lasd0(3)

NAME
lasd0 - lasd0: D&C step: top level solver

SYNOPSIS

  Functions

subroutine dlasd0 (n, sqre, d, e, u, ldu, vt, ldvt, smlsiz, iwork, work, info)
DLASD0 computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e. Used by sbdsdc.
subroutine slasd0 (n, sqre, d, e, u, ldu, vt, ldvt, smlsiz, iwork, work, info)
SLASD0 computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e. Used by sbdsdc.

Detailed Description

Function Documentation

  subroutine dlasd0 (integer n, integer sqre, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldu, * ) u, integer ldu, double precision, dimension( ldvt, * ) vt, integer ldvt, integer smlsiz, integer, dimension( * ) iwork, double precision, dimension( * ) work, integer info)

DLASD0 computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e. Used by sbdsdc.

Purpose:

    !>
    !> Using a divide and conquer approach, DLASD0 computes the singular
    !> value decomposition (SVD) of a real upper bidiagonal N-by-M
    !> matrix B with diagonal D and offdiagonal E, where M = N + SQRE.
    !> The algorithm computes orthogonal matrices U and VT such that
    !> B = U * S * VT. The singular values S are overwritten on D.
    !>
    !> A related subroutine, DLASDA, computes only the singular values,
    !> and optionally, the singular vectors in compact form.
    !>

Parameters
    N

    !>          N is INTEGER
    !>         On entry, the row dimension of the upper bidiagonal matrix.
    !>         This is also the dimension of the main diagonal array D.
    !>

    SQRE

    !>          SQRE is INTEGER
    !>         Specifies the column dimension of the bidiagonal matrix.
    !>         = 0: The bidiagonal matrix has column dimension M = N;
    !>         = 1: The bidiagonal matrix has column dimension M = N+1;
    !>

    D

    !>          D is DOUBLE PRECISION array, dimension (N)
    !>         On entry D contains the main diagonal of the bidiagonal
    !>         matrix.
    !>         On exit D, if INFO = 0, contains its singular values.
    !>

    E

    !>          E is DOUBLE PRECISION array, dimension (M-1)
    !>         Contains the subdiagonal entries of the bidiagonal matrix.
    !>         On exit, E has been destroyed.
    !>

    U

    !>          U is DOUBLE PRECISION array, dimension (LDU, N)
    !>         On exit, U contains the left singular vectors,
    !>          if U passed in as (N, N) Identity.
    !>

    LDU

    !>          LDU is INTEGER
    !>         On entry, leading dimension of U.
    !>

    VT

    !>          VT is DOUBLE PRECISION array, dimension (LDVT, M)
    !>         On exit, VT**T contains the right singular vectors,
    !>          if VT passed in as (M, M) Identity.
    !>

    LDVT

    !>          LDVT is INTEGER
    !>         On entry, leading dimension of VT.
    !>

    SMLSIZ

    !>          SMLSIZ is INTEGER
    !>         On entry, maximum size of the subproblems at the
    !>         bottom of the computation tree.
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (8*N)
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (3*M**2+2*M)
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit.
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
    !>          > 0:  if INFO = 1, a singular value did not converge
    !>

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

  subroutine slasd0 (integer n, integer sqre, real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldvt, * ) vt, integer ldvt, integer smlsiz, integer, dimension( * ) iwork, real, dimension( * ) work, integer info)

SLASD0 computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e. Used by sbdsdc.

Purpose:

    !>
    !> Using a divide and conquer approach, SLASD0 computes the singular
    !> value decomposition (SVD) of a real upper bidiagonal N-by-M
    !> matrix B with diagonal D and offdiagonal E, where M = N + SQRE.
    !> The algorithm computes orthogonal matrices U and VT such that
    !> B = U * S * VT. The singular values S are overwritten on D.
    !>
    !> A related subroutine, SLASDA, computes only the singular values,
    !> and optionally, the singular vectors in compact form.
    !>

Parameters
    N

    !>          N is INTEGER
    !>         On entry, the row dimension of the upper bidiagonal matrix.
    !>         This is also the dimension of the main diagonal array D.
    !>

    SQRE

    !>          SQRE is INTEGER
    !>         Specifies the column dimension of the bidiagonal matrix.
    !>         = 0: The bidiagonal matrix has column dimension M = N;
    !>         = 1: The bidiagonal matrix has column dimension M = N+1;
    !>

    D

    !>          D is REAL array, dimension (N)
    !>         On entry D contains the main diagonal of the bidiagonal
    !>         matrix.
    !>         On exit D, if INFO = 0, contains its singular values.
    !>

    E

    !>          E is REAL array, dimension (M-1)
    !>         Contains the subdiagonal entries of the bidiagonal matrix.
    !>         On exit, E has been destroyed.
    !>

    U

    !>          U is REAL array, dimension (LDU, N)
    !>         On exit, U contains the left singular vectors,
    !>          if U passed in as (N, N) Identity.
    !>

    LDU

    !>          LDU is INTEGER
    !>         On entry, leading dimension of U.
    !>

    VT

    !>          VT is REAL array, dimension (LDVT, M)
    !>         On exit, VT**T contains the right singular vectors,
    !>          if VT passed in as (M, M) Identity.
    !>

    LDVT

    !>          LDVT is INTEGER
    !>         On entry, leading dimension of VT.
    !>

    SMLSIZ

    !>          SMLSIZ is INTEGER
    !>         On entry, maximum size of the subproblems at the
    !>         bottom of the computation tree.
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (8*N)
    !>

    WORK

    !>          WORK is REAL array, dimension (3*M**2+2*M)
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit.
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
    !>          > 0:  if INFO = 1, a singular value did not converge
    !>

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

Author

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