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    1:       SUBROUTINE DLAED7( ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q,
    2:      $                   LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR,
    3:      $                   PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK,
    4:      $                   INFO )
    5: *
    6: *  -- LAPACK routine (version 3.2) --
    7: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    8: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    9: *     November 2006
   10: *
   11: *     .. Scalar Arguments ..
   12:       INTEGER            CURLVL, CURPBM, CUTPNT, ICOMPQ, INFO, LDQ, N,
   13:      $                   QSIZ, TLVLS
   14:       DOUBLE PRECISION   RHO
   15: *     ..
   16: *     .. Array Arguments ..
   17:       INTEGER            GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ),
   18:      $                   IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * )
   19:       DOUBLE PRECISION   D( * ), GIVNUM( 2, * ), Q( LDQ, * ),
   20:      $                   QSTORE( * ), WORK( * )
   21: *     ..
   22: *
   23: *  Purpose
   24: *  =======
   25: *
   26: *  DLAED7 computes the updated eigensystem of a diagonal
   27: *  matrix after modification by a rank-one symmetric matrix. This
   28: *  routine is used only for the eigenproblem which requires all
   29: *  eigenvalues and optionally eigenvectors of a dense symmetric matrix
   30: *  that has been reduced to tridiagonal form.  DLAED1 handles
   31: *  the case in which all eigenvalues and eigenvectors of a symmetric
   32: *  tridiagonal matrix are desired.
   33: *
   34: *    T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out)
   35: *
   36: *     where Z = Q'u, u is a vector of length N with ones in the
   37: *     CUTPNT and CUTPNT + 1 th elements and zeros elsewhere.
   38: *
   39: *     The eigenvectors of the original matrix are stored in Q, and the
   40: *     eigenvalues are in D.  The algorithm consists of three stages:
   41: *
   42: *        The first stage consists of deflating the size of the problem
   43: *        when there are multiple eigenvalues or if there is a zero in
   44: *        the Z vector.  For each such occurence the dimension of the
   45: *        secular equation problem is reduced by one.  This stage is
   46: *        performed by the routine DLAED8.
   47: *
   48: *        The second stage consists of calculating the updated
   49: *        eigenvalues. This is done by finding the roots of the secular
   50: *        equation via the routine DLAED4 (as called by DLAED9).
   51: *        This routine also calculates the eigenvectors of the current
   52: *        problem.
   53: *
   54: *        The final stage consists of computing the updated eigenvectors
   55: *        directly using the updated eigenvalues.  The eigenvectors for
   56: *        the current problem are multiplied with the eigenvectors from
   57: *        the overall problem.
   58: *
   59: *  Arguments
   60: *  =========
   61: *
   62: *  ICOMPQ  (input) INTEGER
   63: *          = 0:  Compute eigenvalues only.
   64: *          = 1:  Compute eigenvectors of original dense symmetric matrix
   65: *                also.  On entry, Q contains the orthogonal matrix used
   66: *                to reduce the original matrix to tridiagonal form.
   67: *
   68: *  N      (input) INTEGER
   69: *         The dimension of the symmetric tridiagonal matrix.  N >= 0.
   70: *
   71: *  QSIZ   (input) INTEGER
   72: *         The dimension of the orthogonal matrix used to reduce
   73: *         the full matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1.
   74: *
   75: *  TLVLS  (input) INTEGER
   76: *         The total number of merging levels in the overall divide and
   77: *         conquer tree.
   78: *
   79: *  CURLVL (input) INTEGER
   80: *         The current level in the overall merge routine,
   81: *         0 <= CURLVL <= TLVLS.
   82: *
   83: *  CURPBM (input) INTEGER
   84: *         The current problem in the current level in the overall
   85: *         merge routine (counting from upper left to lower right).
   86: *
   87: *  D      (input/output) DOUBLE PRECISION array, dimension (N)
   88: *         On entry, the eigenvalues of the rank-1-perturbed matrix.
   89: *         On exit, the eigenvalues of the repaired matrix.
   90: *
   91: *  Q      (input/output) DOUBLE PRECISION array, dimension (LDQ, N)
   92: *         On entry, the eigenvectors of the rank-1-perturbed matrix.
   93: *         On exit, the eigenvectors of the repaired tridiagonal matrix.
   94: *
   95: *  LDQ    (input) INTEGER
   96: *         The leading dimension of the array Q.  LDQ >= max(1,N).
