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version 1.7, 2010/12/21 13:53:55 version 1.8, 2011/11/21 20:43:21
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   *> \brief \b ZSTEGR
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download ZSTEGR + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zstegr.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zstegr.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zstegr.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
   *                  ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
   *                  LIWORK, INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          JOBZ, RANGE
   *       INTEGER            IL, INFO, IU, LDZ, LIWORK, LWORK, M, N
   *       DOUBLE PRECISION ABSTOL, VL, VU
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            ISUPPZ( * ), IWORK( * )
   *       DOUBLE PRECISION   D( * ), E( * ), W( * ), WORK( * )
   *       COMPLEX*16         Z( LDZ, * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZSTEGR computes selected eigenvalues and, optionally, eigenvectors
   *> of a real symmetric tridiagonal matrix T. Any such unreduced matrix has
   *> a well defined set of pairwise different real eigenvalues, the corresponding
   *> real eigenvectors are pairwise orthogonal.
   *>
   *> The spectrum may be computed either completely or partially by specifying
   *> either an interval (VL,VU] or a range of indices IL:IU for the desired
   *> eigenvalues.
   *>
   *> ZSTEGR is a compatability wrapper around the improved ZSTEMR routine.
   *> See DSTEMR for further details.
   *>
   *> One important change is that the ABSTOL parameter no longer provides any
   *> benefit and hence is no longer used.
   *>
   *> Note : ZSTEGR and ZSTEMR work only on machines which follow
   *> IEEE-754 floating-point standard in their handling of infinities and
   *> NaNs.  Normal execution may create these exceptiona values and hence
   *> may abort due to a floating point exception in environments which
   *> do not conform to the IEEE-754 standard.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] JOBZ
   *> \verbatim
   *>          JOBZ is CHARACTER*1
   *>          = 'N':  Compute eigenvalues only;
   *>          = 'V':  Compute eigenvalues and eigenvectors.
   *> \endverbatim
   *>
   *> \param[in] RANGE
   *> \verbatim
   *>          RANGE is CHARACTER*1
   *>          = 'A': all eigenvalues will be found.
   *>          = 'V': all eigenvalues in the half-open interval (VL,VU]
   *>                 will be found.
   *>          = 'I': the IL-th through IU-th eigenvalues will be found.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrix.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in,out] D
   *> \verbatim
   *>          D is DOUBLE PRECISION array, dimension (N)
   *>          On entry, the N diagonal elements of the tridiagonal matrix
   *>          T. On exit, D is overwritten.
   *> \endverbatim
   *>
   *> \param[in,out] E
   *> \verbatim
   *>          E is DOUBLE PRECISION array, dimension (N)
   *>          On entry, the (N-1) subdiagonal elements of the tridiagonal
   *>          matrix T in elements 1 to N-1 of E. E(N) need not be set on
   *>          input, but is used internally as workspace.
   *>          On exit, E is overwritten.
   *> \endverbatim
   *>
   *> \param[in] VL
   *> \verbatim
   *>          VL is DOUBLE PRECISION
   *> \endverbatim
   *>
   *> \param[in] VU
   *> \verbatim
   *>          VU is DOUBLE PRECISION
   *>
   *>          If RANGE='V', the lower and upper bounds of the interval to
   *>          be searched for eigenvalues. VL < VU.
   *>          Not referenced if RANGE = 'A' or 'I'.
   *> \endverbatim
   *>
   *> \param[in] IL
   *> \verbatim
   *>          IL is INTEGER
   *> \endverbatim
   *>
   *> \param[in] IU
   *> \verbatim
   *>          IU is INTEGER
   *>
   *>          If RANGE='I', the indices (in ascending order) of the
   *>          smallest and largest eigenvalues to be returned.
   *>          1 <= IL <= IU <= N, if N > 0.
   *>          Not referenced if RANGE = 'A' or 'V'.
   *> \endverbatim
   *>
   *> \param[in] ABSTOL
   *> \verbatim
   *>          ABSTOL is DOUBLE PRECISION
   *>          Unused.  Was the absolute error tolerance for the
   *>          eigenvalues/eigenvectors in previous versions.
   *> \endverbatim
   *>
   *> \param[out] M
   *> \verbatim
   *>          M is INTEGER
   *>          The total number of eigenvalues found.  0 <= M <= N.
   *>          If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
   *> \endverbatim
   *>
   *> \param[out] W
   *> \verbatim
   *>          W is DOUBLE PRECISION array, dimension (N)
   *>          The first M elements contain the selected eigenvalues in
   *>          ascending order.
   *> \endverbatim
   *>
   *> \param[out] Z
   *> \verbatim
   *>          Z is COMPLEX*16 array, dimension (LDZ, max(1,M) )
   *>          If JOBZ = 'V', and if INFO = 0, then the first M columns of Z
   *>          contain the orthonormal eigenvectors of the matrix T
   *>          corresponding to the selected eigenvalues, with the i-th
   *>          column of Z holding the eigenvector associated with W(i).
