path: root/SRC/slaed7.f

      SUBROUTINE SLAED7( ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q,
     $                   LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR,
     $                   PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK,
     $                   INFO )
*
*  -- LAPACK routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
      INTEGER            CURLVL, CURPBM, CUTPNT, ICOMPQ, INFO, LDQ, N,
     $                   QSIZ, TLVLS
      REAL               RHO
*     ..
*     .. Array Arguments ..
      INTEGER            GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ),
     $                   IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * )
      REAL               D( * ), GIVNUM( 2, * ), Q( LDQ, * ),
     $                   QSTORE( * ), WORK( * )
*     ..
*
*  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' ) Q'(in) = Q(out) * D(out) * Q'(out)
*
*     where Z = Q'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 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.
*
*  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) REAL array, dimension (N)
*         On entry, the eigenvalues of the rank-1-perturbed matrix.
*         On exit, the eigenvalues of the repaired matrix.
*
*  Q      (input/output) 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    (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) REAL
*         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) 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   (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) REAL array, dimension (2, N lg N)
*         Each number indicates the S value to be used in the
*         corresponding Givens rotation.
*
*  WORK   (workspace) REAL 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 ..
      REAL               ONE, ZERO
      PARAMETER          ( ONE = 1.0E0, ZERO = 0.0E0 )
*     ..
*     .. Local Scalars ..
      INTEGER            COLTYP, CURR, I, IDLMDA, INDX, INDXC, INDXP,
     $                   IQ2, IS, IW, IZ, K, LDQ2, N1, N2, PTR
*     ..
*     .. External Subroutines ..
      EXTERNAL           SGEMM, SLAED8, SLAED9, SLAEDA, SLAMRG, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, MIN
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
*
      IF( ICOMPQ.LT.0 .OR. ICOMPQ.GT.1 ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( ICOMPQ.EQ.1 .AND. QSIZ.LT.N ) THEN
         INFO = -4
      ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN
         INFO = -9
      ELSE IF( MIN( 1, N ).GT.CUTPNT .OR. N.LT.CUTPNT ) THEN
         INFO = -12
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'SLAED7', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 )
     $   RETURN
*
*     The following values are for bookkeeping purposes only.  They are
*     integer pointers which indicate the portion of the workspace
*     used by a particular array in SLAED8 and SLAED9.
*
      IF( ICOMPQ.EQ.1 ) THEN
         LDQ2 = QSIZ
      ELSE
         LDQ2 = N
      END IF
*
      IZ = 1
      IDLMDA = IZ + N
      IW = IDLMDA + N
      IQ2 = IW + N
      IS = IQ2 + N*LDQ2
*
      INDX = 1
      INDXC = INDX + N
      COLTYP = INDXC + N
      INDXP = COLTYP + N
*
*     Form the z-vector which consists of the last row of Q_1 and the
*     first row of Q_2.
*
      PTR = 1 + 2**TLVLS
      DO 10 I = 1, CURLVL - 1
         PTR = PTR + 2**( TLVLS-I )
   10 CONTINUE
      CURR = PTR + CURPBM
      CALL SLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR,
     $             GIVCOL, GIVNUM, QSTORE, QPTR, WORK( IZ ),
     $             WORK( IZ+N ), INFO )
*
*     When solving the final problem, we no longer need the stored data,
*     so we will overwrite the data from this level onto the previously
*     used storage space.
*
      IF( CURLVL.EQ.TLVLS ) THEN
         QPTR( CURR ) = 1
         PRMPTR( CURR ) = 1
         GIVPTR( CURR ) = 1
      END IF
*
*     Sort and Deflate eigenvalues.
*
      CALL SLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT,
     $             WORK( IZ ), WORK( IDLMDA ), WORK( IQ2 ), LDQ2,
     $             WORK( IW ), PERM( PRMPTR( CURR ) ), GIVPTR( CURR+1 ),
     $             GIVCOL( 1, GIVPTR( CURR ) ),
     $             GIVNUM( 1, GIVPTR( CURR ) ), IWORK( INDXP ),
     $             IWORK( INDX ), INFO )
      PRMPTR( CURR+1 ) = PRMPTR( CURR ) + N
      GIVPTR( CURR+1 ) = GIVPTR( CURR+1 ) + GIVPTR( CURR )
*
*     Solve Secular Equation.
*
      IF( K.NE.0 ) THEN
         CALL SLAED9( K, 1, K, N, D, WORK( IS ), K, RHO, WORK( IDLMDA ),
     $                WORK( IW ), QSTORE( QPTR( CURR ) ), K, INFO )
         IF( INFO.NE.0 )
     $      GO TO 30
         IF( ICOMPQ.EQ.1 ) THEN
            CALL SGEMM( 'N', 'N', QSIZ, K, K, ONE, WORK( IQ2 ), LDQ2,
     $                  QSTORE( QPTR( CURR ) ), K, ZERO, Q, LDQ )
         END IF
         QPTR( CURR+1 ) = QPTR( CURR ) + K**2
*
*     Prepare the INDXQ sorting permutation.
*
         N1 = K
         N2 = N - K
         CALL SLAMRG( N1, N2, D, 1, -1, INDXQ )
      ELSE
         QPTR( CURR+1 ) = QPTR( CURR )
         DO 20 I = 1, N
            INDXQ( I ) = I
   20    CONTINUE
      END IF
*
   30 CONTINUE
      RETURN
*
*     End of SLAED7
*
      END