1 %# Copyright (C) 2007-2012, Thomas Treichl <treichl@users.sourceforge.net>
2 %# OdePkg - A package for solving ordinary differential equations and more
4 %# This program is free software; you can redistribute it and/or modify
5 %# it under the terms of the GNU General Public License as published by
6 %# the Free Software Foundation; either version 2 of the License, or
7 %# (at your option) any later version.
9 %# This program is distributed in the hope that it will be useful,
10 %# but WITHOUT ANY WARRANTY; without even the implied warranty of
11 %# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
12 %# GNU General Public License for more details.
14 %# You should have received a copy of the GNU General Public License
15 %# along with this program; If not, see <http://www.gnu.org/licenses/>.
18 %# @deftypefn {Function File} {[@var{solution}] =} odepkg_testsuite_pollution (@var{@@solver}, @var{reltol})
20 %# If this function is called with two input arguments and the first input argument @var{@@solver} is a function handle describing an OdePkg solver and the second input argument @var{reltol} is a double scalar describing the relative error tolerance then return the cell array @var{solution} with performance informations about the POLLUTION testsuite of ordinary differential equations after solving (ODE--test).
22 %# Run examples with the command
24 %# demo odepkg_testsuite_pollution
27 %# This function has been ported from the "Test Set for IVP solvers" which is developed by the INdAM Bari unit project group "Codes and Test Problems for Differential Equations", coordinator F. Mazzia.
32 function vret = odepkg_testsuite_pollution (vhandle, vrtol)
34 if (nargin ~= 2) %# Check number and types of all input arguments
35 help ('odepkg_testsuite_pollution');
36 error ('OdePkg:InvalidArgument', ...
37 'Number of input arguments must be exactly two');
38 elseif (~isa (vhandle, 'function_handle') || ~isscalar (vrtol))
42 vret{1} = vhandle; %# The handle for the solver that is used
43 vret{2} = vrtol; %# The value for the realtive tolerance
44 vret{3} = vret{2}; %# The value for the absolute tolerance
45 vret{4} = vret{2}; %# The value for the first time step
46 %# Write a debug message on the screen, because this testsuite function
47 %# may be called more than once from a loop over all solvers present
48 fprintf (1, ['Testsuite POLLUTION, testing solver %7s with relative', ...
49 ' tolerance %2.0e\n'], func2str (vret{1}), vrtol); fflush (1);
51 %# Setting the integration algorithms option values
52 vstart = 0.0; %# The point of time when solving is started
53 vstop = 60.0; %# The point of time when solving is stoped
54 vinit = odepkg_testsuite_pollutioninit; %# The initial values
56 vopt = odeset ('Refine', 0, 'RelTol', vret{2}, 'AbsTol', vret{3}, ...
57 'InitialStep', vret{4}, 'Stats', 'on', 'NormControl', 'off', ...
58 'Jacobian', @odepkg_testsuite_pollutionjac, 'MaxStep', vstop-vstart);
60 %# Calculate the algorithm, start timer and do solving
61 tic; vsol = feval (vhandle, @odepkg_testsuite_pollutionfun, ...
62 [vstart, vstop], vinit, vopt);
63 vret{12} = toc; %# The value for the elapsed time
64 vref = odepkg_testsuite_pollutionref; %# Get the reference solution vector
65 if (exist ('OCTAVE_VERSION') ~= 0)
70 vret{5} = odepkg_testsuite_calcmescd (vlst, vref, vret{3}, vret{2});
71 vret{6} = odepkg_testsuite_calcscd (vlst, vref, vret{3}, vret{2});
72 vret{7} = vsol.stats.nsteps + vsol.stats.nfailed; %# The value for all evals
73 vret{8} = vsol.stats.nsteps; %# The value for success evals
74 vret{9} = vsol.stats.nfevals; %# The value for fun calls
75 vret{10} = vsol.stats.npds; %# The value for partial derivations
76 vret{11} = vsol.stats.ndecomps; %# The value for LU decompositions
78 %# Returns the results for the for the POLLUTION problem
79 function f = odepkg_testsuite_pollutionfun (t, y, varargin)
80 f(01,1) = - 0.350 * y(1) + 0.266e2 * y(2) * y(4) + 0.123e5 * y(2) * y(5) + ...
81 0.165e5 * y(2) * y(11) - 0.900e4 * y(1) * y(11) + 0.220e-1 * y(13) + ...
82 0.120e5 * y(2) * y(10) - 0.163e5 * y(1) * y(6) + 0.578e1 * y(19) - ...
83 0.474e-1 * y(1) * y(4) - 0.178e4 * y(1) * y(19) + 0.312e1 * y(20);
84 f(02,1) = + 0.350 * y(1) - 0.266e2 * y(2) * y(4) - 0.123e5 * y(2) * y(5) - ...
