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

NAME

       LAPACK-3  -  is  an itermediate step in solving the least squares problem by computing the
       SVD of the coefficient matrix in compact  form  (The  singular  vectors  are  computed  as
       products of simple orthorgonal matrices.)

SYNOPSIS

       SUBROUTINE DLALSA( ICOMPQ,  SMLSIZ,  N, NRHS, B, LDB, BX, LDBX, U, LDU, VT, K, DIFL, DIFR,
                          Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, IWORK, INFO
                          )

           INTEGER        ICOMPQ, INFO, LDB, LDBX, LDGCOL, LDU, N, NRHS, SMLSIZ

           INTEGER        GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ), K( * ), PERM( LDGCOL, * )

           DOUBLE         PRECISION  B(  LDB,  *  ), BX( LDBX, * ), C( * ), DIFL( LDU, * ), DIFR(
                          LDU, * ), GIVNUM( LDU, * ), POLES( LDU, * ), S( * ), U( LDU, *  ),  VT(
                          LDU, * ), WORK( * ), Z( LDU, * )

PURPOSE

       DLALSA is an itermediate step in solving the least squares problem by computing the SVD of
       the coefficient matrix in compact form (The singular vectors are computed as  products  of
       simple orthorgonal matrices.).
        If ICOMPQ = 0, DLALSA applies the inverse of the left singular vector
        matrix of an upper bidiagonal matrix to the right hand side; and if
        ICOMPQ = 1, DLALSA applies the right singular vector matrix to the
        right hand side. The singular vector matrices were generated in
        compact form by DLALSA.

ARGUMENTS

        ICOMPQ (input) INTEGER
        Specifies whether the left or the right singular vector
        matrix is involved.
        = 0: Left singular vector matrix
        = 1: Right singular vector matrix
        SMLSIZ (input) INTEGER
        The maximum size of the subproblems at the bottom of the
        computation tree.

        N      (input) INTEGER
               The row and column dimensions of the upper bidiagonal matrix.

        NRHS   (input) INTEGER
               The number of columns of B and BX. NRHS must be at least 1.

        B      (input/output) DOUBLE PRECISION 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 in the calling subprogram.
               LDB must be at least max(1,MAX( M, N ) ).

        BX     (output) DOUBLE PRECISION array, dimension ( LDBX, NRHS )
               On exit, the result of applying the left or right singular
               vector matrix to B.

        LDBX   (input) INTEGER
               The leading dimension of BX.

        U      (input) DOUBLE PRECISION array, dimension ( LDU, SMLSIZ ).
               On entry, U contains the left singular vector matrices of all
               subproblems at the bottom level.

        LDU    (input) INTEGER, LDU = > N.
               The leading dimension of arrays U, VT, DIFL, DIFR,
               POLES, GIVNUM, and Z.

        VT     (input) DOUBLE PRECISION array, dimension ( LDU, SMLSIZ+1 ).
               On entry, VT**T contains the right singular vector matrices of
               all subproblems at the bottom level.

        K      (input) INTEGER array, dimension ( N ).

        DIFL   (input) DOUBLE PRECISION array, dimension ( LDU, NLVL ).
               where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1.

        DIFR   (input) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ).
               On entry, DIFL(*, I) and DIFR(*, 2 * I -1) record
               distances between singular values on the I-th level and
               singular values on the (I -1)-th level, and DIFR(*, 2 * I)
               record the normalizing factors of the right singular vectors
               matrices of subproblems on I-th level.

        Z      (input) DOUBLE PRECISION array, dimension ( LDU, NLVL ).
               On entry, Z(1, I) contains the components of the deflation-
               adjusted updating row vector for subproblems on the I-th
               level.

        POLES  (input) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ).
               On entry, POLES(*, 2 * I -1: 2 * I) contains the new and old
               singular values involved in the secular equations on the I-th
               level.
               GIVPTR (input) INTEGER array, dimension ( N ).
               On entry, GIVPTR( I ) records the number of Givens
               rotations performed on the I-th problem on the computation
               tree.
               GIVCOL (input) INTEGER array, dimension ( LDGCOL, 2 * NLVL ).
               On entry, for each I, GIVCOL(*, 2 * I - 1: 2 * I) records the
               locations of Givens rotations performed on the I-th level on
               the computation tree.
               LDGCOL (input) INTEGER, LDGCOL = > N.
               The leading dimension of arrays GIVCOL and PERM.

        PERM   (input) INTEGER array, dimension ( LDGCOL, NLVL ).
               On entry, PERM(*, I) records permutations done on the I-th
               level of the computation tree.
               GIVNUM (input) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ).
               On entry, GIVNUM(*, 2 *I -1 : 2 * I) records the C- and S-
               values of Givens rotations performed on the I-th level on the
               computation tree.

        C      (input) DOUBLE PRECISION array, dimension ( N ).
               On entry, if the I-th subproblem is not square,
               C( I ) contains the C-value of a Givens rotation related to
               the right null space of the I-th subproblem.

        S      (input) DOUBLE PRECISION array, dimension ( N ).
               On entry, if the I-th subproblem is not square,
               S( I ) contains the S-value of a Givens rotation related to
               the right null space of the I-th subproblem.

        WORK   (workspace) DOUBLE PRECISION array.
               The dimension must be at least N.

        IWORK  (workspace) INTEGER array.
               The dimension must be at least 3 * N

        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                            DLALSA(3lapack)