More About Timing

There are two distinct timing programs for LAPACK routines in each data type, one for the linear equations routines and one for the eigensystem routines. The linear equation timing program also times the Level 2 and 3 BLAS, and the reductions to bidiagonal, tridiagonal, or Hessenberg form for eigenvalue computations. Results from the linear equation timing program are given in megaflops, and the operation counts are computed from a formula (see Appendix  C). Results from the eigensystem timing program are given in execution times, operation counts, and megaflops, where the operation counts are calculated during execution using special versions of the LAPACK routines which have been instrumented to count operations. Each program has its own style of input, and the eigensystem timing program accepts four different sets of parameters, for the generalized nonsymmetric eigenvalue problem, the nonsymmetric eigenvalue problem, the symmetric and generalized symmetric eigenvalue problem, and the singular value decomposition. The following sections describe the different input formats and timing parameters.

Both timing programs, but the linear equation timing program in particular, are intended to be used to collect data to determine optimal values for the block routines. All of the block factorization, inversion, reduction, and orthogonal transformation routines in LAPACK are included in the linear equation timing program. Currently, the block parameters NB and NX, as well as others, are passed to the block routines by the environment inquiry function ILAENV, which in turn receives these values through a common block set in the timing program. Future implementations of ILAENV may be tuned to a specific machine so that users of LAPACK will not have to set the block size. For a brief introduction to ILAENV and guidelines on setting some of the parameters, see the LAPACK Users' Guide [1].

The main timing procedure for the REAL linear equation routines is found in LAPACK/TIMING/LIN/stimaa.f in the Unix version and is the first program unit in SLINTIMF in the non-Unix version. The main timing procedure for the REAL eigenvalue routines is found in LAPACK/TIMING/EIG/stimee.f in the Unix version and is the first program unit in SEIGTIMF in the non-Unix version.