This file is indexed.

/usr/share/octave/packages/optim-1.5.2/jacobs.m is in octave-optim 1.5.2-4.

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
## Copyright (C) 2011 Fotios Kasolis <fotios.kasolis@gmail.com>
## Copyright (C) 2013-2016 Olaf Till <i7tiol@t-online.de>
##
## This program 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.
##
## This program 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
## this program; if not, see <http://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn {Function File} {Df =} jacobs (@var{x}, @var{f})
## @deftypefnx {Function File} {Df =} jacobs (@var{x}, @var{f}, @var{hook})
## Calculate the jacobian of a function using the complex step method.
##
## Let @var{f} be a user-supplied function. Given a point @var{x} at
## which we seek for the Jacobian, the function @command{jacobs} returns
## the Jacobian matrix @code{d(f(1), @dots{}, df(end))/d(x(1), @dots{},
## x(n))}. The function uses the complex step method and thus can be
## applied to real analytic functions.
##
## The optional argument @var{hook} is a structure with additional options. @var{hook}
## can have the following fields:
## @itemize @bullet
## @item
## @code{h} - can be used to define the magnitude of the complex step and defaults
## to 1e-20; steps larger than 1e-3 are not allowed.
## @item
## @code{fixed} - is a logical vector internally usable by some optimization
## functions; it indicates for which elements of @var{x} no gradient should be
## computed, but zero should be returned.
## @end itemize
##
## For example:
## 
## @example
## @group
## f = @@(x) [x(1)^2 + x(2); x(2)*exp(x(1))];
## Df = jacobs ([1, 2], f)
## @end group
## @end example
## @end deftypefn

function Df = jacobs (x, f, hook)

  if ( (nargin < 2) || (nargin > 3) )
    print_usage ();
  endif

  if (ischar (f))
    f = str2func (f, "global");
  endif

  n  = numel (x);

  default_h = 1e-20;
  max_h = 1e-3; # must be positive

  if (nargin > 2)

    if (isfield (hook, "h"))
      if (! (isscalar (hook.h)))
        error ("complex step magnitude must be a scalar");
      endif
      if (abs (hook.h) > max_h)
        warning ("complex step magnitude larger than allowed, set to %e", ...
                 max_h)
        h = max_h;
      else
        h = hook.h;
      endif
    else
      h = default_h;
    endif

    if (isfield (hook, "fixed"))
      if (numel (hook.fixed) != n)
        error ("index of fixed parameters has wrong dimensions");
      endif
      fixed = hook.fixed(:);
    else
      fixed = false (n, 1);
    endif

  else
    h = default_h;
    fixed = false (n, 1);
  endif

  if (all (fixed))
    error ("all elements of 'x' are fixed");
  endif

  x = repmat (x(:), 1, n) + h * 1i * eye (n);

  idx = find (! fixed);

  if (nargin > 2)

    if (isfield (hook, 'parallel_local'))
      parallel_local = hook.parallel_local;
    else
      parallel_local = false;
    end

    if (isfield (hook, "parallel_net"))
      parallel_net = hook.parallel_net;
    else
      parallel_net = [];
    endif

    if (parallel_local || ! isempty (parallel_net))

      parallel = true;
      ## user function
      func = @ (id) {imag(f(x(:, id))(:)) / h, false, []}{:};
      ## error handler
      errh = @ (s, id) {[], true, s}{:};

      if (parallel_local && ! isempty (parallel_net))
        error ("If option 'parallel_net' is not empty, option 'parallel_local' must not be true.");
      endif

      if (parallel_local)

        if (parallel_local > 1)
          npr = parallel_local;
        else
          npr = nproc ("current");
        endif

        parfun = @ () pararrayfun (npr, func, idx,
                                   "UniformOutput", false,
                                   "VerboseLevel", 0,
                                   "ErrorHandler", errh);

      else # ! isempty (parallel_net)
        parfun = @ () netarrayfun (parallel_net, func, idx,
                                   "UniformOutput", false,
                                   "ErrorHandler", errh);
      endif

    else
      parallel = false;
    endif

  else
    parallel = false;
  endif

  if (parallel)

    [t_Df, err, info] = parfun ();

    ## check for errors
    if (any ((err = [err{:}])))
      id = find (err, 1);
      error ("Some subprocesses, calling model function for complex step derivatives, returned and error. Message of first of these (with id %i): %s%s",
             id, info{id}.message, print_stack (info{id}));
    endif

    ## process output
    t_Df = horzcat (t_Df{:});
    Df = zeros (rows (t_Df), n);
    Df(:, idx) = t_Df;

  else # not parallel

    ## after first evaluation, dimensionness of 'f' is known
    t_Df = imag (f (x(:, idx(1)))(:));
    dim = numel (t_Df);

    Df = zeros (dim, n);

    Df(:, idx(1)) = t_Df;

    for count = (idx.')(2:end)
      Df(:, count) = imag (f (x(:, count))(:));
    endfor

    Df /=  h;

  endif

endfunction

function ret = print_stack (info)

  ret = "";

  if (isfield (info, "stack"))
    for id = 1 : numel (info.stack)
      ret = cstrcat (ret, sprintf ("\n    %s at line %i comumn %i",
                                   info.stack(id).name,
                                   info.stack(id).line,
                                   info.stack(id).column));
    endfor
  endif

endfunction

%!assert (jacobs (1, @(x) x), 1)
%!assert (jacobs (6, @(x) x^2), 12)
%!assert (jacobs ([1; 1], @(x) [x(1)^2; x(1)*x(2)]), [2, 0; 1, 1])
%!assert (jacobs ([1; 2], @(x) [x(1)^2 + x(2); x(2)*exp(x(1))]), [2, 1; 2*exp(1), exp(1)])

%% Test input validation
%!error jacobs ()
%!error jacobs (1)
%!error jacobs (1, 2, 3, 4)
%!error jacobs (@sin, 1, [1, 1])
%!error jacobs (@sin, 1, ones(2, 2))

%!demo
%! # Relative error against several h-values
%! k = 3:20; h = 10 .^ (-k); x = 0.3*pi;
%! err = zeros (1, numel (k));
%! for count = 1 : numel (k)
%!   err(count) = abs (jacobs (x, @sin,	struct ("h", h(count))) - cos (x)) / abs (cos (x)) + eps;
%! endfor
%! loglog (h, err); grid minor;
%! xlabel ("h"); ylabel ("|Df(x) - cos(x)| / |cos(x)|")
%! title ("f(x)=sin(x), f'(x)=cos(x) at x = 0.3pi")