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dlaed7.f(3)				      LAPACK				      dlaed7.f(3)

NAME
       dlaed7.f -

SYNOPSIS
   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 (integerICOMPQ, integerN, integerQSIZ, integerTLVLS, integerCURLVL,
       integerCURPBM, double precision, dimension( * )D, double precision, dimension( ldq, * )Q,
       integerLDQ, integer, dimension( * )INDXQ, double precisionRHO, integerCUTPNT, 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, integerINFO)
       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.

       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:
	   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.

	   N

		     N is INTEGER
		    The dimension of the symmetric tridiagonal matrix.	N >= 0.

	   QSIZ

		     QSIZ is INTEGER
		    The dimension of the orthogonal matrix used to reduce
		    the full matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1.

	   TLVLS

		     TLVLS is INTEGER
		    The total number of merging levels in the overall divide and
		    conquer tree.

	   CURLVL

		     CURLVL is INTEGER
		    The current level in the overall merge routine,
		    0 <= CURLVL <= TLVLS.

	   CURPBM

		     CURPBM is INTEGER
		    The current problem in the current level in the overall
		    merge routine (counting from upper left to lower right).

	   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.

	   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.

	   LDQ

		     LDQ is INTEGER
		    The leading dimension of the array Q.  LDQ >= max(1,N).

	   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.

	   RHO

		     RHO is DOUBLE PRECISION
		    The subdiagonal element used to create the rank-1
		    modification.

	   CUTPNT

		     CUTPNT is INTEGER
		    Contains the location of the last eigenvalue in the leading
		    sub-matrix.  min(1,N) <= CUTPNT <= N.

	   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.

	   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.

	   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.

	   PERM

		     PERM is INTEGER array, dimension (N lg N)
		    Contains the permutations (from deflation and sorting) to be
		    applied to each eigenblock.

	   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.

	   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.

	   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.

	   WORK

		     WORK is DOUBLE PRECISION array, dimension (3*N+2*QSIZ*N)

	   IWORK

		     IWORK is INTEGER array, dimension (4*N)

	   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.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      dlaed7.f(3)
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