NAG Library Function Document

nag_zwaxpby (f16ghc)

void	nag_zwaxpby (Integer n, Complex alpha, const Complex x[], Integer incx, Complex beta, const Complex y[], Integer incy, Complex w[], Integer incw, NagError *fail)

3 Description

nag_zwaxpby (f16ghc) performs the operation

w \leftarrow α x + β y,

where

x

and

y

are

n

-element complex vectors, and

α

and

β

are complex scalars.

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 Arguments

1: n – IntegerInput: On entry: $n$ , the number of elements in $x$ , $y$ and $w$ .

Constraint: $n \geq 0$ .
2: alpha – ComplexInput: On entry: the scalar $α$ .
3: x[ $\dim$ ] – const ComplexInput: Note: the dimension, dim, of the array x must be at least $\max (1, 1 + (n - 1) \times |incx|)$ .
On entry: the $n$ -element vector $x$ .
If $incx > 0$ , $x_{i}$ must be stored in $x [(i - 1) \times |incx|]$ , for $i = 1, 2, \dots, n$ .

If $incx < 0$ , $x_{i}$ must be stored in $x [(n - i) \times |incx| - 2]$ , for $i = 1, 2, \dots, n$ .

Intermediate elements of x are not referenced.
4: incx – IntegerInput: On entry: the increment in the subscripts of x between successive elements of $x$ .
Constraint: $incx \neq 0$ .
5: beta – ComplexInput: On entry: the scalar $β$ .
6: y[ $\dim$ ] – const ComplexInput: Note: the dimension, dim, of the array y must be at least $\max (1, 1 + (n - 1) \times |incy|)$ .
On entry: the $n$ -element vector $y$ .
If $incy > 0$ , $y_{i}$ must be stored in $y [1 + (i - 1) \times incy - 1]$ , for $i = 1, 2, \dots, n$ .

If $incy < 0$ , $y_{i}$ must be stored in $y [1 - (n - i) \times incy - 1]$ , for $i = 1, 2, \dots, n$ .

Intermediate elements of y are not referenced.
7: incy – IntegerInput: On entry: the increment in the subscripts of y between successive elements of $y$ .
Constraint: $incy \neq 0$ .
8: w[ $\dim$ ] – ComplexOutput: Note: the dimension, dim, of the array w must be at least $\max (1, 1 + (n - 1) \times |incw|)$ .

On exit: the $n$ -element vector $w$ .
If $incw > 0$ , $w_{i}$ is in $w [1 + (i - 1) \times incw - 1]$ , for $i = 1, 2, \dots, n$ .

If $incw < 0$ , $w_{i}$ is in $w [1 + (n - i) \times incw - 1]$ , for $i = 1, 2, \dots, n$ .

Intermediate elements of w are not referenced.
9: incw – IntegerInput: On entry: the increment in the subscripts of w between successive elements of $w$ .
Constraint: $incw \neq 0$ .
10: fail – NagError *Input/Output: The NAG error argument (see Section 3.6 in the Essential Introduction).

6 Error Indicators and Warnings

NE_BAD_PARAM: On entry, argument $⟨value⟩$ had an illegal value.
NE_INT: On entry, $incw = ⟨value⟩$ .
Constraint: $incw \neq 0$ .
On entry, $incx = ⟨value⟩$ .
Constraint: $incx \neq 0$ .
On entry, $incy = ⟨value⟩$ .
Constraint: $incy \neq 0$ .
On entry, $n = ⟨value⟩$ .
Constraint: $n \geq 0$ .

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)).

8 Parallelism and Performance

Not applicable.

9 Further Comments

None.

10 Example

This example computes the result of a scaled vector accumulation for

\begin{matrix} α = 3 + 2 i, & x = {(- 4 + 2.1 i, 3.7 + 4.5 i, - 6 + 1.2 i)}^{T}, \\ β = - i, & y = {(- 3 - 2.4 i, 6.4 - 5 i, - 5.1)}^{T} . \end{matrix}

NAG Library Function Documentnag_zwaxpby (f16ghc)

+− Contents

1 Purpose

2 Specification