https://pythonhosted.org/uncertainties/
https://pypi.python.org/pypi/soerp
https://pypi.python.org/pypi/mcerp
This last one is one of my favorite Python libraries. My hunch is that it is highly underrated.
I am still looking for/consider implementing error propagation as probability distributions where these are symbolic.
The "free, cross-platform program that transparently handles calculations with numbers with uncertainties" module may not be as strong, but definitely sells and describes itself better.
mcerp might be better rated if it hoisted "easily and transparently track the effects of uncertainty through mathematical calculations" promise to its headline.
I developed a new method using SVD/PCA with some basis rotation method. I can potentially characterize or estimate errors on my input data, but I have no idea how to propagate these errors to my basis vectors. I'm at a bit of a loss as to where to look from here. My only idea is to bootstrap... But that's a bit lame :) and not very rigorous
See if you are able to define each element of your input data as a stochastic variable that you can sample from. Then make a function to generate a set of fixed value input data elements by sampling from the stochastic variables. Then run this many times to generate resulting basis vectors. Calculate relevant measures of variability from these vectors.