load("Eulix.mac")$


/* Lotka-Volterra  
    alpha= 0.1  beta= 0.015  gamma= 0.0225  delta= 0.02

    y1' = y1*(alpha-beta*y2)     y1(0)= 1
    y2' = -y2*(gamma-delta*y1)   y2(0)= 1
*/
 
Rhs(t,y):= block([alpha:0.1,beta:0.015,gamma:0.0225,delta:0.02],
             matrix([y[1,1]*(alpha-beta*y[2,1])],[-y[2,1]*(gamma-delta*y[1,1])]))$

define(Rhs_t('t,'y),diff(Rhs('t,'y),'t))$
gen_jacobian(F,xx,Fdim)::= block([i,n:ev(Fdim),J,X:ev(xx)],
  J: genmatrix(lambda([i,j],diff(F(X,y)[i,1],y[j,1])),n,n),
   buildq([J,t:X],lambda([t,y],J))
)$

Rhs_jac:gen_jacobian(Rhs,t,length(Rhs('t,'y)))$
compile(Rhs,Rhs_t)$

t0:0.0$
y0:matrix([1.0],[1.0])$
/* h:0.1$ */
t_end: 198.0$
debugmode:true$
/*:break Eulix_SplineEval*/
Start:elapsed_real_time()$

Splines: Eulix_Spline(t0,y0,t_end,Rhs,Rhs_t,Rhs_jac,logging=true)$

print("I've used ",elapsed_real_time()-Start,"seconds for computing the Lotka-Volterra orbit")$
Sp1:lambda([tau],first(first(transpose(Eulix_SplineEval(tau,Splines)))));
Sp2:lambda([tau],second(first(transpose(Eulix_SplineEval(tau,Splines)))));
print("end state:",Sp1(t_end), Sp2(t_end))$
plot2d([parametric,Sp1,Sp2,[t,0,t_end],[xlabel,"y1"],[ylabel,"y2"]], [title,"Lotka-Volterra Equation"]);
read("enter ; or $ to quit");
