# NAG Library Routine Document

## 1Purpose

f16glf (blas_zsum) sums the elements of a complex vector.

## 2Specification

Fortran Interface
 Function f16glf ( n, x, incx)
 Complex (Kind=nag_wp) :: f16glf Integer, Intent (In) :: n, incx Complex (Kind=nag_wp), Intent (In) :: x(1+(n-1)*ABS(incx))
#include nagmk26.h
 Complex f16glf_ ( const Integer *n, const Complex x[], const Integer *incx)
The routine may be called by its BLAST name blas_zsum.

## 3Description

f16glf (blas_zsum) returns the sum
 $x1 + x2 + ⋯ + xn$
of the elements of an $n$-element complex vector $x$, via the function name.
If ${\mathbf{n}}\le 0$ on entry, f16glf (blas_zsum) returns the value $0+0i$.

## 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:     $\mathbf{x}\left(1+\left({\mathbf{n}}-1\right)×\left|{\mathbf{incx}}\right|\right)$ – Complex (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

f16glf (blas_zsum) is not threaded in any implementation.

None.

## 10Example

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

### 10.1Program Text

Program Text (f16glfe.f90)

### 10.2Program Data

Program Data (f16glfe.d)

### 10.3Program Results

Program Results (f16glfe.r)

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