```      SUBROUTINE DLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS,
\$                   WORK, IWORK, INFO )
*
*  -- LAPACK routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
INTEGER            ICOMPQ, INFO, LDQ, LDQS, N, QSIZ
*     ..
*     .. Array Arguments ..
INTEGER            IWORK( * )
DOUBLE PRECISION   D( * ), E( * ), Q( LDQ, * ), QSTORE( LDQS, * ),
\$                   WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  DLAED0 computes all eigenvalues and corresponding eigenvectors of a
*  symmetric tridiagonal matrix using the divide and conquer method.
*
*  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.
*          = 2:  Compute eigenvalues and eigenvectors of tridiagonal
*                matrix.
*
*  QSIZ   (input) INTEGER
*         The dimension of the orthogonal matrix used to reduce
*         the full matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1.
*
*  N      (input) INTEGER
*         The dimension of the symmetric tridiagonal matrix.  N >= 0.
*
*  D      (input/output) DOUBLE PRECISION array, dimension (N)
*         On entry, the main diagonal of the tridiagonal matrix.
*         On exit, its eigenvalues.
*
*  E      (input) DOUBLE PRECISION array, dimension (N-1)
*         The off-diagonal elements of the tridiagonal matrix.
*         On exit, E has been destroyed.
*
*  Q      (input/output) 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.
*
*  LDQ    (input) INTEGER
*         The leading dimension of the array Q.  If eigenvectors are
*         desired, then  LDQ >= max(1,N).  In any case,  LDQ >= 1.
*
*  QSTORE (workspace) 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.
*
*  LDQS   (input) INTEGER
*         The leading dimension of the array QSTORE.  If ICOMPQ = 1,
*         then  LDQS >= max(1,N).  In any case,  LDQS >= 1.
*
*  WORK   (workspace) DOUBLE PRECISION array,
*         If ICOMPQ = 0 or 1, the dimension of WORK must be at least
*                     1 + 3*N + 2*N*lg N + 2*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.
*
*  IWORK  (workspace) 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.
*
*  INFO   (output) 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).
*
*  Further Details
*  ===============
*
*  Based on contributions by
*     Jeff Rutter, Computer Science Division, University of California
*     at Berkeley, USA
*
*  =====================================================================
*
*     .. 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

```