NAME

       zlalsd.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zlalsd (UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, RANK, WORK, RWORK, IWORK,
           INFO)
           ZLALSD uses the singular value decomposition of A to solve the least squares problem.

Function/Subroutine Documentation

   subroutine zlalsd (character UPLO, integer SMLSIZ, integer N, integer NRHS, double precision,
       dimension( * ) D, double precision, dimension( * ) E, complex*16, dimension( ldb, * ) B,
       integer LDB, double precision RCOND, integer RANK, complex*16, dimension( * ) WORK, double
       precision, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer INFO)
       ZLALSD uses the singular value decomposition of A to solve the least squares problem.

       Purpose:

            ZLALSD uses the singular value decomposition of A to solve the least
            squares problem of finding X to minimize the Euclidean norm of each
            column of A*X-B, where A is N-by-N upper bidiagonal, and X and B
            are N-by-NRHS. The solution X overwrites B.

            The singular values of A smaller than RCOND times the largest
            singular value are treated as zero in solving the least squares
            problem; in this case a minimum norm solution is returned.
            The actual singular values are returned in D in ascending order.

            This code makes very mild assumptions about floating point
            arithmetic. It will work on machines with a guard digit in
            add/subtract, or on those binary machines without guard digits
            which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2.
            It could conceivably fail on hexadecimal or decimal machines
            without guard digits, but we know of none.

       Parameters:
           UPLO

                     UPLO is CHARACTER*1
                    = 'U': D and E define an upper bidiagonal matrix.
                    = 'L': D and E define a  lower bidiagonal matrix.

           SMLSIZ

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

           N

                     N is INTEGER
                    The dimension of the  bidiagonal matrix.  N >= 0.

           NRHS

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

           D

                     D is DOUBLE PRECISION array, dimension (N)
                    On entry D contains the main diagonal of the bidiagonal
                    matrix. On exit, if INFO = 0, D contains its singular values.

           E

                     E is DOUBLE PRECISION array, dimension (N-1)
                    Contains the super-diagonal entries of the bidiagonal matrix.
                    On exit, E has been destroyed.

           B

                     B is COMPLEX*16 array, dimension (LDB,NRHS)
                    On input, B contains the right hand sides of the least
                    squares problem. On output, B contains the solution X.

           LDB

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

           RCOND

                     RCOND is DOUBLE PRECISION
                    The singular values of A less than or equal to RCOND times
                    the largest singular value are treated as zero in solving
                    the least squares problem. If RCOND is negative,
                    machine precision is used instead.
                    For example, if diag(S)*X=B were the least squares problem,
                    where diag(S) is a diagonal matrix of singular values, the
                    solution would be X(i) = B(i) / S(i) if S(i) is greater than
                    RCOND*max(S), and X(i) = 0 if S(i) is less than or equal to
                    RCOND*max(S).

           RANK

                     RANK is INTEGER
                    The number of singular values of A greater than RCOND times
                    the largest singular value.

           WORK

                     WORK is COMPLEX*16 array, dimension at least
                    (N * NRHS).

           RWORK

                     RWORK is DOUBLE PRECISION array, dimension at least
                    (9*N + 2*N*SMLSIZ + 8*N*NLVL + 3*SMLSIZ*NRHS +
                    MAX( (SMLSIZ+1)**2, N*(1+NRHS) + 2*NRHS ),
                    where
                    NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 )

           IWORK

                     IWORK is INTEGER array, dimension at least
                    (3*N*NLVL + 11*N).

           INFO

                     INFO is INTEGER
                    = 0:  successful exit.
                    < 0:  if INFO = -i, the i-th argument had an illegal value.
                    > 0:  The algorithm failed to compute a singular value while
                          working on the submatrix lying in rows and columns
                          INFO/(N+1) through MOD(INFO,N+1).

       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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