I want to obtain value of "W" for different combination of values of (psi,r) example. "W" for (psi=0.0001,r = 2.1891) ; (psi=0.001,r = 2.1940); (psi=0.01,r = 2.2373) and so on

psi     = 0.001;
alpha = (12*psi)^(1/3);
r = 2.1940;
l1 = (r + alpha)*(r + alpha);
l1a = r*r - r*alpha + alpha*alpha;
L1 = log(l1/l1a);

t1 = (2*r - alpha) / (alpha*sqrt(3));
T1 = atan(t1);

l2 = (1 + alpha)*(1 + alpha);
l2a = (1*1) - (1*alpha) + (alpha*alpha);
L2 = log(l2/l2a);

t2 = (2*1 - alpha) / (alpha*sqrt(3));
T2 = atan(t2);

W1 = 4 * sqrt(3) * (T1 - T2) * log((r+alpha)/(1+alpha));
W2 = (L1 - L2)*log((r*r - r*alpha + alpha*alpha)/(1 - alpha + alpha*alpha)); 
W3 = 4*(T1 -T2)*(T1 -T2);
W4 = (L1 - L2) + 2 * sqrt(3) * (T1 - T2);
W5 = 3 ./ ((r - 1) * (r - 1));
W = ((W1 + W2 -W3) * W5)/W4

[Dyuman Joshi]

Make it a function and call from workspace.

%calling individually
W1=calculateW(0.0001,2.1891)

W1 = 0.1602

W2=calculateW(0.001,2.194)

W2 = 0.1595

W3=calculateW(0.01,2.2373)

W3 = 0.1534

function W = calculateW(psi,r)
alpha = (12*psi)^(1/3);
l1 = (r + alpha)*(r + alpha);
l1a = r*r - r*alpha + alpha*alpha;
L1 = log(l1/l1a);
t1 = (2*r - alpha) / (alpha*sqrt(3));
T1 = atan(t1);
l2 = (1 + alpha)*(1 + alpha);
l2a = (1*1) - (1*alpha) + (alpha*alpha);
L2 = log(l2/l2a);
t2 = (2*1 - alpha) / (alpha*sqrt(3));
T2 = atan(t2);
W1 = 4 * sqrt(3) * (T1 - T2) * log((r+alpha)/(1+alpha));
W2 = (L1 - L2)*log((r*r - r*alpha + alpha*alpha)/(1 - alpha + alpha*alpha)); 
W3 = 4*(T1 -T2)*(T1 -T2);
W4 = (L1 - L2) + 2 * sqrt(3) * (T1 - T2);
W5 = 3 ./ ((r - 1) * (r - 1));
W = ((W1 + W2 -W3) * W5)/W4;
end

[AVINASH SAHU]

thank you for clarification but how can we use loop so that we don't have to enter manually for large dataset?

Answer 1

[Dyuman Joshi]

%loop
psi=[0.0001,0.001,0.01];
r=[2.1891,2.194,2.2373];
for i=1:numel(psi)
    W(i)=calculateW(psi(i),r(i));
end
W

W = 1×3

0.1602 0.1595 0.1534

%arrayfun
W1=arrayfun(@calculateW, psi, r)

W1 = 1×3

0.1602 0.1595 0.1534

function W = calculateW(psi,r)
alpha = (12*psi)^(1/3);
l1 = (r + alpha)*(r + alpha);
l1a = r*r - r*alpha + alpha*alpha;
L1 = log(l1/l1a);
t1 = (2*r - alpha) / (alpha*sqrt(3));
T1 = atan(t1);
l2 = (1 + alpha)*(1 + alpha);
l2a = (1*1) - (1*alpha) + (alpha*alpha);
L2 = log(l2/l2a);
t2 = (2*1 - alpha) / (alpha*sqrt(3));
T2 = atan(t2);
W1 = 4 * sqrt(3) * (T1 - T2) * log((r+alpha)/(1+alpha));
W2 = (L1 - L2)*log((r*r - r*alpha + alpha*alpha)/(1 - alpha + alpha*alpha)); 
W3 = 4*(T1 -T2)*(T1 -T2);
W4 = (L1 - L2) + 2 * sqrt(3) * (T1 - T2);
W5 = 3 ./ ((r - 1) * (r - 1));
W = ((W1 + W2 -W3) * W5)/W4;
end

[AVINASH SAHU]

Thank you so much