NAG Library Routine Document

F16ECF (BLAS_DAXPBY)

Note: before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

6 Error Indicators and Warnings

7 Accuracy

8 Further Comments

+− 9 Example

9.1 Program Text

9.2 Program Data

9.3 Program Results

1 Purpose

F16ECF (BLAS_DAXPBY) computes the sum of two scaled vectors, for real vectors and scalars.

2 Specification

SUBROUTINE F16ECF ( N, ALPHA, X, INCX, BETA, Y, INCY)

INTEGER N, INCX, INCY

REAL (KIND=nag_wp) ALPHA, X(1+(N-1)*ABS(INCX)), BETA, Y(1+(N-1)*ABS(INCY))

The routine may be called by its BLAST name blas_daxpby.

3 Description

F16ECF (BLAS_DAXPBY) performs the operation

y \leftarrow α x + β y

where

x

and

y

are

n

-element real vectors, and

α

and

β

real scalars. If

n

is less than or equal to zero, or if

α

is equal to zero and

β

is equal to

1

, this routine returns immediately.

4 References

Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001) Basic Linear Algebra Subprograms Technical (BLAST) Forum Standard University of Tennessee, Knoxville, Tennessee http://www.netlib.org/blas/blast-forum/blas-report.pdf

5 Parameters

1: N – INTEGERInput: On entry: $n$ , the number of elements in $x$ and $y$ .
2: ALPHA – REAL (KIND=nag_wp)Input: On entry: the scalar $α$ .
3: X( $1 + (N - 1) \times |INCX|$ ) – REAL (KIND=nag_wp) arrayInput: On entry: the $n$ -element vector $x$ .
If $INCX > 0$ , $x_{i}$ must be stored in $X (1 + (i - 1) \times INCX)$ , for $i = 1, 2, \dots, N$ .

If $INCX < 0$ , $x_{i}$ must be stored in $X (1 - (N - i) \times INCX)$ , for $i = 1, 2, \dots, N$ .

Intermediate elements of X are not referenced.
4: INCX – INTEGERInput: On entry: the increment in the subscripts of X between successive elements of $x$ .
Constraint: $INCX \neq 0$ .
5: BETA – REAL (KIND=nag_wp)Input: On entry: the scalar $β$ .
6: Y( $1 + (N - 1) \times |INCY|$ ) – REAL (KIND=nag_wp) arrayInput/Output: On entry: the $n$ -element vector $y$ .
If $INCY > 0$ , $y_{i}$ must be stored in $Y (1 + (i - 1) \times INCY)$ , for $i = 1, 2, \dots, N$ .

If $INCY < 0$ , $y_{i}$ must be stored in $Y (1 - (N - i) \times INCY)$ , for $i = 1, 2, \dots, N$ .

Intermediate elements of Y are not referenced.

On exit: the updated vector $y$ stored in the array elements used to supply the original vector $y$ .
Intermediate elements of Y are unchanged.
7: INCY – INTEGERInput: On entry: the increment in the subscripts of Y between successive elements of $y$ .
Constraint: $INCY \neq 0$ .

6 Error Indicators and Warnings

$IFAIL =$: On entry, $INCX = ⟨value⟩$ .
Constraint: $INCX \neq 0$ .

On entry, $INCY = ⟨value⟩$ .
Constraint: $INCY \neq 0$ .

On entry, $N = ⟨value⟩$ .
Constraint: $N \geq 0$ .

7 Accuracy

The BLAS standard requires accurate implementations which avoid unnecessary over/underflow (see Section 2.7 of Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001)).

8 Further Comments

None.

9 Example

This example computes the result of a scaled vector accumulation for

\begin{matrix} α = 3, & x = {(- 4, 2.1, 3.7, 4.5, - 6)}^{T}, \\ β = - 1, & y = {(- 3, - 2.4, 6.4, - 5, - 5.1)}^{T} . \end{matrix}

NAG Library Routine DocumentF16ECF (BLAS_DAXPBY)