```      SUBROUTINE DSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK,
\$                   LIWORK, INFO )
*
*  -- LAPACK driver routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
CHARACTER          COMPZ
INTEGER            INFO, LDZ, LIWORK, LWORK, N
*     ..
*     .. Array Arguments ..
INTEGER            IWORK( * )
DOUBLE PRECISION   D( * ), E( * ), WORK( * ), Z( LDZ, * )
*     ..
*
*  Purpose
*  =======
*
*  DSTEDC computes all eigenvalues and, optionally, eigenvectors of a
*  symmetric tridiagonal matrix using the divide and conquer method.
*  The eigenvectors of a full or band real symmetric matrix can also be
*  found if DSYTRD or DSPTRD or DSBTRD has been used to reduce this
*  matrix to tridiagonal form.
*
*  This code makes very mild assumptions about floating point
*  arithmetic. It will work on machines with a guard digit in
*  add/subtract, or on those binary machines without guard digits
*  which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
*  It could conceivably fail on hexadecimal or decimal machines
*  without guard digits, but we know of none.  See DLAED3 for details.
*
*  Arguments
*  =========
*
*  COMPZ   (input) CHARACTER*1
*          = 'N':  Compute eigenvalues only.
*          = 'I':  Compute eigenvectors of tridiagonal matrix also.
*          = 'V':  Compute eigenvectors of original dense symmetric
*                  matrix also.  On entry, Z 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.
*
*  D       (input/output) DOUBLE PRECISION array, dimension (N)
*          On entry, the diagonal elements of the tridiagonal matrix.
*          On exit, if INFO = 0, the eigenvalues in ascending order.
*
*  E       (input/output) DOUBLE PRECISION array, dimension (N-1)
*          On entry, the subdiagonal elements of the tridiagonal matrix.
*          On exit, E has been destroyed.
*
*  Z       (input/output) DOUBLE PRECISION array, dimension (LDZ,N)
*          On entry, if COMPZ = 'V', then Z contains the orthogonal
*          matrix used in the reduction to tridiagonal form.
*          On exit, if INFO = 0, then if COMPZ = 'V', Z contains the
*          orthonormal eigenvectors of the original symmetric matrix,
*          and if COMPZ = 'I', Z contains the orthonormal eigenvectors
*          of the symmetric tridiagonal matrix.
*          If  COMPZ = 'N', then Z is not referenced.
*
*  LDZ     (input) INTEGER
*          The leading dimension of the array Z.  LDZ >= 1.
*          If eigenvectors are desired, then LDZ >= max(1,N).
*
*  WORK    (workspace/output) DOUBLE PRECISION array,
*                                         dimension (LWORK)
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK.
*          If COMPZ = 'N' or N <= 1 then LWORK must be at least 1.
*          If COMPZ = 'V' and N > 1 then LWORK must be at least
*                         ( 1 + 3*N + 2*N*lg N + 3*N**2 ),
*                         where lg( N ) = smallest integer k such
*                         that 2**k >= N.
*          If COMPZ = 'I' and N > 1 then LWORK must be at least
*                         ( 1 + 4*N + N**2 ).
*          Note that for COMPZ = 'I' or 'V', then if N is less than or
*          equal to the minimum divide size, usually 25, then LWORK need
*          only be max(1,2*(N-1)).
*
*          If LWORK = -1, then a workspace query is assumed; the routine
*          only calculates the optimal size of the WORK array, returns
*          this value as the first entry of the WORK array, and no error
*          message related to LWORK is issued by XERBLA.
*
*  IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
*          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
*
*  LIWORK  (input) INTEGER
*          The dimension of the array IWORK.
*          If COMPZ = 'N' or N <= 1 then LIWORK must be at least 1.
*          If COMPZ = 'V' and N > 1 then LIWORK must be at least
*                         ( 6 + 6*N + 5*N*lg N ).
*          If COMPZ = 'I' and N > 1 then LIWORK must be at least
*                         ( 3 + 5*N ).
*          Note that for COMPZ = 'I' or 'V', then if N is less than or
*          equal to the minimum divide size, usually 25, then LIWORK
*          need only be 1.
*
*          If LIWORK = -1, then a workspace query is assumed; the
*          routine only calculates the optimal size of the IWORK array,
*          returns this value as the first entry of the IWORK array, and
*          no error message related to LIWORK is issued by XERBLA.
*
*  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
*  Modified by Francoise Tisseur, University of Tennessee.
*
*  =====================================================================
*
*     .. Parameters ..
DOUBLE PRECISION   ZERO, ONE, TWO
PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0 )
*     ..
