/usr/share/octave/packages/control-2.6.2/@lti/prescale.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{scaledsys}, @var{info}] =} prescale (@var{sys})
## Scale state-space model. The scaled model @var{scaledsys} is equivalent to
## @var{sys}, but the state vector is scaled by diagonal transformation matrices
## in order to increase the accuracy of subsequent numerical computations.
## Frequency response commands perform automatic scaling unless model property
## @var{scaled} is set to @var{true}.
##
## @strong{Inputs}
## @table @var
## @item sys
## @acronym{LTI} model.
## @end table
##
## @strong{Outputs}
## @table @var
## @item scaledsys
## Scaled state-space model.
## @item info
## Structure containing additional information.
## @item info.SL
## Left scaling factors. @code{Tl = diag (info.SL)}.
## @item info.SR
## Right scaling factors. @code{Tr = diag (info.SR)}.
## @end table
##
## @strong{Equations}
## @example
## @group
## Es = Tl * E * Tr
## As = Tl * A * Tr
## Bs = Tl * B
## Cs = C * Tr
## Ds = D
## @end group
## @end example
##
## For proper state-space models, @var{Tl} and @var{Tr} are inverse of each other.
##
## @strong{Algorithm}@*
## Uses SLICOT TB01ID and TG01AD by courtesy of
## @uref{http://www.slicot.org, NICONET e.V.}.
## @end deftypefn
## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
## Created: June 2011
## Version: 0.2
function [retsys, varargout] = prescale (sys)
if (nargin != 1)
print_usage ();
endif
if (! isa (sys, "ss"))
warning ("prescale: system not in state-space form");
sys = ss (sys);
endif
[retsys, lscale, rscale] = __prescale__ (sys);
if (nargout > 1)
varargout{1} = struct ("SL", lscale, "SR", rscale);
endif
endfunction
## Scaling of state-space models, direct access to TB01ID
%!shared Ao, Bo, Co, SCALEo, MAXREDo, Ae, Be, Ce, SCALEe, MAXREDe
%! A = [ 0.0 1.0000e+000 0.0 0.0 0.0
%! -1.5800e+006 -1.2570e+003 0.0 0.0 0.0
%! 3.5410e+014 0.0 -1.4340e+003 0.0 -5.3300e+011
%! 0.0 0.0 0.0 0.0 1.0000e+000
%! 0.0 0.0 0.0 -1.8630e+004 -1.4820e+000 ];
%!
%! B = [ 0.0 0.0
%! 1.1030e+002 0.0
%! 0.0 0.0
%! 0.0 0.0
%! 0.0 8.3330e-003 ];
%!
%! C = [ 1.0000e+000 0.0 0.0 0.0 0.0
%! 0.0 0.0 1.0000e+000 0.0 0.0
%! 0.0 0.0 0.0 1.0000e+000 0.0
%! 6.6640e-001 0.0 -6.2000e-013 0.0 0.0
%! 0.0 0.0 -1.0000e-003 1.8960e+006 1.5080e+002 ];
%!
%! MAXRED = 0.0;
%!
%! [Ao, Bo, Co, MAXREDo, SCALEo] = __sl_tb01id__ (A, B, C, MAXRED);
%!
%! Ae = [ 0.0000000D+00 0.1000000D+05 0.0000000D+00 0.0000000D+00 0.0000000D+00
%! -0.1580000D+03 -0.1257000D+04 0.0000000D+00 0.0000000D+00 0.0000000D+00
%! 0.3541000D+05 0.0000000D+00 -0.1434000D+04 0.0000000D+00 -0.5330000D+03
%! 0.0000000D+00 0.0000000D+00 0.0000000D+00 0.0000000D+00 0.1000000D+03
%! 0.0000000D+00 0.0000000D+00 0.0000000D+00 -0.1863000D+03 -0.1482000D+01 ];
%!
%! Be = [ 0.0000000D+00 0.0000000D+00
%! 0.1103000D+04 0.0000000D+00
%! 0.0000000D+00 0.0000000D+00
%! 0.0000000D+00 0.0000000D+00
%! 0.0000000D+00 0.8333000D+02 ];
%!
