八度/ Matlab中的矢量化功能

Question

I have a function that I was wondering if it was possible to vectorize it and not have to use a for loop. The code is below.

a=1:2:8
for jj=1:length(a)
     b(jj)=rtfib(a(jj)); %fibbonacci function
end
b

output below:

a =

   1   3   5   7

>>>b =

    1    3    8   21

I was trying to do it this way

t = 0:.01:10;
y = sin(t);

but doing the code below doesn't work any suggestions? ps: I'm trying to keep the function rtfib because of it's speed and I need to use very large Fibonacci numbers. I'm using octave 3.8.1

 a=1:2:8
 b=rtfib(a)

Here's the rtfib code below as requested

function f = rtfib(n)

if (n == 0)
    f = 0;
elseif (n==1)
    f=1;
elseif (n == 2)
    f = 2;
else
    fOld = 2;
    fOlder = 1;
    for i = 3 : n
        f = fOld + fOlder;
        fOlder = fOld;
        fOld = f;
    end
end
end

Answer 1

You can see that your function rtfib actually computes every Fibonacci number up to n . You can modify it so that is stores and returns all these number, so that you only have to call the function once with the maximum number you need:

function f = rtfib(n)

    f=zeros(1,n+1);
    if (n >= 0)
        f(1) = 0;
    end
    if (n>=1)
        f(2)=1;
    end
    if (n >= 2)
        f(3) = 2;
    end
    if n>2
        fOld = 2;
        fOlder = 1;
        for i = 3 : n
            f(i+1) = fOld + fOlder;
            fOlder = fOld;
            fOld = f(i+1);
        end
    end
end

(It will return fibonnaci(n) in f(n+1), if you don't need the 0 you could change it so that it returns fibonnaci(n) in f(n) if you prefer)

Then you only need to call

>>f=rtfib(max(a));
>>b=f(a+1)
b =

 1     3     8    21

If you don't want to store everything you could modify the function rtfib a little more, so that it takes the the array a as input, compute the Fibonacci numbers up to max(a) but only stores the one needed, and it would directly return b . Both solutions will slow down rtfib itself but it will be a lot faster than calculating the Fibonacci numbers from 0 each time.