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version 1.8, 2011/07/22 07:38:06 version 1.9, 2011/11/21 20:42:54
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   *> \brief \b DLAED7
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DLAED7 + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaed7.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaed7.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaed7.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DLAED7( ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q,
   *                          LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR,
   *                          PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK,
   *                          INFO )
   * 
   *       .. Scalar Arguments ..
   *       INTEGER            CURLVL, CURPBM, CUTPNT, ICOMPQ, INFO, LDQ, N,
   *      $                   QSIZ, TLVLS
   *       DOUBLE PRECISION   RHO
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ),
   *      $                   IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * )
   *       DOUBLE PRECISION   D( * ), GIVNUM( 2, * ), Q( LDQ, * ),
   *      $                   QSTORE( * ), WORK( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> 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.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] ICOMPQ
   *> \verbatim
   *>          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.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>         The dimension of the symmetric tridiagonal matrix.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in] QSIZ
   *> \verbatim
   *>          QSIZ is INTEGER
   *>         The dimension of the orthogonal matrix used to reduce
   *>         the full matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1.
   *> \endverbatim
   *>
   *> \param[in] TLVLS
   *> \verbatim
   *>          TLVLS is INTEGER
   *>         The total number of merging levels in the overall divide and
   *>         conquer tree.
   *> \endverbatim
   *>
   *> \param[in] CURLVL
   *> \verbatim
   *>          CURLVL is INTEGER
   *>         The current level in the overall merge routine,
   *>         0 <= CURLVL <= TLVLS.
   *> \endverbatim
   *>
   *> \param[in] CURPBM
   *> \verbatim
   *>          CURPBM is INTEGER
   *>         The current problem in the current level in the overall
   *>         merge routine (counting from upper left to lower right).
   *> \endverbatim
   *>
   *> \param[in,out] D
   *> \verbatim
   *>          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.
   *> \endverbatim
   *>
   *> \param[in,out] Q
   *> \verbatim
   *>          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.
   *> \endverbatim
   *>
   *> \param[in] LDQ
   *> \verbatim
   *>          LDQ is INTEGER
   *>         The leading dimension of the array Q.  LDQ >= max(1,N).
   *> \endverbatim
   *>
   *> \param[out] INDXQ
   *> \verbatim
   *>          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.
   *> \endverbatim
   *>
   *> \param[in] RHO
   *> \verbatim
   *>          RHO is DOUBLE PRECISION
   *>         The subdiagonal element used to create the rank-1
   *>         modification.
   *> \endverbatim
   *>
   *> \param[in] CUTPNT
   *> \verbatim
   *>          CUTPNT is INTEGER
   *>         Contains the location of the last eigenvalue in the leading
   *>         sub-matrix.  min(1,N) <= CUTPNT <= N.
   *> \endverbatim
   *>
   *> \param[in,out] QSTORE
   *> \verbatim
   *>          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.
   *> \endverbatim
   *>
   *> \param[in,out] QPTR
   *> \verbatim
   *>          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.
   *> \endverbatim
   *>
   *> \param[in] PRMPTR
   *> \verbatim
   *>          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.
   *> \endverbatim
   *>
   *> \param[in] PERM
   *> \verbatim
   *>          PERM is INTEGER array, dimension (N lg N)
   *>         Contains the permutations (from deflation and sorting) to be
   *>         applied to each eigenblock.
   *> \endverbatim
   *>
   *> \param[in] GIVPTR
   *> \verbatim
   *>          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.
   *> \endverbatim
   *>
   *> \param[in] GIVCOL
   *> \verbatim
   *>          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.
   *> \endverbatim
   *>
   *> \param[in] GIVNUM
   *> \verbatim
   *>          GIVNUM is DOUBLE PRECISION array, dimension (2, N lg N)
   *>         Each number indicates the S value to be used in the
   *>         corresponding Givens rotation.
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is DOUBLE PRECISION array, dimension (3*N+2*QSIZ*N)
   *> \endverbatim
   *>
   *> \param[out] IWORK
   *> \verbatim
   *>          IWORK is INTEGER array, dimension (4*N)
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          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
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup auxOTHERcomputational
   *
   *> \par Contributors:
   *  ==================
   *>
   *> Jeff Rutter, Computer Science Division, University of California
   *> at Berkeley, USA
   *
   *  =====================================================================
       SUBROUTINE DLAED7( ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q,        SUBROUTINE DLAED7( ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q,
      $                   LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR,       $                   LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR,
      $                   PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK,       $                   PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK,
      $                   INFO )       $                   INFO )
 *  *
 *  -- LAPACK routine (version 3.3.1) --  *  -- LAPACK computational routine (version 3.4.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *  -- April 2011                                                      --  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER            CURLVL, CURPBM, CUTPNT, ICOMPQ, INFO, LDQ, N,        INTEGER            CURLVL, CURPBM, CUTPNT, ICOMPQ, INFO, LDQ, N,
Line 20 Line 277
      $                   QSTORE( * ), WORK( * )       $                   QSTORE( * ), WORK( * )
 *     ..  *     ..
 *  *
 *  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.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  ICOMPQ  (input) 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      (input) INTEGER  
 *         The dimension of the symmetric tridiagonal matrix.  N >= 0.  
 *  
 *  QSIZ   (input) INTEGER  
 *         The dimension of the orthogonal matrix used to reduce  
 *         the full matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1.  
 *  
 *  TLVLS  (input) INTEGER  
 *         The total number of merging levels in the overall divide and  
 *         conquer tree.  
 *  
 *  CURLVL (input) INTEGER  
 *         The current level in the overall merge routine,  
 *         0 <= CURLVL <= TLVLS.  
 *  
 *  CURPBM (input) INTEGER  
 *         The current problem in the current level in the overall  
 *         merge routine (counting from upper left to lower right).  
 *  
 *  D      (input/output) DOUBLE PRECISION array, dimension (N)  
 *         On entry, the eigenvalues of the rank-1-perturbed matrix.  
 *         On exit, the eigenvalues of the repaired matrix.  
 *  
 *  Q      (input/output) 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    (input) INTEGER  
 *         The leading dimension of the array Q.  LDQ >= max(1,N).  
 *  
 *  INDXQ  (output) 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    (input) DOUBLE PRECISION  
 *         The subdiagonal element used to create the rank-1  
 *         modification.  
 *  
 *  CUTPNT (input) INTEGER  
 *         Contains the location of the last eigenvalue in the leading  
 *         sub-matrix.  min(1,N) <= CUTPNT <= N.  
 *  
 *  QSTORE (input/output) 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   (input/output) 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 (input) 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   (input) INTEGER array, dimension (N lg N)  
 *         Contains the permutations (from deflation and sorting) to be  
 *         applied to each eigenblock.  
 *  
 *  GIVPTR (input) 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 (input) INTEGER array, dimension (2, N lg N)  
 *         Each pair of numbers indicates a pair of columns to take place  
 *         in a Givens rotation.  
 *  
 *  GIVNUM (input) DOUBLE PRECISION array, dimension (2, N lg N)  
 *         Each number indicates the S value to be used in the  
 *         corresponding Givens rotation.  
 *  
 *  WORK   (workspace) DOUBLE PRECISION array, dimension (3*N+QSIZ*N)  
 *  
 *  IWORK  (workspace) INTEGER array, dimension (4*N)  
 *  
 *  INFO   (output) 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  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  Based on contributions by  
 *     Jeff Rutter, Computer Science Division, University of California  
 *     at Berkeley, USA  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.8  
changed lines
  Added in v.1.9

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