sbdsdc.f(3)

NAME
sbdsdc.f -

SYNOPSIS

  Functions/Subroutines
subroutine SBDSDC (UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q, IQ, WORK, IWORK, INFO)
SBDSDC

Function/Subroutine Documentation

  subroutine SBDSDC (CHARACTERUPLO, CHARACTERCOMPQ, INTEGERN, REAL, dimension( * )D, REAL, dimension( * )E, REAL, dimension( ldu, * )U, INTEGERLDU, REAL, dimension( ldvt, * )VT, INTEGERLDVT, REAL, dimension( * )Q, INTEGER, dimension( * )IQ, REAL, dimension( * )WORK, INTEGER, dimension( * )IWORK, INTEGERINFO)

SBDSDC

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.

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 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

              E is 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

              U is 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

              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 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

              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 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

              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 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

              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'.

Date:
    November 2011

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

Definition at line 205 of file sbdsdc.f'.

Author

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