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: $n$ – int64int32nag_int scalar: $n$ , the number of elements in $x$ , $y$ and $w$ .
2: $alpha$ – double scalar: The scalar $α$ .
3: $x (1 + (n - 1) \times |incx|)$ – 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.
4: $incx$ – int64int32nag_int scalar: The increment in the subscripts of x between successive elements of $x$ .

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

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

Intermediate elements of y are not referenced.
7: $incy$ – int64int32nag_int scalar: The increment in the subscripts of y between successive elements of $y$ .

Constraint: $incy \neq 0$ .
8: $incw$ – int64int32nag_int scalar: The increment in the subscripts of w between successive elements of $w$ .

Constraint: $incw \neq 0$ .

Optional Input Parameters

None.

Output Parameters

1: $w (1 + (n - 1) \times |incw|)$ – double array: The $n$ -element vector $w$ .
If $incw > 0$ , $w_{i}$ is in $w (1 + (i - 1) \times incw)$ , for $i = 1, 2, \dots, n$ .

If $incw < 0$ , $w_{i}$ is in $w (1 + (n - i) \times incw)$ , for $i = 1, 2, \dots, n$ .

Intermediate elements of w are not referenced.

Error Indicators and Warnings

incx = 0

incy = 0

incw = 0

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

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)).

Further Comments

None.

Example

This example computes the result of a scaled vector accumulation for

\begin{matrix} α = 3, & x = {(- 6, 4.5, 3.7, 2.1, - 4)}^{T}, \\ β = - 1, & y = {(- 5.1, - 5, 6.4, - 2.4, - 3)}^{T} . \end{matrix}

x

and

y

, and also the sum vector

w

, are stored in reverse order.

Open in the MATLAB editor: f16eh_example

function f16eh_example


fprintf('f16eh example results\n\n');

% real vectors x and y;
n = int64(5);
x = [-4    2.1    3.7    4.5   -6.0];
y = [-3   -2.4    6.4   -5.0   -5.1];

% w = 3x - y;
alpha = 3;
beta = -1;

incx = int64(1);
incy = incx;
incw = incx;

[w] = f16eh(n, alpha, x, incx, beta, y, incy, incw);

fprintf('x = ');
fprintf('%5.1f',x);
fprintf('\ny = ');
fprintf('%5.1f',y);
fprintf('\n%4.1f x %+4.1f y = ',alpha,beta);
fprintf('%7.1f',w);
fprintf('\n');

f16eh example results

x =  -4.0  2.1  3.7  4.5 -6.0
y =  -3.0 -2.4  6.4 -5.0 -5.1
 3.0 x -1.0 y =    -9.0    8.7    4.7   18.5  -12.9

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Chapter Contents

Chapter Introduction

NAG Toolbox