
SLASD2(l) ) SLASD2(l)
NAME
SLASD2  merge the two sets of singular values together into a single sorted set
SYNOPSIS
SUBROUTINE SLASD2( NL, NR, SQRE, K, D, Z, ALPHA, BETA, U, LDU, VT, LDVT, DSIGMA, U2, LDU2,
VT2, LDVT2, IDXP, IDX, IDXC, IDXQ, COLTYP, INFO )
INTEGER INFO, K, LDU, LDU2, LDVT, LDVT2, NL, NR, SQRE
REAL ALPHA, BETA
INTEGER COLTYP( * ), IDX( * ), IDXC( * ), IDXP( * ), IDXQ( * )
REAL D( * ), DSIGMA( * ), U( LDU, * ), U2( LDU2, * ), VT( LDVT, * ), VT2(
LDVT2, * ), Z( * )
PURPOSE
SLASD2 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.
SLASD2 is called from SLASD1.
ARGUMENTS
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.
ALPHA (input) REAL
Contains the diagonal element associated with the added row.
BETA (input) REAL
Contains the offdiagonal element associated with the added row.
U (input/output) REAL array, dimension(LDU,N)
On entry U contains the left singular vectors of two submatrices in the two square
blocks with corners at (1,1), (NL, NL), and (NL+2, NL+2), (N,N). On exit U con
tains the trailing (NK) updated left singular vectors (those which were deflated)
in its last NK columns.
LDU (input) INTEGER
The leading dimension of the array U. LDU >= N.
Z (output) REAL array, dimension(N)
On exit Z contains the updating row vector in the secular equation.
DSIGMA (output) REAL array, dimension (N) Contains a copy of the diagonal elements
(K1 singular values and one zero) in the secular equation.
U2 (output) REAL array, dimension(LDU2,N)
Contains a copy of the first K1 left singular vectors which will be used by SLASD3
in a matrix multiply (SGEMM) to solve for the new left singular vectors. U2 is
arranged into four blocks. The first block contains a column with 1 at NL+1 and
zero everywhere else; the second block contains nonzero entries only at and above
NL; the third contains nonzero entries only below NL+1; and the fourth is dense.
LDU2 (input) INTEGER
The leading dimension of the array U2. LDU2 >= N.
VT (input/output) REAL array, dimension(LDVT,M)
On entry VT' contains the right singular vectors of two submatrices in the two
square blocks with corners at (1,1), (NL+1, NL+1), and (NL+2, NL+2), (M,M). On
exit VT' contains the trailing (NK) updated right singular vectors (those which
were deflated) in its last NK columns. In case SQRE =1, the last row of VT spans
the right null space.
LDVT (input) INTEGER
The leading dimension of the array VT. LDVT >= M.
VT2 (output) REAL array, dimension(LDVT2,N)
VT2' contains a copy of the first K right singular vectors which will be used by
SLASD3 in a matrix multiply (SGEMM) to solve for the new right singular vectors.
VT2 is arranged into three blocks. The first block contains a row that corresponds
to the special 0 diagonal element in SIGMA; the second block contains nonzeros
only at and before NL +1; the third block contains nonzeros only at and after NL
+2.
LDVT2 (input) INTEGER
The leading dimension of the array VT2. LDVT2 >= M.
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.
IDX (workspace) INTEGER array, dimension(N)
This will contain the permutation used to sort the contents of D into ascending
order.
IDXC (output) INTEGER array, dimension(N)
This will contain the permutation used to arrange the columns of the deflated U
matrix into three groups: the first group contains nonzero entries only at and
above NL, the second contains nonzero entries only below NL+2, and the third is
dense.
COLTYP (workspace/output) INTEGER array, dimension(N) As workspace, this will con
tain a label which will indicate which of the following types a column in the U2
matrix or a row in the VT2 matrix is:
1 : nonzero in the upper half only
2 : nonzero in the lower half only
3 : dense
4 : deflated
On exit, it is an array of dimension 4, with COLTYP(I) being the dimension of the
Ith type columns.
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 hlaf 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.
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 SLASD2(l) 
