
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 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 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 offdiagonal element associated with the added row.
DSIGMA (output) REAL array, dimension ( N ) Contains a copy of the diagonal ele
ments (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 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 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 by
Ming Gu and Huan Ren, Computer Science Division, University of
California at Berkeley, USA
LAPACK version 3.0 15 June 2000 SLASD7(l) 
