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, LDG
COL, 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 com
puted 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
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 components of all
right singular vectors of the lower block. On exit,
VF contains the first components of all right sin
gular 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 singu
lar 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 ) Con
tains a copy of the diagonal elements (K-1 singular
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 back
ward; 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 rota
tions which took place in this subproblem. Not ref
erenced 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 refer
enced 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
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an ille
gal value.
FURTHER DETAILS
Based on contributions by
Ming Gu and Huan Ren, Computer Science Division, Uni
versity of
California at Berkeley, USA
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