Poor Performance

We have tried to make the performance of LAPACK ``transportable'' by performing most of the computation within the Level 1, 2, and 3 BLAS, and by isolating all of the machine-dependent tuning parameters in a single integer function ILAENV . To avoid poor performance  from LAPACK routines, note the following recommendations :

BLAS:

One should use BLAS that have been optimized for the machine being used if they are available. Many manufacturers and research institutions have developed, or are developing, efficient versions of the BLAS for particular machines. A portable set of Fortran BLAS is supplied with LAPACK and can always be used if no other BLAS are available or if there is a suspected problem in the local BLAS library, but no attempt has been made to structure the Fortran BLAS for high performance.

ILAENV:

For best performance, the LAPACK routine ILAENV should be set with optimal tuning parameters for the machine being used. The version of ILAENV provided with LAPACK supplies default values for these parameters that give good, but not optimal, average case performance on a range of existing machines. In particular, the performance of xHSEQR is particularly sensitive to        the correct choice of block parameters; the same applies to the driver routines which call xHSEQR, namely xGEES, xGEESX, xGEEV and xGEEVX.                     Further details on setting parameters in ILAENV are found in section 6.

LWORK WORK(1):

The performance of some routines depends on the amount of workspace supplied. In such cases, an argument, usually called WORK, is provided, accompanied by an integer argument LWORK specifying its length as a linear array. On exit, WORK(1) returns the amount of workspace required to use the optimal tuning parameters. If LWORK < WORK(1), then insufficient workspace was provided to use the optimal parameters, and the performance may be less than possible. One should check that LWORK WORK(1) on return from an LAPACK routine requiring user-supplied workspace to see if enough workspace has been provided.   Note that the computation is performed correctly, even if the amount of workspace is less than optimal, unless LWORK is reported as an invalid value by a call to XERBLA as described in Section 7.2.

xLAMCH:

Users should beware of the high cost of the first call to the LAPACK auxiliary routine xLAMCH,   which computes machine characteristics such as epsilon and the smallest invertible number. The first call dynamically determines a set of parameters defining the machine's arithmetic, but these values are saved and subsequent calls incur only a trivial cost. For performance testing, the initial cost can be hidden by including a call to xLAMCH in the main program, before any calls to LAPACK routines that will be timed. A sample use of SLAMCH  is

      XXXXXX = SLAMCH( 'P' )

or in double precision:

      XXXXXX = DLAMCH( 'P' )

A cleaner but less portable solution is for the installer to save the values computed by xLAMCH for a specific machine and create a new version of xLAMCH with these constants set in DATA statements, taking care that no accuracy is lost in the translation.