This section contains performance numbers for selected driver routines. These routines provide complete solutions for the most common problems of numerical linear algebra and are the routines users are most likely to call:

- Solve an
*N*by*N*general system of linear equations with one right-hand side using PDGESV. - Solve an
*N*by*N*symmetric positive definite system of linear equations with one right-hand side using PDPOSV. - Solve an
*N*by*N*linear least squares problem with one right-hand side using PDGELS. item Find the eigenvalues and eigenvectors of an*N*by*N*

Data is provided for a
variety of distributed-memory concurrent
computers. All timings
were obtained by using
the machine-specific
optimized BLAS available
on each machine.
For the IBM Scalable
POWERparallel 2, the
ESSL BLAS were used.
In all cases the data
consisted of 64-bit
floating-point numbers.
For each
machine and each driver,
a range of problems was
run on different number
of processors. Different
physical distribution
block sizes were tried,
with data for the
fastest run reported
in the tables below.
Similarly, whenever
applicable, UPLO=`L'
and UPLO=`U' were timed,
but times are reported only for
UPLO=`U'.
The test matrices were
generated with randomly
distributed entries.
All run times are reported
in seconds, and block size
is denoted by *nb*. The value
of the physical distribution
block size as well as the
process grid shape was
chosen to make *N*=2000
optimal. It is not necessarily
the best choice for the entire
range of problem sizes.

Table 4 presents ``standard'' floating-point operation counts for ScaLAPACK drivers.

**Table 4:** ``Standard'' Floating-Point Operation Counts for Some ScaLAPACK
Drivers for *N* by *N* Matrices

Sat Feb 1 08:18:10 EST 1997