dlaed7.f man page

dlaed7.f —

Synopsis

Functions/Subroutines

subroutine dlaed7 (ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK, INFO)
DLAED7 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 dlaed7 (integerICOMPQ, integerN, integerQSIZ, integerTLVLS, integerCURLVL, integerCURPBM, double precision, dimension( * )D, double precision, dimension( ldq, * )Q, integerLDQ, integer, dimension( * )INDXQ, double precisionRHO, integerCUTPNT, double precision, dimension( * )QSTORE, integer, dimension( * )QPTR, integer, dimension( * )PRMPTR, integer, dimension( * )PERM, integer, dimension( * )GIVPTR, integer, dimension( 2, * )GIVCOL, double precision, dimension( 2, * )GIVNUM, double precision, dimension( * )WORK, integer, dimension( * )IWORK, integerINFO)

DLAED7 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:

DLAED7 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.  DLAED1 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 DLAED8.

      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 DLAED9).
      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 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)
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 DOUBLE PRECISION
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 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.

WORK

WORK is DOUBLE PRECISION 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:

September 2012

Contributors:

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

Definition at line 258 of file dlaed7.f.

Author

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Referenced By

dlaed7(3) is an alias of dlaed7.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK