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// Copyright INRIA
 
Leps=1.e-6;
 
//     dy1/dt = -0.04*y1 + 1.e4*y2*y3
 
//     dy2/dt =0.04*y1 - 1.e4*y2*y3 - 3.e7*y2**2
 
//     dy3/dt = 3.e7*y2**2
 
// on the interval from t = 0.0 to t = 4.e10, with initial conditions
 
// y1 = 1.0, y2 = y3 = 0.  the problem is stiff.
 
//     definition of rhs
 
deff('[ydot]=f(t,y)',...
   'f1=-0.04*y(1)+1e4*y(2)*y(3),...
    f3=3e7*y(2)*y(2),...
    ydot=[f1;-f1-f3;f3]','n')
 
//     jacobian
 
deff('[jac]=j(t,y)',...
'jac(1,1)=-0.04;jac(1,2)=1.e4*y(3);jac(1,3)=1.e4*y(2),...
 jac(3,1)=0;jac(3,2)=6.e7*y(2);jac(3,3)=0;...
 jac(2,1)=-jac(1,1);jac(2,2)=-jac(1,2)-jac(3,2);jac(2,3)=-jac(1,3);','n')
 
//
 
y0=[1;0;0];t0=0;t1=[0.4,4];nt=size(t1,'*');
 
//    solution
 
yref=[0.9851721 0.9055180;0.0000339 0.0000224;0.0147940 0.0944596];
 
//
 
//  1. fortran called by fydot, without jacobian
 
y1=ode(y0,t0,t1,'fex');
 
if maxi(y1-yref) > Leps then bugmes();quit;end
 
//  2. fortran called by fydot, type given (stiff), no jacobian
 
y2=ode('stiff',y0,t0,t1,'fex');
 
if maxi(y2-yref) > Leps then bugmes();quit;end
 
//  3. fortran called by fydot , fjac, type given
 
y3=ode('stiff',y0,t0,t1,'fex','jex');
 
if maxi(y3-yref) > Leps then bugmes();quit;end
 
//   hot restart
 
[z,w,iw]=ode('stiff',y0,0,0.4,'fex','jex');
 
z=ode('stiff',z,0.4,4,'fex','jex',w,iw);
 
if maxi(z-y3(:,2)) > %eps then bugmes();quit;end
 
 
[y1,w,iw]=ode(y0,t0,t1(1),'fex');
 
y2=ode(y0,t1(1),t1(2:nt),'fex',w,iw);
 
if maxi([y1 y2]-yref) > Leps then bugmes();quit;end
 
 
[y1,w,iw]=ode(y0,t0,t1(1),'fex','jex');
 
y2=ode(y0,t1(1),t1(2:nt),'fex','jex',w,iw);
 
if maxi([y1 y2]-yref) > Leps then bugmes();quit;end
 
 
//   variation of tolerances
 
atol=[0.001,0.0001,0.001];rtol=atol;
 
//    externals
 
//  4. type given , scilab lhs ,jacobian not passed
 
y4=ode('stiff',y0,t0,t1(1),atol,rtol,f);
 
if maxi(y4(:,1)-yref(:,1)) > 0.01 then bugmes();quit;end
 
//  5. type non given, rhs and scilab jacobian
 
y5=ode(y0,t0,t1,f,j);
 
if maxi(y5-yref) > Leps then bugmes();quit;end
 
//  6. type given (stiff),rhs and jacobian  by scilab
 
y6=ode('stiff',y0,t0,t1,0.00001,0.00001,f,j);
 
if (y6-yref) > 2*0.00001 then bugmes();quit;end
 
//  7. matrix rhs, type given(adams),jacobian not passed
 
//
 
a=rand(3,3);ea=expm(a);
 
deff('[ydot]=f(t,y)','ydot=a*y')
Warning :redefining function: f                       
 
 
t1=1;y=ode('adams',eye(a),t0,t1,f);
 
if maxi(ea-y) > Leps then bugmes();quit;end
 
//
 
//   DAE's
 
//     dy1/dt = -0.04*y1 + 1.e4*y2*y3
 
//     dy2/dt =0.04*y1 - 1.e4*y2*y3 - 3.e7*y2**2
 
//       0.   = y1 + y2 + y3 - 1.
 
//  y1(0) = 1.0, y2(0) = y3(0) = 0.
 
