How to generate fx value according to number of samples?

I have a matlab code of matrix multiplication with normal distribution

I need a output corresponding to number of samples = 20

I have a thickness data by normal distribution with 10x20 matrix . That number of rows data i used to generate matrix multiplication. I need fx values corresponds with that number of columns data( i.e, i need 20 output values)

How to do this in matlab.

clc
clear
close all

x=pi:0.01:2*pi; %%% x domain

mu=25;
sigma=1.5;
n=10;
num_samples=20;
d0=25;                      %%% thickness of layer 1
d1= normrnd(mu,sigma,[n,num_samples]);  %%% thickness of layer 2 by normal distribution

for i =1:length(x)
    x_value=x(i);
    X1=x_value*d0;
    Fx=[sin(X1) 1i; -1i cos(X1)]; %%% Matrix for layer 1
    Fy = eye(2); % Initialize total matrix as identity for layer 2

    for j = 1:n
        X2=x_value*d1(j);
        M=[sin(X2) 1i; -1i cos(X2)]; %%% Matrix for layer 1
        Fy= Fy * M;
    end

    Fxx=(Fx^n*Fy); %%% Matrix multiplication
    fx=Fxx(1,1)+Fxx(2,2); %%% output

end
disp(fx)

Answer 1

[Ayush Aniket]

Hi Gulzar,

It seems like you are trying to perform matrix multiplication for a layered medium simulation, where the thickness of each layer is determined by a normal distribution. You want to generate 20 output values corresponding to the number of samples in your normal distribution matrix ('d1'), for a given set of 'x' values.

However, your code calculates 'fx' for each value of 'x' in the loop but overwrites it in each iteration, and the final 'disp(fx)' only shows the last computed value of 'fx'.

To achieve 20 distinct output values corresponding to each column in your 'd1' matrix (each sample), you need to adjust your approach as shown below:

clc
clear
close all

x = pi:0.01:2*pi; 
mu = 25;
sigma = 1.5;
n = 10;
num_samples = 20;
d0 = 25;

d1 = normrnd(mu, sigma, [n, num_samples]);

% Initialize an array to store the output values of fx for each sample
fx_values = zeros(1, num_samples);

% Loop over each sample
for sample = 1:num_samples
    Fy = eye(2); % Initialize total matrix as identity for layer 2
    for i = 1:length(x)
        x_value = x(i);
        X1 = x_value * d0;
        Fx = [sin(X1) 1i; -1i cos(X1)]; 
        
        % Reset Fy for each x value
        Fy = eye(2);
        for j = 1:n
            X2 = x_value * d1(j, sample);
            M = [sin(X2) 1i; -1i cos(X2)]; 
            Fy = Fy * M; % Update Fy for each layer
        end
        Fxx = (Fx^n * Fy); 
        fx = Fxx(1,1) + Fxx(2,2); 
    end
    % Store the last computed fx value for this sample
    fx_values(sample) = fx;
end

disp(fx_values)

In the above code, 'fx_values' stores the final 'fx' value for each sample. This is necessary because you want 20 distinct outputs corresponding to your 'num_samples'.