# NAG CL Interfacef16eac (ddot)

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## 1Purpose

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

## 2Specification

 #include
 void f16eac (Nag_ConjType conj, Integer n, double alpha, const double x[], Integer incx, double beta, const double y[], Integer incy, double *r, NagError *fail)
The function may be called by the names: f16eac, nag_blast_ddot or nag_ddot.

## 3Description

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.

## 4References

Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001) Basic Linear Algebra Subprograms Technical (BLAST) Forum Standard University of Tennessee, Knoxville, Tennessee https://www.netlib.org/blas/blast-forum/blas-report.pdf

## 5Arguments

1: $\mathbf{conj}$Nag_ConjType Input
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: $\mathbf{n}$Integer Input
On entry: $n$, the number of elements in $x$ and $y$.
3: $\mathbf{alpha}$double Input
On entry: the scalar $\alpha$.
4: $\mathbf{x}\left[1+\left({\mathbf{n}}-1\right)×|{\mathbf{incx}}|\right]$const double Input
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 ${\mathbf{x}}\left[\left({\mathbf{n}}-\mathit{i}\right)×|{\mathbf{incx}}|\right]$, 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: $\mathbf{incx}$Integer Input
On entry: the increment in the subscripts of x between successive elements of $x$.
Constraint: ${\mathbf{incx}}\ne 0$.
6: $\mathbf{beta}$double Input
On entry: the scalar $\beta$.
7: $\mathbf{y}\left[1+\left({\mathbf{n}}-1\right)×|{\mathbf{incy}}|\right]$const double Input
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 ${\mathbf{y}}\left[\left({\mathbf{n}}-\mathit{i}\right)×|{\mathbf{incy}}|\right]$, 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: $\mathbf{incy}$Integer Input
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 7 in the Introduction to the NAG Library CL Interface).

## 6Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface 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 8 in the Introduction to the NAG Library CL Interface 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

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)