dlaed0.f

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*> \brief \b DLAED0 used by DSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
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*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE DLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS,
*                          WORK, IWORK, INFO )
*
*       .. Scalar Arguments ..
*       INTEGER            ICOMPQ, INFO, LDQ, LDQS, N, QSIZ
*       ..
*       .. Array Arguments ..
*       INTEGER            IWORK( * )
*       DOUBLE PRECISION   D( * ), E( * ), Q( LDQ, * ), QSTORE( LDQS, * ),
*      $                   WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DLAED0 computes all eigenvalues and corresponding eigenvectors of a
*> symmetric tridiagonal matrix using the divide and conquer method.
*> \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.
*>          = 2:  Compute eigenvalues and eigenvectors of tridiagonal
*>                matrix.
*> \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] N
*> \verbatim
*>          N is INTEGER
*>         The dimension of the symmetric tridiagonal matrix.  N >= 0.
*> \endverbatim
*>
*> \param[in,out] D
*> \verbatim
*>          D is DOUBLE PRECISION array, dimension (N)
*>         On entry, the main diagonal of the tridiagonal matrix.
*>         On exit, its eigenvalues.
*> \endverbatim
*>
*> \param[in] E
*> \verbatim
*>          E is DOUBLE PRECISION array, dimension (N-1)
*>         The off-diagonal elements of the tridiagonal matrix.
*>         On exit, E has been destroyed.
*> \endverbatim
*>
*> \param[in,out] Q
*> \verbatim
*>          Q is DOUBLE PRECISION array, dimension (LDQ, N)
*>         On entry, Q must contain an N-by-N orthogonal matrix.
*>         If ICOMPQ = 0    Q is not referenced.
*>         If ICOMPQ = 1    On entry, Q is a subset of the columns of the
*>                          orthogonal matrix used to reduce the full
*>                          matrix to tridiagonal form corresponding to
*>                          the subset of the full matrix which is being
*>                          decomposed at this time.
*>         If ICOMPQ = 2    On entry, Q will be the identity matrix.
*>                          On exit, Q contains the eigenvectors of the
*>                          tridiagonal matrix.
*> \endverbatim
*>
*> \param[in] LDQ
*> \verbatim
*>          LDQ is INTEGER
*>         The leading dimension of the array Q.  If eigenvectors are
*>         desired, then  LDQ >= max(1,N).  In any case,  LDQ >= 1.
*> \endverbatim
*>
*> \param[out] QSTORE
*> \verbatim
*>          QSTORE is DOUBLE PRECISION array, dimension (LDQS, N)
*>         Referenced only when ICOMPQ = 1.  Used to store parts of
*>         the eigenvector matrix when the updating matrix multiplies
*>         take place.
*> \endverbatim
*>
*> \param[in] LDQS
*> \verbatim
*>          LDQS is INTEGER
*>         The leading dimension of the array QSTORE.  If ICOMPQ = 1,
*>         then  LDQS >= max(1,N).  In any case,  LDQS >= 1.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is DOUBLE PRECISION array,
*>         If ICOMPQ = 0 or 1, the dimension of WORK must be at least
*>                     1 + 3*N + 2*N*lg N + 3*N**2
*>                     ( lg( N ) = smallest integer k
*>                                 such that 2^k >= N )
*>         If ICOMPQ = 2, the dimension of WORK must be at least
*>                     4*N + N**2.
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*>          IWORK is INTEGER array,
*>         If ICOMPQ = 0 or 1, the dimension of IWORK must be at least
*>                        6 + 6*N + 5*N*lg N.
*>                        ( lg( N ) = smallest integer k
*>                                    such that 2^k >= N )
*>         If ICOMPQ = 2, the dimension of IWORK must be at least
*>                        3 + 5*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:  The algorithm failed to compute an eigenvalue while
*>                working on the submatrix lying in rows and columns
*>                INFO/(N+1) through mod(INFO,N+1).
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup laed0
*
*> \par Contributors:
*  ==================
*>
*> Jeff Rutter, Computer Science Division, University of California
*> at Berkeley, USA
*
*  =====================================================================
      SUBROUTINE dlaed0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS,
     $                   WORK, IWORK, INFO )
*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      INTEGER            ICOMPQ, INFO, LDQ, LDQS, N, QSIZ
*     ..
*     .. Array Arguments ..
