This file is indexed.

/usr/share/octave/packages/control-3.0.0/lsim.m is in octave-control 3.0.0-2.

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
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
## 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} {} lsim (@var{sys}, @var{u})
## @deftypefnx{Function File} {} lsim (@var{sys1}, @var{sys2}, @dots{}, @var{sysN}, @var{u})
## @deftypefnx{Function File} {} lsim (@var{sys1}, @var{'style1'}, @dots{}, @var{sysN}, @var{'styleN'}, @var{u})
## @deftypefnx{Function File} {} lsim (@var{sys1}, @dots{}, @var{u}, @var{t})
## @deftypefnx{Function File} {} lsim (@var{sys1}, @dots{}, @var{u}, @var{t}, @var{x0})
## @deftypefnx{Function File} {[@var{y}, @var{t}, @var{x}] =} lsim (@var{sys}, @var{u})
## @deftypefnx{Function File} {[@var{y}, @var{t}, @var{x}] =} lsim (@var{sys}, @var{u}, @var{t})
## @deftypefnx{Function File} {[@var{y}, @var{t}, @var{x}] =} lsim (@var{sys}, @var{u}, @var{t}, @var{x0})
## Simulate @acronym{LTI} model response to arbitrary inputs.  If no output arguments are given,
## the system response is plotted on the screen.
##
## @strong{Inputs}
## @table @var
## @item sys
## @acronym{LTI} model.  System must be proper, i.e. it must not have more zeros than poles.
## @item u
## Vector or array of input signal.  Needs @code{length(t)} rows and as many columns
## as there are inputs.  If @var{sys} is a single-input system, row vectors @var{u}
## of length @code{length(t)} are accepted as well.
## @item t
## Time vector.  Should be evenly spaced.  If @var{sys} is a continuous-time system
## and @var{t} is a real scalar, @var{sys} is discretized with sampling time
## @code{tsam = t/(rows(u)-1)}.  If @var{sys} is a discrete-time system and @var{t}
## is not specified, vector @var{t} is assumed to be @code{0 : tsam : tsam*(rows(u)-1)}.
## @item x0
## Vector of initial conditions for each state.  If not specified, a zero vector is assumed.
## @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.  It is always evenly spaced.
## @item x
## State trajectories array.  Has @code{length (t)} rows and as many columns as states.
## @end table
##
## @seealso{impulse, initial, step}
## @end deftypefn

## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
## Created: October 2009
## Version: 0.5

function [y_r, t_r, x_r] = lsim (varargin)

  ## TODO: individual initial state vectors 'x0' for each system
  ##       there would be conflicts with other arguments,
  ##       maybe a cell {x0_1, x0_2, ..., x0_N} would be a solution?

  if (nargin < 2)
    print_usage ();
  endif

  idx = cellfun (@islogical, varargin);
  tmp = cellfun (@double, varargin(idx), "uniformoutput", false);
  varargin(idx) = tmp;

  sys_idx = cellfun (@isa, varargin, {"lti"});          # LTI models
  mat_idx = cellfun (@is_real_matrix, varargin);        # matrices
  sty_idx = cellfun (@ischar, varargin);                # string (style arguments)

  inv_idx = ! (sys_idx | mat_idx | sty_idx);            # invalid arguments

  if (any (inv_idx))
    warning ("lsim: arguments number %s are invalid and are being ignored", ...
             mat2str (find (inv_idx)(:).'));
  endif

  if (nnz (sys_idx) == 0)
    error ("lsim: require at least one LTI model");
  endif

  if (nargout > 0 && (nnz (sys_idx) > 1 || any (sty_idx)))
    print_usage ();
  endif

  if (! size_equal (varargin{sys_idx}))
    error ("lsim: all LTI models must have equal size");
  endif

  if (any (find (sty_idx) < find (sys_idx)(1)))
    warning ("lsim: strings in front of first LTI model are being ignored");
  endif

  t = [];  x0 = [];                                     # default arguments

  switch (nnz (mat_idx))
    case 0
      error ("lsim: require input signal 'u'");
    case 1
      u = varargin{mat_idx};
    case 2
      [u, t] = varargin{mat_idx};
    case 3
      [u, t, x0] = varargin{mat_idx};
    otherwise
      print_usage ();
  endswitch

  if (is_real_vector (u))                               # allow row vectors for single-input systems
    u = vec (u);
  elseif (isempty (u))                                  # ! is_real_matrix (u)  already tested
    error ("lsim: input signal 'u' must be a real-valued matrix");
  endif

  if (! is_real_vector (t) && ! isempty (t))
    error ("lsim: time vector 't' must be real-valued or empty");
  endif

  if (! isequal (t, unique (t)))
    error ("lsim: time vector 't' must be sorted");
  endif
  
  if (! is_real_vector (x0) && ! isempty (x0))
    error ("lsim: initial state vector 'x0' must be empty or a real-valued vector");
  endif


