NAME

       dlaed1.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dlaed1 (N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK, INFO)
           DLAED1 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 dlaed1 (integer N, double precision, dimension( * ) D, double precision, dimension(
       ldq, * ) Q, integer LDQ, integer, dimension( * ) INDXQ, double precision RHO, integer
       CUTPNT, double precision, dimension( * ) WORK, integer, dimension( * ) IWORK, integer
       INFO)
       DLAED1 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:

            DLAED1 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.  DLAED7 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 occurrence the dimension of the
                  secular equation problem is reduced by one.  This stage is
                  performed by the routine DLAED2.

                  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 DLAED3).
                  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 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)
                    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 DOUBLE PRECISION
                    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 DOUBLE PRECISION 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

Author

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