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 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
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: $incy \neq 0$ .
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

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

nag_ddot (f16eac) 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 x06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

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 Document

nag_ddot (f16eac)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

1

Purpose

2

Specification