claed7()

subroutine claed7	(	integer	n,
		integer	cutpnt,
		integer	qsiz,
		integer	tlvls,
		integer	curlvl,
		integer	curpbm,
		real, dimension( * )	d,
		complex, dimension( ldq, * )	q,
		integer	ldq,
		real	rho,
		integer, dimension( * )	indxq,
		real, dimension( * )	qstore,
		integer, dimension( * )	qptr,
		integer, dimension( * )	prmptr,
		integer, dimension( * )	perm,
		integer, dimension( * )	givptr,
		integer, dimension( 2, * )	givcol,
		real, dimension( 2, * )	givnum,
		complex, dimension( * )	work,
		real, dimension( * )	rwork,
		integer, dimension( * )	iwork,
		integer	info )

CLAED7 used by CSTEDC. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is dense.

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Purpose:

!>
!> CLAED7 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 optionally eigenvectors of a dense or banded
!> Hermitian matrix that has been reduced to tridiagonal form.
!>
!>   T = Q(in) ( D(in) + RHO * Z*Z**H ) Q**H(in) = Q(out) * D(out) * Q**H(out)
!>
!>   where Z = Q**Hu, 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]	CUTPNT	!> CUTPNT is INTEGER !> Contains the location of the last eigenvalue in the leading !> sub-matrix. min(1,N) <= CUTPNT <= N. !>
[in]	QSIZ	!> QSIZ is INTEGER !> The dimension of the unitary matrix used to reduce !> the full matrix to tridiagonal form. QSIZ >= N. !>
[in]	TLVLS	!> TLVLS is INTEGER !> The total number of merging levels in the overall divide and !> conquer tree. !>
[in]	CURLVL	!> CURLVL is INTEGER !> The current level in the overall merge routine, !> 0 <= curlvl <= tlvls. !>
[in]	CURPBM	!> CURPBM is INTEGER !> The current problem in the current level in the overall !> merge routine (counting from upper left to lower right). !>
[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 COMPLEX 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]	RHO	!> RHO is REAL !> Contains the subdiagonal element used to create the rank-1 !> modification. !>
[out]	INDXQ	!> INDXQ is INTEGER array, dimension (N) !> This contains the permutation which will reintegrate the !> subproblem just solved back into sorted order, !> ie. D( INDXQ( I = 1, N ) ) will be in ascending order. !>
[out]	IWORK	!> IWORK is INTEGER array, dimension (4*N) !>
[out]	RWORK	!> RWORK is REAL array, !> dimension (3*N+2*QSIZ*N) !>
[out]	WORK	!> WORK is COMPLEX array, dimension (QSIZ*N) !>
[in,out]	QSTORE	!> QSTORE is REAL array, dimension (N**2+1) !> Stores eigenvectors of submatrices encountered during !> divide and conquer, packed together. QPTR points to !> beginning of the submatrices. !>
[in,out]	QPTR	!> QPTR is INTEGER array, dimension (N+2) !> List of indices pointing to beginning of submatrices stored !> in QSTORE. The submatrices are numbered starting at the !> bottom left of the divide and conquer tree, from left to !> right and bottom to top. !>
[in]	PRMPTR	!> PRMPTR is INTEGER array, dimension (N lg N) !> Contains a list of pointers which indicate where in PERM a !> level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) !> indicates the size of the permutation and also the size of !> the full, non-deflated problem. !>
[in]	PERM	!> PERM is INTEGER array, dimension (N lg N) !> Contains the permutations (from deflation and sorting) to be !> applied to each eigenblock. !>
[in]	GIVPTR	!> GIVPTR is INTEGER array, dimension (N lg N) !> Contains a list of pointers which indicate where in GIVCOL a !> level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) !> indicates the number of Givens rotations. !>
[in]	GIVCOL	!> GIVCOL is INTEGER array, dimension (2, N lg N) !> Each pair of numbers indicates a pair of columns to take place !> in a Givens rotation. !>
[in]	GIVNUM	!> GIVNUM is REAL array, dimension (2, N lg N) !> Each number indicates the S value to be used in the !> corresponding Givens rotation. !>
[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.