Eliminating nested loops without repeating input combinations for equation output

Hi,

I have been given an equation with several variables. For each variable I have created a normal distribution using normn. I would like to get all the solutions to the equation using every single possible combination of values without them repeating themselves. Since I want to use distribution fitter and fit a norma distribution to the data, having inputs repeat themselves would not be good. Currently I am using nested for loops but this is very inefficient especially as I start adding variables. does anybody know of a way in which I can speed up my code?

When n gets to be higher than 10 it becomes unbearably slow. I would like n to be at least 500.

t_mean = 9.74; %mm
D_mean = 324; %mm
dm_mean = 3.896; %mm 
sig_u_mean = 542; %MPa
l_mean = 528; %mm

%range of values and number of random inputs
n = 100;
t = 0.01*randn(1, n) + t_mean;
D = 0.25*randn(1, n) + D_mean;
sig_u = 0.25*randn(1, n) + sig_u_mean;
dm = 0.001*randn(1, 100) + dm_mean;
l = 0.25*randn(1, 100) + l_mean;

%initialize the Pb matrix
K = zeros(1,1000);
m = 1;
tic
%loop over all possible input combinations
for i = 1 : length(t)
    for j = 1 : length(D)
        for k = 1 : length(sig_u)
            for n = 1 : length(dm)
                for o = 1 : length(l)
                     M = sqrt(1 + 0.31*(l_mean/sqrt(D(j)*t(i)))^2);
                     K(m) = ((2*t(i))/(D(j)-t(i)))*sig_u(k)*abs((1-(dm_mean/t(i)))/(1-(dm_mean/(t(i)*M))));
                     m = m+1;
                end
            end
        end
    end
end
toc
distributionFitter(K)

[darova]

Preallocate your K variable precisely

K = zeros(1,n^3*1e4);

Answer 1

[Swetha Polemoni]

Hi,

Eliminating nested for loops is possible using “ndgrid()” function. Look into the following code snippet for better understanding.

clear all
x=1:10;
y=10:20;
[A,B]=ndgrid(x,y);

for i= 1:10
    for j=1:10
        out1(i,j)=x(i)+y(j);
    end
end
out2=A+B;

Here out1 and out2 gives same output. Atleast 2 nested loops can be eliminated using this function.