sladiv(l) [redhat man page]

SLADIV(l)								 )								 SLADIV(l)

NAME

       SLADIV - perform complex division in real arithmetic  a + i*b p + i*q = --------- c + i*d  The algorithm is due to Robert L

SYNOPSIS

       SUBROUTINE SLADIV( A, B, C, D, P, Q )

	   REAL 	  A, B, C, D, P, Q

PURPOSE

       SLADIV  performs complex division in real arithmetic a + i*b p + i*q = --------- c + i*d The algorithm is due to Robert L. Smith and can be
       found in D. Knuth, The art of Computer Programming, Vol.2, p.195

ARGUMENTS

       A       (input) REAL
	       B       (input) REAL C	    (input) REAL D	 (input) REAL The scalars a, b, c, and d in the above expression.

       P       (output) REAL
	       Q       (output) REAL The scalars p and q in the above expression.

LAPACK version 3.0						   15 June 2000 							 SLADIV(l)

SLAEIN(l)								 )								 SLAEIN(l)

NAME

       SLAEIN  -  use  inverse	iteration  to  find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg
       matrix H

SYNOPSIS

       SUBROUTINE SLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI, B, LDB, WORK, EPS3, SMLNUM, BIGNUM, INFO )

	   LOGICAL	  NOINIT, RIGHTV

	   INTEGER	  INFO, LDB, LDH, N

	   REAL 	  BIGNUM, EPS3, SMLNUM, WI, WR

	   REAL 	  B( LDB, * ), H( LDH, * ), VI( * ), VR( * ), WORK( * )

PURPOSE

       SLAEIN uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix
       H.

ARGUMENTS

       RIGHTV	(input) LOGICAL
		= .TRUE. : compute right eigenvector;
		= .FALSE.: compute left eigenvector.

       NOINIT	(input) LOGICAL
		= .TRUE. : no initial vector supplied in (VR,VI).
		= .FALSE.: initial vector supplied in (VR,VI).

       N       (input) INTEGER
	       The order of the matrix H.  N >= 0.

       H       (input) REAL array, dimension (LDH,N)
	       The upper Hessenberg matrix H.

       LDH     (input) INTEGER
	       The leading dimension of the array H.  LDH >= max(1,N).

       WR      (input) REAL
	       WI	(input)  REAL  The  real and imaginary parts of the eigenvalue of H whose corresponding right or left eigenvector is to be
	       computed.

       VR      (input/output) REAL array, dimension (N)
	       VI      (input/output) REAL array, dimension (N) On entry, if NOINIT = .FALSE. and WI = 0.0, VR must contain a real starting vector
	       for  inverse  iteration using the real eigenvalue WR; if NOINIT = .FALSE. and WI.ne.0.0, VR and VI must contain the real and imagi-
	       nary parts of a complex starting vector for inverse iteration using the complex eigenvalue (WR,WI); otherwise VR and VI need not be
	       set.   On exit, if WI = 0.0 (real eigenvalue), VR contains the computed real eigenvector; if WI.ne.0.0 (complex eigenvalue), VR and
	       VI contain the real and imaginary parts of the computed complex eigenvector. The eigenvector is normalized so that the component of
	       largest	magnitude has magnitude 1; here the magnitude of a complex number (x,y) is taken to be |x| + |y|.  VI is not referenced if
	       WI = 0.0.

       B       (workspace) REAL array, dimension (LDB,N)

       LDB     (input) INTEGER
	       The leading dimension of the array B.  LDB >= N+1.

       WORK   (workspace) REAL array, dimension (N)

       EPS3    (input) REAL
	       A small machine-dependent value which is used to perturb close eigenvalues, and to replace zero pivots.

       SMLNUM  (input) REAL
	       A machine-dependent value close to the underflow threshold.

       BIGNUM  (input) REAL
	       A machine-dependent value close to the overflow threshold.

       INFO    (output) INTEGER
	       = 0:  successful exit
	       = 1:  inverse iteration did not converge; VR is set to the last iterate, and so is VI if WI.ne.0.0.

LAPACK version 3.0						   15 June 2000 							 SLAEIN(l)