F121 Vector Algebra

Performs various vector manipulations, such as addition of two vectors, multiplication of a vector by a scalar, scalar product, pre- and post-multiplication of a vector by a matrix.

Structure:

SUBROUTINE, and FUNCTION subprograms
User Entry Names:

VADD,	VSUB,	VMUL,	VBIAS,	VSCALE,	VLINCO,	VUNIT,	VMATR,
VMATL,	VCOPYN,	VFIX,	VFLOAT,	VFILL,	VZERO,	VBLANK,	VEXCUM,
VDIST,	VDIST2,	VDOT,	VDOTN,	VDOTN2,	VMOD,	VASUM,	VSUM,
VMAXA,	VMAX,	VMINA,	VMIN,	LVMAXA,	LVMAX,	LVMINA,	LVMIN,
LVSMI,	LVSMX,	LVSDMI,	LVSDMX,	LVSIMI,	LVSIMX

Notes:

VLINE is the original and obsolete name for the linear combination routine VLINCO; it was changed because it clashed with an entry point in some system library.

Usage:

The arguments in the calling sequences below are defined as follows:

A,B,X

( REAL) One-dimensional arrays of length N.

DA

( DOUBLE PRECISION) One-dimensional array of length N.

IA,IX

( INTEGER) One-dimensional arrays of length N.

C,V

( REAL) One-dimensional arrays of length M.

EX

( REAL) One-dimensional array of length 3.

G

( REAL) Two-dimensional array of dimension (M,N).

ALPHA

( REAL) Variable.

F1,F2

( REAL) Variables.

Y

( REAL) Variable.

N,M

( INTEGER) Variables.

Any summation $\sum$ is taken over the index I from 1 to N or over the index J from 1 to M.

Subroutines

CALL VADD(A,B,X,N)	$X(I)=A(I)+B(I)$	$(I=1,2,...,N)$
CALL VSUB(A,B,X,N)	$X(I)=A(I)-B(I)$	$(I=1,2,...,N)$
CALL VMUL(A,B,X,N)	$X(I)=A(I)*B(I)$	$(I=1,2,...,N)$
CALL VBIAS(A,ALPHA,X,N)	$X(I)=A(I)+ALPHA$	$(I=1,2,...,N)$
CALL VSCALE(A,ALPHA,X,N)	$X(I)=A(I)*ALPHA$	$(I=1,2,...,N)$
CALL VLINCO(A,F1,B,F2,X,N)	$X(I)=A(I)*F1+B(I)*F2$	$(I=1,2,...,N)$
CALL VUNIT(A,X,N)	$x\; =\; a\; /\; |a|$
	$X(I)=A(I)/VMOD(A,N)$	$(I=1,2,...,N)$
CALL VMATR(A,G,V,N,M)	$v\; =\; aG$
	$V(J)=\; \sum \; A(I)*G(J,I)$	$(J=1,2,...,M)$
CALL VMATL(G,C,X,N,M)	$x\; =\; Gc$
	$X(I)=\; \sum \; G(J,I)*C(J)$	$(I=1,2,...,N)$
CALL VCOPYN(A,X,N)	$X(I)=-A(I)$	$(I=1,2,...,N)$
CALL VFIX(A,IX,N)	$IX(I)=A(I)$	$(I=1,2,...,N)$
CALL VFLOAT(IA,X,N)	$X(I)=IA(I)$	$(I=1,2,...,N)$
CALL VFILL(X,N,ALPHA)	$X(I)=ALPHA$	$(I=1,2,...,N)$
CALL VZERO(IX,N)	$IX(I)=0$	$(I=1,2,...,N)$
CALL VBLANK(IX,N)	$IX(I)=blank$	$(I=1,2,...,N)$
CALL VEXCUM(A,EX,N)	$EX(1)=min(EX(1),A(1),...,A(N))$
	$EX(2)=max(EX(2),A(1),...,A(N))$
	$EX(3)=EX(3)+\sum \; A(I)$

REAL functions

VDIST2(A,B,N)	$(a-b)2=\sum \; (A(I)-B(I))2$
VDIST(A,B,N)	$|a-b|\; =(a-b)2$
VDOT(A,B,N)	$ab\; =\sum \; A(I)*B(I)$
VDOTN2(A,B,N)	$(ab)2/\; (a2b2)$
VDOTN(A,B,N)	$ab\; /\; |a|\; |b|$
VMOD (A,N)	$|a|\; =a2$
VASUM(A,N)	$\sum \; |A(I)|$
VSUM (A,N)	$\sum \; A(I)$
VMAXA(A,N)	$max(|A(1)|,|A(2)|,...,|A(N)|)$
VMAX (A,N)	$max(A(1),A(2),...,A(N))$
VMINA(A,N)	$min(|A(1)|,|A(2)|,...,|A(N)|)$
VMIN (A,N)	$min(A(1),A(2),...,A(N))$

INTEGER functions

LVMAXA(A,N)	Location of $max|A(I)|$
LVMAX (A,N)	Location of $maxA(I)$
LVMINA(A,N)	Location of $min|A(I)|$
LVMIN (A,N)	Location of $minA(I)$
LVSMI(A,N,INC)	Location of $minA(k)$
LVSMX(A,N,INC)	Location of $maxA(k)$
LVSDMI(DA,N,INC)	Location of $minDA(k)$
LVSDMX(DA,N,INC)	Location of $maxDA(k)$
LVSIMI(IA,N,INC)	Location of $minIA(k)$
LVSIMX(IA,N,INC)	Location of $maxIA(k)$

where $k=1,1+INC,1+2*INC,...,1+(N-1)*INC$

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F122