How to fit parameters of an ode by using ode45 and fmincon

Hi everyone,

I have a system of 3 ODEs with 6 parameters and a 24x3 matrix that contains real data for the 3 variables. My goal is to find the numerical value of the 6 parameters that best fit the model by using ode45 and fmincon.

I've been trying to use the following code but, when I run it, I get my parameters' initial conditions (initialParam) as a result. I've tried to debug my code and [t,y], that are the output of the ode45, are 0 and initialCond respectively so I guess the error is there but i'm not sure about it and moreover i don't know how to fix it.

Can someone please help me find my mistake? Thanks!

% Before this line i've imported by data from .csv files, now i've stored
% it in a 24x3 matrix called xdata
xdata = [GDP(:,2) AL(:,2) HW(:,2)];

initialParam = [1.3; 0.3; 24.84; 1.3; 1.1; 0.04];
A = [-1 0 0 0 0 0;
    0 -1 0 0 0 0;
    0 1 0 0 0 0;
    0 0 -1 0 0 0;
    0 0 0 -1 0 0;
    0 0 0 0 -1 0;
    0 0 0 0 0 -1];
b = [0; 0; 1; 0; 0; 0; 0];

bestParam = fmincon(@(param)objFunction(param,xdata),initialParam,A,b)

function d = objFunction(param,xdata)
timePeriod = linspace(0,24,24);
initialCond = [2000 4000 1800];
epsi = 0.45;

f = @(t,y,p) [1/p(4)*(y(1)^p(2)/y(3)^p(2))*(y(3)*(1-p(2)+p(4))-(1-p(2)));
            y(2)*(p(1)-y(2))-epsi*(y(1))^p(2)*(y(3))^(1-p(2)); 
            (y(3)*(1-y(3))*(p(6)-p(2)*(y(3)^(1-p(2))/y(1)^(1-p(2)))+(p(2)*p(5)*(1/p(4)*(y(1)^p(2)/y(3)^p(2))*(y(3)*(1-p(2)+p(4))-(1-p(2))))/y(1))-(p(3)*(1-p(5))*(y(2)*(p(1)-y(2))-epsi*y(1)^p(2)*y(3)^(1-p(2))))/y(2)))/(((p(4)+1)*p(5)-p(4)-p(2)*p(5))*y(3)+p(2)*p(5))];

[t,y] = ode45(@(t,x)f(t,x,param),timePeriod,initialCond);
d = sum(((y(:,1)-xdata(:,1))).^2)+sum((y(:,2)-xdata(:,2)).^2)+sum((y(:,3)-xdata(:,3)).^2);
end

Answer 1

[Torsten]

Check your differential equations. As you can see, the derivatives for the given constellation (parameters and initial conditions) are in the order of 1e7 to 1e32.

For the fitting, I suggest you use lsqcurvefit instead of fmincon and define the constraints on the parameters as lower and upper bounds. The last remark also applies to fmincon if you want to stick to this optimizer: Don't use A and b, but lb and ub to define the parameter constraints.

p = [1.3; 0.3; 24.84; 1.3; 1.1; 0.04];
timePeriod = linspace(0,24,24);
initialCond = [2000 4000 1800];
[t,y] = ode45(@(t,y)fun(t,y,p),timePeriod,initialCond);

