NAG Library Function Document

nag_ddot (f16eac)

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 \leftarrow β r + α x^{T} y

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

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: conj – Nag_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: n – IntegerInput: On entry: $n$ , the number of elements in $x$ and $y$ .
3: alpha – doubleInput: On entry: the scalar $α$ .
4: x[ $1 + (n - 1) \times |incx|$ ] – const doubleInput: 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 $x [(n - i) \times |incx|]$ , for $i = 1, 2, \dots, n$ .

Intermediate elements of x are not referenced. If $α = 0.0$ or $n = 0$ , x is not referenced and may be NULL.
5: incx – IntegerInput: On entry: the increment in the subscripts of x between successive elements of $x$ .
Constraint: $incx \neq 0$ .
6: beta – doubleInput: On entry: the scalar $β$ .
7: y[ $1 + (n - 1) \times |incy|$ ] – const doubleInput: On entry: the $n$ -element vector $y$ .
If $incy > 0$ , $y_{i}$ must be stored in $y [(i - 1) \times |incy|]$ , for $i = 1, 2, \dots, n$ .

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

Intermediate elements of y are not referenced. If $α = 0.0$ or $n = 0$ , y is not referenced and may be NULL.
8: incy – IntegerInput: On entry: the increment in the subscripts of y between successive elements of $y$ .
Constraint: $incy \neq 0$ .
9: r – double *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: 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, $incx = ⟨value⟩$ .
Constraint: $incx \neq 0$ .
On entry, $incy = ⟨value⟩$ .
Constraint: $incy \neq 0$ .

7 Accuracy

The dot product

x^{T} y

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 = α_{1} x^{T} y + α_{2} u^{T} v

, where

\begin{matrix} α_{1} = 0.3, & x = (1, 2, 3, 4, 5), y = (- 5, - 4, 3, 2, 1), \\ α_{2} = - 7.0, & u = v = (0.4, 0.3, 0.2, 0.1) . \end{matrix}

y

and

v

are stored in reverse order, and

u

is stored in reverse order in every other element of a real array.

NAG Library Function Documentnag_ddot (f16eac)

+− Contents

1 Purpose

2 Specification