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 NRbyNR square matrix.
= 1: the lower block is an NRby(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 nondeflated 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 (NK) 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 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 (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 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 (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 offdiagonal element associated with the added row. DSIGMA (output) REAL array, dimension ( N ) Contains a copy of the diagonal elements (K1 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 Dvalues 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 subproblems 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 indicates 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 Cvalue of a Givens rotation related to the right null space if SQRE = 1.
 S (output) REAL
 S contains garbage if SQRE =0 and the Svalue of a Givens rotation related to the right null space if SQRE = 1.
 INFO (output) INTEGER

= 0: successful exit.
< 0: if INFO = i, the ith argument had an illegal value.
FURTHER DETAILS
Based on contributions byMing Gu and Huan Ren, Computer Science Division, University of
California at Berkeley, USA