Functions/Subroutines
subroutine	zlaed8 (K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA, Q2, LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR, GIVCOL, GIVNUM, INFO)
	ZLAED8 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense.

Function/Subroutine Documentation

subroutine zlaed8	(	integer	K,
		integer	N,
		integer	QSIZ,
		complex16, dimension( ldq, )	Q,
		integer	LDQ,
		double precision, dimension( * )	D,
		double precision	RHO,
		integer	CUTPNT,
		double precision, dimension( * )	Z,
		double precision, dimension( * )	DLAMDA,
		complex16, dimension( ldq2, )	Q2,
		integer	LDQ2,
		double precision, dimension( * )	W,
		integer, dimension( * )	INDXP,
		integer, dimension( * )	INDX,
		integer, dimension( * )	INDXQ,
		integer, dimension( * )	PERM,
		integer	GIVPTR,
		integer, dimension( 2, * )	GIVCOL,
		double precision, dimension( 2, * )	GIVNUM,
		integer	INFO
	)

ZLAED8 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense.

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Purpose:

 ZLAED8 merges the two sets of eigenvalues together into a single
 sorted set.  Then it tries to deflate the size of the problem.
 There are two ways in which deflation can occur:  when two or more
 eigenvalues are close together or if there is a tiny element in the
 Z vector.  For each such occurrence the order of the related secular
 equation problem is reduced by one.

Parameters:

[out]	K	K is INTEGER Contains the number of non-deflated eigenvalues. This is the order of the related secular equation.
[in]	N	N is INTEGER The dimension of the symmetric tridiagonal matrix. N >= 0.
[in]	QSIZ	QSIZ is INTEGER The dimension of the unitary matrix used to reduce the dense or band matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.
[in,out]	Q	Q is COMPLEX*16 array, dimension (LDQ,N) On entry, Q contains the eigenvectors of the partially solved system which has been previously updated in matrix multiplies with other partially solved eigensystems. On exit, Q contains the trailing (N-K) updated eigenvectors (those which were deflated) in its last N-K columns.
[in]	LDQ	LDQ is INTEGER The leading dimension of the array Q. LDQ >= max( 1, N ).
[in,out]	D	D is DOUBLE PRECISION array, dimension (N) On entry, D contains the eigenvalues of the two submatrices to be combined. On exit, D contains the trailing (N-K) updated eigenvalues (those which were deflated) sorted into increasing order.
[in,out]	RHO	RHO is DOUBLE PRECISION Contains the off diagonal element associated with the rank-1 cut which originally split the two submatrices which are now being recombined. RHO is modified during the computation to the value required by DLAED3.
[in]	CUTPNT	CUTPNT is INTEGER Contains the location of the last eigenvalue in the leading sub-matrix. MIN(1,N) <= CUTPNT <= N.
[in]	Z	Z is DOUBLE PRECISION array, dimension (N) On input this vector contains the updating vector (the last row of the first sub-eigenvector matrix and the first row of the second sub-eigenvector matrix). The contents of Z are destroyed during the updating process.
[out]	DLAMDA	DLAMDA is DOUBLE PRECISION array, dimension (N) Contains a copy of the first K eigenvalues which will be used by DLAED3 to form the secular equation.
[out]	Q2	Q2 is COMPLEX*16 array, dimension (LDQ2,N) If ICOMPQ = 0, Q2 is not referenced. Otherwise, Contains a copy of the first K eigenvectors which will be used by DLAED7 in a matrix multiply (DGEMM) to update the new eigenvectors.
[in]	LDQ2	LDQ2 is INTEGER The leading dimension of the array Q2. LDQ2 >= max( 1, N ).
[out]	W	W is DOUBLE PRECISION array, dimension (N) This will hold the first k values of the final deflation-altered z-vector and will be passed to DLAED3.
[out]	INDXP	INDXP is INTEGER array, dimension (N) This will contain the permutation used to place deflated values of D at the end of the array. On output INDXP(1:K) points to the nondeflated D-values and INDXP(K+1:N) points to the deflated eigenvalues.
[out]	INDX	INDX is INTEGER array, dimension (N) This will contain the permutation used to sort the contents of D into ascending order.
[in]	INDXQ	INDXQ is INTEGER array, dimension (N) This contains the permutation which separately sorts the two sub-problems in D into ascending order. Note that elements in the second half of this permutation must first have CUTPNT added to their values in order to be accurate.
[out]	PERM	PERM is INTEGER array, dimension (N) Contains the permutations (from deflation and sorting) to be applied to each eigenblock.
[out]	GIVPTR	GIVPTR is INTEGER Contains the number of Givens rotations which took place in this subproblem.
[out]	GIVCOL	GIVCOL is INTEGER array, dimension (2, N) Each pair of numbers indicates a pair of columns to take place in a Givens rotation.
[out]	GIVNUM	GIVNUM is DOUBLE PRECISION array, dimension (2, 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.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: September 2012

Definition at line 227 of file zlaed8.f.

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