DLASD0(3)      LAPACK routine of NEC Numeric Library Collection      DLASD0(3)



NAME
       DLASD0

SYNOPSIS
       SUBROUTINE DLASD0 (N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK,
           WORK, INFO)



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.




ARGUMENTS
           N         (input)
                     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      (input)
                     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         (input/output)
                     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         (input)
                     E is DOUBLE PRECISION array, dimension (M-1)
                    Contains the subdiagonal entries of the bidiagonal matrix.
                    On exit, E has been destroyed.

           U         (output)
                     U is DOUBLE PRECISION array, dimension at least (LDQ, N)
                    On exit, U contains the left singular vectors.

           LDU       (input)
                     LDU is INTEGER
                    On entry, leading dimension of U.

           VT        (output)
                     VT is DOUBLE PRECISION array, dimension at least (LDVT, M)
                    On exit, VT**T contains the right singular vectors.

           LDVT      (input)
                     LDVT is INTEGER
                    On entry, leading dimension of VT.

           SMLSIZ    (input)
                     SMLSIZ is INTEGER
                    On entry, maximum size of the subproblems at the
                    bottom of the computation tree.

           IWORK     (output)
                     IWORK is INTEGER work array.
                    Dimension must be at least (8 * N)

           WORK      (output)
                     WORK is DOUBLE PRECISION work array.
                    Dimension must be at least (3 * M**2 + 2 * M)

           INFO      (output)
                     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



LAPACK routine                  31 October 2017                      DLASD0(3)