*     .. Local Scalars ..
LOGICAL            LQUERY
INTEGER            FINISH, I, ICOMPZ, II, J, K, LGN, LIWMIN,
\$                   LWMIN, M, SMLSIZ, START, STOREZ, STRTRW
DOUBLE PRECISION   EPS, ORGNRM, P, TINY
*     ..
*     .. External Functions ..
LOGICAL            LSAME
INTEGER            ILAENV
DOUBLE PRECISION   DLAMCH, DLANST
EXTERNAL           LSAME, ILAENV, DLAMCH, DLANST
*     ..
*     .. External Subroutines ..
EXTERNAL           DGEMM, DLACPY, DLAED0, DLASCL, DLASET, DLASRT,
\$                   DSTEQR, DSTERF, DSWAP, XERBLA
*     ..
*     .. Intrinsic Functions ..
INTRINSIC          ABS, DBLE, INT, LOG, MAX, MOD, SQRT
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
INFO = 0
LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
*
IF( LSAME( COMPZ, 'N' ) ) THEN
ICOMPZ = 0
ELSE IF( LSAME( COMPZ, 'V' ) ) THEN
ICOMPZ = 1
ELSE IF( LSAME( COMPZ, 'I' ) ) THEN
ICOMPZ = 2
ELSE
ICOMPZ = -1
END IF
IF( ICOMPZ.LT.0 ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( ( LDZ.LT.1 ) .OR.
\$         ( ICOMPZ.GT.0 .AND. LDZ.LT.MAX( 1, N ) ) ) THEN
INFO = -6
END IF
*
IF( INFO.EQ.0 ) THEN
*
*        Compute the workspace requirements
*
SMLSIZ = ILAENV( 9, 'DSTEDC', ' ', 0, 0, 0, 0 )
IF( N.LE.1 .OR. ICOMPZ.EQ.0 ) THEN
LIWMIN = 1
LWMIN = 1
ELSE IF( N.LE.SMLSIZ ) THEN
LIWMIN = 1
LWMIN = 2*( N - 1 )
ELSE
LGN = INT( LOG( DBLE( N ) )/LOG( TWO ) )
IF( 2**LGN.LT.N )
\$         LGN = LGN + 1
IF( 2**LGN.LT.N )
\$         LGN = LGN + 1
IF( ICOMPZ.EQ.1 ) THEN
LWMIN = 1 + 3*N + 2*N*LGN + 3*N**2
LIWMIN = 6 + 6*N + 5*N*LGN
ELSE IF( ICOMPZ.EQ.2 ) THEN
LWMIN = 1 + 4*N + N**2
LIWMIN = 3 + 5*N
END IF
END IF
WORK( 1 ) = LWMIN
IWORK( 1 ) = LIWMIN
*
IF( LWORK.LT.LWMIN .AND. .NOT. LQUERY ) THEN
INFO = -8
ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT. LQUERY ) THEN
INFO = -10
END IF
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DSTEDC', -INFO )
RETURN
ELSE IF (LQUERY) THEN
RETURN
END IF
*
*     Quick return if possible
*
IF( N.EQ.0 )
\$   RETURN
IF( N.EQ.1 ) THEN
IF( ICOMPZ.NE.0 )
\$      Z( 1, 1 ) = ONE
RETURN
END IF
*
*     If the following conditional clause is removed, then the routine
*     will use the Divide and Conquer routine to compute only the
*     eigenvalues, which requires (3N + 3N**2) real workspace and
*     (2 + 5N + 2N lg(N)) integer workspace.
*     Since on many architectures DSTERF is much faster than any other
*     algorithm for finding eigenvalues only, it is used here
*     as the default. If the conditional clause is removed, then
*     information on the size of workspace needs to be changed.
*
*     If COMPZ = 'N', use DSTERF to compute the eigenvalues.
*
IF( ICOMPZ.EQ.0 ) THEN
CALL DSTERF( N, D, E, INFO )
GO TO 50
END IF
*
*     If N is smaller than the minimum divide size (SMLSIZ+1), then
*     solve the problem with another solver.
*
IF( N.LE.SMLSIZ ) THEN
*
CALL DSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
*
ELSE
*
*        If COMPZ = 'V', the Z matrix must be stored elsewhere for later
*        use.
*
IF( ICOMPZ.EQ.1 ) THEN
STOREZ = 1 + N*N
ELSE
STOREZ = 1
END IF
*
IF( ICOMPZ.EQ.2 ) THEN
CALL DLASET( 'Full', N, N, ZERO, ONE, Z, LDZ )
END IF
*
*        Scale.
