## Code for Figure A.3

### main.m

```
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% Copyright (C) 2001, James B. Rawlings and John G. Ekerdt
%
% 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 2, 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; see the file COPYING.  If not, write to
% the Free Software Foundation, 59 Temple Place - Suite 330, Boston,
% MA 02111-1307, USA.

%
% Illustrate sensitivity calculation in simple first-order reaction
%
% dca/dt = -k ca
% ca(0)  = ca0
%
% theta = [k; ca0]
%
% compute solution to model
% and sensitivities
%
%  ca(t)
%  S1 = d ca / d k
%  S2 = d ca / d ca0
%
%  ca(t) = ca0 exp(-kt)
%  S1 = -t ca0 exp(-kt)
%  S2 = exp(-kt)
%
% jbr,  10/5/01
%
% converted from ddasac to cvodes, 3/31/07, jbr
%
% converted to use paresto, 5/1/2018, jbr
%

ca0 = 2;
k   = 1;
tfinal = 5;
nts    = 100;
tout = linspace(0,tfinal,nts);

model = struct;
model.x = {'ca'};
model.p = {'k'};
model.d = {'dummy'};
model.tout = tout;

model.ode = @(t, y, p) {-p.k*y.ca};
% dummy objective function; just finding sensitivities
model.lsq = @(t, y, p) {y.ca};

pe = paresto(model);

% initialize state and parameters

x0 = ca0;
thetaac = [k; x0];

theta0 = thetaac;
lbtheta = theta0;
ubtheta = theta0;

[est, y, p] = pe.optimize(zeros(1,nts), theta0, lbtheta, ubtheta);

table = [tout(:), y.ca(:), est.dca_dk(:), est.dca_dca0(:)];
save -ascii Sfirstorder.dat table;
% if (~ strcmp (getenv ('OMIT_PLOTS'), 'true')) % PLOTTING
plot (tout, [y.ca', est.dca_dk, est.dca_dca0]);
% % TITLE
% end % PLOTTING

```