DLASD7 (3) - Linux Manuals

NAME

dlasd7.f -

SYNOPSIS


Functions/Subroutines


subroutine dlasd7 (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)
DLASD7 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 dlasd7 (integerICOMPQ, integerNL, integerNR, integerSQRE, integerK, double precision, dimension( * )D, double precision, dimension( * )Z, double precision, dimension( * )ZW, double precision, dimension( * )VF, double precision, dimension( * )VFW, double precision, dimension( * )VL, double precision, dimension( * )VLW, double precisionALPHA, double precisionBETA, double precision, dimension( * )DSIGMA, integer, dimension( * )IDX, integer, dimension( * )IDXP, integer, dimension( * )IDXQ, integer, dimension( * )PERM, integerGIVPTR, integer, dimension( ldgcol, * )GIVCOL, integerLDGCOL, double precision, dimension( ldgnum, * )GIVNUM, integerLDGNUM, double precisionC, double precisionS, integerINFO)

DLASD7 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: 

 DLASD7 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.

 DLASD7 is called from DLASD6.


 

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


ZW 

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


VF 

          VF is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension ( M )
         Workspace for VF.


VL 

          VL is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension ( M )
         Workspace for VL.


ALPHA 

          ALPHA is DOUBLE PRECISION
         Contains the diagonal element associated with the added row.


BETA 

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


DSIGMA 

          DSIGMA is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION
         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 DOUBLE PRECISION
         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 dlasd7.f.

Author

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