/usr/share/octave/packages/control-2.6.2/__slicot_identification__.m is in octave-control 2.6.2-1build1.
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##
## This file is part of LTI Syncope.
##
## LTI Syncope 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.
##
## LTI Syncope 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 LTI Syncope. If not, see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn{Function File} {[@var{sys}, @var{x0}], @var{info} =} __slicot_identification__ (@var{method}, @var{dat}, @dots{})
## Backend for moesp, moen4 and n4sid.
## @end deftypefn
## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
## Created: May 2012
## Version: 0.1
function [sys, x0, info] = __slicot_identification__ (method, nout, dat, varargin)
## determine identification method
switch (method)
case "moesp"
meth = 0;
case "n4sid"
meth = 1;
case "moen4"
meth = 2;
otherwise
error ("ident: invalid method"); # should never happen
endswitch
if (! isa (dat, "iddata") || ! dat.timedomain)
error ("%s: first argument must be a time-domain 'iddata' dataset", method);
endif
if (nargin > 3) # ident (dat, ...)
if (is_real_scalar (varargin{1})) # ident (dat, n, ...)
varargin = horzcat (varargin(2:end), {"order"}, varargin(1));
endif
if (isstruct (varargin{1})) # ident (dat, opt, ...), ident (dat, n, opt, ...)
varargin = horzcat (__opt2cell__ (varargin{1}), varargin(2:end));
endif
endif
nkv = numel (varargin); # number of keys and values
if (rem (nkv, 2))
error ("%s: keys and values must come in pairs", method);
endif
[ns, p, m, e] = size (dat); # dataset dimensions
tsam = dat.tsam;
## multi-experiment data requires equal sampling times
if (e > 1 && ! isequal (tsam{:}))
error ("%s: require equally sampled experiments", method);
else
tsam = tsam{1};
endif
## default arguments
alg = 0;
conct = 1; # no connection between experiments
ctrl = 1; # don't confirm order n
rcond = 0.0;
tol = 0.0; # -1.0;
s = [];
n = [];
conf = [];
noise = "n";
## handle keys and values
for k = 1 : 2 : nkv
key = lower (varargin{k});
val = varargin{k+1};
switch (key)
case {"n", "order"}
if (! issample (val, 0) || val != round (val))
error ("%s: 'n' must be a positive integer", method);
endif
n = val;
case "s"
if (! issample (val, 0) || val != round (val))
error ("%s: 's' must be a positive integer", method);
endif
s = val;
case {"alg", "algorithm"}
if (strncmpi (val, "c", 1))
alg = 0; # Cholesky algorithm applied to correlation matrix
elseif (strncmpi (val, "f", 1))
alg = 1; # fast QR algorithm
elseif (strncmpi (val, "q", 1))
alg = 2; # QR algorithm applied to block Hankel matrices
else
error ("%s: invalid algorithm", method);
endif
case "tol"
if (! is_real_scalar (val))
error ("%s: tolerance 'tol' must be a real scalar", method);
endif
tol = val;
case "rcond"
if (! is_real_scalar (val))
error ("%s: 'rcond' must be a real scalar", method);
endif
rcond = val;
case "confirm"
conf = logical (val);
case {"noiseinput", "noiseinputs", "noise", "input", "inputs"}
noise = val;
otherwise
warning ("%s: invalid property name '%s' ignored", method, key);
endswitch
endfor
## handle s/nobr and n
nsmp = sum (ns); # total number of samples
nobr = fix ((nsmp+1)/(2*(m+p+1)));
if (e > 1)
nobr = min (nobr, fix (min (ns) / 2));
endif
if (isempty (s) && isempty (n))
ctrl = 0; # confirm system order estimate
n = 0;
elseif (isempty (s))
s = min (2*n, n+10); # upper bound for n
nobr = min (nobr, s);
elseif (isempty (n))
nobr = __check_s__ (s, nobr, method);
ctrl = 0; # confirm system order estimate
n = 0;
else # s & n non-empty
nobr = __check_s__ (s, nobr, method);
if (n >= nobr)
error ("%s: n=%d, but require n < %d (s)", method, n, nobr);
endif
endif
if (! isempty (conf))
ctrl = ! conf;
endif
if (nout == 0)
## compute singular values
[sv, nrec] = __sl_ib01ad__ (dat.y, dat.u, nobr, n, meth, alg, conct, ctrl, rcond, tol);
## there is no 'logbar' function
svl = log10 (sv);
base = floor (min (svl));
clf
bar (svl, "basevalue", base)
xlim ([0, length(sv)+1])
yl = ylim;
ylim ([base, yl(2)])
title ("Singular Values")
ylabel ("Logarithm of Singular Values")
xlabel (sprintf ("Estimated System Order with current Tolerance: %d", nrec))
grid on
else
## perform system identification
[a, b, c, d, q, ry, s, k, x0] = __sl_ident__ (dat.y, dat.u, nobr, n, meth, alg, conct, ctrl, rcond, tol);
## compute noise variance matrix factor L
## L L' = Ry, e = L v
## v becomes white noise with identity covariance matrix
l = chol (ry, "lower");
## assemble model
[inname, outname] = get (dat, "inname", "outname");
if (strncmpi (noise, "e", 1)) # add error inputs e, not normalized
sys = ss (a, [b, k], c, [d, eye(p)], tsam);
in_u = __labels__ (inname, "u");
in_e = __labels__ (outname, "y");
in_e = cellfun (@(x) ["e@", x], in_e, "uniformoutput", false);
inname = [in_u; in_e];
elseif (strncmpi (noise, "v", 1)) # add error inputs v, normalized
sys = ss (a, [b, k*l], c, [d, l], tsam);
in_u = __labels__ (inname, "u");
in_v = __labels__ (outname, "y");
in_v = cellfun (@(x) ["v@", x], in_v, "uniformoutput", false);
inname = [in_u; in_v];
elseif (strncmpi (noise, "k", 1)) # Kalman predictor
sys = ss ([a-k*c], [b-k*d, k], c, [d, zeros(p)], tsam);
in_u = __labels__ (inname, "u");
in_y = __labels__ (outname, "y");
inname = [in_u; in_y];
else # no error inputs, default
sys = ss (a, b, c, d, tsam);
endif
sys = set (sys, "inname", inname, "outname", outname);
## return x0 as vector for single-experiment data
## instead of a cell containing one vector
if (numel (x0) == 1)
x0 = x0{1};
endif
## assemble info struct
## Kalman gain matrix K
## state covariance matrix Q
## output covariance matrix Ry
## state-output cross-covariance matrix S
## noise variance matrix factor L
info = struct ("K", k, "Q", q, "Ry", ry, "S", s, "L", l);
endif
endfunction
function nobr = __check_s__ (s, nobr, method)
if (s <= nobr)
nobr = s;
else
error ("%s: require upper bound s <= %d, but the requested s is %d", method, nobr, s);
endif
endfunction
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