NAME

       slasdq.f -

SYNOPSIS

   Functions/Subroutines
       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.

Function/Subroutine Documentation

   subroutine slasdq (characterUPLO, integerSQRE, integerN, integerNCVT, integerNRU, integerNCC,
       real, dimension( * )D, real, dimension( * )E, real, dimension( ldvt, * )VT, integerLDVT,
       real, dimension( ldu, * )U, integerLDU, real, dimension( ldc, * )C, integerLDC, real,
       dimension( * )WORK, integerINFO)
       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 wether 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.

       Date:
           September 2012

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

       Definition at line 211 of file slasdq.f.

Author

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