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 'Computing  Small Singular Values of Bidiagonal Matrices With
     Guaranteed High Relative Accuracy,' 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 'Computing  Small Singular Values of Bidiagonal Matrices With
     Guaranteed High Relative Accuracy,' 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

Generated automatically by Doxygen for LAPACK from the source code.