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RedHat 9 (Linux i386) - man page for slasd7 (redhat section l)

SLASD7(l)					)					SLASD7(l)

NAME
       SLASD7 - merge the two sets of singular values together into a single sorted set

SYNOPSIS
       SUBROUTINE SLASD7( ICOMPQ,  NL,	NR,  SQRE,  K,	D,  Z, ZW, VF, VFW, VL, VLW, ALPHA, BETA,
			  DSIGMA, IDX, IDXP, IDXQ, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM,  LDGNUM,
			  C, S, INFO )

	   INTEGER	  GIVPTR, ICOMPQ, INFO, K, LDGCOL, LDGNUM, NL, NR, SQRE

	   REAL 	  ALPHA, BETA, C, S

	   INTEGER	  GIVCOL( LDGCOL, * ), IDX( * ), IDXP( * ), IDXQ( * ), PERM( * )

	   REAL 	  D(  *  ), DSIGMA( * ), GIVNUM( LDGNUM, * ), VF( * ), VFW( * ), VL( * ),
			  VLW( * ), Z( * ), ZW( * )

PURPOSE
       SLASD7 merges the two sets of singular values together into a single sorted set.  Then  it
       tries to deflate the size of the problem. There are two ways in which deflation can occur:
       when two or more singular values are close together or if there is a tiny entry in  the	Z
       vector.	For  each  such  occurrence  the order of the related secular equation problem is
       reduced by one.

       SLASD7 is called from SLASD6.

ARGUMENTS
       ICOMPQ  (input) INTEGER
	       Specifies whether singular vectors are to be computed in compact form, as follows:
	       = 0: Compute singular values only.
	       = 1: Compute singular vectors of upper bidiagonal matrix in compact form.

       NL     (input) INTEGER
	      The row dimension of the upper block. NL >= 1.

       NR     (input) INTEGER
	      The row dimension of the lower block. NR >= 1.

       SQRE   (input) INTEGER
	      = 0: the lower block is an NR-by-NR square matrix.
	      = 1: the lower block is an NR-by-(NR+1) rectangular matrix.

	      The bidiagonal matrix has N = NL + NR + 1 rows and M = N + SQRE >= N columns.

       K      (output) INTEGER
	      Contains the dimension of the non-deflated matrix, this is the order of the related
	      secular equation. 1 <= K <=N.

       D      (input/output) REAL array, dimension ( N )
	      On  entry  D contains the singular values of the two submatrices to be combined. On
	      exit D contains the trailing  (N-K)  updated  singular  values  (those  which  were
	      deflated) sorted into increasing order.

       Z      (output) REAL array, dimension ( M )
	      On exit Z contains the updating row vector in the secular equation.

       ZW     (workspace) REAL array, dimension ( M )
	      Workspace for Z.

       VF     (input/output) REAL array, dimension ( M )
	      On entry, VF(1:NL+1) contains the first components of all
	      right singular vectors of the upper block; and VF(NL+2:M) contains the first compo-
	      nents of all right singular vectors of the lower block. On exit,	VF  contains  the
	      first components of all right singular vectors of the bidiagonal matrix.

       VFW    (workspace) REAL array, dimension ( M )
	      Workspace for VF.

       VL     (input/output) REAL array, dimension ( M )
	      On entry, VL(1:NL+1) contains the  last components of all
	      right  singular vectors of the upper block; and VL(NL+2:M) contains the last compo-
	      nents of all right singular vectors of the lower block. On exit,	VL  contains  the
	      last components of all right singular vectors of the bidiagonal matrix.

       VLW    (workspace) REAL array, dimension ( M )
	      Workspace for VL.

       ALPHA  (input) REAL
	      Contains the diagonal element associated with the added row.

       BETA   (input) REAL
	      Contains the off-diagonal element associated with the added row.

	      DSIGMA  (output)	REAL  array, dimension ( N ) Contains a copy of the diagonal ele-
	      ments (K-1 singular values and one zero) in the secular equation.

       IDX    (workspace) INTEGER array, dimension ( N )
	      This will contain the permutation used to sort the contents  of  D  into	ascending
	      order.

       IDXP   (workspace) INTEGER array, dimension ( N )
	      This  will contain the permutation used to place deflated values of D at the end of
	      the array. On output IDXP(2:K)
	      points to the nondeflated D-values and IDXP(K+1:N) points to the deflated  singular
	      values.

       IDXQ   (input) INTEGER array, dimension ( N )
	      This contains the permutation which separately sorts the two sub-problems in D into
	      ascending order.	Note that entries in the first	half  of  this	permutation  must
	      first  be  moved	one  position backward; and entries in the second half must first
	      have NL+1 added to their values.

       PERM   (output) INTEGER array, dimension ( N )
	      The permutations (from deflation and sorting) to be applied to each singular block.
	      Not referenced if ICOMPQ = 0.

	      GIVPTR  (output)	INTEGER  The  number of Givens rotations which took place in this
	      subproblem. Not referenced if ICOMPQ = 0.

	      GIVCOL (output) INTEGER array, dimension ( LDGCOL, 2 ) Each pair of  numbers  indi-
	      cates  a	pair  of  columns  to  take place in a Givens rotation. Not referenced if
	      ICOMPQ = 0.

	      LDGCOL (input) INTEGER The leading dimension of GIVCOL, must be at least N.

	      GIVNUM (output) REAL array, dimension ( LDGNUM, 2 ) Each number indicates the C  or
	      S value to be used in the corresponding Givens rotation. Not referenced if ICOMPQ =
	      0.

	      LDGNUM (input) INTEGER The leading dimension of GIVNUM, must be at least N.

       C      (output) REAL
	      C contains garbage if SQRE =0 and the C-value of a Givens rotation related  to  the
	      right null space if SQRE = 1.

       S      (output) REAL
	      S  contains  garbage if SQRE =0 and the S-value of a Givens rotation related to the
	      right null space if SQRE = 1.

       INFO   (output) INTEGER
	      = 0:  successful exit.
	      < 0:  if INFO = -i, the i-th argument had an illegal value.

FURTHER DETAILS
       Based on contributions by
	  Ming Gu and Huan Ren, Computer Science Division, University of
	  California at Berkeley, USA

LAPACK version 3.0			   15 June 2000 				SLASD7(l)


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