slamsh(3) [debian man page]

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

NAME

       SLAMSH - 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 SLAMSH ( S, LDS, NBULGE, JBLK, H, LDH, N, ULP )

	   INTEGER	 LDS, NBULGE, JBLK, LDH, N

	   REAL 	 ULP

	   REAL 	 S(LDS,*), H(LDH,*)

PURPOSE

       SLAMSH 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.  SLAMSH 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) REAL 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) REAL 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) REAL
	       On entry, machine precision Unchanged on exit.

	       Implemented by:	G. Henry, May 1, 1997

LAPACK version 1.5						    12 May 1997 							 SLAMSH(l)

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slaqr1.f(3)							      LAPACK							       slaqr1.f(3)

NAME

       slaqr1.f -

SYNOPSIS

   Functions/Subroutines
       subroutine slaqr1 (N, H, LDH, SR1, SI1, SR2, SI2, V)
	   SLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts.

Function/Subroutine Documentation
   subroutine slaqr1 (integerN, real, dimension( ldh, * )H, integerLDH, realSR1, realSI1, realSR2, realSI2, real, dimension( * )V)
       SLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts.

       Purpose:

		 Given a 2-by-2 or 3-by-3 matrix H, SLAQR1 sets v to a
		 scalar multiple of the first column of the product

		 (*)  K = (H - (sr1 + i*si1)*I)*(H - (sr2 + i*si2)*I)

		 scaling to avoid overflows and most underflows. It
		 is assumed that either

			 1) sr1 = sr2 and si1 = -si2
		     or
			 2) si1 = si2 = 0.

		 This is useful for starting double implicit shift bulges
		 in the QR algorithm.

       Parameters:
	   N

		     N is integer
			 Order of the matrix H. N must be either 2 or 3.

	   H

		     H is REAL array of dimension (LDH,N)
			 The 2-by-2 or 3-by-3 matrix H in (*).

	   LDH

		     LDH is integer
			 The leading dimension of H as declared in
			 the calling procedure.  LDH.GE.N

	   SR1

		     SR1 is REAL

	   SI1

		     SI1 is REAL

	   SR2

		     SR2 is REAL

	   SI2

		     SI2 is REAL
			 The shifts in (*).

	   V

		     V is REAL array of dimension N
			 A scalar multiple of the first column of the
			 matrix K in (*).

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Contributors:
	   Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA

       Definition at line 122 of file slaqr1.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       slaqr1.f(3)

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