%! Ce = [ 0.1000000D-04 0.0000000D+00 0.0000000D+00 0.0000000D+00 0.0000000D+00
%! 0.0000000D+00 0.0000000D+00 0.1000000D+06 0.0000000D+00 0.0000000D+00
%! 0.0000000D+00 0.0000000D+00 0.0000000D+00 0.1000000D-05 0.0000000D+00
%! 0.6664000D-05 0.0000000D+00 -0.6200000D-07 0.0000000D+00 0.0000000D+00
%! 0.0000000D+00 0.0000000D+00 -0.1000000D+03 0.1896000D+01 0.1508000D-01 ];
%!
%! SCALEe = [0.1000000D-04 0.1000000D+00 0.1000000D+06 0.1000000D-05 0.1000000D-03 ];
%!
%! MAXREDe = 0.3488E+10;
%!
%!assert (Ao, Ae, 1e-4);
%!assert (Bo, Be, 1e-4);
%!assert (Co, Ce, 1e-4);
%!assert (MAXREDo, MAXREDe, 1e6);
%!assert (SCALEo, SCALEe.', 1e-4);
## Scaling of descriptor state-space models, direct access to TG01AD
%!shared Ao, Eo, Bo, Co, LSCALEo, RSCALEo, Ae, Ee, Be, Ce, LSCALEe, RSCALEe
%! A = [ -1 0 0 0.003
%! 0 0 0.1000 0.02
%! 100 10 0 0.4
%! 0 0 0 0.0];
%!
%! E = [ 1 0.2 0 0.0
%! 0 1 0 0.01
%! 300 90 6 0.3
%! 0 0 20 0.0];
%!
%! B = [ 10 0
%! 0 0
%! 0 1000
%! 10000 10000];
%!
%! C = [ -0.1 0.0 0.001 0.0
%! 0.0 0.01 -0.001 0.0001];
%!
%! TRESH = 0.0;
%!
%! [Ao, Eo, Bo, Co, LSCALEo, RSCALEo] = __sl_tg01ad__ (A, E, B, C, TRESH);
%!
%! Ae = [ -1.0000 0.0000 0.0000 0.3000
%! 0.0000 0.0000 1.0000 2.0000
%! 1.0000 0.1000 0.0000 0.4000
%! 0.0000 0.0000 0.0000 0.0000];
%!
%! Ee = [ 1.0000 0.2000 0.0000 0.0000
%! 0.0000 1.0000 0.0000 1.0000
%! 3.0000 0.9000 0.6000 0.3000
%! 0.0000 0.0000 0.2000 0.0000 ];
%!
%! Be = [100.0000 0.0000
%! 0.0000 0.0000
%! 0.0000 100.0000
%! 100.0000 100.0000 ];
%!
%! Ce = [ -0.0100 0.0000 0.0010 0.0000
%! 0.0000 0.0010 -0.0010 0.0010];
%!
%! LSCALEe = [ 10.0000 10.0000 0.1000 0.0100 ];
%!
%! RSCALEe = [ 0.1000 0.1000 1.0000 10.0000 ];
%!
%!assert (Ao, Ae, 1e-4);
%!assert (Eo, Ee, 1e-4);
%!assert (Bo, Be, 1e-4);
%!assert (Co, Ce, 1e-4);
%!assert (LSCALEo, LSCALEe.', 1e-4);
%!assert (RSCALEo, RSCALEe.', 1e-4);
## Scaling of state-space models, user function
%!shared Ao, Bo, Co, INFOo, Ae, Be, Ce, SCALEe
%! A = [ 0.0 1.0000e+000 0.0 0.0 0.0
%! -1.5800e+006 -1.2570e+003 0.0 0.0 0.0
%! 3.5410e+014 0.0 -1.4340e+003 0.0 -5.3300e+011
%! 0.0 0.0 0.0 0.0 1.0000e+000
%! 0.0 0.0 0.0 -1.8630e+004 -1.4820e+000 ];
%!
%! B = [ 0.0 0.0
%! 1.1030e+002 0.0
%! 0.0 0.0
%! 0.0 0.0
%! 0.0 8.3330e-003 ];
%!
%! C = [ 1.0000e+000 0.0 0.0 0.0 0.0
%! 0.0 0.0 1.0000e+000 0.0 0.0
%! 0.0 0.0 0.0 1.0000e+000 0.0
%! 6.6640e-001 0.0 -6.2000e-013 0.0 0.0
%! 0.0 0.0 -1.0000e-003 1.8960e+006 1.5080e+002 ];
%!
%! SYS = ss (A, B, C);
%!
%! [SYSo, INFOo] = prescale (SYS);
%!
