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zlaed7.f(3) LAPACK zlaed7.f(3)

zlaed7.f -


subroutine zlaed7 (N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ, RHO, INDXQ, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIVCOL, GIVNUM, WORK, RWORK, IWORK, INFO)
 
ZLAED7 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.

ZLAED7 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:
 ZLAED7 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 or banded
 Hermitian matrix that has been reduced to tridiagonal form.
T = Q(in) ( D(in) + RHO * Z*Z**H ) Q**H(in) = Q(out) * D(out) * Q**H(out)
where Z = Q**Hu, 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 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 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.
CUTPNT
          CUTPNT is INTEGER
         Contains the location of the last eigenvalue in the leading
         sub-matrix.  min(1,N) <= CUTPNT <= N.
QSIZ
          QSIZ is INTEGER
         The dimension of the unitary matrix used to reduce
         the full matrix to tridiagonal form.  QSIZ >= N.
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 COMPLEX*16 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).
RHO
          RHO is DOUBLE PRECISION
         Contains the subdiagonal element used to create the rank-1
         modification.
INDXQ
          INDXQ is INTEGER array, dimension (N)
         This contains the permutation which will reintegrate the
         subproblem just solved back into sorted order,
         ie. D( INDXQ( I = 1, N ) ) will be in ascending order.
IWORK
          IWORK is INTEGER array, dimension (4*N)
RWORK
          RWORK is DOUBLE PRECISION array,
                                 dimension (3*N+2*QSIZ*N)
WORK
          WORK is COMPLEX*16 array, dimension (QSIZ*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.
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
Definition at line 247 of file zlaed7.f.

Generated automatically by Doxygen for LAPACK from the source code.
Sat Nov 16 2013 Version 3.4.2

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