   97: *
   98: *  INDXQ  (output) INTEGER array, dimension (N)
   99: *         The permutation which will reintegrate the subproblem just
  100: *         solved back into sorted order, i.e., D( INDXQ( I = 1, N ) )
  101: *         will be in ascending order.
  102: *
  103: *  RHO    (input) DOUBLE PRECISION
  104: *         The subdiagonal element used to create the rank-1
  105: *         modification.
  106: *
  107: *  CUTPNT (input) INTEGER
  108: *         Contains the location of the last eigenvalue in the leading
  109: *         sub-matrix.  min(1,N) <= CUTPNT <= N.
  110: *
  111: *  QSTORE (input/output) DOUBLE PRECISION array, dimension (N**2+1)
  112: *         Stores eigenvectors of submatrices encountered during
  113: *         divide and conquer, packed together. QPTR points to
  114: *         beginning of the submatrices.
  115: *
  116: *  QPTR   (input/output) INTEGER array, dimension (N+2)
  117: *         List of indices pointing to beginning of submatrices stored
  118: *         in QSTORE. The submatrices are numbered starting at the
  119: *         bottom left of the divide and conquer tree, from left to
  120: *         right and bottom to top.
  121: *
  122: *  PRMPTR (input) INTEGER array, dimension (N lg N)
  123: *         Contains a list of pointers which indicate where in PERM a
  124: *         level's permutation is stored.  PRMPTR(i+1) - PRMPTR(i)
  125: *         indicates the size of the permutation and also the size of
  126: *         the full, non-deflated problem.
  127: *
  128: *  PERM   (input) INTEGER array, dimension (N lg N)
  129: *         Contains the permutations (from deflation and sorting) to be
  130: *         applied to each eigenblock.
  131: *
  132: *  GIVPTR (input) INTEGER array, dimension (N lg N)
  133: *         Contains a list of pointers which indicate where in GIVCOL a
  134: *         level's Givens rotations are stored.  GIVPTR(i+1) - GIVPTR(i)
  135: *         indicates the number of Givens rotations.
  136: *
  137: *  GIVCOL (input) INTEGER array, dimension (2, N lg N)
  138: *         Each pair of numbers indicates a pair of columns to take place
  139: *         in a Givens rotation.
  140: *
  141: *  GIVNUM (input) DOUBLE PRECISION array, dimension (2, N lg N)
  142: *         Each number indicates the S value to be used in the
  143: *         corresponding Givens rotation.
  144: *
  145: *  WORK   (workspace) DOUBLE PRECISION array, dimension (3*N+QSIZ*N)
  146: *
  147: *  IWORK  (workspace) INTEGER array, dimension (4*N)
  148: *
  149: *  INFO   (output) INTEGER
  150: *          = 0:  successful exit.
  151: *          < 0:  if INFO = -i, the i-th argument had an illegal value.
  152: *          > 0:  if INFO = 1, an eigenvalue did not converge
  153: *
  154: *  Further Details
  155: *  ===============
  156: *
  157: *  Based on contributions by
  158: *     Jeff Rutter, Computer Science Division, University of California
  159: *     at Berkeley, USA
  160: *
  161: *  =====================================================================
  162: *
  163: *     .. Parameters ..
  164:       DOUBLE PRECISION   ONE, ZERO
  165:       PARAMETER          ( ONE = 1.0D0, ZERO = 0.0D0 )
  166: *     ..
  167: *     .. Local Scalars ..
  168:       INTEGER            COLTYP, CURR, I, IDLMDA, INDX, INDXC, INDXP,
  169:      $                   IQ2, IS, IW, IZ, K, LDQ2, N1, N2, PTR
  170: *     ..
  171: *     .. External Subroutines ..
  172:       EXTERNAL           DGEMM, DLAED8, DLAED9, DLAEDA, DLAMRG, XERBLA
  173: *     ..
  174: *     .. Intrinsic Functions ..
  175:       INTRINSIC          MAX, MIN
  176: *     ..
  177: *     .. Executable Statements ..
  178: *
  179: *     Test the input parameters.
