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I'm trying to numerically compute the full set of eigenvectors of a large dense matrix, with the freedom to specify the error tolerance and maximum number of iterations. (The default error tolerance has proven too large for my purposes.)

So far I have been working in Python.

Both NumPy's and SciPy's linalg.eig(), which use LAPACK, can solve for the full set of eigenvectors but do not allow me to set the error tolerance or maximum iterations. This seems to be a freely specifiable parameter in LAPACK itself, so I would think there exists a Python package that allows one to specify these, but I don't know what it is.

SciPy's sparse.linalg.eig(), which uses ARPACK, does allow me to set error tolerance and maximum iterations, but cannot solve for all the eigenvectors. And as mentioned, my matrices are dense (50%).

So, how to calculate the full set of eigenvectors for a large dense matrix with arbitrary error tolerance? Is there a package in Python that would allow me to do this?

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