dy = 3×1

1.0e+07 * 0.0003 -1.5996 1.9851

dy = 3×1

1.0e+07 * 0.0003 -1.5533 2.0348

dy = 3×1

1.0e+07 * 0.0003 -1.5319 2.0620

dy = 3×1

1.0e+07 * 0.0003 -1.4278 2.1939

dy = 3×1

1.0e+07 * 0.0003 -1.4097 2.2190

dy = 3×1

1.0e+07 * 0.0003 -1.3886 2.2485

dy = 3×1

1.0e+07 * 0.0003 -1.3897 2.2466

dy = 3×1

1.0e+07 * 0.0004 -1.2339 2.4541

dy = 3×1

1.0e+07 * 0.0004 -1.1780 2.5969

dy = 3×1

1.0e+07 * 0.0005 -0.8998 3.2610

dy = 3×1

1.0e+07 * 0.0005 -0.8251 3.4101

dy = 3×1

1.0e+07 * 0.0005 -0.7841 3.5407

dy = 3×1

1.0e+07 * 0.0005 -0.8371 3.5104

dy = 3×1

1.0e+07 * 0.0006 -0.7433 3.8346

dy = 3×1

1.0e+07 * 0.0006 -0.7096 4.0576

dy = 3×1

1.0e+07 * 0.0008 -0.5421 5.0955

dy = 3×1

1.0e+07 * 0.0009 -0.4971 5.3286

dy = 3×1

1.0e+07 * 0.0009 -0.4725 5.5328

dy = 3×1

1.0e+07 * 0.0009 -0.5043 5.4853

dy = 3×1

1.0e+07 * 0.0010 -0.4478 5.9923

dy = 3×1

1.0e+07 * 0.0010 -0.4276 6.3411

dy = 3×1

1.0e+07 * 0.0013 -0.3267 7.9656

dy = 3×1

1.0e+07 * 0.0014 -0.2996 8.3310

dy = 3×1

1.0e+07 * 0.0015 -0.2848 8.6509

dy = 3×1

1.0e+07 * 0.0014 -0.3039 8.5761

dy = 3×1

1.0e+07 * 0.0016 -0.2699 9.3709

dy = 3×1

1.0e+07 * 0.0017 -0.2577 9.9179

dy = 3×1

1.0e+08 * 0.0002 -0.0197 1.2470

dy = 3×1

1.0e+08 * 0.0002 -0.0181 1.3047

dy = 3×1

1.0e+08 * 0.0002 -0.0172 1.3551

dy = 3×1

1.0e+08 * 0.0002 -0.0183 1.3431

dy = 3×1

1.0e+08 * 0.0003 -0.0163 1.4686

dy = 3×1

1.0e+08 * 0.0003 -0.0156 1.5549

dy = 3×1

1.0e+08 * 0.0004 -0.0119 1.9605

dy = 3×1

1.0e+08 * 0.0004 -0.0109 2.0531

dy = 3×1

1.0e+08 * 0.0004 -0.0104 2.1340

dy = 3×1

1.0e+08 * 0.0004 -0.0111 2.1139

dy = 3×1

1.0e+08 * 0.0004 -0.0099 2.3155

dy = 3×1

1.0e+08 * 0.0004 -0.0094 2.4548

dy = 3×1

1.0e+08 * 0.0006 -0.0072 3.1191

dy = 3×1

1.0e+08 * 0.0006 -0.0067 3.2755

dy = 3×1

1.0e+08 * 0.0006 -0.0063 3.4112

dy = 3×1

1.0e+08 * 0.0006 -0.0067 3.3737

dy = 3×1

1.0e+08 * 0.0007 -0.0060 3.7147

dy = 3×1

1.0e+08 * 0.0007 -0.0058 3.9520

dy = 3×1

1.0e+08 * 0.0010 -0.0045 5.1344

dy = 3×1

1.0e+08 * 0.0010 -0.0041 5.4338

dy = 3×1

1.0e+08 * 0.0011 -0.0039 5.6911

dy = 3×1

1.0e+08 * 0.0010 -0.0042 5.6042

dy = 3×1

1.0e+08 * 0.0012 -0.0038 6.2634

dy = 3×1

1.0e+08 * 0.0012 -0.0036 6.7328

dy = 3×1

1.0e+08 * 0.0017 -0.0029 9.3478

dy = 3×1

1.0e+09 * 0.0002 -0.0003 1.0115

dy = 3×1

1.0e+09 * 0.0002 -0.0003 1.0779

dy = 3×1

1.0e+09 * 0.0002 -0.0003 1.0502

dy = 3×1

1.0e+09 * 0.0002 -0.0003 1.2270

dy = 3×1

1.0e+09 * 0.0002 -0.0002 1.3633

dy = 3×1

1.0e+09 * 0.0003 -0.0002 2.3605

dy = 3×1

1.0e+09 * 0.0003 -0.0002 2.7168

dy = 3×1

1.0e+09 * 0.0004 -0.0002 3.0849

dy = 3×1

1.0e+09 * 0.0004 -0.0002 2.9827

dy = 3×1

1.0e+09 * 0.0004 -0.0002 3.9351

dy = 3×1

1.0e+09 * 0.0005 -0.0002 4.8645

dy = 3×1

1.0e+10 * 0.0001 -0.0000 1.8297

dy = 3×1

1.0e+10 * 0.0001 -0.0000 2.0325

dy = 3×1

1.0e+10 * 0.0001 -0.0000 3.9640

dy = 3×1

1.0e+10 * 0.0001 -0.0000 6.2028

dy = 3×1

1.0e+09 * 0.0004 -0.0002 3.3958

dy = 3×1

1.0e+09 * 0.0004 -0.0002 3.6823

dy = 3×1

1.0e+09 * 0.0005 -0.0002 5.6821

dy = 3×1

1.0e+09 * 0.0005 -0.0002 6.2915

dy = 3×1

1.0e+09 * 0.0005 -0.0002 6.9965

dy = 3×1

1.0e+09 * 0.0005 -0.0002 6.8825

dy = 3×1

1.0e+09 * 0.0006 -0.0002 8.4609

dy = 3×1

1.0e+09 * 0.0006 -0.0002 9.7524

dy = 3×1

1.0e+10 * 0.0001 -0.0000 2.2144

dy = 3×1

1.0e+10 * 0.0001 -0.0000 2.6218

dy = 3×1

1.0e+10 * 0.0001 -0.0000 3.3282

dy = 3×1

1.0e+10 * 0.0001 -0.0000 3.4894

dy = 3×1

1.0e+10 * 0.0001 -0.0000 5.1696

dy = 3×1

1.0e+10 * 0.0001 -0.0000 7.2079

dy = 3×1

1.0e+11 * 0.0000 -0.0000 6.7798

dy = 3×1

1.0e+11 * 0.0000 -0.0000 1.4931

dy = 3×1

1.0e+13 * 0.0000 -0.0000 1.8508

dy = 3×1

1.0e+15 * 0.0000 -0.0000 -6.3514

dy = 3×1

1.0e+10 * 0.0001 -0.0000 3.6378

dy = 3×1

1.0e+10 * 0.0001 -0.0000 3.7200

dy = 3×1

1.0e+10 * 0.0001 -0.0000 4.1622

dy = 3×1

1.0e+10 * 0.0001 -0.0000 4.2529

dy = 3×1

1.0e+10 * 0.0001 -0.0000 4.3645

dy = 3×1

1.0e+10 * 0.0001 -0.0000 4.3591

dy = 3×1

1.0e+10 * 0.0001 -0.0000 4.5683

dy = 3×1

1.0e+10 * 0.0001 -0.0000 4.6856

dy = 3×1

1.0e+10 * 0.0001 -0.0000 5.3240

dy = 3×1

1.0e+10 * 0.0001 -0.0000 5.4578

dy = 3×1

1.0e+10 * 0.0001 -0.0000 5.6215

dy = 3×1

1.0e+10 * 0.0001 -0.0000 5.6119

dy = 3×1

1.0e+10 * 0.0001 -0.0000 7.1055

dy = 3×1

1.0e+10 * 0.0001 -0.0000 8.3942

dy = 3×1

1.0e+11 * 0.0000 -0.0000 2.2295

dy = 3×1

1.0e+11 * 0.0000 -0.0000 2.6589

dy = 3×1

1.0e+11 * 0.0000 -0.0000 3.6371

dy = 3×1

1.0e+11 * 0.0000 -0.0000 4.0686

dy = 3×1

1.0e+10 * 0.0001 -0.0000 6.6194

dy = 3×1

1.0e+10 * 0.0001 -0.0000 7.3620

dy = 3×1

1.0e+11 * 0.0000 -0.0000 1.3194

dy = 3×1

1.0e+11 * 0.0000 -0.0000 1.5091

dy = 3×1

1.0e+11 * 0.0000 -0.0000 1.7503

dy = 3×1

1.0e+11 * 0.0000 -0.0000 1.7340

dy = 3×1

1.0e+11 * 0.0000 -0.0000 2.3243

dy = 3×1

1.0e+11 * 0.0000 -0.0000 2.8996

dy = 3×1

1.0e+12 * 0.0000 -0.0000 1.1291

dy = 3×1

1.0e+12 * 0.0000 -0.0000 1.2517

