SRC/slalsd.f(3)

NAME
SRC/slalsd.f

SYNOPSIS

  Functions/Subroutines
subroutine slalsd (uplo, smlsiz, n, nrhs, d, e, b, ldb, rcond, rank, work, iwork, info)
SLALSD uses the singular value decomposition of A to solve the least squares problem.

Function/Subroutine Documentation

  subroutine slalsd (character uplo, integer smlsiz, integer n, integer nrhs, real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldb, * ) b, integer ldb, real rcond, integer rank, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)

SLALSD uses the singular value decomposition of A to solve the least squares problem.

Purpose:

    !>
    !> SLALSD 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.
    !>
    !>

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 REAL 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 REAL array, dimension (N-1)
    !>         Contains the super-diagonal entries of the bidiagonal matrix.
    !>         On exit, E has been destroyed.
    !>

    B

    !>          B is REAL 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 REAL
    !>         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 REAL array, dimension at least
    !>         (9*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2),
    !>         where NLVL = max(0, INT(log_2 (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.

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

Definition at line 171 of file slalsd.f.

Author

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