85 0.165e5 * y(2) * y(11) - 0.120e5 * y(2) * y(10) + 0.210e1 * y(19);
86 f(03,1) = + 0.350 * y(1) - 0.480e7 * y(3) + 0.175e-1 * y(4) + 0.444e12 * y(16) + 0.578e1 * y(19);
87 f(04,1) = - 0.266e2 * y(2) * y(4) + 0.480e7 * y(3) - 0.350e-3 * y(4) - ...
88 0.175e-1 * y(4) - 0.474e-1 * y(1) * y(4);
89 f(05,1) = - 0.123e5 * y(2) * y(5) + 2*0.860e-3 * y(7) + 0.150e5 * y(6) * y(7) + ...
90 0.130e-3 * y(9) + 0.188e1 * y(14) + 0.124e4 * y(6) * y(17);
91 f(06,1) = + 0.123e5 * y(2) * y(5) - 0.150e5 * y(6) * y(7) - 0.240e5 * y(6) * y(9) - ...
92 0.163e5 * y(1) * y(6) + 2*0.100e9 * y(16) - 0.124e4 * y(6) * y(17);
93 f(07,1) = - 0.860e-3 * y(7) - 0.820e-3 * y(7) - 0.150e5 * y(6) * y(7) + 0.188e1 * y(14);
94 f(08,1) = + 0.860e-3 * y(7) + 0.820e-3 * y(7) + 0.150e5 * y(6) * y(7) + 0.130e-3 * y(9);
95 f(09,1) = - 0.130e-3 * y(9) - 0.240e5 * y(6) * y(9);
96 f(10,1) = + 0.130e-3 * y(9) + 0.165e5 * y(2) * y(11) - 0.120e5 * y(2) * y(10);
97 f(11,1) = + 0.240e5 * y(6) * y(9) - 0.165e5 * y(2) * y(11) - 0.900e4 * y(1) * y(11) + ...
99 f(12,1) = + 0.165e5 * y(2) * y(11);
100 f(13,1) = + 0.900e4 * y(1) * y(11) - 0.220e-1 * y(13);
101 f(14,1) = + 0.120e5 * y(2) * y(10) - 0.188e1 * y(14);
102 f(15,1) = + 0.163e5 * y(1) * y(6);
103 f(16,1) = + 0.350e-3 * y(4) - 0.100e9 * y(16) - 0.444e12 * y(16);
104 f(17,1) = - 0.124e4 * y(6) * y(17);
105 f(18,1) = + 0.124e4 * y(6) * y(17);
106 f(19,1) = - 0.210e1 * y(19) - 0.578e1 * y(19) + 0.474e-1 * y(1) * y(4) - ...
107 0.178e4 * y(1) * y(19) + 0.312e1 * y(20);
108 f(20,1) = + 0.178e4 * y(1) * y(19) - 0.312e1 * y(20);
110 %# Returns the INITIAL values for the POLLUTION problem
111 function vinit = odepkg_testsuite_pollutioninit ()
112 vinit = [0, 0.2, 0, 0.04, 0, 0, 0.1, 0.3, 0.01, ...
113 0, 0, 0, 0, 0, 0, 0, 0.007, 0, 0, 0];
115 %# Returns the JACOBIAN matrix for the POLLUTION problem
116 function dfdy = odepkg_testsuite_pollutionjac (t, y)
117 k1 = 0.35e0; k2 = 0.266e2; k3 = 0.123e5; k4 = 0.86e-3;
118 k5 = 0.82e-3; k6 = 0.15e5; k7 = 0.13e-3; k8 = 0.24e5;
119 k9 = 0.165e5; k10 = 0.9e4; k11 = 0.22e-1; k12 = 0.12e5;
120 k13 = 0.188e1; k14 = 0.163e5; k15 = 0.48e7; k16 = 0.35e-3;
121 k17 = 0.175e-1; k18 = 0.1e9; k19 = 0.444e12; k20 = 0.124e4;
122 k21 = 0.21e1; k22 = 0.578e1; k23 = 0.474e-1; k24 = 0.178e4;
125 dfdy(1,1) = -k1 - k10 * y(11) - k14 * y(6) - k23 * y(4) - k24 * y(19);
126 dfdy(1,11) = -k10 * y(1) + k9 * y(2);
127 dfdy(1,6) = -k14 * y(1);
128 dfdy(1,4) = -k23 * y(1) + k2 * y(2);
129 dfdy(1,19) = -k24 * y(1) + k22;
130 dfdy(1,2) = k2 * y(4) + k9 * y(11) + k3 * y(5) + k12 * y(10);
133 dfdy(1,5) = k3 * y(2);
134 dfdy(1,10) = k12 * y(2);
136 dfdy(2,4) = -k2 * y(2);
137 dfdy(2,5) = -k3 * y(2);
138 dfdy(2,11) = -k9 * y(2);
139 dfdy(2,10) = -k12 * y(2);
142 dfdy(2,2) = -k2 * y(4) - k3 * y(5) - k9 * y(11) - k12 * y(10);
