Functions/Subroutines
subroutine	dlaed7 (ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK, INFO)
	DLAED7 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 dlaed7	(	integer	ICOMPQ,
		integer	N,
		integer	QSIZ,
		integer	TLVLS,
		integer	CURLVL,
		integer	CURPBM,
		double precision, dimension( * )	D,
		double precision, dimension( ldq, * )	Q,
		integer	LDQ,
		integer, dimension( * )	INDXQ,
		double precision	RHO,
		integer	CUTPNT,
		double precision, dimension( * )	QSTORE,
		integer, dimension( * )	QPTR,
		integer, dimension( * )	PRMPTR,
		integer, dimension( * )	PERM,
		integer, dimension( * )	GIVPTR,
		integer, dimension( 2, * )	GIVCOL,
		double precision, dimension( 2, * )	GIVNUM,
		double precision, dimension( * )	WORK,
		integer, dimension( * )	IWORK,
		integer	INFO
	)

DLAED7 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 DLAED7 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

 DLAED7 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 symmetric matrix
 that has been reduced to tridiagonal form.  DLAED1 handles
 the case in which all eigenvalues and eigenvectors of a symmetric
 tridiagonal matrix are desired.

   T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out)

    where Z = Q**Tu, 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 DLAED8.

       The second stage consists of calculating the updated
       eigenvalues. This is done by finding the roots of the secular
       equation via the routine DLAED4 (as called by DLAED9).
       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]	ICOMPQ	ICOMPQ is INTEGER = 0: Compute eigenvalues only. = 1: Compute eigenvectors of original dense symmetric matrix also. On entry, Q contains the orthogonal matrix used to reduce the original matrix to tridiagonal form.
[in]	N	N is INTEGER The dimension of the symmetric tridiagonal matrix. N >= 0.
[in]	QSIZ	QSIZ is INTEGER The dimension of the orthogonal matrix used to reduce the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.
[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 DOUBLE PRECISION 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 DOUBLE PRECISION 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).
[out]	INDXQ	INDXQ is INTEGER array, dimension (N) The permutation which will reintegrate the subproblem just solved back into sorted order, i.e., D( INDXQ( I = 1, N ) ) will be in ascending order.
[in]	RHO	RHO is DOUBLE PRECISION The subdiagonal element used to create the rank-1 modification.
[in]	CUTPNT	CUTPNT is INTEGER Contains the location of the last eigenvalue in the leading sub-matrix. min(1,N) <= CUTPNT <= N.
[in,out]	QSTORE	QSTORE is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (2, N lg N) Each number indicates the S value to be used in the corresponding Givens rotation.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (3N+2QSIZ*N)
[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.

Date:: September 2012

Contributors:: Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

Definition at line 258 of file dlaed7.f.

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Functions/Subroutines

Function/Subroutine Documentation