# NAG C Library Function Document

## 1Purpose

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

## 2Specification

 #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)

## 3Description

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.
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:    $\mathbf{conj}$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 3.7 in How to Use the NAG Library and its Documentation).

## 6Error 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_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.

## 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

nag_ddot (f16eac) 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 function. 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 (f16eace.c)

### 10.2Program Data

Program Data (f16eace.d)

### 10.3Program Results

Program Results (f16eace.r)