Tuning Parameters for Linear Algebra Computations

The object .laenv is a list of parameters used by the functions in the Matrix library. It has the following components:

ARGUMENTS:

NB
optimal blocksize. The default value is 1, indicating that the best performance is expected for unblocked methods.
NBMIN
minimum block size. If the usable block size is less than NBMIN , an unblocked method is used. The value of NBMIN is irrelevant if NB = 1 . The default value is -1.
NX
crossover point. In a block method, when blocks reach dimension less than NX , an unblocked method is used. The value of NX is irrelevant if NB = 1 . The default value is -1.
NS
number of shifts for nonsymmetric eigenvalue computations. The default value is 2.
NXSVD
crossover point for the singular-value computation. When reducing an m by n matrix to bidiagonal form, if max(m,n)/min(m,n) exceeds this value, the matrix is first reduced to triangular form by QR factorization. The default value is 16.
MAXB
crossover point within nonsymmetric eigenvalue computations. The default value is 50.

DETAILS:

The following is from Anderson et al. (1994) : The range of problem sizes needed to determine the optimal block size or crossover point is machine dependent. For algorithms that require a crossover point, it is best to start by finding the best block size with the crossover point set to 0, and then locate the point at which blocked algorithm begins to outperform then unblocked algorithm using this block size. The best crossover point will be somewhat smaller than the latter value. By experimenting with small values, it should be straightforward to choose NBMIN , the smallest block size that gives improvement over an unblocked method. Anderson, E., et al. (1994), LAPACK Users' Guide. 2nd edition, SIAM, Philadelphia.

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