slaed7.f(3)

NAME
slaed7.f -

SYNOPSIS

  Functions/Subroutines
subroutine slaed7 (ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK, INFO)
SLAED7 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 slaed7 (integerICOMPQ, integerN, integerQSIZ, integerTLVLS, integerCURLVL, integerCURPBM, real, dimension( * )D, real, dimension( ldq, * )Q, integerLDQ, integer, dimension( * )INDXQ, realRHO, integerCUTPNT, real, dimension( * )QSTORE, integer, dimension( * )QPTR, integer, dimension( * )PRMPTR, integer, dimension( * )PERM, integer, dimension( * )GIVPTR, integer, dimension( 2, * )GIVCOL, real, dimension( 2, * )GIVNUM, real, dimension( * )WORK, integer, dimension( * )IWORK, integerINFO)

Purpose:

     SLAED7 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.  SLAED1 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 SLAED8.
           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 SLAED9).
           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 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)
             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 REAL
             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 REAL 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 REAL array, dimension (2, N lg N)
             Each number indicates the S value to be used in the
             corresponding Givens rotation.

    WORK

              WORK is REAL 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:
    November 2015

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

Definition at line 258 of file slaed7.f.

Author

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