Calculate f for multiple inputs

I want to calculate the function f for multiple inputs and then find the number of local and global minima.

% Import the excel data into MATLAB

T = readtable('Task1.xlsx','Range','A7:F106');

% Calculate the function f and find the number of local and global minima

q = T(1:99,4);

x = T(1:99,2);

y = T(1:99,3);

cost = T(1:99,6);

u = [0:100];

v = [0:100];

for i = 1:100

f = sum(q(i)*((u-x).^2) + ((v-y).^2))

end

Answer 1

[Sanju]

Hi @Arashdeep Dhillon,

To calculate the function “f” for multiple inputs, I have updated the code as follows,

% Import the excel data into MATLAB
T = readtable('Task1.xlsx','Range','A7:F106');

% Calculate the function f and find the number of local and global minima
q = T(1:99,4);
x = T(1:99,2);
y = T(1:99,3);
cost = T(1:99,6);
u = 0:100;
v = 0:100;

f_values = zeros(length(u), length(v));
for i = 1:length(u)
    for j = 1:length(v)
        f_values(i,j) = sum(q.*((u(i)-x).^2) + ((v(j)-y).^2));
    end
end

To find the number of local and global minima, you can refer to the below implementation,

% Find the number of local and global minima
num_local_minima = sum(imregionalmin(f_values));
num_global_minima = sum(f_values(:) == min(f_values(:)));

You can also refer to the below documentation on “imregionalmin” function if required,

https://www.mathworks.com/help/images/ref/imregionalmin.html

Hope this helps!