dy = 3×1

1.0e+12 * 0.0000 -0.0000 2.4378

dy = 3×1

1.0e+12 * 0.0000 -0.0000 3.8284

dy = 3×1

1.0e+11 * 0.0000 -0.0000 1.9908

dy = 3×1

1.0e+11 * 0.0000 -0.0000 2.1686

dy = 3×1

1.0e+11 * 0.0000 -0.0000 3.4264

dy = 3×1

1.0e+11 * 0.0000 -0.0000 3.8086

dy = 3×1

1.0e+11 * 0.0000 -0.0000 4.2601

dy = 3×1

1.0e+11 * 0.0000 -0.0000 4.1950

dy = 3×1

1.0e+11 * 0.0000 -0.0000 5.2071

dy = 3×1

1.0e+11 * 0.0000 -0.0000 6.0411

dy = 3×1

1.0e+12 * 0.0000 -0.0000 1.4156

dy = 3×1

1.0e+12 * 0.0000 -0.0000 1.6840

dy = 3×1

1.0e+12 * 0.0000 -0.0000 2.1532

dy = 3×1

1.0e+12 * 0.0000 -0.0000 2.2644

dy = 3×1

1.0e+12 * 0.0000 -0.0000 3.3855

dy = 3×1

1.0e+12 * 0.0000 -0.0000 4.7634

dy = 3×1

1.0e+13 * 0.0000 -0.0000 4.7145

dy = 3×1

1.0e+12 * 0.0000 -0.0000 8.0527

dy = 3×1

1.0e+15 * 0.0000 -0.0000 1.9393

dy = 3×1

1.0e+17 * 0.0000 -0.0000 -1.7373

dy = 3×1

1.0e+12 * 0.0000 -0.0000 2.3798

dy = 3×1

1.0e+12 * 0.0000 -0.0000 2.4448

dy = 3×1

1.0e+12 * 0.0000 -0.0000 2.8006

dy = 3×1

1.0e+12 * 0.0000 -0.0000 2.8760

dy = 3×1

1.0e+12 * 0.0000 -0.0000 2.9679

dy = 3×1

1.0e+12 * 0.0000 -0.0000 2.9619

dy = 3×1

1.0e+12 * 0.0000 -0.0000 3.1358

dy = 3×1

1.0e+12 * 0.0000 -0.0000 3.2355

dy = 3×1

1.0e+12 * 0.0000 -0.0000 3.7902

dy = 3×1

1.0e+12 * 0.0000 -0.0000 3.9116

dy = 3×1

1.0e+12 * 0.0000 -0.0000 4.0582

dy = 3×1

1.0e+12 * 0.0000 -0.0000 4.0465

dy = 3×1

1.0e+12 * 0.0000 -0.0000 5.1635

dy = 3×1

1.0e+12 * 0.0000 -0.0000 6.1409

dy = 3×1

1.0e+13 * 0.0000 -0.0000 1.6984

dy = 3×1

1.0e+13 * 0.0000 -0.0000 2.0257

dy = 3×1

1.0e+13 * 0.0000 -0.0000 2.8300

dy = 3×1

1.0e+13 * 0.0000 -0.0000 3.2279

dy = 3×1

1.0e+12 * 0.0000 -0.0000 4.7718

dy = 3×1

1.0e+12 * 0.0000 -0.0000 5.3049

dy = 3×1

1.0e+12 * 0.0000 -0.0000 9.4622

dy = 3×1

1.0e+13 * 0.0000 -0.0000 1.0814

dy = 3×1

1.0e+13 * 0.0000 -0.0000 1.2513

dy = 3×1

1.0e+13 * 0.0000 -0.0000 1.2378

dy = 3×1

1.0e+13 * 0.0000 -0.0000 1.6505

dy = 3×1

1.0e+13 * 0.0000 -0.0000 2.0477

dy = 3×1

1.0e+13 * 0.0000 -0.0000 7.6236

dy = 3×1

1.0e+13 * 0.0000 -0.0000 8.6078

dy = 3×1

1.0e+14 * 0.0000 -0.0000 1.5725

dy = 3×1

1.0e+14 * 0.0000 -0.0000 2.3260

dy = 3×1

1.0e+13 * 0.0000 -0.0000 1.4281

dy = 3×1

1.0e+13 * 0.0000 -0.0000 1.5612

dy = 3×1

1.0e+13 * 0.0000 -0.0000 2.5171

dy = 3×1

1.0e+13 * 0.0000 -0.0000 2.8118

dy = 3×1

1.0e+13 * 0.0000 -0.0000 3.1613

dy = 3×1

1.0e+13 * 0.0000 -0.0000 3.1124

dy = 3×1

1.0e+13 * 0.0000 -0.0000 3.9049

dy = 3×1

1.0e+13 * 0.0000 -0.0000 4.5733

dy = 3×1

1.0e+14 * 0.0000 -0.0000 1.1392

dy = 3×1

1.0e+14 * 0.0000 -0.0000 1.3598

dy = 3×1

1.0e+14 * 0.0000 -0.0000 1.7890

dy = 3×1

1.0e+14 * 0.0000 -0.0000 1.9285

dy = 3×1

1.0e+13 * 0.0000 -0.0000 3.6942

dy = 3×1

1.0e+13 * 0.0000 -0.0000 4.1282

dy = 3×1

1.0e+13 * 0.0000 -0.0000 7.5991

dy = 3×1

1.0e+13 * 0.0000 -0.0000 8.7411

dy = 3×1

1.0e+14 * 0.0000 -0.0000 1.0210

dy = 3×1

1.0e+14 * 0.0000 -0.0000 1.0131

dy = 3×1

1.0e+14 * 0.0000 -0.0000 1.3782

dy = 3×1

1.0e+14 * 0.0000 -0.0000 1.7453

dy = 3×1

1.0e+14 * 0.0000 -0.0000 7.5366

dy = 3×1

1.0e+14 * 0.0000 -0.0000 7.9708

dy = 3×1

1.0e+15 * 0.0000 -0.0000 1.8119

dy = 3×1

1.0e+15 * 0.0000 -0.0000 3.2620

dy = 3×1

1.0e+14 * 0.0000 -0.0000 1.1548

dy = 3×1

1.0e+14 * 0.0000 -0.0000 1.2513

dy = 3×1

1.0e+14 * 0.0000 -0.0000 1.9151

dy = 3×1

1.0e+14 * 0.0000 -0.0000 2.1122

dy = 3×1

1.0e+14 * 0.0000 -0.0000 2.3420

dy = 3×1

1.0e+14 * 0.0000 -0.0000 2.3060

dy = 3×1

1.0e+14 * 0.0000 -0.0000 2.8103

dy = 3×1

1.0e+14 * 0.0000 -0.0000 3.2092

dy = 3×1

1.0e+14 * 0.0000 -0.0000 6.7712

dy = 3×1

1.0e+14 * 0.0000 -0.0000 7.9694

dy = 3×1

1.0e+14 * 0.0000 -0.0000 9.7495

dy = 3×1

1.0e+14 * 0.0000 -0.0000 9.9119

dy = 3×1

1.0e+15 * 0.0000 -0.0000 1.4346

dy = 3×1

1.0e+15 * 0.0000 -0.0000 1.9433

dy = 3×1

1.0e+16 * 0.0000 -0.0000 1.4042

dy = 3×1

1.0e+15 * 0.0000 -0.0000 8.1437

dy = 3×1

1.0e+16 * 0.0000 -0.0000 9.6996

dy = 3×1

1.0e+17 * 0.0000 -0.0000 6.6818

dy = 3×1

1.0e+15 * 0.0000 -0.0000 1.0810

dy = 3×1

1.0e+15 * 0.0000 -0.0000 1.1363

dy = 3×1

1.0e+15 * 0.0000 -0.0000 1.4677

dy = 3×1

1.0e+15 * 0.0000 -0.0000 1.5505

dy = 3×1

1.0e+15 * 0.0000 -0.0000 1.6471

dy = 3×1

1.0e+15 * 0.0000 -0.0000 1.6340

dy = 3×1

1.0e+15 * 0.0000 -0.0000 1.8272

dy = 3×1

1.0e+15 * 0.0000 -0.0000 1.9531

dy = 3×1

1.0e+15 * 0.0000 -0.0000 2.7666

dy = 3×1

1.0e+15 * 0.0000 -0.0000 2.9920

dy = 3×1

1.0e+15 * 0.0000 -0.0000 3.2521

dy = 3×1

1.0e+15 * 0.0000 -0.0000 3.2101

dy = 3×1

1.0e+15 * 0.0000 -0.0000 4.2353

dy = 3×1

1.0e+15 * 0.0000 -0.0000 5.2001

dy = 3×1

1.0e+16 * 0.0000 -0.0000 1.7942

dy = 3×1

1.0e+16 * 0.0000 -0.0000 2.0723

dy = 3×1

1.0e+16 * 0.0000 -0.0000 3.4689

dy = 3×1

1.0e+16 * 0.0000 -0.0000 4.7223

dy = 3×1

1.0e+15 * 0.0000 -0.0000 3.7267

dy = 3×1

1.0e+15 * 0.0000 -0.0000 4.0934

dy = 3×1

1.0e+15 * 0.0000 -0.0000 6.7861

