V which reduces the system state matrix A to a real Schur
// form, as well as some estimates of the reciprocal condition numbers
// of the matrices involved in rank decisions.
//
// B = FINDX0BD(A,C,Y,U,0,0) returns B only, and
// [B,D] = FINDX0BD(A,C,Y,U,0) returns B and D only.
//
// See also FINDBD, INISTATE
//
// V. Sima 13-05-2000.
//
// For efficiency, most errors are checked in the mexfile findBD.
//
// Revisions:
// V. Sima, July 2000.
//
ni = nargin;
nout = nargout;
if ni<4 then
error(msprintf(gettext("%s: Wrong number of input arguments: %d to %d expected.\n"),"findx0BD",4,8));
end
if nout<1 then
error(msprintf(gettext("%s: Wrong number of output arguments: At least %d expected.\n"),"findx0BD",1));
end
//
if ni<8 then
printw = 0;
end
if ni<7 then tol = 0;end
if tol==[] then tol = 0;end
if ni<6 then
withd = 1;
elseif withd ==[] then
withd = 1;
elseif (withd~=0)&(withd~=1) then
warning(msprintf(gettext("%s: Wrong value for input argument #%d: %d or %d expected.\n"),"findx0BD",6,0,1))
end
if ni<5 then withx0 = 1;end
if withx0 ==[] then withx0 = 1;end
job = withd+1;
//
if withx0==1 then
if withd==1 then
[x0,B,D,Vl,rcndl] = findBD(withx0,1,job,A,C,y,u,tol,printw);
if nout>3 then
V = Vl;
end
if nout>4 then
rcnd = rcndl;
end
else
[x0,B,Vl,rcndl] = findBD(withx0,1,job,A,C,y,u,tol,printw);
if nout>2 then
D = Vl;
end
if nout>3 then
V = rcndl;
end
end
else
// Below, x0 means B, and B means D or V !
if withd==1 then
[x0,B,Vl,rcndl] = findBD(withx0,1,job,A,C,y,u,tol,printw);
if nout>2 then
D = Vl;
end
if nout>3 then
V = rcndl;
end
else
[x0,B,Vl] = findBD(withx0,1,job,A,C,y,u,tol,printw);
if nout>2 then
D = Vl;
end
end
end
//
// end findx0BD
endfunction
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