For loop for Covariance of two vectors

I am looking to make a for loop to identify the individual covariance between each point in two lines and plot them as a color map along a line

To make the for loop I have:

x = rand(1, 5521)
y = rand(1, 5521)
for ii = 1:length(x)
    covar(ii) = cov(x,y)
end

I understand that I need to make an empty array to enter the new data into and I understand that I am not calling the covariance to do individual points of the vector, but I am not sure how to fix it.

The plot I want to plot the two variables x and y ontop of eachother with a color map on the bottom showing the differences of variance along the line.

Answer 1

[Walter Roberson]

Individual covariances between two points is always [0 0; 0 0] because there is a constant relationship between the two scalars. Knowing the one possible input scalar tells you the only possible output for that highly restricted population.

You need at least two x and y in order to get meaningful covariances.

Also remember that covariance between two classes (x, y) is a 2 x 2 array, but you want to color the result, which implies you only want one value per x y rather than 4 values.

[Caitlin Bemis]

Thank you. That makes sense

Answer 2

[Torsten]

The covariance between two given vectors is a scalar, namely

cov(x,y) = 1/(n-1) * sum_{i=1}^{i=n} (x(i)-mean(x))*(y(i)-mean(y)):

rng('default')
format long
x = rand(1, 5521);
y = rand(1, 5521);
covariance = 1/5520 * sum((x-mean(x)).*(y-mean(y)))

covariance = 
    -9.473031297795489e-04

or directly with the matlab function

covariance_matrix = cov(x,y);
covariance = covariance_matrix(2,1)

covariance = 
    -9.473031297795485e-04

Calculating the covariance between individual data points does not make sense.

Calculating the covariance between random variables is something different.

So I'm not sure what you are trying to do in your code.