SRC/dbdsdc.f(3)

NAME
SRC/dbdsdc.f

SYNOPSIS

  Functions/Subroutines
subroutine dbdsdc (uplo, compq, n, d, e, u, ldu, vt, ldvt, q, iq, work, iwork, info)
DBDSDC

Function/Subroutine Documentation

  subroutine dbdsdc (character uplo, character compq, integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldu, * ) u, integer ldu, double precision, dimension( ldvt, * ) vt, integer ldvt, double precision, dimension( * ) q, integer, dimension( * ) iq, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)

DBDSDC

Purpose:

    !>
    !> DBDSDC 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. DBDSDC can be used to compute all singular values,
    !> and optionally, singular vectors or singular vectors in compact form.
    !>
    !> The code currently calls DLASDQ if singular values only are desired.
    !> However, it can be slightly modified to compute singular values
    !> using the divide and conquer method.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  B is upper bidiagonal.
    !>          = 'L':  B is lower bidiagonal.
    !>

    COMPQ

    !>          COMPQ is 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

    !>          N is INTEGER
    !>          The order of the matrix B.  N >= 0.
    !>

    D

    !>          D is DOUBLE PRECISION 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

    !>          E is DOUBLE PRECISION 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

    !>          U is DOUBLE PRECISION 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

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

    VT

    !>          VT is DOUBLE PRECISION 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

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

    Q

    !>          Q is DOUBLE PRECISION 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 DOUBLE PRECISION 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

    !>          IQ is 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

    !>          WORK is DOUBLE PRECISION 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

    !>          IWORK is INTEGER array, dimension (8*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.
    !>                The update process of divide and conquer failed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:
    Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

Definition at line 196 of file dbdsdc.f.

Author

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