Recursive method from for loop

Hi!

I have a normal working loop

 clc;
 time =     [0,    1,  2,  3,  4, 10, 12, 18];
 distance = [4.71, 9, 15, 19, 20, 45, 55, 78];
 totaltime = 0;
 totaldistance = 0;
 figure;
 hold on
 for i=1:1:8
     dis = 0.9^(-i) * distance(i);
     totaldistance = dis+totaldistance;
     hold on
     ti = 0.9^(-i) * time(i);
     totaltime = ti+totaltime;
     plot(ti,dis,'p')
      hold on
      plot(totaltime,totaldistance,'o')
     hold on
 end
 v=totaldistance/totaltime;
 estimatedspeed = v
 plot(v,'*')

And I need to get the same result of estimated speed using recursive method. I'm a begginer in Matlab and I need a little bit of help. I tried to write a function as it would be recursive, but nothing goes right. Where I'm making a mistake?

 clc;
 time =     [0,    1,  2,  3,  4, 10, 12, 18];
 distance = [4.71, 9, 15, 19, 20, 45, 55, 78];
 totaltime = 0;
 totaldistance = 0;
 function averagespeed = speed(time, distance)
    for i=1:1:8
        dis = 0.9^(-i) * distance(i);
        ti = 0.9^(-i) * time(i);
        totaldistance = dis+totaldistance;
        totaltime = ti+totaltime;
        averagespeed = speed + totaldistance/totaltime;
    end
 end

Answer 1

[Walter Roberson]

You have

function averagespeed = speed(time, distance)
    for i=1:1:8
        dis = 0.9^(-i) * distance(i);
        ti = 0.9^(-i) * time(i);
        totaldistance = dis+totaldistance;
        totaltime = ti+totaltime;
        averagespeed = speed + totaldistance/totaltime;
    end
 end

In the line

          averagespeed = speed + totaldistance/totaltime;

you have a reference to the function speed, but you are not passing in the time and distance parameters that speed() needs.

Recursive functions always need to have a test for some boundary condition under which they can return a value directly instead of calling itself recursively, and ideally you should be able to give a proof by induction that every branch of the recursion will eventually stop. For example,

function averagespeed = speed(time, distance)
    if time <= eps
       averagespeed = 0.0;
       return
    end
    for i=1:1:8
        dis = 0.9^(-i) * distance(i);
        ti = 0.9^(-i) * time(i);
        totaldistance = dis+totaldistance;
        totaltime = ti+totaltime;
        averagespeed = speed(time/2, distance/2) + totaldistance/totaltime;
    end
 end

Note, though, that you are adding dis to totaldistance before having defined totaldistance inside the function. Perhaps you thought you were using totaldistance as a shared variable, but shared variables need to have been defined inside an outer function and your outer code is a script not a function. Writing to a shared variable (other than perhaps a counter) is more often than not a mistake in a recursive routine, better handled by returning multiple outputs from the recursive routine.