/usr/share/octave/site/m/sundialsTB/kinsol/examples_ser/mkinFerTron_dns.m is in octave-sundials 2.5.0-3+b1.
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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 | function mkinFerTron_dns
% mkinFerTron_dns - Ferraris-Tronconi test problem
%
% Source: "Handbook of Test Problems in Local and Global Optimization",
% C.A. Floudas, P.M. Pardalos et al.
% Kluwer Academic Publishers, 1999.
% Test problem 4 from Section 14.1, Chapter 14: Ferraris and Tronconi
%
% This problem involves a blend of trigonometric and exponential terms.
% 0.5 sin(x1 x2) - 0.25 x2/pi - 0.5 x1 = 0
% (1-0.25/pi) ( exp(2 x1)-e ) + e x2 / pi - 2 e x1 = 0
% such that
% 0.25 <= x1 <=1.0
% 1.5 <= x2 <= 2 pi
%
% The treatment of the bound constraints on x1 and x2 is done using
% the additional variables
% l1 = x1 - x1_min >= 0
% L1 = x1 - x1_max <= 0
% l2 = x2 - x2_min >= 0
% L2 = x2 - x2_max >= 0
%
% and using the constraint feature in KINSOL to impose
% l1 >= 0 l2 >= 0
% L1 <= 0 L2 <= 0
%
% The Ferraris-Tronconi test problem has two known solutions.
% The nonlinear system is solved by KINSOL using different
% combinations of globalization and Jacobian update strategies
% and with different initial guesses (leading to one or the other
% of the known solutions).
%
% Constraints are imposed to make all components of the solution
% positive.
% Radu Serban <radu@llnl.gov>
% Copyright (c) 2007, The Regents of the University of California.
% $Revision: 1.1 $Date: 2007/12/05 21:58:19 $
% Initializations
% ---------------
% User data
lb = [0.25 ; 1.5];
ub = [1.0 ; 2*pi];
data.lb = lb;
data.ub = ub;
% Number of problem variables
nvar = 2;
% Number of equations = number of problem vars. + number of bound variables
neq = nvar + 2*nvar;
% Function tolerance
ftol = 1.0e-5;
% Step tolerance
stol = 1.0e-5;
% Constraints
constraints = [ 0 0 1 -1 1 -1];
% Modified/exact Newton
% msbset = 0 -> modified Newton
% msbset = 1 -> exact Newton
msbset = 0;
% Initialize solver
options = KINSetOptions('UserData', data, ...
'FuncNormTol', ftol, ...
'ScaledStepTol', stol, ...
'Constraints', constraints, ...
'MaxNumSetups', msbset, ...
'LinearSolver', 'Dense');
KINInit(@sysfn, neq, options);
% Initial guess
% -------------
%
% There are two known solutions for this problem
%
% the following initial guess should take us to (0.29945; 2.83693)
x1 = lb(1);
x2 = lb(2);
u1 = [ x1 ; x2 ; x1-lb(1) ; x1-ub(1) ; x2-lb(2) ; x2-ub(2) ];
% while this one should take us to (0.5; 3.1415926)
x1 = 0.5*(lb(1)+ub(1));
x2 = 0.5*(lb(2)+ub(2));
u2 = [ x1 ; x2 ; x1-lb(1) ; x1-ub(1) ; x2-lb(2) ; x2-ub(2) ];
% No Y and F scaling
yscale = ones(neq,1);
fscale = ones(neq,1);
% No globalization
strategy = 'None';
fprintf('\nFerraris and Tronconi test problem\n');
fprintf('Tolerance parameters:\n');
fprintf(' fnormtol = %10.6g\n scsteptol = %10.6g\n', ftol, stol);
if msbset == 1
fprintf('Exact Newton');
else
fprintf('Modified Newton');
end
if strcmp(strategy,'None')
fprintf('\n');
else
fprintf(' with line search\n');
end
% Solve problem starting from the 1st initial guess
% -------------------------------------------------
fprintf('\n------------------------------------------\n');
fprintf('\nInitial guess on lower bounds\n');
fprintf(' [x1,x2] = %8.6g %8.6g', u1(1), u1(2));
[status, u1] = KINSol(u1, strategy, yscale, fscale);
stats = KINGetStats;
fprintf('\nsolution\n');
fprintf(' [x1,x2] = %8.6g %8.6g', u1(1), u1(2));
fprintf('\nSolver statistics:\n');
fprintf(' nni = %5d nfe = %5d \n', stats.nni, stats.nfe);
fprintf(' nje = %5d nfeD = %5d \n', stats.LSInfo.njeD, stats.LSInfo.nfeD);
% Solve problem starting from the 2nd initial guess
% -------------------------------------------------
fprintf('\n------------------------------------------\n');
fprintf('\nInitial guess in middle of feasible region\n');
fprintf(' [x1,x2] = %8.6g %8.6g', u2(1), u2(2));
[status, u2] = KINSol(u2, strategy, yscale, fscale);
stats = KINGetStats;
fprintf('\nsolution\n');
fprintf(' [x1,x2] = %8.6g %8.6g', u2(1), u2(2));
fprintf('\nSolver statistics:\n');
fprintf(' nni = %5d nfe = %5d \n', stats.nni, stats.nfe);
fprintf(' nje = %5d nfeD = %5d \n', stats.LSInfo.njeD, stats.LSInfo.nfeD);
% Free memory
% --------------------------------------
KINFree;
return
% System function
% ---------------
function [fu, flag, new_data] = sysfn(u, data)
lb = data.lb;
ub = data.ub;
x1 = u(1);
x2 = u(2);
l1 = u(3);
L1 = u(4);
l2 = u(5);
L2 = u(6);
e = exp(1);
fu(1) = 0.5 * sin(x1*x2) - 0.25 * x2 / pi - 0.5 * x1;
fu(2) = (1.0 - 0.25/pi)*(exp(2.0*x1)-e) + e*x2/pi - 2.0*e*x1;
fu(3) = l1 - x1 + lb(1);
fu(4) = L1 - x1 + ub(1);
fu(5) = l2 - x2 + lb(2);
fu(6) = L2 - x2 + ub(2);
flag = 0;
new_data = [];
return
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