dy = 3×1

1.0e+15 * 0.0000 -0.0000 7.6308

dy = 3×1

1.0e+15 * 0.0000 -0.0000 8.6441

dy = 3×1

1.0e+15 * 0.0000 -0.0000 8.5145

dy = 3×1

1.0e+16 * 0.0000 -0.0000 1.0854

dy = 3×1

1.0e+16 * 0.0000 -0.0000 1.2896

dy = 3×1

1.0e+16 * 0.0000 -0.0000 3.5397

dy = 3×1

1.0e+16 * 0.0000 -0.0000 4.2234

dy = 3×1

1.0e+16 * 0.0000 -0.0000 5.8680

dy = 3×1

1.0e+16 * 0.0000 -0.0000 6.6582

dy = 3×1

1.0e+16 * 0.0000 -0.0000 1.0048

dy = 3×1

1.0e+16 * 0.0000 -0.0000 1.1177

dy = 3×1

1.0e+16 * 0.0000 -0.0000 2.0000

dy = 3×1

1.0e+16 * 0.0000 -0.0000 2.2873

dy = 3×1

1.0e+16 * 0.0000 -0.0000 2.6485

dy = 3×1

1.0e+16 * 0.0000 -0.0000 2.6203

dy = 3×1

1.0e+16 * 0.0000 -0.0000 3.4991

dy = 3×1

1.0e+16 * 0.0000 -0.0000 4.3480

dy = 3×1

1.0e+17 * 0.0000 -0.0000 1.6344

dy = 3×1

1.0e+17 * 0.0000 -0.0000 1.8392

dy = 3×1

1.0e+17 * 0.0000 -0.0000 3.3978

dy = 3×1

1.0e+17 * 0.0000 -0.0000 5.0776

dy = 3×1

1.0e+16 * 0.0000 -0.0000 3.0214

dy = 3×1

1.0e+16 * 0.0000 -0.0000 3.3018

dy = 3×1

1.0e+16 * 0.0000 -0.0000 5.3105

dy = 3×1

1.0e+16 * 0.0000 -0.0000 5.9289

dy = 3×1

1.0e+16 * 0.0000 -0.0000 6.6607

dy = 3×1

1.0e+16 * 0.0000 -0.0000 6.5568

dy = 3×1

1.0e+16 * 0.0000 -0.0000 8.2130

dy = 3×1

1.0e+16 * 0.0000 -0.0000 9.6049

dy = 3×1

1.0e+17 * 0.0000 -0.0000 2.3683

dy = 3×1

1.0e+17 * 0.0000 -0.0000 2.8259

dy = 3×1

1.0e+17 * 0.0000 -0.0000 3.6976

dy = 3×1

1.0e+17 * 0.0000 -0.0000 3.9664

dy = 3×1

1.0e+16 * 0.0000 -0.0000 7.7875

dy = 3×1

1.0e+16 * 0.0000 -0.0000 8.7070

dy = 3×1

1.0e+17 * 0.0000 -0.0000 1.6076

dy = 3×1

1.0e+17 * 0.0000 -0.0000 1.8504

dy = 3×1

1.0e+17 * 0.0000 -0.0000 2.1631

dy = 3×1

1.0e+17 * 0.0000 -0.0000 2.1467

dy = 3×1

1.0e+17 * 0.0000 -0.0000 2.9253

dy = 3×1

1.0e+17 * 0.0000 -0.0000 3.7107

dy = 3×1

1.0e+18 * 0.0000 -0.0000 1.6210

dy = 3×1

1.0e+18 * 0.0000 -0.0000 1.7034

dy = 3×1

1.0e+18 * 0.0000 -0.0000 3.9486

dy = 3×1

1.0e+18 * 0.0000 -0.0000 7.2274

dy = 3×1

1.0e+17 * 0.0000 -0.0000 2.4451

dy = 3×1

1.0e+17 * 0.0000 -0.0000 2.6479

dy = 3×1

1.0e+17 * 0.0000 -0.0000 4.0392

dy = 3×1

1.0e+17 * 0.0000 -0.0000 4.4513

dy = 3×1

1.0e+17 * 0.0000 -0.0000 4.9308

dy = 3×1

1.0e+17 * 0.0000 -0.0000 4.8551

dy = 3×1

1.0e+17 * 0.0000 -0.0000 5.9054

dy = 3×1

1.0e+17 * 0.0000 -0.0000 6.7328

dy = 3×1

1.0e+18 * 0.0000 -0.0000 1.4056

dy = 3×1

1.0e+18 * 0.0000 -0.0000 1.6519

dy = 3×1

1.0e+18 * 0.0000 -0.0000 2.0126

dy = 3×1

1.0e+18 * 0.0000 -0.0000 2.0406

dy = 3×1

1.0e+18 * 0.0000 -0.0000 2.9435

dy = 3×1

1.0e+18 * 0.0000 -0.0000 3.9720

dy = 3×1

1.0e+19 * 0.0000 -0.0000 2.7801

dy = 3×1

1.0e+19 * 0.0000 -0.0000 1.7214

dy = 3×1

1.0e+20 * 0.0000 -0.0000 1.7343

dy = 3×1

1.0e+21 * 0.0000 -0.0000 1.0330

dy = 3×1

1.0e+18 * 0.0000 -0.0000 2.2327

dy = 3×1

1.0e+18 * 0.0000 -0.0000 2.3518

dy = 3×1

1.0e+18 * 0.0000 -0.0000 3.0727

dy = 3×1

1.0e+18 * 0.0000 -0.0000 3.2552

dy = 3×1

1.0e+18 * 0.0000 -0.0000 3.4677

dy = 3×1

1.0e+18 * 0.0000 -0.0000 3.4377

dy = 3×1

1.0e+18 * 0.0000 -0.0000 3.8650

dy = 3×1

1.0e+18 * 0.0000 -0.0000 4.1469

dy = 3×1

1.0e+18 * 0.0000 -0.0000 5.9999

dy = 3×1

1.0e+18 * 0.0000 -0.0000 6.5238

dy = 3×1

1.0e+18 * 0.0000 -0.0000 7.1289

dy = 3×1

1.0e+18 * 0.0000 -0.0000 7.0303

dy = 3×1

1.0e+18 * 0.0000 -0.0000 9.3110

dy = 3×1

1.0e+19 * 0.0000 -0.0000 1.1475

dy = 3×1

1.0e+19 * 0.0000 -0.0000 4.0648

dy = 3×1

1.0e+19 * 0.0000 -0.0000 4.6615

dy = 3×1

1.0e+19 * 0.0000 -0.0000 8.0253

dy = 3×1

1.0e+20 * 0.0000 -0.0000 1.1222

dy = 3×1

1.0e+18 * 0.0000 -0.0000 8.1455

dy = 3×1

1.0e+18 * 0.0000 -0.0000 8.9336

dy = 3×1

1.0e+19 * 0.0000 -0.0000 1.4677

dy = 3×1

1.0e+19 * 0.0000 -0.0000 1.6470

dy = 3×1

1.0e+19 * 0.0000 -0.0000 1.8609

dy = 3×1

1.0e+19 * 0.0000 -0.0000 1.8325

dy = 3×1

1.0e+19 * 0.0000 -0.0000 2.3235

dy = 3×1

1.0e+19 * 0.0000 -0.0000 2.7473

dy = 3×1

1.0e+19 * 0.0000 -0.0000 7.2922

dy = 3×1

1.0e+19 * 0.0000 -0.0000 8.7089

dy = 3×1

1.0e+20 * 0.0000 -0.0000 1.1856

dy = 3×1

1.0e+20 * 0.0000 -0.0000 1.3194

dy = 3×1

1.0e+19 * 0.0000 -0.0000 2.1672

dy = 3×1

1.0e+19 * 0.0000 -0.0000 2.4148

dy = 3×1

1.0e+19 * 0.0000 -0.0000 4.3653

dy = 3×1

1.0e+19 * 0.0000 -0.0000 5.0032

dy = 3×1

1.0e+19 * 0.0000 -0.0000 5.8108

dy = 3×1

1.0e+19 * 0.0000 -0.0000 5.7540

dy = 3×1

1.0e+19 * 0.0000 -0.0000 7.7334

dy = 3×1

1.0e+19 * 0.0000 -0.0000 9.6720

dy = 3×1

1.0e+20 * 0.0000 -0.0000 3.8090

dy = 3×1

1.0e+20 * 0.0000 -0.0000 4.2104

dy = 3×1

1.0e+20 * 0.0000 -0.0000 8.2770

dy = 3×1

1.0e+21 * 0.0000 -0.0000 1.3095

dy = 3×1

1.0e+19 * 0.0000 -0.0000 6.6101

dy = 3×1

1.0e+19 * 0.0000 -0.0000 7.2036

dy = 3×1

1.0e+20 * 0.0000 -0.0000 1.1398

dy = 3×1

1.0e+20 * 0.0000 -0.0000 1.2675

dy = 3×1

1.0e+20 * 0.0000 -0.0000 1.4177

dy = 3×1

1.0e+20 * 0.0000 -0.0000 1.3954

dy = 3×1

1.0e+20 * 0.0000 -0.0000 1.7318

dy = 3×1

1.0e+20 * 0.0000 -0.0000 2.0088

