F002 Elementary Vector Processing

These subprograms perform elementary vector operations.

Structure:

SUBROUTINE and FUNCTION subprograms
User Entry Names:

RVADD,	RVCPY,	RVDIV,	RVMPA,	RVMPY,	RVMUL,	RVMULA,	RVMUNA,
RVRAN,	RVSCA,	RVSCL,	RVSCS,	RVSET,	RVSUB,	RVSUM,	RVXCH,
DVADD,	DVCPY,	DVDIV,	DVMPA,	DVMPY,	DVMUL,	DVMULA,	DVMUNA,
DVRAN,	DVSCA,	DVSCL,	DVSCS,	DVSET,	DVSUB,	DVSUM,	DVXCH,
CVADD,	CVCPY,	CVDIV,	CVMPA,	CVMPY,	CVMUL,	CVMULA,	CVMUNA,
CVRAN,	CVSCA,	CVSCL,	CVSCS,	CVSET,	CVSUB,	CVSUM,	CVXCH,
CVMPYC,	CVMPAC

External References: LOCF (N100), RANF, DRANF (G900) (some Fortran versions only).

Usage:

For $t=R$ (type REAL), $t=D$ (type DOUBLE PRECISION), $t=C$ (type COMPLEX):

CALL tVSET (N,S,Z1,Z2)	$z$j=s
CALL tVRAN (N,A,B,Z1,Z2)	$z$j= random (see Note2)
CALL tVCPY (N,X1,X2,Z1,Z2)	$z$j=xj
CALL tVXCH (N,X1,X2,Y1,Y2)	interchanges $x$j with $y$j
CALL tVADD (N,X1,X2,Y1,Y2,Z1,Z2)	$z$j=xj+yj
CALL tVSUB (N,X1,X2,Y1,Y2,Z1,Z2)	$z$j=xj-yj
CALL tVMUL (N,X1,X2,Y1,Y2,Z1,Z2)	$z$j=xjyj
CALL tVMULA(N,X1,X2,Y1,Y2,Z1,Z2)	$z$j=xjyj+zj
CALL tVMUNA(N,X1,X2,Y1,Y2,Z1,Z2)	$z$j=-xjyj+zj
CALL tVDIV (N,X1,X2,Y1,Y2,Z1,Z2,IFAIL)	$z$j=xj/yj (see Note3)
CALL tVSCL (N,S,X1,X2,Z1,Z2)	$z$j=sxj
CALL tVSCA (N,S,X1,X2,Y1,Y2,Z1,Z2)	$z$j=sxj+yj
CALL tVSCS (N,S,X1,X2,Y1,Y2,Z1,Z2)	$z$j=sxj-yj
F = tVSUM (N,X1,X2)	$f\; =\; x$1+ ...+xn
F = tVMPY (N,X1,X2,Y1,Y2)	$f\; =\; x$1y1+ ...+xnyn
F = tVMPA (N,X1,X2,Y1,Y2,S)	$f\; =\; x$1y1+ ...+xnyn+s
F = CVMPYC(N,X1,X2,Y1,Y2)	$f\; =\; x$1y1+ ...+xnyn
F = CVMPAC(N,X1,X2,Y1,Y2,S)	$f\; =\; x$1y1+ ...+xnyn+s

where $y$_j is the complex conjugate of $y$_j .

N

( INTEGER) The mathematical dimension of the vectors $(j\; =\; 1,2,...,N)$ .

S,A,B

(Type according to t) The scalar values s, a, and b, respectively.

X1,X2

(Type according to t) Array elements. They must contain the elements $x$₁,x₂ of the vector $(x$_j) .

Y1,Y2

(Type according to t) Array elements. They must contain the elements $y$₁,y₂ of the vector $(y$_j) .

Z1,Z2

(Type according to t) Array elements. On exit, they will contain the elements $z$₁,z₂ of the result vector $(z$_j) .

IFAIL

( INTEGER) On exit, IFAIL is set to zero if all elements $y$_j are non-zero. Otherwise IFAIL is set to the smallest index k for which $y$_k= 0 .

Restrictions:

If vector $(z$_j) overlaps with vector $(x$_j) or $(y$_j) , results will be correct provided each element $z$_j coincides with an element $x$_k

or $y$_k , where k<j.

Accuracy:

On computers with IBM 370 architecture, RVMPY, RVMPA, CVMPY and CVMPA accumulate the inner product using double-precision arithmetic internally; the final result is then rounded to single precision.

Notes:

1. The vectors $(x$_j) etc. need not be packed: any equidistant spacing of their elements is permitted. The subprograms determine the location of the vector element $x$_j from the actual arguments X1 and X2.
2. tVRAN sets $z$_j to a random value of type t that is uniformly distributed in the interval (A,B). For CVRAN, the real and imaginary parts of $z$_j are distributed uniformly and independently in (REAL(A),REAL(B)) and in (AIMAG(A),AIMAG(B)).
3. If $y$_k= 0 and $y$₁,...,y_k-1 are non-zero, tVDIV computes only $z$₁,...,z_k-1 and sets $IFAIL=\; k$ .
4. The use of an in-line DO loop will be more efficient than calling the equivalent vector processing subprogram when the vector length is sufficiently small, due to the overhead of the subprogram call.

F003

H. Lipps