NAME

       zlalsa.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zlalsa (ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, LDU, VT, K, DIFL, DIFR,
           Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, RWORK, IWORK, INFO)
           ZLALSA computes the SVD of the coefficient matrix in compact form. Used by sgelsd.

Function/Subroutine Documentation

   subroutine zlalsa (integer ICOMPQ, integer SMLSIZ, integer N, integer NRHS, complex*16,
       dimension( ldb, * ) B, integer LDB, complex*16, dimension( ldbx, * ) BX, integer LDBX,
       double precision, dimension( ldu, * ) U, integer LDU, double precision, dimension( ldu, *
       ) VT, integer, dimension( * ) K, double precision, dimension( ldu, * ) DIFL, double
       precision, dimension( ldu, * ) DIFR, double precision, dimension( ldu, * ) Z, double
       precision, dimension( ldu, * ) POLES, integer, dimension( * ) GIVPTR, integer, dimension(
       ldgcol, * ) GIVCOL, integer LDGCOL, integer, dimension( ldgcol, * ) PERM, double
       precision, dimension( ldu, * ) GIVNUM, double precision, dimension( * ) C, double
       precision, dimension( * ) S, double precision, dimension( * ) RWORK, integer, dimension( *
       ) IWORK, integer INFO)
       ZLALSA computes the SVD of the coefficient matrix in compact form. Used by sgelsd.

       Purpose:

            ZLALSA 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, ZLALSA applies the inverse of the left singular vector
            matrix of an upper bidiagonal matrix to the right hand side; and if
            ICOMPQ = 1, ZLALSA applies the right singular vector matrix to the
            right hand side. The singular vector matrices were generated in
            compact form by ZLALSA.

       Parameters:
           ICOMPQ

                     ICOMPQ is INTEGER
                    Specifies whether the left or the right singular vector
                    matrix is involved.
                    = 0: Left singular vector matrix
                    = 1: Right singular vector matrix

           SMLSIZ

                     SMLSIZ is INTEGER
                    The maximum size of the subproblems at the bottom of the
                    computation tree.

           N

                     N is INTEGER
                    The row and column dimensions of the upper bidiagonal matrix.

           NRHS

                     NRHS is INTEGER
                    The number of columns of B and BX. NRHS must be at least 1.

           B

                     B is 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

                     LDB is INTEGER
                    The leading dimension of B in the calling subprogram.
                    LDB must be at least max(1,MAX( M, N ) ).

           BX

                     BX is COMPLEX*16 array, dimension ( LDBX, NRHS )
                    On exit, the result of applying the left or right singular
                    vector matrix to B.

           LDBX

                     LDBX is INTEGER
                    The leading dimension of BX.

           U

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

           LDU

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

           VT

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

           K

                     K is INTEGER array, dimension ( N ).

           DIFL

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

           DIFR

                     DIFR is 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

                     Z is 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

                     POLES is 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

                     GIVPTR is 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

                     GIVCOL is 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

                     LDGCOL is INTEGER, LDGCOL = > N.
                    The leading dimension of arrays GIVCOL and PERM.

           PERM

                     PERM is INTEGER array, dimension ( LDGCOL, NLVL ).
                    On entry, PERM(*, I) records permutations done on the I-th
                    level of the computation tree.

           GIVNUM

                     GIVNUM is 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

                     C is 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

                     S is 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.

           RWORK

                     RWORK is DOUBLE PRECISION array, dimension at least
                    MAX( (SMLSZ+1)*NRHS*3, N*(1+NRHS) + 2*NRHS ).

           IWORK

                     IWORK is INTEGER array.
                    The dimension must be at least 3 * N

           INFO

                     INFO is INTEGER
                     = 0:  successful exit.
                     < 0:  if INFO = -i, the i-th argument had an illegal value.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

       Contributors:
           Ming Gu and Ren-Cang Li, Computer Science Division, University of California at
           Berkeley, USA
            Osni Marques, LBNL/NERSC, USA

Author

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