// scilab macros
 
deff('[r]=resid(t,y,s)','...
r(1)=-0.04*y(1)+1.d4*y(2)*y(3)-s(1),...
r(2)=0.04*y(1)-1.d4*y(2)*y(3)-3.d7*y(2)*y(2)-s(2),...
r(3)=y(1)+y(2)+y(3)-1')
 
deff('[p]=aplusp(t,y,p)','...
p(1,1)=p(1,1)+1,...
p(2,2)=p(2,2)+1')
 
deff('[p]=dgbydy(t,y,s)','[-0.04,1.d4*y(3),1.d4*y(2);...
0.04,-1.d4*y(3)-6.d7*y(2),-1.d4*y(2);...
1,1,1]')
 
//        %ODEOPTIONS tests
 
//
 
rand('seed',0);rand('normal');
 
nx=20;A=rand(nx,nx);A=A-4.5*eye();
 
deff('y=f(t,x)','y=A*x')
Warning :redefining function: f                       
 
 
deff('J=j(t,x)','J=A')
Warning :redefining function: j                       
 
 
x0=ones(nx,1);t0=0;t=[1,2,3,4,5];
 
nt=size(t,'*');
 
eAt=expm(A*t(nt));
 
 
//        Test itask=%ODEOPTIONS(1)
 
 
//itask=1  --->  usual call (t=vector of instants, solution at all t)
 
//========================
 
itask=1;tcrit=0;h0=0;hmax=0;hmin=0;ixpr=0;mxstep=0;maxordn=0;maxords=0;
 
jacflag=2;ml=-1;mu=-1;
 
%ODEOPTIONS=[itask,tcrit,h0,hmax,hmin,jacflag,mxstep,maxordn,maxords,ixpr,ml,mu];
 
xf=ode(x0,t0,t,f);   //lsoda
 
if norm(xf(:,nt)-eAt*x0)>Leps then bugmes();quit;end
 
xfj=ode(x0,t0,t,f,j);   //lsoda with jacobian
 Warning: Jacobian external is given, but 
 not used!,  see %ODEOPTIONS(6)
 
 
if norm(xfj(:,nt)-eAt*x0)>Leps then bugmes();quit;end
 
 
 
//itask=2;   --->  solution at mesh points  ---> t=tmax
 
//========================
 
%ODEOPTIONS(1)=2;tmax=t(5);
 
xft=ode(x0,t0,tmax,f);
 
[p,q]=size(xft);
 
xlast=xft(2:nx+1,q);
 
if xft(1,q)<tmax then bugmes();quit;end
 
if norm(xlast-expm(A*xft(1,q))*x0)>Leps then bugmes();quit;end
 
 
//itask=3;   ---> solution at first mesh point beyond t=tmax
 
%ODEOPTIONS(1)=3;
 
x3=ode(x0,t0,tmax,f);
 
if norm(x3(2:nx+1)-xlast,1)>Leps then bugmes();quit;end
 
 
//itask=4; test with %ODEOPTIONS(2)=tcrit
 
%ODEOPTIONS(1)=4; //---> computation at all t and t>tcrit are not called
 
tcrit=2.5;%ODEOPTIONS(2)=tcrit;
 
chk=0;
 
deff('y=fcrit(t,x)',['if t<=tcrit then'
                      ' y=A*x;'
                      'else'
                      ' y=A*x;chk=resume(1);end'])
 
x42=ode(x0,t0,t,fcrit);
 Warning: integration up to tcrit
 
 
if chk==1 then bugmes();quit;end
 
[p,q]=size(x42);
 
if norm(x42(:,q)-ode(x0,t0,tcrit,f),1)>Leps then bugmes();quit;end
 
 
//itask=5; test with %ODEOPTIONS(2)=tcrit
 
%ODEOPTIONS(1)=5;  //---> computation at mesh points and t>tcrit are not called
 
%ODEOPTIONS(6)=2;  // Estimated jacobian
 
chk=0;
 
x52=ode(x0,t0,2.3,fcrit);
 
if chk==1 then bugmes();quit;end
 
[p,q]=size(x52);
 
if x52(1,q)>tcrit then bugmes();quit;end
 
 
//test of %ODEOPTIONS(3:5)=[h0,hmax,hmin]
 
%ODEOPTIONS(1)=1;
 
h0=0.0;hmax=0.1;hmin=0.0001;
 
%ODEOPTIONS(3:5)=[h0,hmax,hmin];
 
x35=ode(x0,t0,t,f);
 
if norm(x35-xf,1)>Leps then bugmes();quit;end
 
 
//test of %ODEOPTIONS(6)=jacflag
 
%ODEOPTIONS(6)=1;//Jacobian given
 
%ODEOPTIONS(3:5)=[0 0 0];
 
x61=ode('st',x0,t0,t,f,j);   //with Jacobian
 
if norm(x61-xf,1)>10*Leps then bugmes();quit;end
 
 
 
%ODEOPTIONS(6)=0; // jacobian nor called nor estimated
 
x60=ode('st',x0,t0,t,f,j);   //Jacobian not used (warning)
 Warning: Jacobian external is given, but 
 not used!,  see %ODEOPTIONS(6)
 
 
x60=ode('st',x0,t0,t,f);    //Jacobian not used
 
if norm(x60-x61,1)>10*Leps then bugmes();quit;end
 
 
 