  180: *
  181:       INFO = 0
  182: *
  183:       IF( ICOMPQ.LT.0 .OR. ICOMPQ.GT.1 ) THEN
  184:          INFO = -1
  185:       ELSE IF( N.LT.0 ) THEN
  186:          INFO = -2
  187:       ELSE IF( ICOMPQ.EQ.1 .AND. QSIZ.LT.N ) THEN
  188:          INFO = -4
  189:       ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN
  190:          INFO = -9
  191:       ELSE IF( MIN( 1, N ).GT.CUTPNT .OR. N.LT.CUTPNT ) THEN
  192:          INFO = -12
  193:       END IF
  194:       IF( INFO.NE.0 ) THEN
  195:          CALL XERBLA( 'DLAED7', -INFO )
  196:          RETURN
  197:       END IF
  198: *
  199: *     Quick return if possible
  200: *
  201:       IF( N.EQ.0 )
  202:      $   RETURN
  203: *
  204: *     The following values are for bookkeeping purposes only.  They are
  205: *     integer pointers which indicate the portion of the workspace
  206: *     used by a particular array in DLAED8 and DLAED9.
  207: *
  208:       IF( ICOMPQ.EQ.1 ) THEN
  209:          LDQ2 = QSIZ
  210:       ELSE
  211:          LDQ2 = N
  212:       END IF
  213: *
  214:       IZ = 1
  215:       IDLMDA = IZ + N
  216:       IW = IDLMDA + N
  217:       IQ2 = IW + N
  218:       IS = IQ2 + N*LDQ2
  219: *
  220:       INDX = 1
  221:       INDXC = INDX + N
  222:       COLTYP = INDXC + N
  223:       INDXP = COLTYP + N
  224: *
  225: *     Form the z-vector which consists of the last row of Q_1 and the
  226: *     first row of Q_2.
  227: *
  228:       PTR = 1 + 2**TLVLS
  229:       DO 10 I = 1, CURLVL - 1
  230:          PTR = PTR + 2**( TLVLS-I )
  231:    10 CONTINUE
  232:       CURR = PTR + CURPBM
  233:       CALL DLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR,
  234:      $             GIVCOL, GIVNUM, QSTORE, QPTR, WORK( IZ ),
  235:      $             WORK( IZ+N ), INFO )
  236: *
  237: *     When solving the final problem, we no longer need the stored data,
  238: *     so we will overwrite the data from this level onto the previously
  239: *     used storage space.
  240: *
  241:       IF( CURLVL.EQ.TLVLS ) THEN
  242:          QPTR( CURR ) = 1
  243:          PRMPTR( CURR ) = 1
  244:          GIVPTR( CURR ) = 1
  245:       END IF
  246: *
  247: *     Sort and Deflate eigenvalues.
  248: *
  249:       CALL DLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT,
  250:      $             WORK( IZ ), WORK( IDLMDA ), WORK( IQ2 ), LDQ2,
  251:      $             WORK( IW ), PERM( PRMPTR( CURR ) ), GIVPTR( CURR+1 ),
  252:      $             GIVCOL( 1, GIVPTR( CURR ) ),
  253:      $             GIVNUM( 1, GIVPTR( CURR ) ), IWORK( INDXP ),
  254:      $             IWORK( INDX ), INFO )
  255:       PRMPTR( CURR+1 ) = PRMPTR( CURR ) + N
  256:       GIVPTR( CURR+1 ) = GIVPTR( CURR+1 ) + GIVPTR( CURR )
  257: *
  258: *     Solve Secular Equation.
  259: *
  260:       IF( K.NE.0 ) THEN
  261:          CALL DLAED9( K, 1, K, N, D, WORK( IS ), K, RHO, WORK( IDLMDA ),
  262:      $                WORK( IW ), QSTORE( QPTR( CURR ) ), K, INFO )
  263:          IF( INFO.NE.0 )
  264:      $      GO TO 30
  265:          IF( ICOMPQ.EQ.1 ) THEN
  266:             CALL DGEMM( 'N', 'N', QSIZ, K, K, ONE, WORK( IQ2 ), LDQ2,
  267:      $                  QSTORE( QPTR( CURR ) ), K, ZERO, Q, LDQ )
  268:          END IF
  269:          QPTR( CURR+1 ) = QPTR( CURR ) + K**2
  270: *
  271: *     Prepare the INDXQ sorting permutation.
  272: *
  273:          N1 = K
  274:          N2 = N - K
  275:          CALL DLAMRG( N1, N2, D, 1, -1, INDXQ )
  276:       ELSE
  277:          QPTR( CURR+1 ) = QPTR( CURR )
  278:          DO 20 I = 1, N
  279:             INDXQ( I ) = I
  280:    20    CONTINUE
  281:       END IF
  282: *
  283:    30 CONTINUE
  284:       RETURN
  285: *
  286: *     End of DLAED7
  287: *
  288:       END