      INTEGER            IWORK( * )
      DOUBLE PRECISION   D( * ), E( * ), Q( LDQ, * ), QSTORE( LDQS, * ),
     $                   work( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE, TWO
      parameter( zero = 0.d0, one = 1.d0, two = 2.d0 )
*     ..
*     .. Local Scalars ..
      INTEGER            CURLVL, CURPRB, CURR, I, IGIVCL, IGIVNM,
     $                   igivpt, indxq, iperm, iprmpt, iq, iqptr, iwrem,
     $                   j, k, lgn, matsiz, msd2, smlsiz, smm1, spm1,
     $                   spm2, submat, subpbs, tlvls
      DOUBLE PRECISION   TEMP
*     ..
*     .. External Subroutines ..
      EXTERNAL           dcopy, dgemm, dlacpy, dlaed1, dlaed7, dsteqr,
     $                   xerbla
*     ..
*     .. External Functions ..
      INTEGER            ILAENV
      EXTERNAL           ilaenv
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, dble, int, log, max
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      info = 0
*
      IF( icompq.LT.0 .OR. icompq.GT.2 ) THEN
         info = -1
      ELSE IF( ( icompq.EQ.1 ) .AND. ( qsiz.LT.max( 0, n ) ) ) THEN
         info = -2
      ELSE IF( n.LT.0 ) THEN
         info = -3
      ELSE IF( ldq.LT.max( 1, n ) ) THEN
         info = -7
      ELSE IF( ldqs.LT.max( 1, n ) ) THEN
         info = -9
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'DLAED0', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 )
     $   RETURN
*
      smlsiz = ilaenv( 9, 'DLAED0', ' ', 0, 0, 0, 0 )
*
*     Determine the size and placement of the submatrices, and save in
*     the leading elements of IWORK.
*
      iwork( 1 ) = n
      subpbs = 1
      tlvls = 0
   10 CONTINUE
      IF( iwork( subpbs ).GT.smlsiz ) THEN
         DO 20 j = subpbs, 1, -1
            iwork( 2*j ) = ( iwork( j )+1 ) / 2
            iwork( 2*j-1 ) = iwork( j ) / 2
   20    CONTINUE
         tlvls = tlvls + 1
         subpbs = 2*subpbs
         GO TO 10
      END IF
      DO 30 j = 2, subpbs
         iwork( j ) = iwork( j ) + iwork( j-1 )
   30 CONTINUE
*
*     Divide the matrix into SUBPBS submatrices of size at most SMLSIZ+1
*     using rank-1 modifications (cuts).
*
      spm1 = subpbs - 1
      DO 40 i = 1, spm1
         submat = iwork( i ) + 1
         smm1 = submat - 1
         d( smm1 ) = d( smm1 ) - abs( e( smm1 ) )
         d( submat ) = d( submat ) - abs( e( smm1 ) )
   40 CONTINUE
*
      indxq = 4*n + 3
      IF( icompq.NE.2 ) THEN
*
*        Set up workspaces for eigenvalues only/accumulate new vectors
*        routine
*
         temp = log( dble( n ) ) / log( two )
         lgn = int( temp )
         IF( 2**lgn.LT.n )
     $      lgn = lgn + 1
         IF( 2**lgn.LT.n )
     $      lgn = lgn + 1
         iprmpt = indxq + n + 1
         iperm = iprmpt + n*lgn
         iqptr = iperm + n*lgn
         igivpt = iqptr + n + 2
         igivcl = igivpt + n*lgn
*
         igivnm = 1
         iq = igivnm + 2*n*lgn
         iwrem = iq + n**2 + 1
*
*        Initialize pointers
*
         DO 50 i = 0, subpbs
            iwork( iprmpt+i ) = 1
            iwork( igivpt+i ) = 1
   50    CONTINUE
         iwork( iqptr ) = 1
      END IF
*
*     Solve each submatrix eigenproblem at the bottom of the divide and
*     conquer tree.
