I would like to analyze some well-used scientific codes that make heavy use of LAPACK. I.e. I'm looking for codes that both spend a lot of time within LAPACK functions and use LAPACK non-trivially (i.e. calling more than just DGEMM). I would be interested in applications that use either sequential LAPACK or ScaLAPACK or any other implementation that exposes the same interface.
What are some good examples that are easy to obtain? Ideally they would be open source or available-on-request.
ATLAS does a pretty brutal group of grinding metrics on LAPACK and BLAS. You might be able to snag some code out of there that meets your needs.
I might also suggest checking out Numpy and Scipy as both have very large unit-tests that likely span large parts of that phase-space. Additionally, they provide hooks down to the LAPACK functions if you want to call those directly on arrays of your creation.