Engineering and Scientific Subroutine Library for AIX Version 3 Release 3: Guide and Reference

SNAXPY and DNAXPY--Compute SAXPY or DAXPY N Times

These subprograms compute SAXPY or DAXPY, respectively, n times:

y_i <-- y_i + alpha_ix_i    for i = 1, n

where each alpha_i is a scalar value, contained in the vector a, and each x_i and y_i are vectors, contained in vectors (or matrices) x and y, respectively. For an explanation of the SAXPY and DAXPY computations, see SAXPY, DAXPY, CAXPY, and ZAXPY--Multiply a Vector X by a Scalar, Add to a Vector Y, and Store in the Vector Y.

Table 44. Data Types

Syntax

On Entry

n

is the number of SAXPY or DAXPY computations to be performed and the number of elements in vector a. Specified as: a fullword integer; n >= 0.

m

is the number of elements in vectors x_i and y_i for each SAXPY or DAXPY computation. Specified as: a fullword integer; m >= 0.

a

is the vector a of length n, containing the scalar values alpha_i, used in each computation of y_i + alpha_ix_i. Specified as: a one-dimensional array of (at least) length 1+(n-1)|inca|, containing numbers of the data type indicated in Table 44.

inca

is the stride for vector a. Specified as: a fullword integer. It can have any value.

x

is the vector (or matrix) x, containing the x_i vectors of length m, used in the n computations of y_i + alpha_ix_i. Specified as: a one- or two-dimensional array of (at least) length (1+(n-1)(incxo)) + (m-1)|incxi|, containing numbers of the data type indicated in Table 44.

incxi

is the stride for x in the inner loop--that is, the stride identifying the elements in each vector x_i. Specified as: a fullword integer. It can have any value.

incxo

is the stride for x in the outer loop--that is, the stride identifying each vector x_i in x. Specified as: a fullword integer; incxo >= 0.

y

is the vector (or matrix) y, containing the y_i vectors of length m, used in the n computations of y_i + alpha_ix_i. Specified as: a one- or two-dimensional array of (at least) length (1+(n-1)(incyo)) + (m-1)|incyi|, containing numbers of the data type indicated in Table 44.

incyi

is the stride for y in the inner loop--that is, the stride identifying the elements in each vector y_i in y. Specified as: a fullword integer; incyi > 0 or incyi < 0.

incyo

is the stride for y in the outer loop--that is, the stride identifying each vector y_i in y. Specified as: a fullword integer; incyo >= 0.

On Return

y

is the vector (or matrix) y, containing the y_i vectors of length m, which contain the results of the n SAXPY or DAXPY computations, y_i + alpha_ix_i for i = 1, n. Returned as: a one- or two-dimensional array, containing numbers of the data type indicated in Table 44.

Note

Vector y must have no common elements with vector a or vector x; otherwise, results are unpredictable. See Concepts.

Function

The SAXPY or DAXPY computations:

y <-- y + alphax

are performed n times. This is expressed as follows:

y_i <-- y_i + alpha_ix_i    for i = 1, n

where each alpha_i is a scalar value, contained in the vector a, and each x_i and y_i are vectors, contained in vectors (or matrices) x and y, respectively.

Each computation of SAXPY or DAXPY on page SAXPY, DAXPY, CAXPY, and ZAXPY--Multiply a Vector X by a Scalar, Add to a Vector Y, and Store in the Vector Y uses the length of the x_i and y_i vectors, m, for its input argument, n. It also uses the strides for the inner loop, incxi and incyi, for its parameters incx and incy, respectively. See Function for a description of how the computation is done.

The outer loop of the SNAXPY or DNAXPY computation uses the strides of inca, incxo, and incyo to locate the elements in a and vectors in x and y for each i-th computation. These are:

For i = 1, n:

alpha_{((i-1)inca+1)}    for inca >= 0

alpha_{((i-n)inca+1)}    for inca < 0

x_{((i-1)incxo+1)}

y_{((i-1)incyo+1)}

If m or n is 0, no computation is performed.

Error Conditions

Computational Errors

None

Input-Argument Errors

1. n < 0
2. m < 0
3. incxo < 0
4. incyi = 0
5. incyo < 0

Example 1

This example shows vectors, contained in matrices, with the stride of the inner loops incxi and incyi equal to 1.

