SLASD7(1) LAPACK auxiliary routine (version 3.2) SLASD7(1)NAME
SLASD7 - merges 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 val‐
ues 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 com‐
pact 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 M = N + SQRE >= N
columns.
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 increas‐
ing order.
Z (output) REAL array, dimension ( M )
On exit Z contains the updating row vector in the secular equa‐
tion.
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) con‐
tains 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) con‐
tains 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 off-diagonal element associated with the added row.
DSIGMA (output) REAL array, dimension ( N ) Contains a copy of
the diagonal elements (K-1 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 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 posi‐
tion 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 (out‐
put) 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 lead‐
ing 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 C-value of a Givens rota‐
tion 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 rota‐
tion related to the right null space if SQRE = 1.
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th 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 auxiliary routine (versioNovember 2008 SLASD7(1)
