dlasq1.f(3)

NAME
dlasq1.f

SYNOPSIS

  Functions/Subroutines
subroutine dlasq1 (N, D, E, WORK, INFO)
DLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr.

Function/Subroutine Documentation

  subroutine dlasq1 (integer N, double precision, dimension( * ) D, double precision, dimension( * ) E, double precision, dimension( * ) WORK, integer INFO)

Purpose:

     DLASQ1 computes the singular values of a real N-by-N bidiagonal
     matrix with diagonal D and off-diagonal E. The singular values
     are computed to high relative accuracy, in the absence of
     denormalization, underflow and overflow. The algorithm was first
     presented in
     'Accurate singular values and differential qd algorithms' by K. V.
     Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2, pp. 191-230,
     1994,
     and the present implementation is described in 'An implementation of
     the dqds Algorithm (Positive Case)', LAPACK Working Note.

Parameters
    N

              N is INTEGER
            The number of rows and columns in the matrix. N >= 0.

    D

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

    E

              E is DOUBLE PRECISION array, dimension (N)
            On entry, elements E(1:N-1) contain the off-diagonal elements
            of the bidiagonal matrix whose SVD is desired.
            On exit, E is overwritten.

    WORK

              WORK is DOUBLE PRECISION array, dimension (4*N)

    INFO

              INFO is INTEGER
            = 0: successful exit
            < 0: if INFO = -i, the i-th argument had an illegal value
            > 0: the algorithm failed
                 = 1, a split was marked by a positive value in E
                 = 2, current block of Z not diagonalized after 100*N
                      iterations (in inner while loop)  On exit D and E
                      represent a matrix with the same singular values
                      which the calling subroutine could use to finish the
                      computation, or even feed back into DLASQ1
                 = 3, termination criterion of outer while loop not met
                      (program created more than N unreduced blocks)

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 107 of file dlasq1.f.

Author

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