Calculating Integral using Array Input

Hi there,

I'm trying to calculate the following, and was wondering whether anyone could suggest a quicker way of doing it, other than introducing a loop. Ideally, I want something that is similar to integral but can work with an array input also (an "elementwise" integral?).

Thanks a lot!

R = [5e-07,1e-06,1.75e-06,2.5e-06,3.5e-06]
phi = 40.2594
b = R/cosd(phi)
n = [1,3,10,17,35]

R_1 = R(1)
b_1 = b(1)
n_1 = n(1)

fun = @(x) (1-(R_1-x).*(b_1-x)/(R_1*b_1)).^(n_1-1).*(((R_1-x)+(b_1-x))/(R_1*b_1)).*n_1.*x
lambda_max = integral(fun,0,R_1)

R_2 = R(2)
b_2 = b(2)
n_2 = n(2)

fun = @(x) (1-(R_2-x).*(b_2-x)/(R_2*b_2)).^(n_2-1).*(((R_2-x)+(b_2-x))/(R_2*b_2)).*n_2.*x
lambda_max = integral(fun,0,R_2)

%...

Answer 1

[Jan]

You do need a loop to get the best solution. Remember that integral is an adaptive method, which creates finer grids until a certain accuracy is reached. Using a set of different parameters does not allow to use the optimal grid for all values, such that it is expected, that you need more function evaluations and get a less accurate solution due to the accumulated rounding errors.

Use a loop and provide the parameters one after the other.

You can use parfor to accelerate the computations.

[J_P]

Ah fair enough, I did not think of the grid itself. Well, worth a try, thanks a lot!