dy = 3×1

1.0e+20 * 0.0000 -0.0000 4.6908

dy = 3×1

1.0e+20 * 0.0000 -0.0000 5.5799

dy = 3×1

1.0e+20 * 0.0000 -0.0000 7.1149

dy = 3×1

1.0e+20 * 0.0000 -0.0000 7.4637

dy = 3×1

1.0e+21 * 0.0000 -0.0000 1.1126

dy = 3×1

1.0e+21 * 0.0000 -0.0000 1.5599

dy = 3×1

1.0e+22 * 0.0000 -0.0000 1.4874

dy = 3×1

1.0e+21 * 0.0000 -0.0000 3.2511

dy = 3×1

1.0e+23 * 0.0000 -0.0000 4.1664

dy = 3×1

1.0e+26 * 0.0000 -0.0000 -3.1817

dy = 3×1

1.0e+20 * 0.0000 -0.0000 7.7879

dy = 3×1

1.0e+20 * 0.0000 -0.0000 7.9676

dy = 3×1

1.0e+20 * 0.0000 -0.0000 8.9353

dy = 3×1

1.0e+20 * 0.0000 -0.0000 9.1340

dy = 3×1

1.0e+20 * 0.0000 -0.0000 9.3784

dy = 3×1

1.0e+20 * 0.0000 -0.0000 9.3660

dy = 3×1

1.0e+20 * 0.0000 -0.0000 9.8241

dy = 3×1

1.0e+21 * 0.0000 -0.0000 1.0081

dy = 3×1

1.0e+21 * 0.0000 -0.0000 1.1481

dy = 3×1

1.0e+21 * 0.0000 -0.0000 1.1775

dy = 3×1

1.0e+21 * 0.0000 -0.0000 1.2134

dy = 3×1

1.0e+21 * 0.0000 -0.0000 1.2113

dy = 3×1

1.0e+21 * 0.0000 -0.0000 1.5367

dy = 3×1

1.0e+21 * 0.0000 -0.0000 1.8180

dy = 3×1

1.0e+21 * 0.0000 -0.0000 4.8434

dy = 3×1

1.0e+21 * 0.0000 -0.0000 5.7839

dy = 3×1

1.0e+21 * 0.0000 -0.0000 7.8912

dy = 3×1

1.0e+21 * 0.0000 -0.0000 8.7992

dy = 3×1

1.0e+21 * 0.0000 -0.0000 1.4321

dy = 3×1

1.0e+21 * 0.0000 -0.0000 1.5955

dy = 3×1

1.0e+21 * 0.0000 -0.0000 2.8811

dy = 3×1

1.0e+21 * 0.0000 -0.0000 3.3013

dy = 3×1

1.0e+21 * 0.0000 -0.0000 3.8329

dy = 3×1

1.0e+21 * 0.0000 -0.0000 3.7951

dy = 3×1

1.0e+21 * 0.0000 -0.0000 5.0969

dy = 3×1

1.0e+21 * 0.0000 -0.0000 6.3700

dy = 3×1

1.0e+22 * 0.0000 -0.0000 2.4953

dy = 3×1

1.0e+22 * 0.0000 -0.0000 2.7643

dy = 3×1

1.0e+22 * 0.0000 -0.0000 5.3937

dy = 3×1

1.0e+22 * 0.0000 -0.0000 8.4751

dy = 3×1

1.0e+21 * 0.0000 -0.0000 4.3617

dy = 3×1

1.0e+21 * 0.0000 -0.0000 4.7548

dy = 3×1

1.0e+21 * 0.0000 -0.0000 7.5381

dy = 3×1

1.0e+21 * 0.0000 -0.0000 8.3866

dy = 3×1

1.0e+21 * 0.0000 -0.0000 9.3849

dy = 3×1

1.0e+21 * 0.0000 -0.0000 9.2375

dy = 3×1

1.0e+22 * 0.0000 -0.0000 1.1476

dy = 3×1

1.0e+22 * 0.0000 -0.0000 1.3324

dy = 3×1

1.0e+22 * 0.0000 -0.0000 3.1307

dy = 3×1

1.0e+22 * 0.0000 -0.0000 3.7258

dy = 3×1

1.0e+22 * 0.0000 -0.0000 4.7639

dy = 3×1

1.0e+22 * 0.0000 -0.0000 5.0090

dy = 3×1

1.0e+22 * 0.0000 -0.0000 1.1000

dy = 3×1

1.0e+22 * 0.0000 -0.0000 1.2325

dy = 3×1

1.0e+22 * 0.0000 -0.0000 2.3056

dy = 3×1

1.0e+22 * 0.0000 -0.0000 2.6606

dy = 3×1

1.0e+22 * 0.0000 -0.0000 3.1227

dy = 3×1

1.0e+22 * 0.0000 -0.0000 3.1039

dy = 3×1

1.0e+22 * 0.0000 -0.0000 4.2658

dy = 3×1

1.0e+22 * 0.0000 -0.0000 5.4597

dy = 3×1

1.0e+23 * 0.0000 -0.0000 2.5473

dy = 3×1

1.0e+23 * 0.0000 -0.0000 2.5694

dy = 3×1

1.0e+23 * 0.0000 -0.0000 6.7561

dy = 3×1

1.0e+24 * 0.0000 -0.0000 1.3757

dy = 3×1

1.0e+22 * 0.0000 -0.0000 3.5162

dy = 3×1

1.0e+22 * 0.0000 -0.0000 3.7930

dy = 3×1

1.0e+22 * 0.0000 -0.0000 5.6578

dy = 3×1

1.0e+22 * 0.0000 -0.0000 6.1998

dy = 3×1

1.0e+22 * 0.0000 -0.0000 6.8278

dy = 3×1

1.0e+22 * 0.0000 -0.0000 6.7264

dy = 3×1

1.0e+22 * 0.0000 -0.0000 8.0835

dy = 3×1

1.0e+22 * 0.0000 -0.0000 9.1245

dy = 3×1

1.0e+23 * 0.0000 -0.0000 1.7877

dy = 3×1

1.0e+23 * 0.0000 -0.0000 2.0803

dy = 3×1

1.0e+23 * 0.0000 -0.0000 2.4785

dy = 3×1

1.0e+23 * 0.0000 -0.0000 2.4806

dy = 3×1

1.0e+23 * 0.0000 -0.0000 3.5171

dy = 3×1

1.0e+23 * 0.0000 -0.0000 4.6553

dy = 3×1

1.0e+24 * 0.0000 -0.0000 2.8022

dy = 3×1

1.0e+24 * 0.0000 -0.0000 2.2115

dy = 3×1

1.0e+25 * 0.0000 -0.0000 1.1728

dy = 3×1

1.0e+25 * 0.0000 -0.0000 4.1710

dy = 3×1

1.0e+23 * 0.0000 -0.0000 2.7510

dy = 3×1

1.0e+23 * 0.0000 -0.0000 2.9239

dy = 3×1

1.0e+23 * 0.0000 -0.0000 4.0127

dy = 3×1

1.0e+23 * 0.0000 -0.0000 4.3045

dy = 3×1

1.0e+23 * 0.0000 -0.0000 4.6416

dy = 3×1

1.0e+23 * 0.0000 -0.0000 4.5887

dy = 3×1

1.0e+23 * 0.0000 -0.0000 5.2840

dy = 3×1

1.0e+23 * 0.0000 -0.0000 5.7685

dy = 3×1

1.0e+23 * 0.0000 -0.0000 9.2220

dy = 3×1

1.0e+24 * 0.0000 -0.0000 1.0281

dy = 3×1

1.0e+24 * 0.0000 -0.0000 1.1531

dy = 3×1

1.0e+24 * 0.0000 -0.0000 1.1350

dy = 3×1

1.0e+24 * 0.0000 -0.0000 1.5339

dy = 3×1

1.0e+24 * 0.0000 -0.0000 1.9293

dy = 3×1

1.0e+24 * 0.0000 -0.0000 7.9167

dy = 3×1

1.0e+24 * 0.0000 -0.0000 8.5932

dy = 3×1

1.0e+25 * 0.0000 -0.0000 1.7949

dy = 3×1

1.0e+25 * 0.0000 -0.0000 2.9986

dy = 3×1

1.0e+24 * 0.0000 -0.0000 1.2995

dy = 3×1

1.0e+24 * 0.0000 -0.0000 1.4127

dy = 3×1

1.0e+24 * 0.0000 -0.0000 2.2032

dy = 3×1

1.0e+24 * 0.0000 -0.0000 2.4413

dy = 3×1

1.0e+24 * 0.0000 -0.0000 2.7200

dy = 3×1

1.0e+24 * 0.0000 -0.0000 2.6774

dy = 3×1

1.0e+24 * 0.0000 -0.0000 3.2961

dy = 3×1

1.0e+24 * 0.0000 -0.0000 3.7967

dy = 3×1

1.0e+24 * 0.0000 -0.0000 8.4685

dy = 3×1

1.0e+25 * 0.0000 -0.0000 1.0033

dy = 3×1

1.0e+25 * 0.0000 -0.0000 1.2543

dy = 3×1

1.0e+25 * 0.0000 -0.0000 1.2951

dy = 3×1

1.0e+25 * 0.0000 -0.0000 1.9038

