nag_daxpby (f16ecc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG Library Manual

NAG Library Function Document

nag_daxpby (f16ecc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_daxpby (f16ecc) computes the sum of two scaled vectors, for real vectors and scalars.
nag_daxpby (f16ecc) performs the operation
yαx+β y .

2  Specification

#include <nag.h>
#include <nagf16.h>
void  nag_daxpby (Integer n, double alpha, const double x[], Integer incx, double beta, const double y[], Integer incy, NagError *fail)

3  Description

nag_daxpby (f16ecc) performs the operation
yα x+β y
where x and y are n-element real vectors, and α and β real scalars. If n is equal to zero, or if α is equal to zero and β is equal to 1, this function 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 http://www.netlib.org/blas/blast-forum/blas-report.pdf

5  Arguments

1:     nIntegerInput
On entry: n, the number of elements in x and y.
Constraint: n0.
2:     alphadoubleInput
On entry: the scalar α.
3:     x[dim]const doubleInput
Note: the dimension, dim, of the array x must be at least max1,1+n-1×incx.
On entry: the n-element vector x.
If incx>0, xi must be stored in x[i-1×incx], for i=1,2,,n.
If incx<0, xi must be stored in x[n-i×incx-2], for i=1,2,,n.
Intermediate elements of x are not referenced.
4:     incxIntegerInput
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx0.
5:     betadoubleInput
On entry: the scalar β.
6:     y[dim]const doubleInput
Note: the dimension, dim, of the array y must be at least max1,1+n-1×incy.
On entry: the n-element vector y.
If incy>0, yi must be stored in y[1+i-1×incy], for i=1,2,,n.
If incy<0, yi must be stored in y[1-n-i×incy], for i=1,2,,n.
Intermediate elements of y are not referenced.
On exit: the updated vector y stored in the array elements used to supply the original vector y.
Intermediate elements of y are unchanged.
7:     incyIntegerInput
On entry: the increment in the subscripts of y between successive elements of y.
Constraint: incy0.
8:     failNagError *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, incx=value.
Constraint: incx0.
On entry, incy=value.
Constraint: incy0.
On entry, n=value.
Constraint: n0.

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

nag_daxpby (f16ecc) is not threaded by NAG in any implementation.
nag_daxpby (f16ecc) 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 Users' Note for your implementation for any additional implementation-specific information.

9  Further Comments

None.

10  Example

This example computes the result of a scaled vector accumulation for
α=3,   x = -4,2.1,3.7,4.5,-6T , β=-1,   y = -3,-2.4,6.4,-5,-5.1T .
See Section 10 in nag_real_banded_sparse_eigensystem_sol (f12agc) and nag_real_symm_banded_sparse_eigensystem_sol (f12fgc).

10.1  Program Text

Program Text (f16ecce.c)

10.2  Program Data

Program Data (f16ecce.d)

10.3  Program Results

Program Results (f16ecce.r)


nag_daxpby (f16ecc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2014