slaed1()

subroutine slaed1	(	integer	n,
		real, dimension( * )	d,
		real, dimension( ldq, * )	q,
		integer	ldq,
		integer, dimension( * )	indxq,
		real	rho,
		integer	cutpnt,
		real, dimension( * )	work,
		integer, dimension( * )	iwork,
		integer	info )

SLAED1 used by SSTEDC. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is tridiagonal.

Download SLAED1 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

!>
!> SLAED1 computes the updated eigensystem of a diagonal
!> matrix after modification by a rank-one symmetric matrix.  This
!> routine is used only for the eigenproblem which requires all
!> eigenvalues and eigenvectors of a tridiagonal matrix.  SLAED7 handles
!> the case in which eigenvalues only or eigenvalues and eigenvectors
!> of a full symmetric matrix (which was reduced to tridiagonal form)
!> are desired.
!>
!>   T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out)
!>
!>    where Z = Q**T*u, u is a vector of length N with ones in the
!>    CUTPNT and CUTPNT + 1 th elements and zeros elsewhere.
!>
!>    The eigenvectors of the original matrix are stored in Q, and the
!>    eigenvalues are in D.  The algorithm consists of three stages:
!>
!>       The first stage consists of deflating the size of the problem
!>       when there are multiple eigenvalues or if there is a zero in
!>       the Z vector.  For each such occurrence the dimension of the
!>       secular equation problem is reduced by one.  This stage is
!>       performed by the routine SLAED2.
!>
!>       The second stage consists of calculating the updated
!>       eigenvalues. This is done by finding the roots of the secular
!>       equation via the routine SLAED4 (as called by SLAED3).
!>       This routine also calculates the eigenvectors of the current
!>       problem.
!>
!>       The final stage consists of computing the updated eigenvectors
!>       directly using the updated eigenvalues.  The eigenvectors for
!>       the current problem are multiplied with the eigenvectors from
!>       the overall problem.
!> 

Parameters

[in]	N	!> N is INTEGER !> The dimension of the symmetric tridiagonal matrix. N >= 0. !>
[in,out]	D	!> D is REAL array, dimension (N) !> On entry, the eigenvalues of the rank-1-perturbed matrix. !> On exit, the eigenvalues of the repaired matrix. !>
[in,out]	Q	!> Q is REAL array, dimension (LDQ,N) !> On entry, the eigenvectors of the rank-1-perturbed matrix. !> On exit, the eigenvectors of the repaired tridiagonal matrix. !>
[in]	LDQ	!> LDQ is INTEGER !> The leading dimension of the array Q. LDQ >= max(1,N). !>
[in,out]	INDXQ	!> INDXQ is INTEGER array, dimension (N) !> On entry, the permutation which separately sorts the two !> subproblems in D into ascending order. !> On exit, the permutation which will reintegrate the !> subproblems back into sorted order, !> i.e. D( INDXQ( I = 1, N ) ) will be in ascending order. !>
[in]	RHO	!> RHO is REAL !> The subdiagonal entry used to create the rank-1 modification. !>
[in]	CUTPNT	!> CUTPNT is INTEGER !> The location of the last eigenvalue in the leading sub-matrix. !> min(1,N) <= CUTPNT <= N/2. !>
[out]	WORK	!> WORK is REAL array, dimension (4*N + N**2) !>
[out]	IWORK	!> IWORK is INTEGER array, dimension (4*N) !>
[out]	INFO	!> INFO is INTEGER !> = 0: successful exit. !> < 0: if INFO = -i, the i-th argument had an illegal value. !> > 0: if INFO = 1, an eigenvalue did not converge !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
Modified by Francoise Tisseur, University of Tennessee