/usr/share/octave/packages/control-3.0.0/initial.m is in octave-control 3.0.0-5.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 | ## Copyright (C) 2009-2015 Lukas F. Reichlin
##
## 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} {} initial (@var{sys}, @var{x0})
## @deftypefnx{Function File} {} initial (@var{sys1}, @var{sys2}, @dots{}, @var{sysN}, @var{x0})
## @deftypefnx{Function File} {} initial (@var{sys1}, @var{'style1'}, @dots{}, @var{sysN}, @var{'styleN'}, @var{x0})
## @deftypefnx{Function File} {} initial (@var{sys1}, @dots{}, @var{x0}, @var{t})
## @deftypefnx{Function File} {} initial (@var{sys1}, @dots{}, @var{x0}, @var{tfinal})
## @deftypefnx{Function File} {} initial (@var{sys1}, @dots{}, @var{x0}, @var{tfinal}, @var{dt})
## @deftypefnx{Function File} {[@var{y}, @var{t}, @var{x}] =} initial (@var{sys}, @var{x0})
## @deftypefnx{Function File} {[@var{y}, @var{t}, @var{x}] =} initial (@var{sys}, @var{x0}, @var{t})
## @deftypefnx{Function File} {[@var{y}, @var{t}, @var{x}] =} initial (@var{sys}, @var{x0}, @var{tfinal})
## @deftypefnx{Function File} {[@var{y}, @var{t}, @var{x}] =} initial (@var{sys}, @var{x0}, @var{tfinal}, @var{dt})
## Initial condition response of state-space model.
## If no output arguments are given, the response is printed on the screen.
##
## @strong{Inputs}
## @table @var
## @item sys
## State-space model.
## @item x0
## Vector of initial conditions for each state.
## @item t
## Optional time vector. Should be evenly spaced. If not specified, it is calculated
## by the poles of the system to reflect adequately the response transients.
## @item tfinal
## Optional simulation horizon. If not specified, it is calculated by
## the poles of the system to reflect adequately the response transients.
## @item dt
## Optional sampling time. Be sure to choose it small enough to capture transient
## phenomena. If not specified, it is calculated by the poles of the system.
## @item 'style'
## Line style and color, e.g. 'r' for a solid red line or '-.k' for a dash-dotted
## black line. See @command{help plot} for details.
## @end table
##
## @strong{Outputs}
## @table @var
## @item y
## Output response array. Has as many rows as time samples (length of t)
## and as many columns as outputs.
## @item t
## Time row vector.
## @item x
## State trajectories array. Has @code{length (t)} rows and as many columns as states.
## @end table
##
## @strong{Example}
## @example
## @group
## .
## Continuous Time: x = A x , y = C x , x(0) = x0
##
## Discrete Time: x[k+1] = A x[k] , y[k] = C x[k] , x[0] = x0
## @end group
## @end example
##
## @seealso{impulse, lsim, step}
## @end deftypefn
## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
## Created: October 2009
## Version: 1.0
function [y_r, t_r, x_r] = initial (varargin)
if (nargin < 2)
print_usage ();
endif
[y, t, x] = __time_response__ ("initial", varargin, nargout);
if (nargout)
y_r = y{1};
t_r = t{1};
x_r = x{1};
endif
endfunction
%!shared initial_c, initial_c_exp, initial_d, initial_d_exp
%!
%! A = [ -2.8 2.0 -1.8
%! -2.4 -2.0 0.8
%! 1.1 1.7 -1.0 ];
%!
%! B = [ -0.8 0.5 0
%! 0 0.7 2.3
%! -0.3 -0.1 0.5 ];
%!
%! C = [ -0.1 0 -0.3
%! 0.9 0.5 1.2
%! 0.1 -0.1 1.9 ];
%!
%! D = [ -0.5 0 0
%! 0.1 0 0.3
%! -0.8 0 0 ];
%!
%! x_0 = [1, 2, 3];
%!
%! sysc = ss (A, B, C, D);
%!
%! [yc, tc, xc] = initial (sysc, x_0, 0.2, 0.1);
%! initial_c = [yc, tc, xc];
%!
%! sysd = c2d (sysc, 2);
%!
%! [yd, td, xd] = initial (sysd, x_0, 4);
%! initial_d = [yd, td, xd];
%!
%! ## expected values computed by the "dark side"
%!
%! yc_exp = [ -1.0000 5.5000 5.6000
%! -0.9872 5.0898 5.7671
%! -0.9536 4.6931 5.7598 ];
%!
%! tc_exp = [ 0.0000
%! 0.1000
%! 0.2000 ];
%!
%! xc_exp = [ 1.0000 2.0000 3.0000
%! 0.5937 1.6879 3.0929
%! 0.2390 1.5187 3.0988 ];
%!
%! initial_c_exp = [yc_exp, tc_exp, xc_exp];
%!
%! yd_exp = [ -1.0000 5.5000 5.6000
%! -0.6550 3.1673 4.2228
%! -0.5421 2.6186 3.4968 ];
%!
%! td_exp = [ 0
%! 2
%! 4 ];
%!
%! xd_exp = [ 1.0000 2.0000 3.0000
%! -0.4247 1.5194 2.3249
%! -0.3538 1.2540 1.9250 ];
%!
%! initial_d_exp = [yd_exp, td_exp, xd_exp];
%!
%!assert (initial_c, initial_c_exp, 1e-4)
%!assert (initial_d, initial_d_exp, 1e-4)
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