
CLALS0(l) ) CLALS0(l)
NAME
CLALS0  applie back the multiplying factors of either the left or the right singular vec
tor matrix of a diagonal matrix appended by a row to the right hand side matrix B in solv
ing the least squares problem using the divideandconquer SVD approach
SYNOPSIS
SUBROUTINE CLALS0( ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX, PERM, GIVPTR, GIVCOL,
LDGCOL, GIVNUM, LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, RWORK, INFO )
INTEGER GIVPTR, ICOMPQ, INFO, K, LDB, LDBX, LDGCOL, LDGNUM, NL, NR, NRHS, SQRE
REAL C, S
INTEGER GIVCOL( LDGCOL, * ), PERM( * )
REAL DIFL( * ), DIFR( LDGNUM, * ), GIVNUM( LDGNUM, * ), POLES( LDGNUM, * ),
RWORK( * ), Z( * )
COMPLEX B( LDB, * ), BX( LDBX, * )
PURPOSE
CLALS0 applies back the multiplying factors of either the left or the right singular vec
tor matrix of a diagonal matrix appended by a row to the right hand side matrix B in solv
ing the least squares problem using the divideandconquer SVD approach. For the left
singular vector matrix, three types of orthogonal matrices are involved:
(1L) Givens rotations: the number of such rotations is GIVPTR; the
pairs of columns/rows they were applied to are stored in GIVCOL;
and the C and Svalues of these rotations are stored in GIVNUM.
(2L) Permutation. The (NL+1)st row of B is to be moved to the first
row, and for J=2:N, PERM(J)th row of B is to be moved to the
Jth row.
(3L) The left singular vector matrix of the remaining matrix.
For the right singular vector matrix, four types of orthogonal matrices are involved:
(1R) The right singular vector matrix of the remaining matrix.
(2R) If SQRE = 1, one extra Givens rotation to generate the right
null space.
(3R) The inverse transformation of (2L).
(4R) The inverse transformation of (1L).
ARGUMENTS
ICOMPQ (input) INTEGER Specifies whether singular vectors are to be computed in factored
form:
= 0: Left singular vector matrix.
= 1: Right singular vector matrix.
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 row dimension N = NL + NR + 1, and column dimension M = N
+ SQRE.
NRHS (input) INTEGER
The number of columns of B and BX. NRHS must be at least 1.
B (input/output) COMPLEX array, dimension ( LDB, NRHS )
On input, B contains the right hand sides of the least squares problem in rows 1
through M. On output, B contains the solution X in rows 1 through N.
LDB (input) INTEGER
The leading dimension of B. LDB must be at least max(1,MAX( M, N ) ).
BX (workspace) COMPLEX array, dimension ( LDBX, NRHS )
LDBX (input) INTEGER
The leading dimension of BX.
PERM (input) INTEGER array, dimension ( N )
The permutations (from deflation and sorting) applied to the two blocks.
GIVPTR (input) INTEGER The number of Givens rotations which took place in this sub
problem.
GIVCOL (input) INTEGER array, dimension ( LDGCOL, 2 ) Each pair of numbers indi
cates a pair of rows/columns involved in a Givens rotation.
LDGCOL (input) INTEGER The leading dimension of GIVCOL, must be at least N.
GIVNUM (input) REAL array, dimension ( LDGNUM, 2 ) Each number indicates the C or S
value used in the corresponding Givens rotation.
LDGNUM (input) INTEGER The leading dimension of arrays DIFR, POLES and GIVNUM, must
be at least K.
POLES (input) REAL array, dimension ( LDGNUM, 2 )
On entry, POLES(1:K, 1) contains the new singular values obtained from solving the
secular equation, and POLES(1:K, 2) is an array containing the poles in the secular
equation.
DIFL (input) REAL array, dimension ( K ).
On entry, DIFL(I) is the distance between Ith updated (undeflated) singular value
and the Ith (undeflated) old singular value.
DIFR (input) REAL array, dimension ( LDGNUM, 2 ).
On entry, DIFR(I, 1) contains the distances between Ith updated (undeflated) sin
gular value and the I+1th (undeflated) old singular value. And DIFR(I, 2) is the
normalizing factor for the Ith right singular vector.
Z (input) REAL array, dimension ( K )
Contain the components of the deflationadjusted updating row vector.
K (input) INTEGER
Contains the dimension of the nondeflated matrix, This is the order of the related
secular equation. 1 <= K <=N.
C (input) REAL
C contains garbage if SQRE =0 and the Cvalue of a Givens rotation related to the
right null space if SQRE = 1.
S (input) REAL
S contains garbage if SQRE =0 and the Svalue of a Givens rotation related to the
right null space if SQRE = 1.
RWORK (workspace) REAL array, dimension
( K*(1+NRHS) + 2*NRHS )
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 RenCang Li, Computer Science Division, University of
California at Berkeley, USA
Osni Marques, LBNL/NERSC, USA
LAPACK version 3.0 15 June 2000 CLALS0(l) 
