```      SUBROUTINE ZLAED0( QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, RWORK,
\$                   IWORK, INFO )
*
*  -- LAPACK routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
INTEGER            INFO, LDQ, LDQS, N, QSIZ
*     ..
*     .. Array Arguments ..
INTEGER            IWORK( * )
DOUBLE PRECISION   D( * ), E( * ), RWORK( * )
COMPLEX*16         Q( LDQ, * ), QSTORE( LDQS, * )
*     ..
*
*  Purpose
*  =======
*
*  Using the divide and conquer method, ZLAED0 computes all eigenvalues
*  of a symmetric tridiagonal matrix which is one diagonal block of
*  those from reducing a dense or band Hermitian matrix and
*  corresponding eigenvectors of the dense or band matrix.
*
*  Arguments
*  =========
*
*  QSIZ   (input) INTEGER
*         The dimension of the unitary 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 diagonal elements of the tridiagonal matrix.
*         On exit, the eigenvalues in ascending order.
*
*  E      (input/output) DOUBLE PRECISION array, dimension (N-1)
*         On entry, the off-diagonal elements of the tridiagonal matrix.
*         On exit, E has been destroyed.
*
*  Q      (input/output) COMPLEX*16 array, dimension (LDQ,N)
*         On entry, Q must contain an QSIZ x N matrix whose columns
*         unitarily orthonormal. It is a part of the unitary matrix
*         that reduces the full dense Hermitian matrix to a
*         (reducible) symmetric tridiagonal matrix.
*
*  LDQ    (input) INTEGER
*         The leading dimension of the array Q.  LDQ >= max(1,N).
*
*  IWORK  (workspace) INTEGER array,
*         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 )
*
*  RWORK  (workspace) DOUBLE PRECISION array,
*                               dimension (1 + 3*N + 2*N*lg N + 3*N**2)
*                        ( lg( N ) = smallest integer k
*                                    such that 2^k >= N )
*
*  QSTORE (workspace) COMPLEX*16 array, dimension (LDQS, N)
*         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.
*         LDQS >= max(1,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).
*
*  =====================================================================
*
*  Warning:      N could be as big as QSIZ!
*
*     .. Parameters ..
DOUBLE PRECISION   TWO
PARAMETER          ( TWO = 2.D+0 )
*     ..
*     .. Local Scalars ..
INTEGER            CURLVL, CURPRB, CURR, I, IGIVCL, IGIVNM,
\$                   IGIVPT, INDXQ, IPERM, IPRMPT, IQ, IQPTR, IWREM,
\$                   J, K, LGN, LL, MATSIZ, MSD2, SMLSIZ, SMM1,
\$                   SPM1, SPM2, SUBMAT, SUBPBS, TLVLS
DOUBLE PRECISION   TEMP
*     ..
*     .. External Subroutines ..
EXTERNAL           DCOPY, DSTEQR, XERBLA, ZCOPY, ZLACRM, ZLAED7
*     ..
*     .. 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
IF( QSIZ.LT.MAX( 0, N ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN
INFO = -6
ELSE IF( LDQS.LT.MAX( 1, N ) ) THEN
INFO = -8
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZLAED0', -INFO )
RETURN
END IF
*
*     Quick return if possible
*
IF( N.EQ.0 )
\$   RETURN
*
SMLSIZ = ILAENV( 9, 'ZLAED0', ' ', 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
*
*     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
*
*     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
LL = IQ - 1 + IWORK( IQPTR+CURR )
CALL DSTEQR( 'I', MATSIZ, D( SUBMAT ), E( SUBMAT ),
\$                RWORK( LL ), MATSIZ, RWORK, INFO )
CALL ZLACRM( QSIZ, MATSIZ, Q( 1, SUBMAT ), LDQ, RWORK( LL ),
\$                MATSIZ, QSTORE( 1, SUBMAT ), LDQS,
\$                RWORK( IWREM ) )
IWORK( IQPTR+CURR+1 ) = IWORK( IQPTR+CURR ) + MATSIZ**2
CURR = CURR + 1
IF( INFO.GT.0 ) THEN
INFO = SUBMAT*( N+1 ) + SUBMAT + MATSIZ - 1
RETURN
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.  ZLAED7 handles the case
*     when the eigenvectors of a full or band Hermitian matrix (which
*     was reduced to tridiagonal form) are desired.
*
*     I am free to use Q as a valuable working space until Loop 150.
*
CALL ZLAED7( MATSIZ, MSD2, QSIZ, TLVLS, CURLVL, CURPRB,
\$                   D( SUBMAT ), QSTORE( 1, SUBMAT ), LDQS,
\$                   E( SUBMAT+MSD2-1 ), IWORK( INDXQ+SUBMAT ),
\$                   RWORK( IQ ), IWORK( IQPTR ), IWORK( IPRMPT ),
\$                   IWORK( IPERM ), IWORK( IGIVPT ),
\$                   IWORK( IGIVCL ), RWORK( IGIVNM ),
\$                   Q( 1, SUBMAT ), RWORK( IWREM ),
\$                   IWORK( SUBPBS+1 ), INFO )
IF( INFO.GT.0 ) THEN
INFO = SUBMAT*( N+1 ) + SUBMAT + MATSIZ - 1
RETURN
END IF
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.
*
DO 100 I = 1, N
J = IWORK( INDXQ+I )
RWORK( I ) = D( J )
CALL ZCOPY( QSIZ, QSTORE( 1, J ), 1, Q( 1, I ), 1 )
100 CONTINUE
CALL DCOPY( N, RWORK, 1, D, 1 )
*
RETURN
*
*     End of ZLAED0
*
END

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