f16 Chapter Contents
f16 Chapter Introduction
NAG Library Manual

# NAG Library Function Documentnag_ddot (f16eac)

## 1  Purpose

nag_ddot (f16eac) updates a scalar by a scaled dot product of two real vectors, by performing
 $r←βr+α xT y .$

## 2  Specification

 #include #include
 void nag_ddot (Nag_ConjType conj, Integer n, double alpha, const double x[], Integer incx, double beta, const double y[], Integer incy, double *r, NagError *fail)

## 3  Description

nag_ddot (f16eac) 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 function 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:    $\mathbf{conj}$Nag_ConjTypeInput
On entry: conj is not used. The presence of this argument in the BLAST standard is for consistency with the interface of the complex variant of this function.
Constraint: ${\mathbf{conj}}=\mathrm{Nag_NoConj}$ or $\mathrm{Nag_Conj}$.
2:    $\mathbf{n}$IntegerInput
On entry: $n$, the number of elements in $x$ and $y$.
3:    $\mathbf{alpha}$doubleInput
On entry: the scalar $\alpha$.
4:    $\mathbf{x}\left[1+\left({\mathbf{n}}-1\right)×\left|{\mathbf{incx}}\right|\right]$const doubleInput
On entry: the $n$-element vector $x$.
If ${\mathbf{incx}}>0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{x}}\left[\left(\mathit{i}-1\right)×{\mathbf{incx}}\right]$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
If ${\mathbf{incx}}<0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{x}}\left[\left({\mathbf{n}}-\mathit{i}\right)×\left|{\mathbf{incx}}\right|\right]$, 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 and may be NULL.
5:    $\mathbf{incx}$IntegerInput
On entry: the increment in the subscripts of x between successive elements of $x$.
Constraint: ${\mathbf{incx}}\ne 0$.
6:    $\mathbf{beta}$doubleInput
On entry: the scalar $\beta$.
7:    $\mathbf{y}\left[1+\left({\mathbf{n}}-1\right)×\left|{\mathbf{incy}}\right|\right]$const doubleInput
On entry: the $n$-element vector $y$.
If ${\mathbf{incy}}>0$, ${y}_{\mathit{i}}$ must be stored in ${\mathbf{y}}\left[\left(\mathit{i}-1\right)×{\mathbf{incy}}\right]$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
If ${\mathbf{incy}}<0$, ${y}_{\mathit{i}}$ must be stored in ${\mathbf{y}}\left[\left({\mathbf{n}}-\mathit{i}\right)×\left|{\mathbf{incy}}\right|\right]$, 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 and may be NULL.
8:    $\mathbf{incy}$IntegerInput
On entry: the increment in the subscripts of y between successive elements of $y$.
Constraint: ${\mathbf{incy}}\ne 0$.
9:    $\mathbf{r}$double *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 $y$.
10:  $\mathbf{fail}$NagError *Input/Output
The NAG error argument (see Section 2.7 in How to Use the NAG Library and its Documentation).

## 6  Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.
NE_INT
On entry, ${\mathbf{incx}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{incx}}\ne 0$.
On entry, ${\mathbf{incy}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{incy}}\ne 0$.
NE_INTERNAL_ERROR
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

## 7  Accuracy

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)).

## 8  Parallelism and Performance

nag_ddot (f16eac) is not threaded in any implementation.

None.

## 10  Example

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.

### 10.1  Program Text

Program Text (f16eace.c)

### 10.2  Program Data

Program Data (f16eace.d)

### 10.3  Program Results

Program Results (f16eace.r)