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 $x$ and $y$ .
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 $y ((i - 1) \times incy + 1)$ , 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.
7: $incy$ – int64int32nag_int scalar: The increment in the subscripts of y between successive elements of $y$ .

Constraint: $incy \neq 0$ .

Optional Input Parameters

None.

Output Parameters

1: $y (1 + (n - 1) \times |incy|)$ – complex array: The updated vector $y$ stored in the array elements used to supply the original vector $y$ .
Intermediate elements of y are unchanged.

Error Indicators and Warnings

incx = 0

incy = 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

are stored in reverse order.

Open in the MATLAB editor: f16gc_example

function f16gc_example


fprintf('f16gc 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;

incx = int64(-1);
incy = int64(-1);
[z] = f16gc( ...
	     n, alpha, x, incx, beta, y, incy);

disp('x, y:');
fprintf('  x = ');
for j = 1:n
  fprintf('%11.4f %+ 8.4fi',real(x(j)),imag(x(j)));
end
fprintf('\n  y = ');
for j = 1:n
  fprintf('%11.4f %+ 8.4fi',real(y(j)),imag(y(j)));
end

fprintf('\n\nalpha = %5.1f%+5.1fi      beta = %5.1f%+5.1fi\n', ...
	real(alpha), imag(alpha), real(beta), imag(beta));
fprintf('\nalpha*x + beta*y = \n      ');
for j = 1:n
  fprintf('%11.4f %+ 8.4fi',real(z(j)),imag(z(j)));
end
fprintf('\n');

f16gc example results

x, y:
  x =     -4.0000  +2.1000i     3.7000  +4.5000i    -6.0000  +1.2000i
  y =     -3.0000  -2.4000i     6.4000  -5.0000i    -5.1000  +0.0000i

alpha =   3.0 +2.0i      beta =   0.0 -1.0i

alpha*x + beta*y = 
         -18.6000  +1.3000i    -2.9000 +14.5000i   -20.4000  -3.3000i

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

Chapter Contents

Chapter Introduction

NAG Toolbox