NAG Library Routine Document

F16EAF (BLAS_DDOT)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

▸▿ 10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

1 Purpose

F16EAF (BLAS_DDOT) updates a scalar by a scaled dot product of two real vectors.

2 Specification

SUBROUTINE F16EAF (

CONJ, N, ALPHA, X, INCX, BETA, Y, INCY, R)

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

The routine may be called by its BLAST name blas_ddot.

3 Description

F16EAF (BLAS_DDOT) performs the operation

r \leftarrow β r + α x^{T} y

where

x

and

y

are

n

-element real vectors, and

r

α

and

β

real scalars. If

n

is less than zero, or, if

β

is equal to one and either

α

n

is equal to zero, 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: $CONJ$ – INTEGERInput: On entry: CONJ is not referenced and need not be set. The presence of this parameter in the BLAST standard is for consistency with the interface of the complex variant of this routine.
2: $N$ – INTEGERInput: On entry: $n$ , the number of elements in $x$ and $y$ .
3: $ALPHA$ – REAL (KIND=nag_wp)Input: On entry: the scalar $α$ .
4: $X (1 + (N - 1) \times |INCX|)$ – REAL (KIND=nag_wp) arrayInput: On entry: the $n$ -element vector $x$ .
If $INCX > 0$ , $x_{i}$ must be stored in $X ((i - 1) \times |INCX| + 1)$ , for $i = 1, 2, \dots, N$ .

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

Intermediate elements of X are not referenced. If $α = 0.0$ or $N = 0$ , X is not referenced.
5: $INCX$ – INTEGERInput: On entry: the increment in the subscripts of X between successive elements of $x$ .

Constraint: $INCX \neq 0$ .
6: $BETA$ – REAL (KIND=nag_wp)Input: On entry: the scalar $β$ .
7: $Y (1 + (N - 1) \times |INCY|)$ – REAL (KIND=nag_wp) arrayInput: On entry: the $n$ -element vector $y$ .
If $INCY > 0$ , $y_{i}$ must be stored in $Y ((i - 1) \times |INCY| + 1)$ , for $i = 1, 2, \dots, N$ .

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

Intermediate elements of Y are not referenced. If $α = 0.0$ or $N = 0$ , Y is not referenced.
8: $INCY$ – INTEGERInput: On entry: the increment in the subscripts of Y between successive elements of $y$ .

Constraint: $INCY \neq 0$ .
9: $R$ – REAL (KIND=nag_wp)Input/Output: On entry: the initial value, $r$ , to be updated. If $β = 0.0$ , R need not be set on entry.

On exit: the value $r$ , scaled by $β$ and updated by the scaled dot product of $x$ and $y$ .

6 Error Indicators and Warnings

INCX = 0

INCY = 0

, an error message is printed and program execution is terminated.

7 Accuracy

The dot product

x^{T} y

is computed using the BLAS routine DDOT.

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 Parallelism and Performance

Not applicable.

9 Further Comments

None.

10 Example

This example computes the scaled sum of two dot products,

r = α_{1} x^{T} y + α_{2} u^{T} v

, where

\begin{matrix} α_{1} = 0.3, & x = (1, 2, 3, 4, 5), y = (- 5, - 4, 3, 2, 1), \\ α_{2} = - 7.0, & u = v = (0.4, 0.3, 0.2, 0.1) . \end{matrix}

y

and

v

are stored in reverse order, and

u

is stored in reverse order in every other element of a real array.

NAG Library Routine DocumentF16EAF (BLAS_DDOT)