%ODEOPTIONS(6)=1;//Jacobian estimated
 
x60=ode('st',x0,t0,t,f)  ;
 Warning: No Jacobian external given but 
 one is required by %ODEOPTIONS(6) value!
 
 
if norm(x60-x61,1)>10*Leps then bugmes();quit;end
 
 
//test of %ODEOPTIONS(6)=jacflag   (adams)
 
%ODEOPTIONS(6)=1;//with given Jacobian
 
x60=ode('ad',x0,t0,t,f,j) ;
 
if norm(x60-x61,1)>10*Leps then bugmes();quit;end
 
 
 
%ODEOPTIONS(6)=0;// jacobian nor called nor estimated
 
x60=ode('ad',x0,t0,t,f,j);   //Jacobian not used (warning)
 Warning: Jacobian external is given, but 
 not used!,  see %ODEOPTIONS(6)
 
 
x60=ode('ad',x0,t0,t,f);    //Jacobian not used
 
if norm(x60-x61,1)>10*Leps then bugmes();quit;end
 
 
// test lsoda
 
%ODEOPTIONS(6)=2;// jacobian  estimated
 
x60=ode(x0,t0,t,f);
 
if norm(x60-x61,1)>10*Leps then bugmes();quit;end
 
 
%ODEOPTIONS(6)=1;//Jacobian estimated
 
x60=ode(x0,t0,t,f);
 Warning: No Jacobian external given but 
 one is required by %ODEOPTIONS(6) value!
 
 
if norm(x60-x61,1)>10*Leps then bugmes();quit;end
 
 
 
//   Banded Jacobian
 
itask=1;tcrit=0;h0=0;hmax=0;hmin=0;ixpr=0;mxstep=0;maxordn=0;maxords=0;
 
//provisional values as default
 
jacflag=2;ml=-1;mu=-1;
 
 
%ODEOPTIONS=[itask,tcrit,h0,hmax,hmin,jacflag,mxstep,maxordn,maxords,ixpr,ml,mu];
 
jacflag=2;%ODEOPTIONS(6)=jacflag;   //Banded Jacobian, given
 
nx=20;A=diag(-[1:nx]);x0=ones(nx,1);
 
t0=0;t=[1,2,3,4,5];
 
for k=1:nx-1, A(k,k+1)=1;end
 
for k=1:nx-2, A(k,k+2)=-2;end
 
for k=1:nx-1, A(k+1,k)=-1;end
 
for k=1:nx-2, A(k+2,k)=2;end
 
for k=1:nx-3, A(k+3,k)=-3;end
 
deff('xd=f(t,x)','xd=A*x')
Warning :redefining function: f                       
 
 
ml=3;mu=2;
 
%ODEOPTIONS(11:12)=[ml,mu];
 
for i=1:nx;
    for j=1:nx;
if A(i,j)<>0 then J(i-j+mu+1,j)=A(i,j);end
end;end;
Warning :redefining function: j                       
 
 
// J is a ml+mu+1 x ny matrix.
 
// Column 1 of J is made of mu zeros followed by df1/dx1, df2/dx1, df3/dx1,
 
// i.e. 1 + ml possibly nonzeros entries.
 
// Column 2 of J is made of mu-1 zeros followed by df1/dx2, df2/dx2,0...
 
// etc...
 
%ODEOPTIONS(6)=1;%ODEOPTIONS(11:12)=[-1,-1];
 
deff('jj=j1(t,x)','jj=A')
 
xnotband=ode('st',x0,t0,t,f,j1);
 
 
 
%ODEOPTIONS(6)=4;//banded jacobian external given
 
%ODEOPTIONS(11:12)=[3,2];
 
deff('jj=j(t,x)','jj=J')
 
xband=ode('st',x0,t0,t,f,j);
 
if norm(xnotband-xband,1)>Leps then bugmes();quit;end
 
 
%ODEOPTIONS(6)=5;//banded jacobian evaluated
 
%ODEOPTIONS(11:12)=[3,2];
 
deff('jj=j(t,x)','jj=J')
 
xband=ode('st',x0,t0,t,f,j);
 Warning: Jacobian external is given, but 
 not used!,  see %ODEOPTIONS(6)
 
 
if norm(xnotband-xband,1)>Leps then bugmes();quit;end
 
 
 
//            Test of %ODEOPTIONS(7)
 
//%ODEOPTIONS(7)=mxstep  ---> maximum number od steps allowed
 
itask=1;tcrit=0;h0=0;hmax=0;hmin=0;ixpr=0;mxstep=0;maxordn=0;maxords=0;
 
