NAG Library Routine Document

1Purpose

f16elf (blas_dsum) sums the elements of a real vector.

2Specification

Fortran Interface
 Function f16elf ( n, x, incx)
 Real (Kind=nag_wp) :: f16elf Integer, Intent (In) :: n, incx Real (Kind=nag_wp), Intent (In) :: x(1+(n-1)*ABS(incx))
#include nagmk26.h
 double f16elf_ (const Integer *n, const double x[], const Integer *incx)
The routine may be called by its BLAST name blas_dsum.

3Description

f16elf (blas_dsum) returns the sum
 $x1 + x2 + ⋯ + xn$
of the elements of an $n$-element real vector $x$, via the function name.
If ${\mathbf{n}}\le 0$ on entry, f16elf (blas_dsum) returns the value $0$.

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:     $\mathbf{n}$ – IntegerInput
On entry: $n$, the number of elements in $x$.
2:     $\mathbf{x}\left(1+\left({\mathbf{n}}-1\right)×\left|{\mathbf{incx}}\right|\right)$ – 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 ${\mathbf{n}}=0$, x is not referenced.
3:     $\mathbf{incx}$ – IntegerInput
On entry: the increment in the subscripts of x between successive elements of $x$.
Constraint: ${\mathbf{incx}}\ne 0$.

6Error Indicators and Warnings

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

7Accuracy

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

f16elf (blas_dsum) is not threaded in any implementation.

None.

10Example

This example computes the sum of the elements of
 $x = 1.1,10.2,11.5,-2.7,9.2T .$

10.1Program Text

Program Text (f16elfe.f90)

10.2Program Data

Program Data (f16elfe.d)

10.3Program Results

Program Results (f16elfe.r)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017