# NAG Library Routine Document

## 1Purpose

f16eaf (blas_ddot) updates a scalar by a scaled dot product of two real vectors.

## 2Specification

Fortran Interface
 Subroutine f16eaf ( conj, n, x, incx, beta, y, incy, r)
 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
#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.

## 3Description

f16eaf (blas_ddot) performs the operation
 $r← βr+ αxTy$
where $x$ and $y$ are $n$-element real vectors, and $r$, $\alpha$ and $\beta$ real scalars. If $n$ is less than zero, or, if $\beta$ is equal to one and either $\alpha$ or $n$ is equal to zero, this routine returns immediately.

## 4References

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

## 5Arguments

1:     $\mathbf{conj}$ – 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:     $\mathbf{n}$ – IntegerInput
On entry: $n$, the number of elements in $x$ and $y$.
3:     $\mathbf{alpha}$ – Real (Kind=nag_wp)Input
On entry: the scalar $\alpha$.
4:     $\mathbf{x}\left(1+\left({\mathbf{n}}-1\right)×\left|{\mathbf{incx}}\right|\right)$ – Real (Kind=nag_wp) arrayInput
On entry: the $n$-element vector $x$.
If ${\mathbf{incx}}>0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{x}}\left(\left(\mathit{i}-1\right)×{\mathbf{incx}}+1\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
If ${\mathbf{incx}}<0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{x}}\left(\left({\mathbf{n}}-\mathit{i}\right)×\left|{\mathbf{incx}}\right|+1\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
Intermediate elements of x are not referenced. If $\alpha =0.0$ or ${\mathbf{n}}=0$, x is not referenced.
5:     $\mathbf{incx}$ – IntegerInput
On entry: the increment in the subscripts of x between successive elements of $x$.
Constraint: ${\mathbf{incx}}\ne 0$.
6:     $\mathbf{beta}$ – Real (Kind=nag_wp)Input
On entry: the scalar $\beta$.
7:     $\mathbf{y}\left(1+\left({\mathbf{n}}-1\right)×\left|{\mathbf{incy}}\right|\right)$ – Real (Kind=nag_wp) arrayInput
On entry: the $n$-element vector $y$.
If ${\mathbf{incy}}>0$, ${y}_{\mathit{i}}$ must be stored in ${\mathbf{y}}\left(\left(\mathit{i}-1\right)×{\mathbf{incy}}+1\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
If ${\mathbf{incy}}<0$, ${y}_{\mathit{i}}$ must be stored in ${\mathbf{y}}\left(\left({\mathbf{n}}-\mathit{i}\right)×\left|{\mathbf{incy}}\right|+1\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
Intermediate elements of y are not referenced. If $\alpha =0.0$ or ${\mathbf{n}}=0$, y is not referenced.
8:     $\mathbf{incy}$ – IntegerInput
On entry: the increment in the subscripts of y between successive elements of $y$.
Constraint: ${\mathbf{incy}}\ne 0$.
9:     $\mathbf{r}$ – Real (Kind=nag_wp)Input/Output
On entry: the initial value, $r$, to be updated. If $\beta =0.0$, r need not be set on entry.
On exit: the value $r$, scaled by $\beta$ and updated by the scaled dot product of $x$ and $y$.

## 6Error Indicators and Warnings

If ${\mathbf{incx}}=0$ or ${\mathbf{incy}}=0$, an error message is printed and program execution is terminated.

## 7Accuracy

The dot product ${x}^{\mathrm{T}}y$ 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)).

## 8Parallelism 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.

None.

## 10Example

This example computes the scaled sum of two dot products, $r={\alpha }_{1}{x}^{\mathrm{T}}y+{\alpha }_{2}{u}^{\mathrm{T}}v$, where
 $α1=0.3 , x= 1,2,3,4,5 , y= -5,-4,3,2,1 , α2 = -7.0 , u=v= 0.4,0.3,0.2,0.1 .$
$y$ and $v$ are stored in reverse order, and $u$ is stored in reverse order in every other element of a real array.

### 10.1Program Text

Program Text (f16eafe.f90)

### 10.2Program Data

Program Data (f16eafe.d)

### 10.3Program Results

Program Results (f16eafe.r)