/usr/share/octave/site/m/sundialsTB/idas/examples_ser/midasPendI1_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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 | function midasPendI1_dns
%midasPendI1_dns - Simple pendulum modeled as an index-1 DAE
% The pendulum is modeled using the x and y positions with
% the constraint x^2 + y^2 = L^2
% The index-1 DAE formulation (in first-order form) includes
% differential equations for the positions and velocities and
% the acceleration-level constraint.
% Radu Serban <radu@llnl.gov>
% Copyright (c) 2007, The Regents of the University of California.
% $Revision: 1.2 $Date: 2007/12/05 21:58:19 $
% x, y, vx, vy, lam
neq = 5;
t0 = 0.0;
tf = 10.0;
id = ones(neq,1);
id(5) = 0;
options = IDASetOptions('RelTol',1.e-6,...
'AbsTol',1.e-6,...
'VariableTypes',id,...
'MaxNumSteps', 1000,...
'LinearSolver','Dense',...
'JacobianFn',@pend_J);
%mondata.update = 100;
%options = IDASetOptions(options,'MonitorFn',@IDAMonitor,'MonitorData',mondata);
y0 = zeros(neq,1);
y0(1) = 1.0;
y0(5) = 0.1;
yp0 = zeros(neq,1);
fprintf('Estimated IC\n');
disp([y0 yp0])
IDAInit(@pend_f,t0,y0,yp0,options);
[status, y0_mod, yp0_mod] = IDACalcIC(tf, 'FindAlgebraic');
fprintf('Corrected IC\n');
disp([y0_mod yp0_mod])
it = 1;
time(it) = t0;
sol_y(it,:) = y0_mod';
[pc(it) vc(it)] = pend_constr(t0,y0_mod);
%t = t0;
%t_start = clock;
%while t < tf
% [status,t,y] = IDASolve(tf,'OneStep');
% it = it+1;
% time(it) = t;
% sol_y(it,:) = y';
% % Compute position and velocity constraint violations
% [pc(it) vc(it)] = pend_constr(t,y);
%end
%runtime = etime(clock,t_start);
dt = 0.1;
nt = ceil((tf-t0)/dt);
t_start = clock;
for it = 1:nt
tout = t0 + it*dt;
[status,t,y] = IDASolve(tout,'Normal');
time(it) = t;
sol_y(it,:) = y';
% Compute position and velocity constraint violations
[pc(it) vc(it)] = pend_constr(t,y);
end
runtime = etime(clock,t_start);
fprintf('Solver stats:\n');
disp(IDAGetStats);
fprintf('Run time: %f\n',runtime);
figure;
subplot(3,1,1)
hold on
plot(time,sol_y(:,1),'b');
plot(time,sol_y(:,2),'r');
box on
set(gca,'XLim',[t0 tf])
title('position');
legend('x','y');
subplot(3,1,2)
hold on
plot(time,sol_y(:,3),'b');
plot(time,sol_y(:,4),'r');
box on
set(gca,'XLim',[t0 tf])
title('velocity');
legend('v_x', 'v_y');
subplot(3,1,3)
plot(time,sol_y(:,5));
box on
set(gca,'XLim',[t0 tf])
title('Lagrange multiplier');
figure
plotyy(time, pc, time, vc);
box on
title('position and velocity constraint violations');
figure
subplot(2,1,1)
plot(sol_y(:,1),sol_y(:,2));
axis equal
axis tight
box on
grid on
xlabel('x');
ylabel('y');
title('trajectory');
phi = atan2( sol_y(:,1) , sol_y(:,2) );
phi_d = ( sol_y(:,1).*sol_y(:,4) - sol_y(:,2).*sol_y(:,3) ) ./ ( sol_y(:,1).^2 + sol_y(:,2).^2 ) ;
subplot(2,1,2)
plot3(time,phi, phi_d);
xlabel('time');
ylabel('\phi');
zlabel('\phi^\prime');
view(-30,15);
set(gca,'XLim',[t0 tf])
grid on
box on
title('phase plot');
IDAFree;
% ================================================================================
function [res, flag, new_data] = pend_f(t,y,yp)
% Residual function for a simple pendulum
% mass = 1.0
% length = 1.0
% damping coeff. = 0.3
% g = 9.81
res = [
-yp(1) + y(3)
-yp(2) + y(4)
-yp(3) - 2*y(1)*y(5) - 0.3*y(3)
-yp(4) + 9.81 - 2*y(2)*y(5) - 0.3*y(4)
-2*y(5) + y(3)^2 - 0.3*y(1)*y(3) + y(4)^2 + y(2)*(9.81-0.3*y(4))
];
flag = 0;
new_data = [];
% ================================================================================
function [J, flag, new_data] = pend_J(t,y,yp, rr, cj)
J = [
-cj 0 1 0 0
0 -cj 0 1 0
-2*y(5) 0 -cj-0.3 0 -2*y(1)
0 -2*y(5) 0 -cj-0.3 -2*y(2)
-0.3*y(3) 9.81-0.3*y(4) 2*y(3)-0.3*y(1) 2*y(4)-0.3*y(2) -2
];
flag = 0;
new_data = [];
% ================================================================================
function [pc, vc] = pend_constr(t,y)
% Position and velocity constraints
%
pc = y(1)^2 + y(2)^2 - 1.0;
vc = y(1)*y(3) + y(2)*y(4);
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