slasorte(3) [debian man page]

SLASORTE(l)						   LAPACK routine (version 1.5) 					       SLASORTE(l)

NAME

       SLASORTE - sort eigenpairs so that real eigenpairs are together and  complex are together

SYNOPSIS

       SUBROUTINE SLASORTE ( S, LDS, J, OUT, INFO )

	   INTEGER	   INFO, J, LDS

	   REAL 	   OUT( J, * ), S( LDS, * )

PURPOSE

       SLASORTE sorts eigenpairs so that real eigenpairs are together and
	 complex are together.	This way one can employ 2x2 shifts easily
	 since every 2nd subdiagonal is guaranteed to be zero.
       This routine does no parallel work and makes no calls.

ARGUMENTS

       S       (local input/output) REAL array, dimension LDS
	       On  entry,  a  matrix  already  in Schur form.  On exit, the diagonal blocks of S have been rewritten to pair the eigenvalues.  The
	       resulting matrix is no longer similar to the input.

       LDS     (local input) INTEGER
	       On entry, the leading dimension of the local array S.  Unchanged on exit.

       J       (local input) INTEGER
	       On entry, the order of the matrix S.  Unchanged on exit.

       OUT     (local input/output) REAL array, dimension Jx2
	       This is the work buffer required by this routine.

       INFO    (local input) INTEGER
	       This is set if the input matrix had an odd number of real eigenvalues and things couldn't be paired or if the input  matrix  S  was
	       not originally in Schur form.  0 indicates successful completion.

	       Implemented by:	G. Henry, May 1, 1997

LAPACK version 1.5						    12 May 1997 						       SLASORTE(l)

DLAMSH(l)					      LAPACK auxiliary routine (version 1.5)						 DLAMSH(l)

NAME

       DLAMSH - send multiple shifts through a small (single node) matrix to  see how consecutive small subdiagonal elements are modified by  sub-
       sequent shifts in an effort to maximize the number of bulges  that can be sent through

SYNOPSIS

       SUBROUTINE DLAMSH ( S, LDS, NBULGE, JBLK, H, LDH, N, ULP )

	   INTEGER	 LDS, NBULGE, JBLK, LDH, N

	   DOUBLE	 PRECISION ULP

	   DOUBLE	 PRECISION S(LDS,*), H(LDH,*)

PURPOSE

       DLAMSH sends multiple shifts through a small (single node) matrix to
	  see how consecutive small subdiagonal elements are modified by
	  subsequent shifts in an effort to maximize the number of bulges
	  that can be sent through.  DLAMSH should only be called when there are multiple shifts/bulges
	  (NBULGE > 1) and the first shift is starting in the middle of an
	  unreduced Hessenberg matrix because of two or more consecutive small
	  subdiagonal elements.

ARGUMENTS

       S       (local input/output) DOUBLE PRECISION array, (LDS,*)
	       On entry, the matrix of shifts.	Only the 2x2 diagonal of S is referenced.  It is assumed that S has JBLK double shifts	(size  2).
	       On exit, the data is rearranged in the best order for applying.

       LDS     (local input) INTEGER
	       On entry, the leading dimension of S.  Unchanged on exit.  1 < NBULGE <= JBLK <= LDS/2

       NBULGE  (local input/output) INTEGER
	       On  entry, the number of bulges to send through H ( >1 ).  NBULGE should be less than the maximum determined (JBLK).  1 < NBULGE <=
	       JBLK <= LDS/2 On exit, the maximum number of bulges that can be sent through.

       JBLK    (local input) INTEGER
	       On entry, the number of shifts determined for S.  Unchanged on exit.

       H       (local input/output) DOUBLE PRECISION array (LDH,N)
	       On entry, the local matrix to apply the shifts on.  H should be aligned so that the starting row  is  2.   On  exit,  the  data	is
	       destroyed.

       LDS     (local input) INTEGER
	       On entry, the leading dimension of S.  Unchanged on exit.

       N       (local input) INTEGER
	       On  entry, the size of H.  If all the bulges are expected to go through, N should be at least 4*NBULGE+2.  Otherwise, NBULGE may be
	       reduced by this routine.

       ULP     (local input) DOUBLE PRECISION
	       On entry, machine precision Unchanged on exit.

	       Implemented by:	G. Henry, May 1, 1997

LAPACK version 1.5						    12 May 1997 							 DLAMSH(l)