Define the size of the matrix (n): Set a variable "n" to the desired size of the matrix.
Create an empty n*n matrix: Use the zeros function to create a matrix filled with zeros.
W = zeros(n,n);
Fill the matrix with random values satisfying the conditions: Use a loop to iterate through the elements of the matrix and assign random values between 0 and -1.
Enforce the condition Σj∈E, Wij < 1/Umax, i = 1,..., n: You can modify the loop to check the sum of the elements in each row and ensure it is less than "1/Umax".
Umax = ...; % Set an upper bound for the second derivatives
for i = 1:n
% Initialize the sum of elements in the current row
row_sum = 0;
for j = 1:n
% Generate a random number between 0 and -1
Wij = rand(1) - 1;
% Assign the random number to the matrix element
W(i, j) = Wij;
% Update the row sum
row_sum = row_sum + Wij;
end
% Check if the row sum is less than 1/Umax
if row_sum >= 1/Umax
% If not, keep generating random numbers for this row until the condition is met
while row_sum >= 1/Umax
for j = 1:n
% Generate a new random number
Wij = rand(1) - 1;
% Update the matrix element and row sum
W(i, j) = Wij;
row_sum = sum(W(i, :));
end
end
end
end
This code creates an n*n matrix filled with random values between 0 and -1, ensuring that the sum of elements in each row is less than the specified "Umax".