dy = 3×1

1.0e+25 * 0.0000 -0.0000 2.6255

dy = 3×1

1.0e+26 * 0.0000 -0.0000 2.1857

dy = 3×1

1.0e+25 * 0.0000 -0.0000 8.6769

dy = 3×1

1.0e+27 * 0.0000 -0.0000 2.6224

dy = 3×1

1.0e+28 * 0.0000 -0.0000 4.5250

dy = 3×1

1.0e+25 * 0.0000 -0.0000 1.3898

dy = 3×1

1.0e+25 * 0.0000 -0.0000 1.4458

dy = 3×1

1.0e+25 * 0.0000 -0.0000 1.7678

dy = 3×1

1.0e+25 * 0.0000 -0.0000 1.8426

dy = 3×1

1.0e+25 * 0.0000 -0.0000 1.9315

dy = 3×1

1.0e+25 * 0.0000 -0.0000 1.9219

dy = 3×1

1.0e+25 * 0.0000 -0.0000 2.0949

dy = 3×1

1.0e+25 * 0.0000 -0.0000 2.2012

dy = 3×1

1.0e+25 * 0.0000 -0.0000 2.8376

dy = 3×1

1.0e+25 * 0.0000 -0.0000 2.9961

dy = 3×1

1.0e+25 * 0.0000 -0.0000 3.1812

dy = 3×1

1.0e+25 * 0.0000 -0.0000 3.1561

dy = 3×1

1.0e+25 * 0.0000 -0.0000 4.0906

dy = 3×1

1.0e+25 * 0.0000 -0.0000 4.9368

dy = 3×1

1.0e+26 * 0.0000 -0.0000 1.5084

dy = 3×1

1.0e+26 * 0.0000 -0.0000 1.7832

dy = 3×1

1.0e+26 * 0.0000 -0.0000 2.6713

dy = 3×1

1.0e+26 * 0.0000 -0.0000 3.2631

dy = 3×1

1.0e+25 * 0.0000 -0.0000 3.6978

dy = 3×1

1.0e+25 * 0.0000 -0.0000 4.0904

dy = 3×1

1.0e+25 * 0.0000 -0.0000 7.0731

dy = 3×1

1.0e+25 * 0.0000 -0.0000 8.0303

dy = 3×1

1.0e+25 * 0.0000 -0.0000 9.2050

dy = 3×1

1.0e+25 * 0.0000 -0.0000 9.0836

dy = 3×1

1.0e+26 * 0.0000 -0.0000 1.1873

dy = 3×1

1.0e+26 * 0.0000 -0.0000 1.4446

dy = 3×1

1.0e+26 * 0.0000 -0.0000 4.6715

dy = 3×1

1.0e+26 * 0.0000 -0.0000 5.4728

dy = 3×1

1.0e+26 * 0.0000 -0.0000 8.6008

dy = 3×1

1.0e+27 * 0.0000 -0.0000 1.1012

dy = 3×1

1.0e+26 * 0.0000 -0.0000 1.0599

dy = 3×1

1.0e+26 * 0.0000 -0.0000 1.1687

dy = 3×1

1.0e+26 * 0.0000 -0.0000 1.9824

dy = 3×1

1.0e+26 * 0.0000 -0.0000 2.2410

dy = 3×1

1.0e+26 * 0.0000 -0.0000 2.5548

dy = 3×1

1.0e+26 * 0.0000 -0.0000 2.5185

dy = 3×1

1.0e+26 * 0.0000 -0.0000 3.2539

dy = 3×1

1.0e+26 * 0.0000 -0.0000 3.9152

dy = 3×1

1.0e+27 * 0.0000 -0.0000 1.1715

dy = 3×1

1.0e+27 * 0.0000 -0.0000 1.3885

dy = 3×1

1.0e+27 * 0.0000 -0.0000 2.0468

dy = 3×1

1.0e+27 * 0.0000 -0.0000 2.4608

dy = 3×1

1.0e+26 * 0.0000 -0.0000 2.9551

dy = 3×1

1.0e+26 * 0.0000 -0.0000 3.2726

dy = 3×1

1.0e+26 * 0.0000 -0.0000 5.6983

dy = 3×1

1.0e+26 * 0.0000 -0.0000 6.4793

dy = 3×1

1.0e+26 * 0.0000 -0.0000 7.4419

dy = 3×1

1.0e+26 * 0.0000 -0.0000 7.3470

dy = 3×1

1.0e+26 * 0.0000 -0.0000 9.6440

dy = 3×1

1.0e+27 * 0.0000 -0.0000 1.1782

dy = 3×1

1.0e+27 * 0.0000 -0.0000 3.9221

dy = 3×1

1.0e+27 * 0.0000 -0.0000 4.5681

dy = 3×1

1.0e+27 * 0.0000 -0.0000 7.3751

dy = 3×1

1.0e+27 * 0.0000 -0.0000 9.6944

dy = 3×1

1.0e+26 * 0.0000 -0.0000 8.5537

dy = 3×1

1.0e+26 * 0.0000 -0.0000 9.4159

dy = 3×1

1.0e+27 * 0.0000 -0.0000 1.5813

dy = 3×1

1.0e+27 * 0.0000 -0.0000 1.7835

dy = 3×1

1.0e+27 * 0.0000 -0.0000 2.0275

dy = 3×1

1.0e+27 * 0.0000 -0.0000 1.9979

dy = 3×1

1.0e+27 * 0.0000 -0.0000 2.5658

dy = 3×1

1.0e+27 * 0.0000 -0.0000 3.0700

dy = 3×1

1.0e+27 * 0.0000 -0.0000 8.8361

dy = 3×1

1.0e+28 * 0.0000 -0.0000 1.0512

dy = 3×1

1.0e+28 * 0.0000 -0.0000 1.5066

dy = 3×1

1.0e+28 * 0.0000 -0.0000 1.7621

dy = 3×1

1.0e+27 * 0.0000 -0.0000 2.3504

dy = 3×1

1.0e+27 * 0.0000 -0.0000 2.6083

dy = 3×1

1.0e+27 * 0.0000 -0.0000 4.5992

dy = 3×1

1.0e+27 * 0.0000 -0.0000 5.2438

dy = 3×1

1.0e+27 * 0.0000 -0.0000 6.0450

dy = 3×1

1.0e+27 * 0.0000 -0.0000 5.9731

dy = 3×1

1.0e+27 * 0.0000 -0.0000 7.9021

dy = 3×1

1.0e+27 * 0.0000 -0.0000 9.7279

dy = 3×1

1.0e+28 * 0.0000 -0.0000 3.4188

dy = 3×1

1.0e+28 * 0.0000 -0.0000 3.9293

dy = 3×1

1.0e+28 * 0.0000 -0.0000 6.7056

dy = 3×1

1.0e+28 * 0.0000 -0.0000 9.2984

dy = 3×1

1.0e+27 * 0.0000 -0.0000 6.9251

dy = 3×1

1.0e+27 * 0.0000 -0.0000 7.5988

dy = 3×1

1.0e+28 * 0.0000 -0.0000 1.2521

dy = 3×1

1.0e+28 * 0.0000 -0.0000 1.4059

dy = 3×1

1.0e+28 * 0.0000 -0.0000 1.5899

dy = 3×1

1.0e+28 * 0.0000 -0.0000 1.5657

dy = 3×1

1.0e+28 * 0.0000 -0.0000 1.9884

dy = 3×1

1.0e+28 * 0.0000 -0.0000 2.3547

dy = 3×1

1.0e+28 * 0.0000 -0.0000 6.3143

dy = 3×1

1.0e+28 * 0.0000 -0.0000 7.5395

dy = 3×1

1.0e+29 * 0.0000 -0.0000 1.0326

dy = 3×1

1.0e+29 * 0.0000 -0.0000 1.1556

dy = 3×1

1.0e+28 * 0.0000 -0.0000 1.8504

dy = 3×1

1.0e+28 * 0.0000 -0.0000 2.0608

dy = 3×1

1.0e+28 * 0.0000 -0.0000 3.7143

dy = 3×1

1.0e+28 * 0.0000 -0.0000 4.2544

dy = 3×1

1.0e+28 * 0.0000 -0.0000 4.9365

dy = 3×1

1.0e+28 * 0.0000 -0.0000 4.8868

dy = 3×1

1.0e+28 * 0.0000 -0.0000 6.5549

dy = 3×1

1.0e+28 * 0.0000 -0.0000 8.1818

dy = 3×1

1.0e+29 * 0.0000 -0.0000 3.1755

dy = 3×1

1.0e+29 * 0.0000 -0.0000 3.5309

dy = 3×1

1.0e+29 * 0.0000 -0.0000 6.8018

dy = 3×1

1.0e+30 * 0.0000 -0.0000 1.0563

dy = 3×1

1.0e+28 * 0.0000 -0.0000 5.6207

dy = 3×1

1.0e+28 * 0.0000 -0.0000 6.1308

dy = 3×1

1.0e+28 * 0.0000 -0.0000 9.7519

dy = 3×1

1.0e+29 * 0.0000 -0.0000 1.0858

dy = 3×1

1.0e+29 * 0.0000 -0.0000 1.2162

dy = 3×1

1.0e+29 * 0.0000 -0.0000 1.1971

