lasdq(3)

NAME
lasdq - lasdq: D&C step: leaf using bdsqr

SYNOPSIS

  Functions
subroutine dlasdq (uplo, sqre, n, ncvt, nru, ncc, d, e, vt, ldvt, u, ldu, c, ldc, work, info)
DLASDQ computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc.
subroutine slasdq (uplo, sqre, n, ncvt, nru, ncc, d, e, vt, ldvt, u, ldu, c, ldc, work, info)
SLASDQ computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc.

Detailed Description

Function Documentation

  subroutine dlasdq (character uplo, integer sqre, integer n, integer ncvt, integer nru, integer ncc, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldvt, * ) vt, integer ldvt, double precision, dimension( ldu, * ) u, integer ldu, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer info)

DLASDQ computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc.

Purpose:

    !>
    !> DLASDQ computes the singular value decomposition (SVD) of a real
    !> (upper or lower) bidiagonal matrix with diagonal D and offdiagonal
    !> E, accumulating the transformations if desired. Letting B denote
    !> the input bidiagonal matrix, the algorithm computes orthogonal
    !> matrices Q and P such that B = Q * S * P**T (P**T denotes the transpose
    !> of P). The singular values S are overwritten on D.
    !>
    !> The input matrix U  is changed to U  * Q  if desired.
    !> The input matrix VT is changed to P**T * VT if desired.
    !> The input matrix C  is changed to Q**T * C  if desired.
    !>
    !> See  by J. Demmel and W. Kahan,
    !> LAPACK Working Note #3, for a detailed description of the algorithm.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>        On entry, UPLO specifies whether the input bidiagonal matrix
    !>        is upper or lower bidiagonal, and whether it is square are
    !>        not.
    !>           UPLO = 'U' or 'u'   B is upper bidiagonal.
    !>           UPLO = 'L' or 'l'   B is lower bidiagonal.
    !>

    SQRE

    !>          SQRE is INTEGER
    !>        = 0: then the input matrix is N-by-N.
    !>        = 1: then the input matrix is N-by-(N+1) if UPLU = 'U' and
    !>             (N+1)-by-N if UPLU = 'L'.
    !>
    !>        The bidiagonal matrix has
    !>        N = NL + NR + 1 rows and
    !>        M = N + SQRE >= N columns.
    !>

    N

    !>          N is INTEGER
    !>        On entry, N specifies the number of rows and columns
    !>        in the matrix. N must be at least 0.
    !>

    NCVT

    !>          NCVT is INTEGER
    !>        On entry, NCVT specifies the number of columns of
    !>        the matrix VT. NCVT must be at least 0.
    !>

    NRU

    !>          NRU is INTEGER
    !>        On entry, NRU specifies the number of rows of
    !>        the matrix U. NRU must be at least 0.
    !>

    NCC

    !>          NCC is INTEGER
    !>        On entry, NCC specifies the number of columns of
    !>        the matrix C. NCC must be at least 0.
    !>

    D

    !>          D is DOUBLE PRECISION array, dimension (N)
    !>        On entry, D contains the diagonal entries of the
    !>        bidiagonal matrix whose SVD is desired. On normal exit,
    !>        D contains the singular values in ascending order.
    !>

    E

    !>          E is DOUBLE PRECISION array.
    !>        dimension is (N-1) if SQRE = 0 and N if SQRE = 1.
    !>        On entry, the entries of E contain the offdiagonal entries
    !>        of the bidiagonal matrix whose SVD is desired. On normal
    !>        exit, E will contain 0. If the algorithm does not converge,
    !>        D and E will contain the diagonal and superdiagonal entries
    !>        of a bidiagonal matrix orthogonally equivalent to the one
    !>        given as input.
    !>

    VT

    !>          VT is DOUBLE PRECISION array, dimension (LDVT, NCVT)
    !>        On entry, contains a matrix which on exit has been
    !>        premultiplied by P**T, dimension N-by-NCVT if SQRE = 0
    !>        and (N+1)-by-NCVT if SQRE = 1 (not referenced if NCVT=0).
    !>

    LDVT

    !>          LDVT is INTEGER
    !>        On entry, LDVT specifies the leading dimension of VT as
    !>        declared in the calling (sub) program. LDVT must be at
    !>        least 1. If NCVT is nonzero LDVT must also be at least N.
    !>

    U

    !>          U is DOUBLE PRECISION array, dimension (LDU, N)
    !>        On entry, contains a  matrix which on exit has been
    !>        postmultiplied by Q, dimension NRU-by-N if SQRE = 0
    !>        and NRU-by-(N+1) if SQRE = 1 (not referenced if NRU=0).
    !>

    LDU

    !>          LDU is INTEGER
    !>        On entry, LDU  specifies the leading dimension of U as
    !>        declared in the calling (sub) program. LDU must be at
    !>        least max( 1, NRU ) .
    !>

    C

    !>          C is DOUBLE PRECISION array, dimension (LDC, NCC)
    !>        On entry, contains an N-by-NCC matrix which on exit
    !>        has been premultiplied by Q**T  dimension N-by-NCC if SQRE = 0
    !>        and (N+1)-by-NCC if SQRE = 1 (not referenced if NCC=0).
    !>

    LDC

    !>          LDC is INTEGER
    !>        On entry, LDC  specifies the leading dimension of C as
    !>        declared in the calling (sub) program. LDC must be at
    !>        least 1. If NCC is nonzero, LDC must also be at least N.
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (4*N)
    !>        Workspace. Only referenced if one of NCVT, NRU, or NCC is
    !>        nonzero, and if N is at least 2.
    !>

    INFO

    !>          INFO is INTEGER
    !>        On exit, a value of 0 indicates a successful exit.
    !>        If INFO < 0, argument number -INFO is illegal.
    !>        If INFO > 0, the algorithm did not converge, and INFO
    !>        specifies how many superdiagonals 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

Definition at line 209 of file dlasdq.f.

  subroutine slasdq (character uplo, integer sqre, integer n, integer ncvt, integer nru, integer ncc, real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldvt, * ) vt, integer ldvt, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer info)

SLASDQ computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc.

