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slaed1.f(3)				      LAPACK				      slaed1.f(3)

NAME
       slaed1.f -

SYNOPSIS
   Functions/Subroutines
       subroutine slaed1 (N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK, INFO)
	   SLAED1 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
	   tridiagonal.

Function/Subroutine Documentation
   subroutine slaed1 (integerN, real, dimension( * )D, real, dimension( ldq, * )Q, integerLDQ,
       integer, dimension( * )INDXQ, realRHO, integerCUTPNT, real, dimension( * )WORK, integer,
       dimension( * )IWORK, integerINFO)
       SLAED1 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 tridiagonal.

       Purpose:

	    SLAED1 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 eigenvectors of a tridiagonal matrix.  SLAED7 handles
	    the case in which eigenvalues only or eigenvalues and eigenvectors
	    of a full symmetric matrix (which was reduced to tridiagonal form)
	    are desired.

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

	       where Z = Q**T*u, 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:
	   N

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

	   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.

	   Q

		     Q is REAL 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)
		    On entry, the permutation which separately sorts the two
		    subproblems in D into ascending order.
		    On exit, the permutation which will reintegrate the
		    subproblems back into sorted order,
		    i.e. D( INDXQ( I = 1, N ) ) will be in ascending order.

	   RHO

		     RHO is REAL
		    The subdiagonal entry used to create the rank-1 modification.

	   CUTPNT

		     CUTPNT is INTEGER
		    The location of the last eigenvalue in the leading sub-matrix.
		    min(1,N) <= CUTPNT <= N/2.

	   WORK

		     WORK is REAL array, dimension (4*N + N**2)

	   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
	    Modified by Francoise Tisseur, University of Tennessee

       Definition at line 163 of file slaed1.f.

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

Version 3.4.2				 Tue Sep 25 2012			      slaed1.f(3)
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