bdsdc(3)

NAME
bdsdc - bdsdc: bidiagonal SVD, divide and conquer

SYNOPSIS

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

Detailed Description

Function 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.

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

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.
     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.

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

Definition at line 196 of file sbdsdc.f.

Author

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