a deval function for octave

[philippe]

Hi to all

the syntax to solve a differential equation in matlab has recently
changed and became incompatible with the octave one ! Actually you
should do :

%% solving y''(t)+y(t)=0  y(0)=y'(0)=1 => y(t)=cos(t)+sin(t)
y0=[1;1];T=40;  %%
t=[0:0.1:T];  %%  you choose times t(k)  where solution is evaluated
sol=ode45(@(t,y) [y(2);-y(1)],[0,T],y0);   %%  solving (E)
tt=sol.x;y=sol.y;   %% retrieve tt and y(tt) vectors
clf ;  %% plotting numerical and exact solutions
plot(tt,y(1,:),'xr',t,cos(t)+sin(t),'-b')

but the problem is that you can’t choose times tt computed with ode45 ,
if you want more points you need to do an interpolation between those
computed by ode45 … in matlab this is done by deval function :


y0=[1;1];T=40;%%
t=[0:0.1:T];%%  you choose times t(k)  where solution is evaluated
sol=ode45(@(t,y) [y(2);-y(1)],[0,T],y0);
y=deval(t,sol);
clf ; %% plotting numerical and exact solutions
plot(t,y(1,:),'xr',t,cos(t)+sin(t),'-b')

but deval has not yet been implemented in octave !!! So I’ve tried to
implement my own one (see below), can it be useful to share it here?

sincerely yours ,
Philippe

function y=deval(t,sol)
       %% y=deval(t,sol)
       %% sol= solution of ode y'(t)=f(t,y(t))  y(0)=y0
       %%       obtained with sol=ode45(@f,[t0,T],y0)
       %%   t=  vector of times [t(1) ...t(n)]
       %%   y= vector of solution values [y(t(1)) ... y(t(n))]
       %%      interpolated  from sol data

       Y=sol.y;
       x=sol.x;
       n=length(t);
       l=size(Y,1);
       y=zeros(l,n);
       K=5;
       for k=1:l
              x_tmp=x(1:3);
              ind=find((t<x(2)));
              P=polyfit(x_tmp,Y(k,1:3),K);
              new_y=polyval(P,t(ind)) ;
              for p=2:length(x)-2
                     x_tmp=x(p-1:p+2);
                     ind=find((t>=x(p))&(t<x(p+1)));
                     P=polyfit(x_tmp,Y(k,p-1:p+2),K);
                     new_y=[new_y polyval(P,t(ind))];
              end
              x_tmp=x(end-2:end);
              ind=find((t>=x(end-1)));
              P=polyfit(x_tmp,Y(k,end-2:end),K);
              new_y=[new_y polyval(P,t(ind))];
              y(k,:)=new_y;
       end