Purpose:

    !>
    !> SLASDQ computes the singular value decomposition (SVD) of a real
    !> (upper or lower) bidiagonal matrix with diagonal D and offdiagonal
    !> E, accumulating the transformations if desired. Letting B denote
    !> the input bidiagonal matrix, the algorithm computes orthogonal
    !> matrices Q and P such that B = Q * S * P**T (P**T denotes the transpose
    !> of P). The singular values S are overwritten on D.
    !>
    !> The input matrix U  is changed to U  * Q  if desired.
    !> The input matrix VT is changed to P**T * VT if desired.
    !> The input matrix C  is changed to Q**T * C  if desired.
    !>
    !> See  by J. Demmel and W. Kahan,
    !> LAPACK Working Note #3, for a detailed description of the algorithm.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>        On entry, UPLO specifies whether the input bidiagonal matrix
    !>        is upper or lower bidiagonal, and whether it is square are
    !>        not.
    !>           UPLO = 'U' or 'u'   B is upper bidiagonal.
    !>           UPLO = 'L' or 'l'   B is lower bidiagonal.
    !>

    SQRE

    !>          SQRE is INTEGER
    !>        = 0: then the input matrix is N-by-N.
    !>        = 1: then the input matrix is N-by-(N+1) if UPLU = 'U' and
    !>             (N+1)-by-N if UPLU = 'L'.
    !>
    !>        The bidiagonal matrix has
    !>        N = NL + NR + 1 rows and
    !>        M = N + SQRE >= N columns.
    !>

    N

    !>          N is INTEGER
    !>        On entry, N specifies the number of rows and columns
    !>        in the matrix. N must be at least 0.
    !>

    NCVT

    !>          NCVT is INTEGER
    !>        On entry, NCVT specifies the number of columns of
    !>        the matrix VT. NCVT must be at least 0.
    !>

    NRU

    !>          NRU is INTEGER
    !>        On entry, NRU specifies the number of rows of
    !>        the matrix U. NRU must be at least 0.
    !>

    NCC

    !>          NCC is INTEGER
    !>        On entry, NCC specifies the number of columns of
    !>        the matrix C. NCC must be at least 0.
    !>

    D

    !>          D is REAL array, dimension (N)
    !>        On entry, D contains the diagonal entries of the
    !>        bidiagonal matrix whose SVD is desired. On normal exit,
    !>        D contains the singular values in ascending order.
    !>

    E

    !>          E is REAL array.
    !>        dimension is (N-1) if SQRE = 0 and N if SQRE = 1.
    !>        On entry, the entries of E contain the offdiagonal entries
    !>        of the bidiagonal matrix whose SVD is desired. On normal
    !>        exit, E will contain 0. If the algorithm does not converge,
    !>        D and E will contain the diagonal and superdiagonal entries
    !>        of a bidiagonal matrix orthogonally equivalent to the one
    !>        given as input.
    !>

    VT

    !>          VT is REAL array, dimension (LDVT, NCVT)
    !>        On entry, contains a matrix which on exit has been
    !>        premultiplied by P**T, dimension N-by-NCVT if SQRE = 0
    !>        and (N+1)-by-NCVT if SQRE = 1 (not referenced if NCVT=0).
    !>

    LDVT

    !>          LDVT is INTEGER
    !>        On entry, LDVT specifies the leading dimension of VT as
    !>        declared in the calling (sub) program. LDVT must be at
    !>        least 1. If NCVT is nonzero LDVT must also be at least N.
    !>

    U

    !>          U is REAL array, dimension (LDU, N)
    !>        On entry, contains a  matrix which on exit has been
    !>        postmultiplied by Q, dimension NRU-by-N if SQRE = 0
    !>        and NRU-by-(N+1) if SQRE = 1 (not referenced if NRU=0).
    !>

    LDU

    !>          LDU is INTEGER
    !>        On entry, LDU  specifies the leading dimension of U as
    !>        declared in the calling (sub) program. LDU must be at
    !>        least max( 1, NRU ) .
    !>

    C

    !>          C is REAL array, dimension (LDC, NCC)
    !>        On entry, contains an N-by-NCC matrix which on exit
    !>        has been premultiplied by Q**T  dimension N-by-NCC if SQRE = 0
    !>        and (N+1)-by-NCC if SQRE = 1 (not referenced if NCC=0).
    !>

    LDC

    !>          LDC is INTEGER
    !>        On entry, LDC  specifies the leading dimension of C as
    !>        declared in the calling (sub) program. LDC must be at
    !>        least 1. If NCC is nonzero, LDC must also be at least N.
    !>

    WORK

    !>          WORK is REAL array, dimension (4*N)
    !>        Workspace. Only referenced if one of NCVT, NRU, or NCC is
    !>        nonzero, and if N is at least 2.
    !>

    INFO

    !>          INFO is INTEGER
    !>        On exit, a value of 0 indicates a successful exit.
    !>        If INFO < 0, argument number -INFO is illegal.
    !>        If INFO > 0, the algorithm did not converge, and INFO
    !>        specifies how many superdiagonals 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

Definition at line 209 of file slasdq.f.

Author

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