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version 1.7, 2010/08/13 21:04:05 version 1.22, 2023/08/07 08:39:23
Line 1 Line 1
   *> \brief <b> ZHEEVR computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices</b>
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at
   *            http://www.netlib.org/lapack/explore-html/
   *
   *> \htmlonly
   *> Download ZHEEVR + dependencies
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zheevr.f">
   *> [TGZ]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zheevr.f">
   *> [ZIP]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zheevr.f">
   *> [TXT]</a>
   *> \endhtmlonly
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZHEEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
   *                          ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK,
   *                          RWORK, LRWORK, IWORK, LIWORK, INFO )
   *
   *       .. Scalar Arguments ..
   *       CHARACTER          JOBZ, RANGE, UPLO
   *       INTEGER            IL, INFO, IU, LDA, LDZ, LIWORK, LRWORK, LWORK,
   *      $                   M, N
   *       DOUBLE PRECISION   ABSTOL, VL, VU
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            ISUPPZ( * ), IWORK( * )
   *       DOUBLE PRECISION   RWORK( * ), W( * )
   *       COMPLEX*16         A( LDA, * ), WORK( * ), Z( LDZ, * )
   *       ..
   *
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZHEEVR computes selected eigenvalues and, optionally, eigenvectors
   *> of a complex Hermitian matrix A.  Eigenvalues and eigenvectors can
   *> be selected by specifying either a range of values or a range of
   *> indices for the desired eigenvalues.
   *>
   *> ZHEEVR first reduces the matrix A to tridiagonal form T with a call
   *> to ZHETRD.  Then, whenever possible, ZHEEVR calls ZSTEMR to compute
   *> eigenspectrum using Relatively Robust Representations.  ZSTEMR
   *> computes eigenvalues by the dqds algorithm, while orthogonal
   *> eigenvectors are computed from various "good" L D L^T representations
   *> (also known as Relatively Robust Representations). Gram-Schmidt
   *> orthogonalization is avoided as far as possible. More specifically,
   *> the various steps of the algorithm are as follows.
   *>
   *> For each unreduced block (submatrix) of T,
   *>    (a) Compute T - sigma I  = L D L^T, so that L and D
   *>        define all the wanted eigenvalues to high relative accuracy.
   *>        This means that small relative changes in the entries of D and L
   *>        cause only small relative changes in the eigenvalues and
   *>        eigenvectors. The standard (unfactored) representation of the
   *>        tridiagonal matrix T does not have this property in general.
   *>    (b) Compute the eigenvalues to suitable accuracy.
   *>        If the eigenvectors are desired, the algorithm attains full
   *>        accuracy of the computed eigenvalues only right before
   *>        the corresponding vectors have to be computed, see steps c) and d).
   *>    (c) For each cluster of close eigenvalues, select a new
   *>        shift close to the cluster, find a new factorization, and refine
   *>        the shifted eigenvalues to suitable accuracy.
   *>    (d) For each eigenvalue with a large enough relative separation compute
   *>        the corresponding eigenvector by forming a rank revealing twisted
   *>        factorization. Go back to (c) for any clusters that remain.
   *>
   *> The desired accuracy of the output can be specified by the input
   *> parameter ABSTOL.
   *>
   *> For more details, see ZSTEMR's documentation and:
   *> - Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representations
   *>   to compute orthogonal eigenvectors of symmetric tridiagonal matrices,"
   *>   Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004.
   *> - Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors and
   *>   Relative Gaps," SIAM Journal on Matrix Analysis and Applications, Vol. 25,
   *>   2004.  Also LAPACK Working Note 154.
   *> - Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric
   *>   tridiagonal eigenvalue/eigenvector problem",
   *>   Computer Science Division Technical Report No. UCB/CSD-97-971,
   *>   UC Berkeley, May 1997.
   *>
   *>
   *> Note 1 : ZHEEVR calls ZSTEMR when the full spectrum is requested
   *> on machines which conform to the ieee-754 floating point standard.
   *> ZHEEVR calls DSTEBZ and ZSTEIN on non-ieee machines and
   *> when partial spectrum requests are made.
   *>
   *> Normal execution of ZSTEMR may create NaNs and infinities and
   *> hence may abort due to a floating point exception in environments
   *> which do not handle NaNs and infinities in the ieee standard default
   *> manner.
   *> \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.
   *>          For RANGE = 'V' or 'I' and IU - IL < N - 1, DSTEBZ and
   *>          ZSTEIN are called
   *> \endverbatim
   *>
   *> \param[in] UPLO
   *> \verbatim
   *>          UPLO is CHARACTER*1
   *>          = 'U':  Upper triangle of A is stored;
   *>          = 'L':  Lower triangle of A is stored.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrix A.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in,out] A
   *> \verbatim
   *>          A is COMPLEX*16 array, dimension (LDA, N)
   *>          On entry, the Hermitian matrix A.  If UPLO = 'U', the
   *>          leading N-by-N upper triangular part of A contains the
   *>          upper triangular part of the matrix A.  If UPLO = 'L',
   *>          the leading N-by-N lower triangular part of A contains
   *>          the lower triangular part of the matrix A.
   *>          On exit, the lower triangle (if UPLO='L') or the upper
   *>          triangle (if UPLO='U') of A, including the diagonal, is
   *>          destroyed.
