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Vector Arguments in BLAS

Vector arguments are passed in one-dimensional arrays. The array dimension ( length) and vector increment are passed as integer variables. The length determines the number of elements in the vector. The increment (also called stride ) determines the spacing between vector elements and the order of the elements in the array in which the vector is passed.
A vector of length
n
and increment
incx
is passed in a one-dimensional array
x
whose values are defined as
x
[0],
x
[|
incx
|], ...,
x
[(
n
-1)* |
incx
|]
If
incx
is positive, then the elements in array
x
are stored in increasing order. If
incx
is negative, the elements in array
x
are stored in decreasing order with the first element defined as
x
[(
n
-1)* |
incx
|]
. If
incx
is zero, then all elements of the vector have the same value,
x
[0]
. The size of the one-dimensional array that stores the vector must always be at least
idimx
= 1 + (
n
-1)* |
incx
|
Example.
One-dimensional Real Array
Let
x
[0:6]
be the one-dimensional real array
x
=
[
1.0, 3.0, 5.0, 7.0, 9.0, 11.0, 13.0
]
.
If
incx
=2
and
n
= 3
, then the vector argument with elements in order from first to last is
[
1.0, 5.0, 9.0
]
.
If
incx
= -2
and
n
= 4
, then the vector elements in order from first to last is
[
13.0, 9.0, 5.0, 1.0
]
.
If
incx
= 0
and
n
= 4
, then the vector elements in order from first to last is
[
1.0, 1.0, 1.0, 1.0
]
.
One-dimensional substructures of a matrix, such as the rows, columns, and diagonals, can be passed as vector arguments with the starting address and increment specified.
Storage of the
m
-by-
n
matrix can be based on either column-major ordering where the increment between elements in the same column is
1
, the increment between elements in the same row is
m
, and the increment between elements on the same diagonal is
m
+ 1
; or row-major ordering where the increment between elements in the same row is
1
, the increment between elements in the same column is
n
, and the increment between elements on the same diagonal is
n
+ 1
.
Example.
Two-dimensional Real Matrix
Let
a
be a real 5 x 4 matrix declared as .
To scale the third column of
a
by 2.0, use the BLAS routine
sscal
with the following calling sequence:
cblas_sscal
(5, 2.0, a[2], 4)
To scale the second row, use the statement:
cblas_sscal
(4, 2.0, a[4], 1)
To scale the main diagonal of
a
by 2.0, use the statement:
cblas_sscal
(4, 2.0, a[0], 5)
The default vector argument is assumed to be 1.

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Notice revision #20110804