dy = 3×1

1.0e+29 * 0.0000 -0.0000 1.4900

dy = 3×1

1.0e+29 * 0.0000 -0.0000 1.7328

dy = 3×1

1.0e+29 * 0.0000 -0.0000 4.1154

dy = 3×1

1.0e+29 * 0.0000 -0.0000 4.9012

dy = 3×1

1.0e+29 * 0.0000 -0.0000 6.2979

dy = 3×1

1.0e+29 * 0.0000 -0.0000 6.6498

dy = 3×1

1.0e+29 * 0.0000 -0.0000 1.4247

dy = 3×1

1.0e+29 * 0.0000 -0.0000 1.5956

dy = 3×1

1.0e+29 * 0.0000 -0.0000 2.9761

dy = 3×1

1.0e+29 * 0.0000 -0.0000 3.4323

dy = 3×1

1.0e+29 * 0.0000 -0.0000 4.0248

dy = 3×1

1.0e+29 * 0.0000 -0.0000 3.9991

dy = 3×1

1.0e+29 * 0.0000 -0.0000 5.4856

dy = 3×1

1.0e+29 * 0.0000 -0.0000 7.0065

dy = 3×1

1.0e+30 * 0.0000 -0.0000 3.2197

dy = 3×1

1.0e+30 * 0.0000 -0.0000 3.2806

dy = 3×1

1.0e+30 * 0.0000 -0.0000 8.3641

dy = 3×1

1.0e+31 * 0.0000 -0.0000 1.6597

dy = 3×1

1.0e+29 * 0.0000 -0.0000 4.5361

dy = 3×1

1.0e+29 * 0.0000 -0.0000 4.8976

dy = 3×1

1.0e+29 * 0.0000 -0.0000 7.3437

dy = 3×1

1.0e+29 * 0.0000 -0.0000 8.0579

dy = 3×1

1.0e+29 * 0.0000 -0.0000 8.8860

dy = 3×1

1.0e+29 * 0.0000 -0.0000 8.7527

dy = 3×1

1.0e+30 * 0.0000 -0.0000 1.0548

dy = 3×1

1.0e+30 * 0.0000 -0.0000 1.1933

dy = 3×1

1.0e+30 * 0.0000 -0.0000 2.3717

dy = 3×1

1.0e+30 * 0.0000 -0.0000 2.7666

dy = 3×1

1.0e+30 * 0.0000 -0.0000 3.3122

dy = 3×1

1.0e+30 * 0.0000 -0.0000 3.3234

dy = 3×1

1.0e+30 * 0.0000 -0.0000 4.7296

dy = 3×1

1.0e+30 * 0.0000 -0.0000 6.2860

dy = 3×1

1.0e+31 * 0.0000 -0.0000 3.9058

dy = 3×1

1.0e+31 * 0.0000 -0.0000 2.9517

dy = 3×1

1.0e+32 * 0.0000 -0.0000 1.7608

dy = 3×1

1.0e+32 * 0.0000 -0.0000 6.8662

dy = 3×1

1.0e+30 * 0.0000 -0.0000 3.6757

dy = 3×1

1.0e+30 * 0.0000 -0.0000 3.8996

dy = 3×1

1.0e+30 * 0.0000 -0.0000 5.2977

dy = 3×1

1.0e+30 * 0.0000 -0.0000 5.6683

dy = 3×1

1.0e+30 * 0.0000 -0.0000 6.0968

dy = 3×1

1.0e+30 * 0.0000 -0.0000 6.0307

dy = 3×1

1.0e+30 * 0.0000 -0.0000 6.9098

dy = 3×1

1.0e+30 * 0.0000 -0.0000 7.5155

dy = 3×1

1.0e+31 * 0.0000 -0.0000 1.1757

dy = 3×1

1.0e+31 * 0.0000 -0.0000 1.3038

dy = 3×1

1.0e+31 * 0.0000 -0.0000 1.4539

dy = 3×1

1.0e+31 * 0.0000 -0.0000 1.4311

dy = 3×1

1.0e+31 * 0.0000 -0.0000 1.9251

dy = 3×1

1.0e+31 * 0.0000 -0.0000 2.4099

dy = 3×1

1.0e+31 * 0.0000 -0.0000 9.5541

dy = 3×1

1.0e+32 * 0.0000 -0.0000 1.0531

dy = 3×1

1.0e+32 * 0.0000 -0.0000 2.0898

dy = 3×1

1.0e+32 * 0.0000 -0.0000 3.3345

dy = 3×1

1.0e+31 * 0.0000 -0.0000 1.6431

dy = 3×1

1.0e+31 * 0.0000 -0.0000 1.7899

dy = 3×1

1.0e+31 * 0.0000 -0.0000 2.8257

dy = 3×1

1.0e+31 * 0.0000 -0.0000 3.1405

dy = 3×1

1.0e+31 * 0.0000 -0.0000 3.5103

dy = 3×1

1.0e+31 * 0.0000 -0.0000 3.4553

dy = 3×1

1.0e+31 * 0.0000 -0.0000 4.2826

dy = 3×1

1.0e+31 * 0.0000 -0.0000 4.9619

dy = 3×1

1.0e+32 * 0.0000 -0.0000 1.1500

dy = 3×1

1.0e+32 * 0.0000 -0.0000 1.3672

dy = 3×1

1.0e+32 * 0.0000 -0.0000 1.7374

dy = 3×1

1.0e+32 * 0.0000 -0.0000 1.8177

dy = 3×1

1.0e+32 * 0.0000 -0.0000 2.7025

dy = 3×1

1.0e+32 * 0.0000 -0.0000 3.7773

dy = 3×1

1.0e+33 * 0.0000 -0.0000 3.5095

dy = 3×1

1.0e+32 * 0.0000 -0.0000 8.8409

dy = 3×1

1.0e+34 * 0.0000 -0.0000 7.9783

dy = 3×1

1.0e+37 * 0.0000 -0.0000 1.0949

dy = 3×1

1.0e+32 * 0.0000 -0.0000 1.9034

dy = 3×1

1.0e+32 * 0.0000 -0.0000 1.9513

dy = 3×1

1.0e+32 * 0.0000 -0.0000 2.2113

dy = 3×1

1.0e+32 * 0.0000 -0.0000 2.2655

dy = 3×1

1.0e+32 * 0.0000 -0.0000 2.3319

dy = 3×1

1.0e+32 * 0.0000 -0.0000 2.3280

dy = 3×1

1.0e+32 * 0.0000 -0.0000 2.4530

dy = 3×1

1.0e+32 * 0.0000 -0.0000 2.5239

dy = 3×1

1.0e+32 * 0.0000 -0.0000 2.9138

dy = 3×1

1.0e+32 * 0.0000 -0.0000 2.9974

dy = 3×1

1.0e+32 * 0.0000 -0.0000 3.0989

dy = 3×1

1.0e+32 * 0.0000 -0.0000 3.0917

dy = 3×1

1.0e+32 * 0.0000 -0.0000 3.9161

dy = 3×1

1.0e+32 * 0.0000 -0.0000 4.6261

dy = 3×1

1.0e+33 * 0.0000 -0.0000 1.2202

dy = 3×1

1.0e+33 * 0.0000 -0.0000 1.4573

dy = 3×1

1.0e+33 * 0.0000 -0.0000 1.9768

dy = 3×1

1.0e+33 * 0.0000 -0.0000 2.1913

dy = 3×1

1.0e+32 * 0.0000 -0.0000 3.6586

dy = 3×1

1.0e+32 * 0.0000 -0.0000 4.0786

dy = 3×1

1.0e+32 * 0.0000 -0.0000 7.3956

dy = 3×1

1.0e+32 * 0.0000 -0.0000 8.4816

dy = 3×1

1.0e+32 * 0.0000 -0.0000 9.8595

dy = 3×1

1.0e+32 * 0.0000 -0.0000 9.7657

dy = 3×1

1.0e+33 * 0.0000 -0.0000 1.3150

dy = 3×1

1.0e+33 * 0.0000 -0.0000 1.6479

dy = 3×1

1.0e+33 * 0.0000 -0.0000 6.5811

dy = 3×1

1.0e+33 * 0.0000 -0.0000 7.2315

dy = 3×1

1.0e+34 * 0.0000 -0.0000 1.4503

dy = 3×1

1.0e+34 * 0.0000 -0.0000 2.3361

dy = 3×1

1.0e+33 * 0.0000 -0.0000 1.1206

dy = 3×1

1.0e+33 * 0.0000 -0.0000 1.2202

dy = 3×1

1.0e+33 * 0.0000 -0.0000 1.9214

dy = 3×1

1.0e+33 * 0.0000 -0.0000 2.1342

dy = 3×1

1.0e+33 * 0.0000 -0.0000 2.3839

dy = 3×1

1.0e+33 * 0.0000 -0.0000 2.3460

dy = 3×1

1.0e+33 * 0.0000 -0.0000 2.9034

dy = 3×1

1.0e+33 * 0.0000 -0.0000 3.3597

dy = 3×1

1.0e+33 * 0.0000 -0.0000 7.7226

dy = 3×1

1.0e+33 * 0.0000 -0.0000 9.1750

dy = 3×1

