Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  applies back the multiplying factors of either the left or the right singular
       vector matrix of a diagonal matrix appended by a row to the right hand side  matrix  B  in
       solving the least squares problem using the divide-and-conquer SVD approach

SYNOPSIS

       SUBROUTINE ZLALS0( 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

           DOUBLE         PRECISION C, S

           INTEGER        GIVCOL( LDGCOL, * ), PERM( * )

           DOUBLE         PRECISION DIFL( * ), DIFR( LDGNUM, * ), GIVNUM(  LDGNUM,  *  ),  POLES(
                          LDGNUM, * ), RWORK( * ), Z( * )

           COMPLEX*16     B( LDB, * ), BX( LDBX, * )

PURPOSE

       ZLALS0  applies  back  the  multiplying  factors  of either the left or the right singular
       vector matrix of a diagonal matrix appended by a row to the right hand side  matrix  B  in
       solving the least squares problem using the divide-and-conquer 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 S-values 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
             J-th 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 NR-by-NR square matrix.
               = 1: the lower block is an NR-by-(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*16 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*16 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
               subproblem.
               GIVCOL (input) INTEGER array, dimension ( LDGCOL, 2 )
               Each pair of numbers indicates 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension ( K ).
               On entry, DIFL(I) is the distance between I-th updated
               (undeflated) singular value and the I-th (undeflated) old
               singular value.

        DIFR   (input) DOUBLE PRECISION array, dimension ( LDGNUM, 2 ).
               On entry, DIFR(I, 1) contains the distances between I-th
               updated (undeflated) singular value and the I+1-th
               (undeflated) old singular value. And DIFR(I, 2) is the
               normalizing factor for the I-th right singular vector.

        Z      (input) DOUBLE PRECISION array, dimension ( K )
               Contain the components of the deflation-adjusted updating row
               vector.

        K      (input) INTEGER
               Contains the dimension of the non-deflated matrix,
               This is the order of the related secular equation. 1 <= K <=N.

        C      (input) DOUBLE PRECISION
               C contains garbage if SQRE =0 and the C-value of a Givens
               rotation related to the right null space if SQRE = 1.

        S      (input) DOUBLE PRECISION
               S contains garbage if SQRE =0 and the S-value of a Givens
               rotation related to the right null space if SQRE = 1.

        RWORK  (workspace) DOUBLE PRECISION array, dimension
               ( K*(1+NRHS) + 2*NRHS )

        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 Ren-Cang Li, Computer Science Division, University of
             California at Berkeley, USA
           Osni Marques, LBNL/NERSC, USA

 LAPACK routine (version 3.2)               April 2011                            ZLALS0(3lapack)