NAG FL Interface
f16eaf (ddot)

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1 Purpose

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

2 Specification

Fortran Interface
Subroutine f16eaf ( conj, n, alpha, 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
C Header Interface
#include <nag.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 the names f16eaf, nagf_blast_ddot or its BLAST name blas_ddot.

3 Description

f16eaf performs the operation
r βr+ αxTy  
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 or 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 https://www.netlib.org/blas/blast-forum/blas-report.pdf

5 Arguments

1: conj Integer Input
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 Integer Input
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)×|incx|) Real (Kind=nag_wp) array Input
On entry: the n-element vector x.
If incx>0, xi must be stored in x((i-1)×incx+1), for i=1,2,,n.
If incx<0, xi must be stored in x((n-i)×|incx|+1), for i=1,2,,n.
Intermediate elements of x are not referenced. If α=0.0 or n=0, x is not referenced.
5: incx Integer Input
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx0.
6: beta Real (Kind=nag_wp) Input
On entry: the scalar β.
7: y(1+(n-1)×|incy|) Real (Kind=nag_wp) array Input
On entry: the n-element vector y.
If incy>0, yi must be stored in y((i-1)×incy+1), for i=1,2,,n.
If incy<0, yi must be stored in y((n-i)×|incy|+1), for i=1,2,,n.
Intermediate elements of y are not referenced. If α=0.0 or n=0, y is not referenced.
8: incy Integer Input
On entry: the increment in the subscripts of y between successive elements of y.
Constraint: incy0.
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

If incx=0 or incy=0, an error message is printed and program execution is terminated.

7 Accuracy

The dot product xTy 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

Background information to multithreading can be found in the Multithreading documentation.
f16eaf 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= α1 xTy+ α2 uTv , 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 (f16eafe.f90)

10.2 Program Data

Program Data (f16eafe.d)

10.3 Program Results

Program Results (f16eafe.r)