1.0e+34 * 0.0000 -0.0000 1.1617

dy = 3×1

1.0e+34 * 0.0000 -0.0000 1.2112

dy = 3×1

1.0e+34 * 0.0000 -0.0000 1.7982

dy = 3×1

1.0e+34 * 0.0000 -0.0000 2.5090

dy = 3×1

1.0e+35 * 0.0000 -0.0000 2.2977

dy = 3×1

1.0e+34 * 0.0000 -0.0000 6.2201

dy = 3×1

1.0e+36 * 0.0000 -0.0000 4.7128

dy = 3×1

1.0e+38 * 0.0000 -0.0000 3.6124

dy = 3×1

1.0e+34 * 0.0000 -0.0000 1.2756

dy = 3×1

1.0e+34 * 0.0000 -0.0000 1.3121

dy = 3×1

1.0e+34 * 0.0000 -0.0000 1.5126

dy = 3×1

1.0e+34 * 0.0000 -0.0000 1.5555

dy = 3×1

1.0e+34 * 0.0000 -0.0000 1.6076

dy = 3×1

1.0e+34 * 0.0000 -0.0000 1.6011

dy = 3×1

1.0e+34 * 0.0000 -0.0000 1.6996

dy = 3×1

1.0e+34 * 0.0000 -0.0000 1.7565

dy = 3×1

1.0e+34 * 0.0000 -0.0000 2.0748

dy = 3×1

1.0e+34 * 0.0000 -0.0000 2.1452

dy = 3×1

1.0e+34 * 0.0000 -0.0000 2.2301

dy = 3×1

1.0e+34 * 0.0000 -0.0000 2.2181

dy = 3×1

1.0e+34 * 0.0000 -0.0000 2.5621

dy = 3×1

1.0e+34 * 0.0000 -0.0000 2.8036

dy = 3×1

1.0e+34 * 0.0000 -0.0000 4.5441

dy = 3×1

1.0e+34 * 0.0000 -0.0000 5.0827

dy = 3×1

1.0e+34 * 0.0000 -0.0000 5.7217

dy = 3×1

1.0e+34 * 0.0000 -0.0000 5.6325

dy = 3×1

1.0e+34 * 0.0000 -0.0000 7.6399

dy = 3×1

1.0e+34 * 0.0000 -0.0000 9.6451

dy = 3×1

1.0e+35 * 0.0000 -0.0000 4.0670

dy = 3×1

1.0e+35 * 0.0000 -0.0000 4.3559

dy = 3×1

1.0e+35 * 0.0000 -0.0000 9.5022

dy = 3×1

1.0e+36 * 0.0000 -0.0000 1.6439

dy = 3×1

1.0e+34 * 0.0000 -0.0000 6.4369

dy = 3×1

1.0e+34 * 0.0000 -0.0000 6.9879

dy = 3×1

1.0e+35 * 0.0000 -0.0000 1.0812

dy = 3×1

1.0e+35 * 0.0000 -0.0000 1.1958

dy = 3×1

1.0e+35 * 0.0000 -0.0000 1.3295

dy = 3×1

1.0e+35 * 0.0000 -0.0000 1.3107

dy = 3×1

1.0e+35 * 0.0000 -0.0000 1.6068

dy = 3×1

1.0e+35 * 0.0000 -0.0000 1.8441

dy = 3×1

1.0e+35 * 0.0000 -0.0000 4.0181

dy = 3×1

1.0e+35 * 0.0000 -0.0000 4.7482

dy = 3×1

1.0e+35 * 0.0000 -0.0000 5.8800

dy = 3×1

1.0e+35 * 0.0000 -0.0000 6.0431

dy = 3×1

1.0e+35 * 0.0000 -0.0000 8.7663

dy = 3×1

1.0e+36 * 0.0000 -0.0000 1.1906

dy = 3×1

1.0e+36 * 0.0000 -0.0000 8.7669

dy = 3×1

1.0e+36 * 0.0000 -0.0000 4.8791

dy = 3×1

1.0e+37 * 0.0000 -0.0000 6.4429

dy = 3×1

1.0e+38 * 0.0000 -0.0000 4.8504

dy = 3×1

1.0e+35 * 0.0000 -0.0000 6.8969

dy = 3×1

1.0e+35 * 0.0000 -0.0000 7.4800

dy = 3×1

1.0e+36 * 0.0000 -0.0000 1.1509

dy = 3×1

1.0e+36 * 0.0000 -0.0000 1.2710

dy = 3×1

1.0e+36 * 0.0000 -0.0000 1.4110

dy = 3×1

1.0e+36 * 0.0000 -0.0000 1.3891

dy = 3×1

1.0e+36 * 0.0000 -0.0000 1.6974

dy = 3×1

1.0e+36 * 0.0000 -0.0000 1.9428

dy = 3×1

1.0e+36 * 0.0000 -0.0000 4.1583

dy = 3×1

1.0e+36 * 0.0000 -0.0000 4.9033

dy = 3×1

1.0e+36 * 0.0000 -0.0000 6.0300

dy = 3×1

1.0e+36 * 0.0000 -0.0000 6.1523

dy = 3×1

1.0e+36 * 0.0000 -0.0000 9.3226

dy = 3×1

1.0e+37 * 0.0000 -0.0000 1.3332

dy = 3×1

1.0e+38 * 0.0000 -0.0000 1.5011

dy = 3×1

1.0e+36 * 0.0000 -0.0000 5.6836

dy = 3×1

1.0e+40 * 0.0000 -0.0000 -1.3114

dy = 
   1.0e+41 *

  -0.0000 + 0.0000i
   0.0000 - 0.0000i
  -2.3797 + 3.2753i

Warning: Failure at t=3.144359e-03. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (6.938894e-18) at time t.

function dy = fun(t,y,p)
epsi = 0.45;
dy = [1/p(4)*(y(1)^p(2)/y(3)^p(2))*(y(3)*(1-p(2)+p(4))-(1-p(2)));
      y(2)*(p(1)-y(2))-epsi*(y(1))^p(2)*(y(3))^(1-p(2)); 
      (y(3)*(1-y(3))*(p(6)-p(2)*(y(3)^(1-p(2))/y(1)^(1-p(2)))+(p(2)*p(5)*(1/p(4)*(y(1)^p(2)/y(3)^p(2))*(y(3)*(1-p(2)+p(4))-(1-p(2))))/y(1))-(p(3)*(1-p(5))*(y(2)*(p(1)-y(2))-epsi*y(1)^p(2)*y(3)^(1-p(2))))/y(2)))/(((p(4)+1)*p(5)-p(4)-p(2)*p(5))*y(3)+p(2)*p(5))]
end

[Francesca Valentini]

The differential equations and the parameters' initial guess are given by the model so i can't change them. What i can change is the matrix of real data, namely xdata, that as things stand has 3 columns of the order of magnitude of 1e4, 1e3, 1e3. If i'm not mistaken, the code itself does not have syntax/conceptual errors but the numerical values that i have used are not compatible with the differential equations of my system, right?

Can it be that the data that i have used is not suitable for my variables and that i should look for data that has smaller order of magnitude? Or the mistake may be elsewhere?

Thanks for the advice on lsqcurvefit and lb/ub, i'll surely take that into consideration.

[Torsten]

I didn't use your data in the test code. I only used your differential equations with initial conditions and the initial guess for the parameters to see how the first step of the optimization would look like. But the integrator already failed for this "introductionary problem".

The initial conditions set as

initialCond = [2000 4000 1800];

look very big. Maybe you didn't get the units correctly ?

[Francesca Valentini]

I have tried to change the dataset I use to calibrate to one that takes into account smaller quantities and so i work with smaller values and smaller initial conditions and it seems to work. Thanks for your help!