◆ dlasq2()

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.

Download DLASQ2 + dependencies [TGZ] [ZIP] [TXT]

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

[in]

N

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

[in,out]

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.
!>

[out]

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).
!>