Functions/Subroutines
subroutine	claed7 (N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ, RHO, INDXQ, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIVCOL, GIVNUM, WORK, RWORK, IWORK, INFO)
	CLAED7 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 dense.

Function/Subroutine Documentation

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

Download CLAED7 + dependencies [TGZ] [ZIP] [TXT]

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 occurence 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 (3N+2QSIZ*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.

Date:: September 2012

Definition at line 247 of file claed7.f.

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Functions/Subroutines

Function/Subroutine Documentation