HP MLIB User's Guide Vol. 1 7th Ed.
Chapter 2 Basic Vector Operations 35
What you need to know to use vector subprograms
BLAS indexing conventions
This section describes handling stride arguments and forward and backward
storage.
A vector in the BLAS is defined by three quantities:
• Vector length
• Array or starting element within an array
• Increment, sometimes called stride—defines the number of storage units
between successive vector elements
Forward storage
Suppose that X is a real array. Let N be the vector length and let INCX be the
increment. Suppose that a vector x with components x
i
, i= 1, 2, ..., N, is stored
in X. If INCX ≥ 0, then x
i
is stored in
X(1 + (I−1) × INCX). This is forward storage starting from X(1) with stride
equal to INCX, ending with X(1 + (N−1) × INCX). Thus, if N = 4 and
INCX = 2, the vector components x
1
, x
2
, x
3
, and x
4
are stored in the array
elements X(1), X(3), X(5), and X(7), respectively.
Backward storage
Some BLAS subprograms permit the backward storage of vectors, which is
specified by using a negative INCX. If INCX < 0, then x
i
is stored in X(1 +
(N−I) × |INCX|) or equivalently in X(1 − (N−I) × INCX). This is
backward storage starting from X(1 − (N−1) × INCX) with stride equal to
INCX, ending with X(1). Thus, if N = 4 and INCX = −2, the vector components
x
1
, x
2
, x
3
, and x
4
are stored in the array elements
X(7), X(5), X(3), and X(1), respectively.
INCX = 0 is only permitted by COPY routines in the legacy BLAS subprograms.
When INCX = 0 is allowed, it means that x is a vector of length N, whose
components all equal the value of X(1).
The notation (N,X,INCX) describes a BLAS vector. For example, if X is an
array of dimension N, then (N,X,1) represents forward storage and (N,X,−1)
represents backward storage. If A is an M-by-N array, then (M,A(1,J),1)
represents column J and (N,A(I,1),M) represents row I. Finally, if an M-by-N
matrix is embedded in the upper left-hand corner of an array B of size LDB by
NMAX, then column J is (M,B(1,J),1) and row is I(N,B(I,1),LDB).