/usr/share/octave/packages/optim-1.5.2/linprog.m is in octave-optim 1.5.2-1.
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 | ## Copyright (C) 2009 Luca Favatella <slackydeb@gmail.com>
##
## 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} {@var{x} =} linprog (@var{f}, @var{A}, @var{b})
## @deftypefnx{Function File} {@var{x} =} linprog (@var{f}, @var{A}, @var{b}, @var{Aeq}, @var{beq})
## @deftypefnx{Function File} {@var{x} =} linprog (@var{f}, @var{A}, @var{b}, @var{Aeq}, @var{beq}, @var{lb}, @var{ub})
## @deftypefnx{Function File} {[@var{x}, @var{fval}] =} linprog (@dots{})
## Solve a linear problem.
##
## Finds
##
## @example
## min (f' * x)
## @end example
##
## (both f and x are column vectors) subject to
##
## @example
## @group
## A * x <= b
## Aeq * x = beq
## lb <= x <= ub
## @end group
## @end example
##
## If not specified, @var{Aeq} and @var{beq} default to empty matrices.
##
## If not specified, the lower bound @var{lb} defaults to minus infinite
## and the upper bound @var{ub} defaults to infinite.
##
## @c Will be cut out in optims info file and replaced with the same
## @c refernces explicitely there, since references to core Octave
## @c functions are not automatically transformed from here to there.
## @c BEGIN_CUT_TEXINFO
## @seealso{glpk}
## @c END_CUT_TEXINFO
## @end deftypefn
function [x fval] = linprog (f, A, b,
Aeq = [], beq = [],
lb = [], ub = [])
if (((nargin != 3) && (nargin != 5) && (nargin != 7)) ||
(nargout > 2))
print_usage ();
endif
nr_f = rows(f);
# Sanitize A and b
if (isempty (A) && isempty (b))
A = zeros (0, nr_f);
b = zeros (rows (A), 1);
endif
nr_A = rows (A);
if (columns (f) != 1)
error ("f must be a column vector");
elseif (columns (A) != nr_f)
error ("columns (A) != rows (f)");
elseif (size (b) != [nr_A 1])
error ("size (b) != [(rows (A)) 1]");
else
## Sanitize Aeq
if (isempty (Aeq))
Aeq = zeros (0, nr_f);
endif
if (columns (Aeq) != nr_f)
error ("columns (Aeq) != rows (f)");
endif
## Sanitize beq
if (isempty (beq))
beq = zeros (0, 1);
endif
nr_Aeq = rows (Aeq);
if (size (beq) != [nr_Aeq 1])
error ("size (beq) != [(rows (Aeq)) 1]");
endif
## Sanitize lb
if (isempty (lb))
lb = - Inf (nr_f, 1);
endif
if (size (lb) != [nr_f 1])
error ("size (lb) != [(rows (f)) 1]");
endif
## Sanitize ub
if (isempty (ub))
ub = Inf (nr_f, 1);
endif
if (size (ub) != [nr_f 1])
error ("size (ub) != [(rows (f)) 1]");
endif
## Call glpk
ctype = [(repmat ("U", nr_A, 1));
(repmat ("S", nr_Aeq, 1))];
[x(1:nr_f, 1) fval(1, 1)] = glpk (f, [A; Aeq], [b; beq], lb, ub, ctype);
endif
endfunction
%!test
%! f = [1; -1];
%! A = [];
%! b = [];
%! Aeq = [1, 0];
%! beq = [2];
%! lb = [0; Inf];
%! ub = [-Inf; 0];
%! x_exp = [2; 0];
%! assert (linprog (f, A, b, Aeq, beq, lb, ub), x_exp);
%!shared f, A, b, lb, ub, x_exp, fval_exp
%! f = [21 25 31 34 23 19 32 36 27 25 19]';
%!
%! A1 = [ 1 0 0 0 1 0 0 1 0 0 0;
%! 0 1 0 0 0 1 0 0 1 0 0;
%! 0 0 1 0 0 0 0 0 0 1 0;
%! 0 0 0 1 0 0 1 0 0 0 1];
%! A2 = [ 1 1 1 1 0 0 0 0 0 0 0;
%! 0 0 0 0 1 1 1 0 0 0 0;
%! 0 0 0 0 0 0 0 1 1 1 1];
%! A = [-A1; A2];
%!
%! b1 = [40; 50; 50; 70];
%! b2 = [100; 60; 50];
%! b = [-b1; b2];
%!
%! lb = zeros (rows (f), 1);
%! ub = Inf (rows (f), 1);
%!
%! x_exp = [40 0 50 10 0 50 10 0 0 0 50]';
%! fval_exp = f' * x_exp;
%!
%!test
%! Aeq = [];
%! beq = [];
%! [x_obs fval_obs] = linprog (f, A, b, Aeq, beq, lb, ub);
%! assert ([x_obs; fval_obs], [x_exp; fval_exp]);
%!
%!test
%! Aeq = zeros (1, rows (f));
%! beq = 0;
%! assert (linprog (f, A, b, Aeq, beq, lb, ub), x_exp);
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