  ## function [y, t, x_arr] = __linear_simulation__ (sys, u, t, x0)
  
  [y, t, x] = cellfun (@__linear_simulation__, varargin(sys_idx), {u}, {t}, {x0}, "uniformoutput", false);


  if (nargout == 0)                                     # plot information
    ## extract plotting styles
    tmp = cumsum (sys_idx);
    tmp(sys_idx | ! sty_idx) = 0;
    n_sys = nnz (sys_idx);
    sty = arrayfun (@(x) varargin(tmp == x), 1:n_sys, "uniformoutput", false);

    ## default plotting styles if empty
    colororder = get (gca, "colororder");
    rc = rows (colororder);
    def = arrayfun (@(k) {"color", colororder(1+rem (k-1, rc), :)}, 1:n_sys, "uniformoutput", false);
    idx = cellfun (@isempty, sty);
    sty(idx) = def(idx);
  
    ## get system names for legend
    ## leg = cellfun (@inputname, find (sys_idx), "uniformoutput", false);
    leg = cell (1, n_sys);
    idx = find (sys_idx);
    for k = 1 : n_sys
      try
        leg{k} = inputname (idx(k));
      catch
        leg{k} = "";                                    # catch case  lsim (lticell{:}, ...)
      end_try_catch
    endfor
    
    [p, m] = size (varargin(sys_idx){1});
    ct_idx = cellfun (@isct, varargin(sys_idx));
    str = "Linear Simulation Results";
    outname = get (varargin(sys_idx){end}, "outname");
    outname = __labels__ (outname, "y");

    for k = 1 : n_sys                                   # for every system
      if (ct_idx(k))                                    # continuous-time system                                           
        for i = 1 : p                                   # for every output
          if (p != 1)
            subplot (p, 1, i);
          endif
          plot (t{k}, y{k}(:, i), sty{k}{:});
          hold on;
          grid on;
          if (k == n_sys)
            axis tight
            ylim (__axis_margin__ (ylim))
            ylabel (outname{i});
            if (i == 1)
              title (str);
            endif
          endif
        endfor
      else                                              # discrete-time system
        for i = 1 : p                                   # for every output
          if (p != 1)
            subplot (p, 1, i);
          endif
          stairs (t{k}, y{k}(:, i), sty{k}{:});
          hold on;
          grid on;
          if (k == n_sys)
            axis tight;
            ylim (__axis_margin__ (ylim))
            ylabel (outname{i});
            if (i == 1)
              title (str);
            endif
          endif
        endfor
      endif
    endfor
    xlabel ("Time [s]");
    if (p == 1 && m == 1)
      legend (leg)
    endif
    hold off;
  else                                                  # return values
    y_r = y{1};
    t_r = t{1};
    x_r = x{1};
  endif
  
endfunction


function [y, t, x_arr] = __linear_simulation__ (sys, u, t, x0)

  method = "zoh";
  [urows, ucols] = size (u);
  len_t = length (t);

  if (isct (sys))                               # continuous-time system
    if (isempty (t))                            # lsim (sys, u, [], ...)
      error ("lsim: time vector 't' must not be empty");
    elseif (len_t == 1)                         # lsim (sys, u, tfinal, ...)
      dt = t / (urows - 1);
      t = vec (linspace (0, t, urows));
    elseif (len_t != urows)
      error ("lsim: length of time vector (%d) doesn't match input signal (%dx%d)", ...
             len_t, urows, ucols);
    else                                        # lsim (sys, u, t, ...)
      dt = abs (t(end) - t(1)) / (urows - 1);   # assume that t is regularly spaced
      t = vec (linspace (t(1), t(end), urows));
    endif
    sys = c2d (sys, dt, method);                # convert to discrete-time model
  else                                          # discrete-time system
    dt = abs (get (sys, "tsam"));               # use 1 second as default if tsam is unspecified (-1)
    if (isempty (t))                            # lsim (sys, u)
      t = vec (linspace (0, dt*(urows-1), urows));
    elseif (len_t == 1)                         # lsim (sys, u, tfinal)
      ## TODO: maybe raise warning if  abs (tfinal - dt*(urows-1)) > dt
      t = vec (linspace (0, dt*(urows-1), urows));
    elseif (len_t != urows)
      error ("lsim: length of time vector (%d) doesn't match input signal (%dx%d)", ...
             len_t, urows, ucols);
    else                                        # lsim (sys, u, t, ...)
      t = vec (linspace (t(1), t(end), len_t));
    endif
  endif

  [A, B, C, D] = ssdata (sys);
  [p, m] = size (D);                            # number of outputs and inputs
  n = rows (A);                                 # number of states

  if (ucols != m)
    error ("lsim: input vector 'u' must have %d columns", m);
  endif

  ## preallocate memory
  y = zeros (urows, p);
  x_arr = zeros (urows, n);

  ## initial conditions
  if (isempty (x0))
    x0 = zeros (n, 1);
  elseif (n != length (x0) || ! is_real_vector (x0))
    error ("lsim: 'x0' must be a vector with %d elements", n);
  endif

  x = vec (x0);                                 # make sure that x is a column vector

  ## simulation
  for k = 1 : urows
    y(k, :) = C * x  +  D * u(k, :).';
    x_arr(k, :) = x;
    x = A * x  +  B * u(k, :).';
  endfor

endfunction


## TODO: add test cases