find magnitude of approximate percent relative error

I am asked to find 7 estimates of sin(x) and errors using a for loop.

I can get my code to run good for the 7 estimates and true error of each but im not sure how to separate the estimates apart to get the magnitude of approx. percent relative error. I put the equation for MAPRE for reference but im not sure how to write the 'sum' inside to give me each estimates MAPRE.

x=pi/5;
sum=0;

% using a for loop to find the first seven estimates of sin(x)
for k = 0:6;
    
    sum = sum + (-1)^k*(x^(2*k+1)/factorial(2*k+1))
    
    % finding magnitude of true error
    f_exact = sin(pi/5);    % True value
    MagTrueerr = abs(sum - f_exact)
    
    % finding magnitude of approximate percent relative error
    
    MAPRE = abs((sum1-sum0)/sum1)*100
    
end

[David Hill]

Just make arrays for sum, MagTrueerr, and MAPRE that stores the answers during each loop.

[Tiffany Lodge]

I dont completely understand, because if i put sum(k) to make sum an array. i get an error saying array indices need to be postive integers or logical values. is this not what you meant?

Answer 1

[David Hill]

a=(-1).^k.*(x.^(2*k+1)./factorial(2*k+1));
MagTrueerr=abs(cumsum(a)-f_exact);
MAPRE=100*MagTrueerr./cumsum(a);

No loops needed.

[Tiffany Lodge]

Yes i would love to do this, but i am told i have to do everything in a for loop.

[David Hill]

Use for loop

for k=0:6
    a(k+1)=(-1)^k*(x^(2*k+1)/factorial(2*k+1));
    MagTrueerr(k+1)=abs(sum(a)-f_exact);
    MAPRE(k+1)=100*MagTrueerr(k+1)/sum(a);
end

[Tiffany Lodge]

i put that in my code and im still geting an error about the array indices.

[David Hill]

It works. Make sure you preallocate a.

a=zeros(1,7);

[Tiffany Lodge]

alright that works thank you