F16 Chapter Contents
F16 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF16GLF (BLAS_ZSUM)

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

## 1  Purpose

F16GLF (BLAS_ZSUM) sums the elements of a complex vector.

## 2  Specification

 FUNCTION F16GLF ( N, X, INCX)
 COMPLEX (KIND=nag_wp) F16GLF
 INTEGER N, INCX COMPLEX (KIND=nag_wp) X(1+(N-1)*ABS(INCX))
The routine may be called by its BLAST name blas_zsum.

## 3  Description

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 $0+0i$.

## 4  References

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

## 5  Parameters

1:     N – INTEGERInput
On entry: $n$, the number of elements in $x$.
2:     X($1+\left({\mathbf{N}}-1\right)×\left|{\mathbf{INCX}}\right|$) – COMPLEX (KIND=nag_wp) arrayInput
On entry: the vector $x$. Element ${x}_{\mathit{i}}$ is stored in ${\mathbf{X}}\left(\left(\mathit{i}-1\right)×\left|{\mathbf{INCX}}\right|+1\right)$, for $\mathit{i}=1,2,\dots ,n$.
3:     INCX – INTEGERInput
On entry: the increment in the subscripts of X between successive elements of $x$.
Constraint: ${\mathbf{INCX}}\ne 0$.

## 6  Error Indicators and Warnings

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

## 7  Accuracy

The BLAS standard requires accurate implementations which avoid unnecessary over/underflow (see Section 2.7 of Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001)).

None.

## 9  Example

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

### 9.1  Program Text

Program Text (f16glfe.f90)

### 9.2  Program Data

Program Data (f16glfe.d)

### 9.3  Program Results

Program Results (f16glfe.r)