   *>          If JOBZ = 'N', then Z is not referenced.
   *>          Note: the user must ensure that at least max(1,M) columns are
   *>          supplied in the array Z; if RANGE = 'V', the exact value of M
   *>          is not known in advance and an upper bound must be used.
   *>          Supplying N columns is always safe.
   *> \endverbatim
   *>
   *> \param[in] LDZ
   *> \verbatim
   *>          LDZ is INTEGER
   *>          The leading dimension of the array Z.  LDZ >= 1, and if
   *>          JOBZ = 'V', then LDZ >= max(1,N).
   *> \endverbatim
   *>
   *> \param[out] ISUPPZ
   *> \verbatim
   *>          ISUPPZ is INTEGER ARRAY, dimension ( 2*max(1,M) )
   *>          The support of the eigenvectors in Z, i.e., the indices
   *>          indicating the nonzero elements in Z. The i-th computed eigenvector
   *>          is nonzero only in elements ISUPPZ( 2*i-1 ) through
   *>          ISUPPZ( 2*i ). This is relevant in the case when the matrix
   *>          is split. ISUPPZ is only accessed when JOBZ is 'V' and N > 0.
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is DOUBLE PRECISION array, dimension (LWORK)
   *>          On exit, if INFO = 0, WORK(1) returns the optimal
   *>          (and minimal) LWORK.
   *> \endverbatim
   *>
   *> \param[in] LWORK
   *> \verbatim
   *>          LWORK is INTEGER
   *>          The dimension of the array WORK. LWORK >= max(1,18*N)
   *>          if JOBZ = 'V', and LWORK >= max(1,12*N) if JOBZ = 'N'.
   *>          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.
   *> \endverbatim
   *>
   *> \param[out] IWORK
   *> \verbatim
   *>          IWORK is INTEGER array, dimension (LIWORK)
   *>          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
   *> \endverbatim
   *>
   *> \param[in] LIWORK
   *> \verbatim
   *>          LIWORK is INTEGER
   *>          The dimension of the array IWORK.  LIWORK >= max(1,10*N)
   *>          if the eigenvectors are desired, and LIWORK >= max(1,8*N)
   *>          if only the eigenvalues are to be computed.
   *>          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.
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>          On exit, INFO
   *>          = 0:  successful exit
   *>          < 0:  if INFO = -i, the i-th argument had an illegal value
   *>          > 0:  if INFO = 1X, internal error in DLARRE,
   *>                if INFO = 2X, internal error in ZLARRV.
   *>                Here, the digit X = ABS( IINFO ) < 10, where IINFO is
   *>                the nonzero error code returned by DLARRE or
   *>                ZLARRV, respectively.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup complex16OTHERcomputational
   *
   *> \par Contributors:
   *  ==================
   *>
   *> Inderjit Dhillon, IBM Almaden, USA \n
   *> Osni Marques, LBNL/NERSC, USA \n
   *> Christof Voemel, LBNL/NERSC, USA \n
   *
   *  =====================================================================
       SUBROUTINE ZSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,        SUBROUTINE ZSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
      $           ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,       $           ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
      $           LIWORK, INFO )       $           LIWORK, INFO )
   
       IMPLICIT NONE  
 *  
 *  *
 *  -- LAPACK computational routine (version 3.2) --  *  -- LAPACK computational routine (version 3.4.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     November 2006  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          JOBZ, RANGE        CHARACTER          JOBZ, RANGE
Line 21 Line 272
       COMPLEX*16         Z( LDZ, * )        COMPLEX*16         Z( LDZ, * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZSTEGR computes selected eigenvalues and, optionally, eigenvectors  
 *  of a real symmetric tridiagonal matrix T. Any such unreduced matrix has  
 *  a well defined set of pairwise different real eigenvalues, the corresponding  
 *  real eigenvectors are pairwise orthogonal.  
 *  
 *  The spectrum may be computed either completely or partially by specifying  
 *  either an interval (VL,VU] or a range of indices IL:IU for the desired  
 *  eigenvalues.  
 *  
 *  ZSTEGR is a compatability wrapper around the improved ZSTEMR routine.  
 *  See DSTEMR for further details.  
 *  
 *  One important change is that the ABSTOL parameter no longer provides any  
 *  benefit and hence is no longer used.  
 *  
 *  Note : ZSTEGR and ZSTEMR work only on machines which follow  
 *  IEEE-754 floating-point standard in their handling of infinities and  
 *  NaNs.  Normal execution may create these exceptiona values and hence  
 *  may abort due to a floating point exception in environments which  
 *  do not conform to the IEEE-754 standard.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  JOBZ    (input) CHARACTER*1  
 *          = 'N':  Compute eigenvalues only;  
 *          = 'V':  Compute eigenvalues and eigenvectors.  
 *  
 *  RANGE   (input) CHARACTER*1  
 *          = 'A': all eigenvalues will be found.  
