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

NAME

       LAPACK-3  -  computes  the  singular  value decomposition (SVD) of a real N-by-N (upper or
       lower) bidiagonal matrix B

SYNOPSIS

       SUBROUTINE SBDSDC( UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q, IQ, WORK, IWORK, INFO )

           CHARACTER      COMPQ, UPLO

           INTEGER        INFO, LDU, LDVT, N

           INTEGER        IQ( * ), IWORK( * )

           REAL           D( * ), E( * ), Q( * ), U( LDU, * ), VT( LDVT, * ), WORK( * )

PURPOSE

       SBDSDC computes the singular value decomposition (SVD) of a real N-by-N (upper  or  lower)
       bidiagonal matrix B:  B = U * S * VT,
        using a divide and conquer method, where S is a diagonal matrix
        with non-negative diagonal elements (the singular values of B), and
        U and VT are orthogonal matrices of left and right singular vectors,
        respectively. SBDSDC can be used to compute all singular values,
        and optionally, singular vectors or singular vectors in compact form.
        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 X-MP, Cray Y-MP, Cray C-90, or Cray-2.
        It could conceivably fail on hexadecimal or decimal machines
        without guard digits, but we know of none.  See SLASD3 for details.
        The code currently calls SLASDQ if singular values only are desired.
        However, it can be slightly modified to compute singular values
        using the divide and conquer method.

ARGUMENTS

        UPLO    (input) CHARACTER*1
                = 'U':  B is upper bidiagonal.
                = 'L':  B is lower bidiagonal.

        COMPQ   (input) CHARACTER*1
                Specifies whether singular vectors are to be computed
                as follows:
                = 'N':  Compute singular values only;
                = 'P':  Compute singular values and compute singular
                vectors in compact form;
                = 'I':  Compute singular values and singular vectors.

        N       (input) INTEGER
                The order of the matrix B.  N >= 0.

        D       (input/output) REAL array, dimension (N)
                On entry, the n diagonal elements of the bidiagonal matrix B.
                On exit, if INFO=0, the singular values of B.

        E       (input/output) REAL array, dimension (N-1)
                On entry, the elements of E contain the offdiagonal
                elements of the bidiagonal matrix whose SVD is desired.
                On exit, E has been destroyed.

        U       (output) REAL array, dimension (LDU,N)
                If  COMPQ = 'I', then:
                On exit, if INFO = 0, U contains the left singular vectors
                of the bidiagonal matrix.
                For other values of COMPQ, U is not referenced.

        LDU     (input) INTEGER
                The leading dimension of the array U.  LDU >= 1.
                If singular vectors are desired, then LDU >= max( 1, N ).

        VT      (output) REAL array, dimension (LDVT,N)
                If  COMPQ = 'I', then:
                On exit, if INFO = 0, VT**T contains the right singular
                vectors of the bidiagonal matrix.
                For other values of COMPQ, VT is not referenced.

        LDVT    (input) INTEGER
                The leading dimension of the array VT.  LDVT >= 1.
                If singular vectors are desired, then LDVT >= max( 1, N ).

        Q       (output) REAL array, dimension (LDQ)
                If  COMPQ = 'P', then:
                On exit, if INFO = 0, Q and IQ contain the left
                and right singular vectors in a compact form,
                requiring O(N log N) space instead of 2*N**2.
                In particular, Q contains all the REAL data in
                LDQ >= N*(11 + 2*SMLSIZ + 8*INT(LOG_2(N/(SMLSIZ+1))))
                words of memory, where SMLSIZ is returned by ILAENV and
                is equal to the maximum size of the subproblems at the
                bottom of the computation tree (usually about 25).
                For other values of COMPQ, Q is not referenced.

        IQ      (output) INTEGER array, dimension (LDIQ)
                If  COMPQ = 'P', then:
                On exit, if INFO = 0, Q and IQ contain the left
                and right singular vectors in a compact form,
                requiring O(N log N) space instead of 2*N**2.
                In particular, IQ contains all INTEGER data in
                LDIQ >= N*(3 + 3*INT(LOG_2(N/(SMLSIZ+1))))
                words of memory, where SMLSIZ is returned by ILAENV and
                is equal to the maximum size of the subproblems at the
                bottom of the computation tree (usually about 25).
                For other values of COMPQ, IQ is not referenced.

        WORK    (workspace) REAL array, dimension (MAX(1,LWORK))
                If COMPQ = 'N' then LWORK >= (4 * N).
                If COMPQ = 'P' then LWORK >= (6 * N).
                If COMPQ = 'I' then LWORK >= (3 * N**2 + 4 * N).

        IWORK   (workspace) INTEGER array, dimension (8*N)

        INFO    (output) 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.
                The update process of divide and conquer failed.

FURTHER DETAILS

        Based on contributions by
           Ming Gu and Huan Ren, Computer Science Division, University of
           California at Berkeley, USA

 LAPACK routine (version 3.2.2)             April 2011                            SBDSDC(3lapack)