SRC/dlasq2.f(3)            Library Functions Manual            SRC/dlasq2.f(3)

NAME
       SRC/dlasq2.f

SYNOPSIS
   Functions/Subroutines
       subroutine dlasq2 (n, z, info)
           DLASQ2 computes all the eigenvalues of the symmetric positive
           definite tridiagonal matrix associated with the qd Array Z to high
           relative accuracy. Used by sbdsqr and sstegr.

Function/Subroutine Documentation
   subroutine dlasq2 (integer n, double precision, dimension( * ) z, integer
       info)
       DLASQ2 computes all the eigenvalues of the symmetric positive definite
       tridiagonal matrix associated with the qd Array Z to high relative
       accuracy. Used by sbdsqr and sstegr.

       Purpose:


           !>
           !> DLASQ2 computes all the eigenvalues of the symmetric positive
           !> definite tridiagonal matrix associated with the qd array Z to high
           !> relative accuracy are computed to high relative accuracy, in the
           !> absence of denormalization, underflow and overflow.
           !>
           !> To see the relation of Z to the tridiagonal matrix, let L be a
           !> unit lower bidiagonal matrix with subdiagonals Z(2,4,6,,..) and
           !> let U be an upper bidiagonal matrix with 1's above and diagonal
           !> Z(1,3,5,,..). The tridiagonal is L*U or, if you prefer, the
           !> symmetric tridiagonal to which it is similar.
           !>
           !> Note : DLASQ2 defines a logical variable, IEEE, which is true
           !> on machines which follow ieee-754 floating-point standard in their
           !> handling of infinities and NaNs, and false otherwise. This variable
           !> is passed to DLASQ3.
           !>

       Parameters
           N

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

           Z

           !>          Z is DOUBLE PRECISION array, dimension ( 4*N )
           !>        On entry Z holds the qd array. On exit, entries 1 to N hold
           !>        the eigenvalues in decreasing order, Z( 2*N+1 ) holds the
           !>        trace, and Z( 2*N+2 ) holds the sum of the eigenvalues. If
           !>        N > 2, then Z( 2*N+3 ) holds the iteration count, Z( 2*N+4 )
           !>        holds NDIVS/NIN^2, and Z( 2*N+5 ) holds the percentage of
           !>        shifts that failed.
           !>

           INFO

           !>          INFO is INTEGER
           !>        = 0: successful exit
           !>        < 0: if the i-th argument is a scalar and had an illegal
           !>             value, then INFO = -i, if the i-th argument is an
           !>             array and the j-entry had an illegal value, then
           !>             INFO = -(i*100+j)
           !>        > 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 Z holds
           !>                   a qd array with the same eigenvalues as the given Z.
           !>              = 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.

       Further Details:


           !>
           !>  Local Variables: I0:N0 defines a current unreduced segment of Z.
           !>  The shifts are accumulated in SIGMA. Iteration count is in ITER.
           !>  Ping-pong is controlled by PP (alternates between 0 and 1).
           !>

       Definition at line 111 of file dlasq2.f.

Author
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LAPACK                          Version 3.12.0                 SRC/dlasq2.f(3)