How do I preallocate for speed in the following code?

clc

clear

N = 9;

S = 18.1;

AR = 7;

lambda = 0.8;

alpha_twist = -1.5;

i_w = 10;

a_2d = 6.3;

a_0 = -3;

a_0_fd = -6;

b = sqrt(AR*S);

bf_b=0.6;

MAC = S/b;

Croot = (1.5*(1+lambda)*MAC)/(1+lambda+lambda^2);

theta = pi/(2*N):pi/(2*N):pi/2;

alpha=i_w+alpha_twist:-alpha_twist/(N-1):i_w;

for i=1:N

if (i/N)>(1-bf_b)

alpha_0(i)=a_0_fd;

else

alpha_0(i)=a_0;

end

end

z = (b/2)*cos(theta);

c = Croot * (1 - (1-lambda)*cos(theta));

mu = c * a_2d / (4 * b);

LHS = mu .* (alpha-alpha_0)/57.3;

for i=1 : N

for j=1 : N

B(i,j) = sin((2*j-1) * theta(i)) * (1 + (mu(i) *(2*j-1)) / sin(theta(i)));

end

end

A=B\transpose(LHS);

for i = 1 : N

sum1(i) = 0;

sum2(i) = 0;

for j = 1 : N

sum1(i) = sum1(i) + (2*j-1) * A(j)*sin((2*j-1)*theta(i));

sum2(i) = sum2(i) + A(j)*sin((2*j-1)*theta(i));

end

end

CL_TO = pi * AR * A(1);

Answer 1

[Askic V]

The most basic approach is given here:

clc
clear
N = 9;         
S = 18.1;        
AR = 7;             
lambda = 0.8;            
alpha_twist = -1.5;            
i_w = 10;                  
a_2d = 6.3;                       
a_0 = -3;                  
a_0_fd = -6;                 
b = sqrt(AR*S);               
bf_b=0.6;     
MAC = S/b;                  
Croot = (1.5*(1+lambda)*MAC)/(1+lambda+lambda^2);       
theta = pi/(2*N):pi/(2*N):pi/2;
alpha=i_w+alpha_twist:-alpha_twist/(N-1):i_w;  
alpha_0 = zeros(1,N);
for i=1:N
    if (i/N)>(1-bf_b)
        alpha_0(i)=a_0_fd;                
    else
        alpha_0(i)=a_0;   
    end
end
z = (b/2)*cos(theta);
c = Croot * (1 - (1-lambda)*cos(theta)); 
mu = c * a_2d / (4 * b);
LHS = mu .* (alpha-alpha_0)/57.3; 
B = zeros(N,N);
for i=1 : N
    for j=1 : N
        B(i,j) = sin((2*j-1) * theta(i)) * (1 + (mu(i) *(2*j-1)) / sin(theta(i)));	
    end
end
A=B\transpose(LHS);
sum1 = zeros(1, N);
sum2 = zeros(1, N);
for i = 1 : N
    for j = 1 : N
        sum1(i) = sum1(i) + (2*j-1) * A(j)*sin((2*j-1)*theta(i));
        sum2(i) = sum2(i) + A(j)*sin((2*j-1)*theta(i));
    end
end
CL_TO = pi * AR * A(1);