LAPACK/ScaLAPACK Development

When I contributed pzlahqr and pztrevc a few years back, it was known (see
reference below) that pztrevc had scaling issues. If I remember correctly,
I created a subroutine pzlatrs that was used to do numerical scaling
(similar to the serial zlatrs), but this routine does not scale in parallel
sense. If numerical scaling is not needed, then a direct call to the level
2 PB LAS pztrsv rather pztrevc would be much faster.

Since contribution of pzlahqr and pztrevc, I have not revisited pztrevc.

@Article{Fahey:2003:APE,
author = "Mark R. Fahey",
title = "Algorithm 826: A Parallel Eigenvalue Routine for Complex
{Hessenberg} Matrices",
journal = "{ACM} Transactions on Mathematical Software",
volume = "29",
number = "3",
pages = "326--336",
month = sep,
year = "2003",
URL = "http://doi.acm.org/10.1145/838250.838256",
abstract = "A code for computing the eigenvalues of a complex
Hessenberg matrix is presented. This code computes the Schur decomposition
of a complex Hessenberg matrix. Together with existing ScaLAPACK routines,
the eigenvalues of dense complex matrices can be directly computed using a
parallel QR algorithm. This parallel complex Schur decomposition routine
was developed to fill a void in the ScaLAPACK library and was based on the
parallel real Schur decomposition routine already in ScaLAPACK. The
real-arithmetic version was appropriately modified to make it work with
complex arithmetic and implement a complex multiple bulge QR algorithm.
This
also required the development of new auxiliary routines that perform
essential operations for the complex Schur decomposition, and that will
provide additional linear algebra computation capability to the parallel
numerical library community.",
}