uncertiantly calculation in matlab

To perform uncertainty calculation in MATLAB, there are several approaches you can take. One common technique is error propagation, which involves propagating the uncertainties from the input variables through the mathematical operations to estimate the uncertainty in the final result. Here's an example of how to calculate the uncertainty of a function using error propagation:

main.m
% Define input variables and their uncertainties
x = 5.0; dx = 0.1; % x with uncertainty dx
y = 3.0; dy = 0.05; % y with uncertainty dy

% Calculate the uncertainty in the function z = f(x,y) = x^2 + 2*y
% using error propagation
dz_dx = 2*x; % partial derivative of z with respect to x
dz_dy = 2;   % partial derivative of z with respect to y
dz = sqrt((dz_dx*dx)^2 + (dz_dy*dy)^2); % total uncertainty in z

% Calculate the function value and its uncertainty
z = x^2 + 2*y;
disp(['The result is z = ', num2str(z), ' +/- ', num2str(dz)]);
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This code defines two input variables x and y, along with their uncertainties dx and dy. The function z = f(x,y) = x^2 + 2*y is then evaluated at these values, and the uncertainty in the result is calculated using error propagation. Finally, the function value and its uncertainty are displayed using the disp() function.

Alternatively, you can use MATLAB's built-in statistical functions to calculate uncertainties. Here's an example using the std() function to calculate the standard deviation of a set of data:

main.m
% Generate a set of random data with known mean and standard deviation
mu = 10.0;  % true mean
sigma = 2.0; % true standard deviation
x = mu + sigma*randn(100,1); % generate 100 data points from a normal distribution

% Calculate the mean and standard deviation of the data
x_bar = mean(x); % sample mean
s = std(x);      % sample standard deviation

% Display the results and compare to the true values
disp(['The sample mean is ', num2str(x_bar)]);
disp(['The sample standard deviation is ', num2str(s)]);
disp(['The true mean is ', num2str(mu)]);
disp(['The true standard deviation is ', num2str(sigma)]);
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This code generates a set of 100 random data points from a normal distribution with a known mean and standard deviation. It then calculates the sample mean and standard deviation using the mean() and std() functions, respectively. Finally, the results are displayed along with the true mean and standard deviation for comparison.