Call Statement and Input

             N   M   A  INCA  X  INCXI INCXO  Y  INCYI INCYO
             |   |   |   |    |    |     |    |    |     |
CALL SNAXPY( 3 , 4 , A , 1  , X ,  1  , 10  , Y ,  1  ,  5  )
 
A        =  (3.0, 2.0, 4.0)

        *               *
        | 1.0  4.0  3.0 |
        | 2.0  3.0  4.0 |
        | 3.0  2.0  2.0 |
        | 4.0  1.0  1.0 |
X    =  |  .    .    .  |
        |  .    .    .  |
        |  .    .    .  |
        |  .    .    .  |
        |  .    .    .  |
        |  .    .    .  |
        *               *

        *               *
        | 4.0  1.0  3.0 |
        | 3.0  2.0  4.0 |
Y    =  | 2.0  3.0  2.0 |
        | 1.0  4.0  1.0 |
        |  .    .    .  |
        *               *

Output

        *                 *
        |  7.0  9.0  15.0 |
        |  9.0  8.0  20.0 |
Y    =  | 11.0  7.0  10.0 |
        | 13.0  6.0   5.0 |
        |   .    .     .  |
        *                 *

Example 2

This example shows vectors, contained in matrices, with a stride of the inner loop incxi greater than 1.

Call Statement and Input

             N   M   A  INCA  X  INCXI INCXO  Y  INCYI INCYO
             |   |   |   |    |    |     |    |    |     |
CALL SNAXPY( 3 , 4 , A , 1  , X ,  2  , 10  , Y ,  1  ,  5  )
 
A        =  (3.0, 2.0, 4.0)

        *               *
        | 1.0  4.0  3.0 |
        |  .    .    .  |
        | 2.0  3.0  4.0 |
        |  .    .    .  |
X    =  | 3.0  2.0  2.0 |
        |  .    .    .  |
        | 4.0  1.0  1.0 |
        |  .    .    .  |
        |  .    .    .  |
        |  .    .    .  |
        *               *

        *               *
        | 4.0  1.0  3.0 |
        | 3.0  2.0  4.0 |
Y    =  | 2.0  3.0  2.0 |
        | 1.0  4.0  1.0 |
        |  .    .    .  |
        *               *

Output

Example 3

This example shows vectors, contained in matrices, with a negative stride, incyi, for the inner loop.

Call Statement and Input

             N   M   A  INCA  X  INCXI INCXO  Y  INCYI INCYO
             |   |   |   |    |    |     |    |    |     |
CALL SNAXPY( 3 , 4 , A , 1  , X ,  1  , 10  , Y , -1  ,  5  )
 
A        =  (3.0, 2.0, 4.0)

        *               *
        | 1.0  4.0  3.0 |
        | 2.0  3.0  4.0 |
        | 3.0  2.0  2.0 |
        | 4.0  1.0  1.0 |
X    =  |  .    .    .  |
        |  .    .    .  |
        |  .    .    .  |
        |  .    .    .  |
        |  .    .    .  |
        |  .    .    .  |
        *               *

        *               *
        | 1.0  4.0  1.0 |
        | 2.0  3.0  2.0 |
Y    =  | 3.0  2.0  4.0 |
        | 4.0  1.0  3.0 |
        |  .    .    .  |
        *               *

Output

        *                 *
        | 13.0  6.0   5.0 |
        | 11.0  7.0  10.0 |
Y    =  |  9.0  8.0  20.0 |
        |  7.0  9.0  15.0 |
        |   .    .     .  |
        *                 *

Example 4

This example shows vectors, contained in matrices, with a negative stride, inca, for vector a. For vector a, processing begins at element A(5), which is 3.0.

Call Statement and Input

             N   M   A   INCA  X  INCXI INCXO  Y  INCYI INCYO
             |   |   |    |    |    |     |    |    |     |
CALL SNAXPY( 3 , 4 , A , -2  , X ,  1  , 10  , Y ,  1  ,  5  )
 
A        =  (4.0, . , 2.0, . , 3.0)

        *               *
        | 1.0  4.0  3.0 |
        | 2.0  3.0  4.0 |
        | 3.0  2.0  2.0 |
        | 4.0  1.0  1.0 |
X    =  |  .    .    .  |
        |  .    .    .  |
        |  .    .    .  |
        |  .    .    .  |
        |  .    .    .  |
        |  .    .    .  |
        *               *

        *               *
        | 4.0  1.0  3.0 |
        | 3.0  2.0  4.0 |
Y    =  | 2.0  3.0  2.0 |
        | 1.0  4.0  1.0 |
        |  .    .    .  |
        *               *

Output