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

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