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CentOS 7.0 - man page for slasd7 (centos section 3)

slasd7.f(3)				      LAPACK				      slasd7.f(3)

NAME
       slasd7.f -

SYNOPSIS
   Functions/Subroutines
       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)
	   SLASD7 merges the two sets of singular values together into a single sorted set. Then
	   it tries to deflate the size of the problem. Used by sbdsdc.

Function/Subroutine Documentation
   subroutine slasd7 (integerICOMPQ, integerNL, integerNR, integerSQRE, integerK, real,
       dimension( * )D, real, dimension( * )Z, real, dimension( * )ZW, real, dimension( * )VF,
       real, dimension( * )VFW, real, dimension( * )VL, real, dimension( * )VLW, realALPHA,
       realBETA, real, dimension( * )DSIGMA, integer, dimension( * )IDX, integer, dimension( *
       )IDXP, integer, dimension( * )IDXQ, integer, dimension( * )PERM, integerGIVPTR, integer,
       dimension( ldgcol, * )GIVCOL, integerLDGCOL, real, dimension( ldgnum, * )GIVNUM,
       integerLDGNUM, realC, realS, integerINFO)
       SLASD7 merges the two sets of singular values together into a single sorted set. Then it
       tries to deflate the size of the problem. Used by sbdsdc.

       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.

       Parameters:
	   ICOMPQ

		     ICOMPQ is 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

		     NL is INTEGER
		    The row dimension of the upper block. NL >= 1.

	   NR

		     NR is INTEGER
		    The row dimension of the lower block. NR >= 1.

	   SQRE

		     SQRE is 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

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

	   D

		     D is 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

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

	   ZW

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

	   VF

		     VF is 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 components 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

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

	   VL

		     VL is 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 components 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

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

	   ALPHA

		     ALPHA is REAL
		    Contains the diagonal element associated with the added row.

	   BETA

		     BETA is REAL
		    Contains the off-diagonal element associated with the added
		    row.

	   DSIGMA

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

	   IDX

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

	   IDXP

		     IDXP is 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

		     IDXQ is 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

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

	   GIVPTR

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

	   GIVCOL

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

	   LDGCOL

		     LDGCOL is INTEGER
		    The leading dimension of GIVCOL, must be at least N.

	   GIVNUM

		     GIVNUM is 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

		     LDGNUM is INTEGER
		    The leading dimension of GIVNUM, must be at least N.

	   C

		     C is 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

		     S is 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

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

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Contributors:
	   Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley,
	   USA

       Definition at line 278 of file slasd7.f.

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

Version 3.4.2				 Tue Sep 25 2012			      slasd7.f(3)


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