# How to create matrix from a function

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Gabriella Gonnella on 14 Feb 2021
Hi guys, I need to create a matrix (in my script is "array"), deriving from a function, depending on three variables, which alternate.
clear all
Var; %from which I derive T1 and m1
beta= 0.05;
k0 = 1.67*10^13;
R = 0.0083;
for j = 1:length(T1)
alpha1_tga(j) = (m1(1,1)-m1(j))./(m1(1,1)-m1(end,end));
alpha1_tga(j) = 1 - alpha1_tga(j);
end
E1= 150;
E2 = 300;
Estep = 5;
sigma1 = 10;
sigma2 = 70;
sigmastep = 5;
[alpha_daem,h2,array] = solvedaem(T1,beta,k0,R,E1,Estep,E2,sigma1,sigmastep,sigma2,alpha1_tga);
Here, there's the function.
function [alpha_daem,h2,array] = solvedaem(T1,beta,k0,R,E1,Estep,E2,sigma1,sigmastep,sigma2,alpha1_tga)
for E0 = E1:Estep:E2
for sigma = sigma1:sigmastep:sigma2
h2 = 0;
array = [];
for j = 1:length(T1)
f = @(x) (exp(-k0./beta.*R.*T1(j).^2./x.*exp(-x./R./T1(j))))./(sigma.*sqrt(2*pi)).*exp(-(x-E0).^2./(2.*sigma.^2));
a = E0-25; b = E0+25; %lower and upper limits
nSimp = 100; %number of intervals
hSimp = (b - a)/nSimp; %length of each interval
s = 0;
for i=0:nSimp
if i==0 || i==nSimp
p = 1;
elseif mod(i,2) ~= 0
p = 4;
else
p = 2;
end
x = a + i*hSimp;
s = s + p*f(x);
end
alpha_daem(j) = hSimp/3*s;
h2 = h2+(alpha1_tga(j) - alpha_daem(j)).^2;
end
array = [E0,sigma,h2];
end
end
end
I mean that I need to create the matrix "array", in which the first column in equal to E1 ( from 150 to 300 with step 5), the second column equal to sigma (from 10 to 70 with step 5, that should repeat for each value of E1), and third column equal to h2.
Could anyone help me?

Abhishek Gupta on 17 Feb 2021
Hi,
As per my understanding, you want to create a matrix containing E1, sigma, and h2 values. The simple way would be as follows:-
Approach 1 - size of the output matrix is known
output = zeros(size(E1:Estep:E2,2)*size(sigma1:sigmastep:sigma2,2), 3); % initialize the matrix
count = 1;
for E0 = E1:Estep:E2
for sigma = sigma1:sigmastep:sigma2
%-------%
end
output(count, :) = [E0,sigma,h2]; % append the array
count = count + 1;
end
Approach 2 - size of the output matrix is unknown
output = []; % initialize the matrix
for E0 = E1:Estep:E2
for sigma = sigma1:sigmastep:sigma2
%-------%
end
output = [output; [E0,sigma,h2]]; % append the array
end
Gabriella Gonnella on 25 Feb 2021
I need to find three values of E and sigma which minimize h2. For this reason I would create the matrix with all the values inside. Could be a faster way to find them?