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: $alpha$ – complex scalar: The scalar $α$ .
3: $x (1 + (n - 1) \times |incx|)$ – complex 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: $beta$ – complex scalar: The scalar $β$ .
6: $y (1 + (n - 1) \times |incy|)$ – complex 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: $w (1 + (n - 1) \times |incw|)$ – complex 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 + 2 i, & x = {(- 6 + 1.2 i, 3.7 + 4.5 i, - 4 + 2.1 i)}^{T}, \\ β = - i, & y = {(- 5.1, 6.4 - 5 i, - 3 - 2.4 i)}^{T} . \end{matrix}

x

and

y

, and also the sum vector

w

, are stored in reverse order.

Open in the MATLAB editor: f16gh_example

function f16gh_example


fprintf('f16gh example results\n\n');

n = int64(3);
x = [ -4 + 2.1i    3.7 + 4.5i     -6   + 1.2i];
y = [ -3 - 2.4i    6.4 - 5.0i     -5.1 + 0.0i];

% z = alpha*x +beta*y;
alpha =  3 + 2i;
beta  =  0 - 1i;

fprintf('w = alpha*x + beta*y\n');
fprintf('alpha = %5.1f%+5.1fi      beta = %5.1f%+5.1fi\n', ...
	real(alpha), imag(alpha), real(beta), imag(beta));

incx = int64(1);
incy = int64(1);
incw = int64(1);
[w] = f16gh( ...
	     n, alpha, x, incx, beta, y, incy, incw);

disp('          x                  y                  w');
disp([x; y; w']');

f16gh example results

w = alpha*x + beta*y
alpha =   3.0 +2.0i      beta =   0.0 -1.0i
          x                  y                  w
  -4.0000 - 2.1000i  -3.0000 + 2.4000i -18.6000 + 1.3000i
   3.7000 - 4.5000i   6.4000 + 5.0000i  -2.9000 +14.5000i
  -6.0000 - 1.2000i  -5.1000 + 0.0000i -20.4000 - 3.3000i

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

Chapter Contents

Chapter Introduction

NAG Toolbox