//provisional values as default
 
jacflag=2;ml=-1;mu=-1;
 
%ODEOPTIONS=[itask,tcrit,h0,hmax,hmin,jacflag,mxstep,maxordn,maxords,ixpr,ml,mu];
 
%ODEOPTIONS(7)=10;
 
//ode(x0,t0,t,f);  // ---> Non convergence
 
 
//            Test of %ODEOPTIONS(8:9)
 
//%ODEOPTIONS(8:9)=[maxordn,maxords] ---> maximum order for nonstiff and stiff
 
itask=1;tcrit=0;h0=0;hmax=0;hmin=0;ixpr=0;mxstep=0;maxordn=0;maxords=0;
 
//provisional values as default
 
jacflag=2;ml=-1;mu=-1;
 
%ODEOPTIONS=[itask,tcrit,h0,hmax,hmin,jacflag,mxstep,maxordn,maxords,ixpr,ml,mu];
 
%ODEOPTIONS(8:9)=[0,0]; //---> default values
 
wref=ode(x0,t0,t,f); //just for computing reference
 
 
%ODEOPTIONS(8:9)=[4,3];
 
ww=ode(x0,t0,t,f);norm(wref-ww,1);
 
 
%ODEOPTIONS(8:9)=[12,5];
 
if norm(wref-ode(x0,t0,t,f),1)>Leps then bugmes();quit;end
 
 
//using stiff method
 
 
%ODEOPTIONS(9)=0;
 
wref=ode('st',x0,t0,t,f);
 
%ODEOPTIONS(9)=5;
 
if norm(wref-ode('st',x0,t0,t,f),1) >Leps then bugmes();quit;end //=0
 
%ODEOPTIONS(9)=4;
 
if norm(wref-ode('st',x0,t0,t,f),1)  >Leps then bugmes();quit;end  //small
 
 
 
//using nonstiff method
 
 
%ODEOPTIONS(8)=0;
 
wref=ode('ad',x0,t0,t,f);
 
%ODEOPTIONS(8)=12;
 
if norm(wref-ode('ad',x0,t0,t,f),1) >Leps then bugmes();quit;end  //=0
 
%ODEOPTIONS(8)=5;
 
if norm(wref-ode('ad',x0,t0,t,f),1) >Leps then bugmes();quit;end   //small
 
 
//mixed
 
%ODEOPTIONS(8:9)=[5,12];
 
wref=ode(x0,t0,t,f);
 
%ODEOPTIONS(8:9)=[4,10];
 
if norm(ode(x0,t0,t,f)-wref,1)>Leps then bugmes();quit;end   //small
 
 
 
A=diag([-10,-0.01,-1]);
 
deff('uu=u(t)','uu=sin(t)');
 
B=rand(3,1);
 
deff('y=f(t,x)','y=A*x+B*u(t)')
Warning :redefining function: f                       
 
 
%ODEOPTIONS(1)=2;
 
yy1=ode('stiff',[1;1;1],0,1,f);
 
yy2=ode('stiff',[1;1;1],0,2,f);
 
%ODEOPTIONS(1)=3;
 
yy1=ode('stiff',[1;1;1],0,1,f);
 
yy2=ode('stiff',[1;1;1],0,2,f);
 
 
clear %ODEOPTIONS;
 
rand('seed',0);rand('normal');
 
nx=20;A=rand(nx,nx);A=A-4.5*eye();
 
deff('y=f(t,x)','y=A*x')
Warning :redefining function: f                       
 
 
deff('J=j(t,x)','J=A')
Warning :redefining function: j                       
 
 
//%ODEOPTIONS(1)=1;
 
y2=ode('stiff',ones(nx,1),0,2,f,j);
 
[y1,w,iw]=ode('stiff',ones(nx,1),0,1,f,j);
 
y2p=ode('stiff',y1,1,2,f,j,w,iw);
 
y12=ode('stiff',ones(nx,1),0,[1,2],f,j);
 
norm(y12(:,2)-y2p);
 
yaf=ode('adams',ones(nx,1),0,2,f,j);
 
yaj=ode('adams',ones(nx,1),0,2,f,j);
 
ysf=ode('stiff',ones(nx,1),0,2,f,j);
 
ysj=ode('stiff',ones(nx,1),0,2,f,j);
 
 
deff('xd=f(t,x)','xd=A*x+B*sin(3*t)')
Warning :redefining function: f                       
 
 
A=rand(10,10)-4.5*eye();B=rand(10,1);
 
x=ode(ones(10,1),0,[1,2,3],f);
 
//link('fexab.o','fexab')
 
if norm(x-ode(ones(10,1),0,[1,2,3],'fexab'),1) > 1.d-9 then bugmes();quit;end