nag_ddot (f16eac) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG Library Manual

NAG Library Function Document

nag_ddot (f16eac)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_ddot (f16eac) updates a scalar by a scaled dot product of two real vectors, by performing
rβr+α xT y .

2  Specification

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

3  Description

nag_ddot (f16eac) performs the operation
r βr+ αxTy
where x and y are n-element real vectors, and r, α and β real scalars. If n is less than zero, or, if β is equal to one and either α or n is equal to zero, 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:     conjNag_ConjTypeInput
On entry: conj is not used. The presence of this argument in the BLAST standard is for consistency with the interface of the complex variant of this function.
Constraint: conj=Nag_NoConj or Nag_Conj.
2:     nIntegerInput
On entry: n, the number of elements in x and y.
3:     alphadoubleInput
On entry: the scalar α.
4:     x[1+n-1×incx]const doubleInput
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], for i=1,2,,n.
Intermediate elements of x are not referenced. If α=0.0 or n=0, x is not referenced and may be NULL.
5:     incxIntegerInput
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx0.
6:     betadoubleInput
On entry: the scalar β.
7:     y[1+n-1×incy]const doubleInput
On entry: the n-element vector y.
If incy>0, yi must be stored in y[i-1×incy], for i=1,2,,n.
If incy<0, yi must be stored in y[n-i×incy], for i=1,2,,n.
Intermediate elements of y are not referenced. If α=0.0 or n=0, y is not referenced and may be NULL.
8:     incyIntegerInput
On entry: the increment in the subscripts of y between successive elements of y.
Constraint: incy0.
9:     rdouble *Input/Output
On entry: the initial value, r, to be updated. If β=0.0, r need not be set on entry.
On exit: the value r, scaled by β and updated by the scaled dot product of x and y.
10:   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.

7  Accuracy

The dot product xTy  is computed using the BLAS routine DDOT.
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 scaled sum of two dot products, r= α1 xTy+ α2 uTv , where
α1=0.3 ,  x= 1,2,3,4,5 ,  y= -5,-4,3,2,1 ,  α2 = -7.0 ,  u=v= 0.4,0.3,0.2,0.1 .
y and v are stored in reverse order, and u is stored in reverse order in every other element of a real array.

10.1  Program Text

Program Text (f16eace.c)

10.2  Program Data

Program Data (f16eace.d)

10.3  Program Results

Program Results (f16eace.r)


nag_ddot (f16eac) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG Library Manual

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