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