*
      curr = 0
      DO 70 i = 0, spm1
         IF( i.EQ.0 ) THEN
            submat = 1
            matsiz = iwork( 1 )
         ELSE
            submat = iwork( i ) + 1
            matsiz = iwork( i+1 ) - iwork( i )
         END IF
         IF( icompq.EQ.2 ) THEN
            CALL dsteqr( 'I', matsiz, d( submat ), e( submat ),
     $                   q( submat, submat ), ldq, work, info )
            IF( info.NE.0 )
     $         GO TO 130
         ELSE
            CALL dsteqr( 'I', matsiz, d( submat ), e( submat ),
     $                   work( iq-1+iwork( iqptr+curr ) ), matsiz, work,
     $                   info )
            IF( info.NE.0 )
     $         GO TO 130
            IF( icompq.EQ.1 ) THEN
               CALL dgemm( 'N', 'N', qsiz, matsiz, matsiz, one,
     $                     q( 1, submat ), ldq, work( iq-1+iwork( iqptr+
     $                     curr ) ), matsiz, zero, qstore( 1, submat ),
     $                     ldqs )
            END IF
            iwork( iqptr+curr+1 ) = iwork( iqptr+curr ) + matsiz**2
            curr = curr + 1
         END IF
         k = 1
         DO 60 j = submat, iwork( i+1 )
            iwork( indxq+j ) = k
            k = k + 1
   60    CONTINUE
   70 CONTINUE
*
*     Successively merge eigensystems of adjacent submatrices
*     into eigensystem for the corresponding larger matrix.
*
*     while ( SUBPBS > 1 )
*
      curlvl = 1
   80 CONTINUE
      IF( subpbs.GT.1 ) THEN
         spm2 = subpbs - 2
         DO 90 i = 0, spm2, 2
            IF( i.EQ.0 ) THEN
               submat = 1
               matsiz = iwork( 2 )
               msd2 = iwork( 1 )
               curprb = 0
            ELSE
               submat = iwork( i ) + 1
               matsiz = iwork( i+2 ) - iwork( i )
               msd2 = matsiz / 2
               curprb = curprb + 1
            END IF
*
*     Merge lower order eigensystems (of size MSD2 and MATSIZ - MSD2)
*     into an eigensystem of size MATSIZ.
*     DLAED1 is used only for the full eigensystem of a tridiagonal
*     matrix.
*     DLAED7 handles the cases in which eigenvalues only or eigenvalues
*     and eigenvectors of a full symmetric matrix (which was reduced to
*     tridiagonal form) are desired.
*
            IF( icompq.EQ.2 ) THEN
               CALL dlaed1( matsiz, d( submat ), q( submat, submat ),
     $                      ldq, iwork( indxq+submat ),
     $                      e( submat+msd2-1 ), msd2, work,
     $                      iwork( subpbs+1 ), info )
            ELSE
               CALL dlaed7( icompq, matsiz, qsiz, tlvls, curlvl, curprb,
     $                      d( submat ), qstore( 1, submat ), ldqs,
     $                      iwork( indxq+submat ), e( submat+msd2-1 ),
     $                      msd2, work( iq ), iwork( iqptr ),
     $                      iwork( iprmpt ), iwork( iperm ),
     $                      iwork( igivpt ), iwork( igivcl ),
     $                      work( igivnm ), work( iwrem ),
     $                      iwork( subpbs+1 ), info )
            END IF
            IF( info.NE.0 )
     $         GO TO 130
            iwork( i / 2+1 ) = iwork( i+2 )
   90    CONTINUE
         subpbs = subpbs / 2
         curlvl = curlvl + 1
         GO TO 80
      END IF
*
*     end while
*
*     Re-merge the eigenvalues/vectors which were deflated at the final
*     merge step.
*
      IF( icompq.EQ.1 ) THEN
         DO 100 i = 1, n
            j = iwork( indxq+i )
            work( i ) = d( j )
            CALL dcopy( qsiz, qstore( 1, j ), 1, q( 1, i ), 1 )
  100    CONTINUE
         CALL dcopy( n, work, 1, d, 1 )
      ELSE IF( icompq.EQ.2 ) THEN
         DO 110 i = 1, n
            j = iwork( indxq+i )
            work( i ) = d( j )
            CALL dcopy( n, q( 1, j ), 1, work( n*i+1 ), 1 )
  110    CONTINUE
         CALL dcopy( n, work, 1, d, 1 )
         CALL dlacpy( 'A', n, n, work( n+1 ), n, q, ldq )
      ELSE
         DO 120 i = 1, n
            j = iwork( indxq+i )
            work( i ) = d( j )
  120    CONTINUE
         CALL dcopy( n, work, 1, d, 1 )
      END IF
      GO TO 140
*
  130 CONTINUE
      info = submat*( n+1 ) + submat + matsiz - 1
*
  140 CONTINUE
      RETURN
*
*     End of DLAED0
*
      END