Can someone convert this to matlab code?

[James Tursa]

What have you tried so far?

[Kevin Wood]

Lag_Poly = 0;
for i = 1:N
    for k = 1:N
        while k~= i
        Lag_Poly = Lag_Poly + prod((p - x(k))/(x(i)-x(k)));
        end
    end
    Lag_Poly = Lag_Poly + y(i) * Lag_Poly;
end

Answer 1

[James Tursa]

So, you don't need any loops for this. Just use the automatic array expansion feature. E.g., take a look at what happens with this calculation:

>> n = 5;
>> x = 1:n
x =
     1     2     3     4     5
>> p = rand
p =
    0.9134
>> M = (p - x)./(x' - x) % using automic array expansion
M =
      -Inf    1.0866    1.0433    1.0289    1.0217
   -0.0866      -Inf    2.0866    1.5433    1.3622
   -0.0433   -1.0866      -Inf    3.0866    2.0433
   -0.0289   -0.5433   -2.0866      -Inf    4.0866
   -0.0217   -0.3622   -1.0433   -3.0866      -Inf
>> M(1:n+1:end) = 1 % set diagonals to 1 so they don't influence the product
M =
    1.0000    1.0866    1.0433    1.0289    1.0217
   -0.0866    1.0000    2.0866    1.5433    1.3622
   -0.0433   -1.0866    1.0000    3.0866    2.0433
   -0.0289   -0.5433   -2.0866    1.0000    4.0866
   -0.0217   -0.3622   -1.0433   -3.0866    1.0000
>> prod(M,2)
ans =
    1.1917
   -0.3800
    0.2968
   -0.1338
    0.0253

Then just take the dot product of this with your y vector.

This should be OK as long as n isn't too large. If n is too large, then you may need to resort to a loop for part of the calculation.