*
ORGNRM = DLANST( 'M', N, D, E )
IF( ORGNRM.EQ.ZERO )
\$      GO TO 50
*
EPS = DLAMCH( 'Epsilon' )
*
START = 1
*
*        while ( START <= N )
*
10    CONTINUE
IF( START.LE.N ) THEN
*
*           Let FINISH be the position of the next subdiagonal entry
*           such that E( FINISH ) <= TINY or FINISH = N if no such
*           subdiagonal exists.  The matrix identified by the elements
*           between START and FINISH constitutes an independent
*           sub-problem.
*
FINISH = START
20       CONTINUE
IF( FINISH.LT.N ) THEN
TINY = EPS*SQRT( ABS( D( FINISH ) ) )*
\$                    SQRT( ABS( D( FINISH+1 ) ) )
IF( ABS( E( FINISH ) ).GT.TINY ) THEN
FINISH = FINISH + 1
GO TO 20
END IF
END IF
*
*           (Sub) Problem determined.  Compute its size and solve it.
*
M = FINISH - START + 1
IF( M.EQ.1 ) THEN
START = FINISH + 1
GO TO 10
END IF
IF( M.GT.SMLSIZ ) THEN
*
*              Scale.
*
ORGNRM = DLANST( 'M', M, D( START ), E( START ) )
CALL DLASCL( 'G', 0, 0, ORGNRM, ONE, M, 1, D( START ), M,
\$                      INFO )
CALL DLASCL( 'G', 0, 0, ORGNRM, ONE, M-1, 1, E( START ),
\$                      M-1, INFO )
*
IF( ICOMPZ.EQ.1 ) THEN
STRTRW = 1
ELSE
STRTRW = START
END IF
CALL DLAED0( ICOMPZ, N, M, D( START ), E( START ),
\$                      Z( STRTRW, START ), LDZ, WORK( 1 ), N,
\$                      WORK( STOREZ ), IWORK, INFO )
IF( INFO.NE.0 ) THEN
INFO = ( INFO / ( M+1 )+START-1 )*( N+1 ) +
\$                   MOD( INFO, ( M+1 ) ) + START - 1
GO TO 50
END IF
*
*              Scale back.
*
CALL DLASCL( 'G', 0, 0, ONE, ORGNRM, M, 1, D( START ), M,
\$                      INFO )
*
ELSE
IF( ICOMPZ.EQ.1 ) THEN
*
*                 Since QR won't update a Z matrix which is larger than
*                 the length of D, we must solve the sub-problem in a
*                 workspace and then multiply back into Z.
*
CALL DSTEQR( 'I', M, D( START ), E( START ), WORK, M,
\$                         WORK( M*M+1 ), INFO )
CALL DLACPY( 'A', N, M, Z( 1, START ), LDZ,
\$                         WORK( STOREZ ), N )
CALL DGEMM( 'N', 'N', N, M, M, ONE,
\$                        WORK( STOREZ ), N, WORK, M, ZERO,
\$                        Z( 1, START ), LDZ )
ELSE IF( ICOMPZ.EQ.2 ) THEN
CALL DSTEQR( 'I', M, D( START ), E( START ),
\$                         Z( START, START ), LDZ, WORK, INFO )
ELSE
CALL DSTERF( M, D( START ), E( START ), INFO )
END IF
IF( INFO.NE.0 ) THEN
INFO = START*( N+1 ) + FINISH
GO TO 50
END IF
END IF
*
START = FINISH + 1
GO TO 10
END IF
*
*        endwhile
*
*        If the problem split any number of times, then the eigenvalues
*        will not be properly ordered.  Here we permute the eigenvalues
*        (and the associated eigenvectors) into ascending order.
*
IF( M.NE.N ) THEN
IF( ICOMPZ.EQ.0 ) THEN
*
*              Use Quick Sort
*
CALL DLASRT( 'I', N, D, INFO )
*
ELSE
*
*              Use Selection Sort to minimize swaps of eigenvectors
*
DO 40 II = 2, N
I = II - 1
K = I
P = D( I )
DO 30 J = II, N
IF( D( J ).LT.P ) THEN
K = J
P = D( J )
END IF
30             CONTINUE
IF( K.NE.I ) THEN
D( K ) = D( I )
D( I ) = P
CALL DSWAP( N, Z( 1, I ), 1, Z( 1, K ), 1 )
END IF
40          CONTINUE
END IF
END IF
END IF
*
50 CONTINUE
WORK( 1 ) = LWMIN
IWORK( 1 ) = LIWMIN
*
RETURN
*
*     End of DSTEDC
*
END

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