Hi, I'm trying to estimate the uncertainty in my model parameters for a large NLSQ problem (~2M measurements, ~10k unknowns), so I'm constantly struggling to manage RAM even with 128GB on my machine. I have the algorithm working reasonably well using the Jacobian Multiply function interface, but now when it returns I'd like to estimate the parameter covariance in order to assess the fit and the uncertainties. Normally, if one does:

[xCurrent,Resnorm,FVAL,EXITFLAG,OUTPUT,LAMBDA,JACOB] = lsqnonlin(problem);

xCov = inv(JACOB.'*JACOB)*Resnorm/(numel(FVAL)-numel(xCurrent));

You can get the covariance, or you can just send the Jacobian into nlparci() and get confidence intervals. However, if I try that, I get "out of memory" errors, which is why I'm using the JM functions in the first place. I tried sending in eye(numel(xCurrent)) with flag zero to get the JM function to compute the inner product of the Jacobian, but same out of memory error. Is there a loop method I should use to build up the rows/columns of J.'*J? Do I try using a sparse identity matrix? I notice the JACOB returned is a sparse matrix class, but I'm not sure how sparse my native Jacobian really is (some cases moderately sparse, other times it can be pretty full rank). Is there a lower-footprint means of building up the covariance?