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

Parameters

Compulsory Input Parameters

1: $conj$ – int64int32nag_int scalar: conj is not referenced and need not be set. The presence of this argument in the BLAST standard is for consistency with the interface of the complex variant of this function.
2: $n$ – int64int32nag_int scalar: $n$ , the number of elements in $x$ and $y$ .
3: $alpha$ – double scalar: The scalar $α$ .
4: $x (1 + (n - 1) \times |incx|)$ – double array: The $n$ -element vector $x$ .
If $incx > 0$ , $x_{i}$ must be stored in $x ((i - 1) \times |incx| + 1)$ , for $i = 1, 2, \dots, n$ .

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

Intermediate elements of x are not referenced. If $α = 0.0$ or $n = 0$ , x is not referenced.
5: $incx$ – int64int32nag_int scalar: The increment in the subscripts of x between successive elements of $x$ .

Constraint: $incx \neq 0$ .
6: $beta$ – double scalar: The scalar $β$ .
7: $y (1 + (n - 1) \times |incy|)$ – double array: The $n$ -element vector $y$ .
If $incy > 0$ , $y_{i}$ must be stored in $y ((i - 1) \times |incy| + 1)$ , for $i = 1, 2, \dots, n$ .

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

Intermediate elements of y are not referenced. If $α = 0.0$ or $n = 0$ , y is not referenced.
8: $incy$ – int64int32nag_int scalar: The increment in the subscripts of y between successive elements of $y$ .

Constraint: $incy \neq 0$ .
9: $r$ – double scalar: The initial value, $r$ , to be updated. If $β = 0.0$ , r need not be set on entry.

Optional Input Parameters

None.

Output Parameters

1: $r$ – double scalar: The value $r$ , scaled by $β$ and updated by the scaled dot product of $x$ and $y$ .

Error Indicators and Warnings

incx = 0

incy = 0

, an error message is printed and program execution is terminated.

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)).

Further Comments

None.

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.

Open in the MATLAB editor: f16ea_example

function f16ea_example


fprintf('f16ea example results\n\n');

% First dot product; equivalent of
% r =  0*r + 0.3*x*y(n:-1:1)'
n     = int64(5);
incx  = int64(1);
incy  = int64(-1);
x     = [1   2   3   4   5];
y     = [1   2   3  -4  -5];
alpha = 0.3;
beta  = 0;
conj  = int64(0);
r     = 0;

[r] = f16ea(...
            conj, n, alpha, x, incx, beta, y, incy, r);

fprintf('      first dot product = %7.2f\n',r); 

% Second ddot to be added to first; equivalent of
% r = r -7*x(2*(n-1)+1:-2:1)*y(n:-1:1)'
n     = int64(4);
incx  = int64(-2);
incy  = int64(-1);
alpha = -7.0;
beta  = 1;
x     = [0.1   9.9   0.2   9.9   0.3  9.9  0.4];
y     = [0.1   0.2   0.3   0.4];

[r] = f16ea(...
            conj, n, alpha, x, incx, beta, y, incy, r);

fprintf('Accumulated dot product = %7.2f\n',r);

f16ea example results

      first dot product =    2.70
Accumulated dot product =    0.60

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox