Figure 9.15:

Model fit to a single adsorption experiment.

Code for Figure 9.15

Text of the GNU GPL.

main.m


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% 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.

%
% jbr,  11/28/01
%
global X Y grad Ypred dYdtheta lb ub

Hgas1 = [2.659, 27.590, 141.038, ...
	332.613, 546.857, 608.583, 875.353, 991.072, 1080.134, ...
	1142.782, 1203.178, 1256.244]';

Hads1 = [32.31, 40.02, 45.40, 48.49 ...
	50.19, 53.86, 52.77, 53.19, 53.67, 54.15, 54.51, 54.73]';


Hgas2 = [3.755, 36.331, 189.904, ...
	 413.881, 624.665, 817.592]';

Hads2 = [33.17, 40.90, 45.59, 47.72, ...
	 48.74, 49.43]';

Hgas3 = [12.794, 119.331, 339.917, ...
	 545.227, 735.746, 890.642]';

Hads3 = [36.91, 42.90, 45.65, 47.00, ...
	 47.82, 48.60]';

Hgas4 = [7.424, 73.312, 251.177, ...
	 491.691, 707.806, 873.926]';

Hads4 = [39.11, 46.06, 49.87, 51.57, ...
	 52.48, 53.18]';

Hgas5 = [9.176, 72.065, 259.002, ...
	 475.250, 670.034, 818.669]';

Hads5 = [39.52, 46.06, 49.92, 51.86, ...
	 52.96, 53.88]';

Hgas6 = [2.962, 34.350, 176.860, 405.233, ...
	 607.476, 799.723, 946.765]';

Hads6 = [32.70, 40.11, 44.92, 47.40, 48.62, ...
	 49.50, 50.12]';

Hgas7 = [3.159, 38.528, 200.877, 433.924, ...
	 647.630, 820.673]';

Hads7 = [32.42, 39.81, 44.51, 46.79, 48.14, ...
	 48.95]';

Hgas8 = [34.127, 172.316, ...
	 385.633, 616.149, 812.932, 961.191, 1061.967, 1155.829, 1219.299]';

Hads8 = [43.79, 48.97, 51.57, ...
	 53.09, 54.05, 54.67, 55.20, 55.60, 55.93]';

%
% choose a dataset or datasets to fit
%
X = [Hgas4];
Y = [Hads4];
%X = [Hgas1; Hgas2; Hgas3; Hgas4; Hgas5; Hgas6; Hgas7; Hgas8];
%Y = [Hads1; Hads2; Hads3; Hads4; Hads5; Hads6; Hads7; Hads8];

Ks0 = 2;
cms0 = 40;
cmp0 = 0;
theta0 = [Ks0; cms0; cmp0];



small = 1e-5;
large = 1000;
lb = [small; small; small];
ub = [large; large; large];

model.m


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function obj = model(theta)
  global X Y grad Ypred dYdtheta
  Ks = theta(1);
  cms = theta(2);
  cmp = theta(3);
  %
  % choose associative or dissociative adsorption
  %
%  Ypred = cm*K*X./(1+K*X);
  Ypred = cms*Ks*sqrt(X)./(1+Ks*sqrt(X)) + cmp;
  resid = Y - Ypred;
  obj = resid'*resid;
  %
  % while here, compute the gradient and store in global
  %
%  dYdtheta = [Ypred.*(1/Ks - X./(1+Ks*X)), Ypred/cms];
  dYdtheta =  ...
[ cms*Ks*sqrt(X)./(1+Ks*sqrt(X)).*(1/Ks - sqrt(X)./(1+Ks*sqrt(X))), ...
	Ks*sqrt(X)./(1+Ks*sqrt(X)), ones(size(Ypred)) ];
  grad = -2*dYdtheta'*resid;

gradient.m


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function retval = gradient(theta)
global X Y grad Ypred dYdtheta
  %
  % grad was just computed in model so take it from
  % global and return
  %
  obj = model(theta);
  retval = grad;