%! [Ao, Bo, Co] = ssdata (SYSo);
%!
%! Ae = [ 0.0000000D+00 0.1000000D+05 0.0000000D+00 0.0000000D+00 0.0000000D+00
%! -0.1580000D+03 -0.1257000D+04 0.0000000D+00 0.0000000D+00 0.0000000D+00
%! 0.3541000D+05 0.0000000D+00 -0.1434000D+04 0.0000000D+00 -0.5330000D+03
%! 0.0000000D+00 0.0000000D+00 0.0000000D+00 0.0000000D+00 0.1000000D+03
%! 0.0000000D+00 0.0000000D+00 0.0000000D+00 -0.1863000D+03 -0.1482000D+01 ];
%!
%! Be = [ 0.0000000D+00 0.0000000D+00
%! 0.1103000D+04 0.0000000D+00
%! 0.0000000D+00 0.0000000D+00
%! 0.0000000D+00 0.0000000D+00
%! 0.0000000D+00 0.8333000D+02 ];
%!
%! Ce = [ 0.1000000D-04 0.0000000D+00 0.0000000D+00 0.0000000D+00 0.0000000D+00
%! 0.0000000D+00 0.0000000D+00 0.1000000D+06 0.0000000D+00 0.0000000D+00
%! 0.0000000D+00 0.0000000D+00 0.0000000D+00 0.1000000D-05 0.0000000D+00
%! 0.6664000D-05 0.0000000D+00 -0.6200000D-07 0.0000000D+00 0.0000000D+00
%! 0.0000000D+00 0.0000000D+00 -0.1000000D+03 0.1896000D+01 0.1508000D-01 ];
%!
%! SCALEe = [0.1000000D-04 0.1000000D+00 0.1000000D+06 0.1000000D-05 0.1000000D-03 ];
%!
%!assert (Ao, Ae, 1e-4);
%!assert (Bo, Be, 1e-4);
%!assert (Co, Ce, 1e-4);
%!assert (INFOo.SL.^-1, SCALEe.', 1e-4);
%!assert (INFOo.SR, SCALEe.', 1e-4);
## Scaling of descriptor state-space models, user function
%!shared Ao, Eo, Bo, Co, INFOo, Ae, Ee, Be, Ce, LSCALEe, RSCALEe
%! A = [ -1 0 0 0.003
%! 0 0 0.1000 0.02
%! 100 10 0 0.4
%! 0 0 0 0.0];
%!
%! E = [ 1 0.2 0 0.0
%! 0 1 0 0.01
%! 300 90 6 0.3
%! 0 0 20 0.0];
%!
%! B = [ 10 0
%! 0 0
%! 0 1000
%! 10000 10000];
%!
%! C = [ -0.1 0.0 0.001 0.0
%! 0.0 0.01 -0.001 0.0001];
%!
%! SYS = dss (A, B, C, [], E);
%!
%! [SYSo, INFOo] = prescale (SYS);
%!
%! [Ao, Bo, Co, ~, Eo] = dssdata (SYSo);
%!
%! Ae = [ -1.0000 0.0000 0.0000 0.3000
%! 0.0000 0.0000 1.0000 2.0000
%! 1.0000 0.1000 0.0000 0.4000
%! 0.0000 0.0000 0.0000 0.0000];
%!
%! Ee = [ 1.0000 0.2000 0.0000 0.0000
%! 0.0000 1.0000 0.0000 1.0000
%! 3.0000 0.9000 0.6000 0.3000
%! 0.0000 0.0000 0.2000 0.0000 ];
%!
%! Be = [100.0000 0.0000
%! 0.0000 0.0000
%! 0.0000 100.0000
%! 100.0000 100.0000 ];
%!
%! Ce = [ -0.0100 0.0000 0.0010 0.0000
%! 0.0000 0.0010 -0.0010 0.0010];
%!
%! LSCALEe = [ 10.0000 10.0000 0.1000 0.0100 ];
%!
%! RSCALEe = [ 0.1000 0.1000 1.0000 10.0000 ];
%!
%!assert (Ao, Ae, 1e-4);
%!assert (Eo, Ee, 1e-4);
%!assert (Bo, Be, 1e-4);
%!assert (Co, Ce, 1e-4);
%!assert (INFOo.SL, LSCALEe.', 1e-4);
%!assert (INFOo.SR, RSCALEe.', 1e-4);
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