Integer, Intent (In)	::	conj, n, incx, incy
Real (Kind=nag_wp), Intent (In)	::	alpha, x(1+(n-1)ABS(incx)), beta, y(1+(n-1)ABS(incy))
Real (Kind=nag_wp), Intent (Inout)	::	r

C Header Interface

#include nagmk26.h

void	f16eaf_ ( const Integer conj, const Integer n, const double alpha, const double x[], const Integer incx, const double beta, const double y[], const Integer incy, double *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

Arguments

1: $conj$ – IntegerInput: On entry: conj is not referenced and need not be set. The presence of this argument 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

f16eaf (blas_ddot) makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.

Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

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 Document

f16eaf (ddot)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

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

2

Specification