Posterior covariance from GPML toolbox I am currently using the GPML toolbox to perform regression.
Generally, after learning the hyperparameters we can extract the posterior mean and variance by using the function in the toolbox as
[m s2] = gp(hyp2, @infExact, [], covfunc, likfunc, x, y, z);

Here, we can say that m is the Posterior mean and s2 is the posterior variance.
But the code only gives out the self-variance or variance at the target points and not the full covariance matrix. 
$s2 = diagonal(k(x_{target},x_{target}'))$
A vector with only the diagonal terms.
How can I get the full covariance matrix between all the target points i.e. $k(x_{target},x_{target}')$?
I tried writing something like:
kTT = feval(covFunc{:}, hyp2.cov, xTarget);
kTI = feval(covFunc{:}, hyp2.cov, xTarget,x);
kII = feval(covFunc{:}, hyp2.cov, x);
sigma = exp(2*hypProd.lik)*eye(max(size(x))); 

% Posterior covariance matrix
kPost = kTT - kTI/(kII+sigma)*kTI';

But the diagonal variance values in the kPost matrix don't match those with the s2 matrix.
What am I doing wrong?
 A: As you already answered yourself, the m and s2 output variables are just the means and variances of prediction at the given points z.
However, I'd like to add that you can also get a posterior structure by calling the function as
[predmeans, predvars, latentmeans, latentvars, [], poststr] = gp(hyp, inffun, meanfun, covfun, likfun, xtrain, ytrain, xtest)

In this case, poststr is going to be a structure consisting of three fields: alpha, sW and L which are supposed to be used to construct the posterior means and variances using the formula given in the GPML toolbox for Matlab manual, page 4.
Also of note: this posterior structure can also be returned when training (instead of predicting, as in your example as well as the one I wrote out above), using a function call like 
[negloglik, derivnegloglik, poststr] = gp(hyp, inffun, meanfun, covfun, likfun, xtrain, ytrain)

A: I finally got the problem, just writing the answer here so that it might be helpful to others. 
After enough digging around I figured that:
s2 is the variance of $y_*$
Whereas, kPost is the covariance of $f_{*}$
If we write the posterior of "f"
$f_{*} | x_{*}, y, x = GP(K_{*}(K+\sigma_{n}^{2}I)^{-1}y, K_{**}-K_{*}^{T}(K+\sigma_{n}^{2}I)^{-1}K_{*})$
This is equivalent to the kPost that I calculate in the question above.
But the GPML gives as an output 
$y_{*} | x_{*}, y, x = GP(K_{*}(K+\sigma_{n}^{2}I)^{-1}y, K_{**}-K_{*}^{T}(K+\sigma_{n}^{2}I)^{-1}K_{*}+\sigma_{n}^{2}I)$  
The $y_*$ has an extra term in the covariance matrix which is the noise in the measurements.
Hence, 
$s2 = diagonal(kPost+\sigma_{n}^{2}I)$