 *          = 'V': all eigenvalues in the half-open interval (VL,VU]  
 *                 will be found.  
 *          = 'I': the IL-th through IU-th eigenvalues will be found.  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrix.  N >= 0.  
 *  
 *  D       (input/output) DOUBLE PRECISION array, dimension (N)  
 *          On entry, the N diagonal elements of the tridiagonal matrix  
 *          T. On exit, D is overwritten.  
 *  
 *  E       (input/output) DOUBLE PRECISION array, dimension (N)  
 *          On entry, the (N-1) subdiagonal elements of the tridiagonal  
 *          matrix T in elements 1 to N-1 of E. E(N) need not be set on  
 *          input, but is used internally as workspace.  
 *          On exit, E is overwritten.  
 *  
 *  VL      (input) DOUBLE PRECISION  
 *  VU      (input) DOUBLE PRECISION  
 *          If RANGE='V', the lower and upper bounds of the interval to  
 *          be searched for eigenvalues. VL < VU.  
 *          Not referenced if RANGE = 'A' or 'I'.  
 *  
 *  IL      (input) INTEGER  
 *  IU      (input) INTEGER  
 *          If RANGE='I', the indices (in ascending order) of the  
 *          smallest and largest eigenvalues to be returned.  
 *          1 <= IL <= IU <= N, if N > 0.  
 *          Not referenced if RANGE = 'A' or 'V'.  
 *  
 *  ABSTOL  (input) DOUBLE PRECISION  
 *          Unused.  Was the absolute error tolerance for the  
 *          eigenvalues/eigenvectors in previous versions.  
 *  
 *  M       (output) INTEGER  
 *          The total number of eigenvalues found.  0 <= M <= N.  
 *          If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.  
 *  
 *  W       (output) DOUBLE PRECISION array, dimension (N)  
 *          The first M elements contain the selected eigenvalues in  
 *          ascending order.  
 *  
 *  Z       (output) COMPLEX*16 array, dimension (LDZ, max(1,M) )  
 *          If JOBZ = 'V', and if INFO = 0, then the first M columns of Z  
 *          contain the orthonormal eigenvectors of the matrix T  
 *          corresponding to the selected eigenvalues, with the i-th  
 *          column of Z holding the eigenvector associated with W(i).  
 *          If JOBZ = 'N', then Z is not referenced.  
 *          Note: the user must ensure that at least max(1,M) columns are  
 *          supplied in the array Z; if RANGE = 'V', the exact value of M  
 *          is not known in advance and an upper bound must be used.  
 *          Supplying N columns is always safe.  
 *  
 *  LDZ     (input) INTEGER  
 *          The leading dimension of the array Z.  LDZ >= 1, and if  
 *          JOBZ = 'V', then LDZ >= max(1,N).  
 *  
 *  ISUPPZ  (output) INTEGER ARRAY, dimension ( 2*max(1,M) )  
 *          The support of the eigenvectors in Z, i.e., the indices  
 *          indicating the nonzero elements in Z. The i-th computed eigenvector  
 *          is nonzero only in elements ISUPPZ( 2*i-1 ) through  
 *          ISUPPZ( 2*i ). This is relevant in the case when the matrix  
 *          is split. ISUPPZ is only accessed when JOBZ is 'V' and N > 0.  
 *  
 *  WORK    (workspace/output) DOUBLE PRECISION array, dimension (LWORK)  
 *          On exit, if INFO = 0, WORK(1) returns the optimal  
 *          (and minimal) LWORK.  
 *  
 *  LWORK   (input) INTEGER  
 *          The dimension of the array WORK. LWORK >= max(1,18*N)  
 *          if JOBZ = 'V', and LWORK >= max(1,12*N) if JOBZ = 'N'.  
 *          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 (LIWORK)  
 *          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.  
 *  
 *  LIWORK  (input) INTEGER  
 *          The dimension of the array IWORK.  LIWORK >= max(1,10*N)  
 *          if the eigenvectors are desired, and LIWORK >= max(1,8*N)  
 *          if only the eigenvalues are to be computed.  
 *          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  
 *          On exit, INFO  
 *          = 0:  successful exit  
 *          < 0:  if INFO = -i, the i-th argument had an illegal value  
 *          > 0:  if INFO = 1X, internal error in DLARRE,  
 *                if INFO = 2X, internal error in ZLARRV.  
 *                Here, the digit X = ABS( IINFO ) < 10, where IINFO is  
 *                the nonzero error code returned by DLARRE or  
 *                ZLARRV, respectively.  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  Based on contributions by  
 *     Inderjit Dhillon, IBM Almaden, USA  
 *     Osni Marques, LBNL/NERSC, USA  
 *     Christof Voemel, LBNL/NERSC, USA  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Local Scalars ..  *     .. Local Scalars ..
Removed from v.1.7  
changed lines
  Added in v.1.8

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