150 dfdy(4,4) = -k2 * y(2) - k16 - k17 - k23 * y(1);
151 dfdy(4,2) = -k2 * y(4);
152 dfdy(4,1) = -k23 * y(4);
155 dfdy(5,5) = -k3 * y(2);
156 dfdy(5,2) = -k3 * y(5);
157 dfdy(5,7) = 2d0 * k4 + k6 * y(6);
158 dfdy(5,6) = k6 * y(7) + k20 * y(17);
161 dfdy(5,17) = k20 * y(6);
163 dfdy(6,6) = -k6 * y(7) - k8 * y(9) - k14 * y(1) - k20 * y(17);
164 dfdy(6,7) = -k6 * y(6);
165 dfdy(6,9) = -k8 * y(6);
166 dfdy(6,1) = -k14 * y(6);
167 dfdy(6,17) = -k20 * y(6);
168 dfdy(6,2) = k3 * y(5);
169 dfdy(6,5) = k3 * y(2);
170 dfdy(6,16) = 2d0 * k18;
172 dfdy(7,7) = -k4 - k5 - k6 * y(6);
173 dfdy(7,6) = -k6 * y(7);
176 dfdy(8,7) = k4 + k5 + k6 * y(6);
177 dfdy(8,6) = k6 * y(7);
180 dfdy(9,9) = -k7 - k8 * y(6);
181 dfdy(9,6) = -k8 * y(9);
183 dfdy(10,10) = -k12 * y(2);
184 dfdy(10,2) = -k12 * y(10) + k9 * y(11);
186 dfdy(10,11) = k9 * y(2);
188 dfdy(11,11) = -k9 * y(2) - k10 * y(1);
189 dfdy(11,2) = -k9 * y(11);
190 dfdy(11,1) = -k10 * y(11);
191 dfdy(11,9) = k8 * y(6);
192 dfdy(11,6) = k8 * y(9);
195 dfdy(12,11) = k9 * y(2);
196 dfdy(12,2) = k9 * y(11);
199 dfdy(13,11) = k10 * y(1);
200 dfdy(13,1) = k10 * y(11);
203 dfdy(14,10) = k12 * y(2);
204 dfdy(14,2) = k12 * y(10);
206 dfdy(15,1) = k14 * y(6);
207 dfdy(15,6) = k14 * y(1);
209 dfdy(16,16) = -k18 - k19;
212 dfdy(17,17) = -k20 * y(6);
213 dfdy(17,6) = -k20 * y(17);
215 dfdy(18,17) = k20 * y(6);
216 dfdy(18,6) = k20 * y(17);
218 dfdy(19,19) = -k21 - k22 - k24 * y(1);
219 dfdy(19,1) = -k24 * y(19) + k23 * y(4);
220 dfdy(19,4) = k23 * y(1);
224 dfdy(20,1) = k24 * y(19);
225 dfdy(20,19) = k24 * y(1);
227 %# Returns the REFERENCE values for the POLLUTION problem
228 function y = odepkg_testsuite_pollutionref ()
229 y(01,1) = 0.56462554800227 * 10^(-1);
230 y(02,1) = 0.13424841304223 * 10^(+0);
231 y(03,1) = 0.41397343310994 * 10^(-8);
232 y(04,1) = 0.55231402074843 * 10^(-2);
233 y(05,1) = 0.20189772623021 * 10^(-6);
234 y(06,1) = 0.20189772623021 * 10^(-6);
235 y(07,1) = 0.77842491189979 * 10^(-1);
236 y(08,1) = 0.77842491189979 * 10^(+0);
237 y(09,1) = 0.74940133838804 * 10^(-2);
238 y(10,1) = 0.16222931573015 * 10^(-7);
239 y(11,1) = 0.11358638332570 * 10^(-7);
240 y(12,1) = 0.22305059757213 * 10^(-2);
241 y(13,1) = 0.20871628827986 * 10^(-3);
242 y(14,1) = 0.13969210168401 * 10^(-4);
243 y(15,1) = 0.89648848568982 * 10^(-2);
244 y(16,1) = 0.43528463693301 * 10^(-17);
245 y(17,1) = 0.68992196962634 * 10^(-2);
246 y(18,1) = 0.10078030373659 * 10^(-3);
247 y(19,1) = 0.17721465139699 * 10^(-5);
248 y(20,1) = 0.56829432923163 * 10^(-4);
251 %! %% vsolver = {@ode23, @ode45, @ode54, @ode78, ...
252 %! %% @odebda, @oders, @ode2r, @ode5r, @odesx};
253 %! vsolver = {@odebda, @oders, @ode2r, @ode5r, @odesx};
254 %! for vcnt=1:length (vsolver)
255 %! poll{vcnt,1} = odepkg_testsuite_pollution (vsolver{vcnt}, 1e-7);
259 %# Local Variables: ***