HP MLIB User's Guide Vol. 1 7th Ed.

Chapter 2 Basic Vector Operations 37

What you need to know to use vector subprograms

In BLAS Standard routines, you specify an operator argument with a named

constant value. The actual numeric value assigned to the named constant is

deﬁned in the appropriate language’s include ﬁle. Operator arguments are

represented in the Fortran 77 interface as INTEGERs. This speciﬁcation is

different from the legacy BLAS, where operator arguments are deﬁned as

CHARACTER*1.

Refer to individual routines in “BLAS Standard routines” on page 152 for the

named constants you can use to specify operator arguments for basic vector

subprograms.

Representation of a permutation matrix

This section explains how the BLAS Standard represents a permutation

matrix.

An n-by-n permutation matrix P is represented as a product of at most n

interchange permutations. An interchange permutation E is a permutation

obtained by swapping two rows of the identity matrix. An efﬁcient way to

represent a general permutation matrix P is with an integer vector p of length

n. In other words, P = E

...E

and each E

is the identity with rows i and p

interchanged:

For i = n to 1 and incp < 0,

For i = 1 to n and incp > 0,

xi() xpi()()↔