   *> \endverbatim
   *>
   *> \param[in] LDA
   *> \verbatim
   *>          LDA is INTEGER
   *>          The leading dimension of the array A.  LDA >= max(1,N).
   *> \endverbatim
   *>
   *> \param[in] VL
   *> \verbatim
   *>          VL is DOUBLE PRECISION
   *>          If RANGE='V', the lower bound of the interval to
   *>          be searched for eigenvalues. VL < VU.
   *>          Not referenced if RANGE = 'A' or 'I'.
   *> \endverbatim
   *>
   *> \param[in] VU
   *> \verbatim
   *>          VU is DOUBLE PRECISION
   *>          If RANGE='V', the upper bound 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
   *>          If RANGE='I', the index of the
   *>          smallest eigenvalue to be returned.
   *>          1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
   *>          Not referenced if RANGE = 'A' or 'V'.
   *> \endverbatim
   *>
   *> \param[in] IU
   *> \verbatim
   *>          IU is INTEGER
   *>          If RANGE='I', the index of the
   *>          largest eigenvalue to be returned.
   *>          1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
   *>          Not referenced if RANGE = 'A' or 'V'.
   *> \endverbatim
   *>
   *> \param[in] ABSTOL
   *> \verbatim
   *>          ABSTOL is DOUBLE PRECISION
   *>          The absolute error tolerance for the eigenvalues.
   *>          An approximate eigenvalue is accepted as converged
   *>          when it is determined to lie in an interval [a,b]
   *>          of width less than or equal to
   *>
   *>                  ABSTOL + EPS *   max( |a|,|b| ) ,
   *>
   *>          where EPS is the machine precision.  If ABSTOL is less than
   *>          or equal to zero, then  EPS*|T|  will be used in its place,
   *>          where |T| is the 1-norm of the tridiagonal matrix obtained
   *>          by reducing A to tridiagonal form.
   *>
   *>          See "Computing Small Singular Values of Bidiagonal Matrices
   *>          with Guaranteed High Relative Accuracy," by Demmel and
   *>          Kahan, LAPACK Working Note #3.
   *>
   *>          If high relative accuracy is important, set ABSTOL to
   *>          DLAMCH( 'Safe minimum' ).  Doing so will guarantee that
   *>          eigenvalues are computed to high relative accuracy when
   *>          possible in future releases.  The current code does not
   *>          make any guarantees about high relative accuracy, but
   *>          future releases will. See J. Barlow and J. Demmel,
   *>          "Computing Accurate Eigensystems of Scaled Diagonally
   *>          Dominant Matrices", LAPACK Working Note #7, for a discussion
   *>          of which matrices define their eigenvalues to high relative
   *>          accuracy.
   *> \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', then if INFO = 0, the first M columns of Z
   *>          contain the orthonormal eigenvectors of the matrix A
   *>          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.
   *> \endverbatim
   *>
   *> \param[in] LDZ
   *> \verbatim
   *>          LDZ is INTEGER
   *>          The leading dimension of the array Z.  LDZ >= 1, and if
   *>          JOBZ = 'V', 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 eigenvector
   *>          is nonzero only in elements ISUPPZ( 2*i-1 ) through
   *>          ISUPPZ( 2*i ). This is an output of ZSTEMR (tridiagonal
   *>          matrix). The support of the eigenvectors of A is typically
   *>          1:N because of the unitary transformations applied by ZUNMTR.
   *>          Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
   *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
   *> \endverbatim
   *>
   *> \param[in] LWORK
   *> \verbatim
   *>          LWORK is INTEGER
   *>          The length of the array WORK.  LWORK >= max(1,2*N).
   *>          For optimal efficiency, LWORK >= (NB+1)*N,
   *>          where NB is the max of the blocksize for ZHETRD and for
   *>          ZUNMTR as returned by ILAENV.
   *>
   *>          If LWORK = -1, then a workspace query is assumed; the routine
   *>          only calculates the optimal sizes of the WORK, RWORK and
   *>          IWORK arrays, returns these values as the first entries of
   *>          the WORK, RWORK and IWORK arrays, and no error message
   *>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
   *> \endverbatim
   *>
   *> \param[out] RWORK
   *> \verbatim
   *>          RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
   *>          On exit, if INFO = 0, RWORK(1) returns the optimal
   *>          (and minimal) LRWORK.
   *> \endverbatim
   *>
   *> \param[in] LRWORK
   *> \verbatim
   *>          LRWORK is INTEGER
   *>          The length of the array RWORK.  LRWORK >= max(1,24*N).
   *>
   *>          If LRWORK = -1, then a workspace query is assumed; the
   *>          routine only calculates the optimal sizes of the WORK, RWORK
   *>          and IWORK arrays, returns these values as the first entries
   *>          of the WORK, RWORK and IWORK arrays, and no error message
   *>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
   *> \endverbatim
   *>
   *> \param[out] IWORK
   *> \verbatim
   *>          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
   *>          On exit, if INFO = 0, IWORK(1) returns the optimal
   *>          (and minimal) LIWORK.
   *> \endverbatim
   *>
   *> \param[in] LIWORK
   *> \verbatim
   *>          LIWORK is INTEGER
   *>          The dimension of the array IWORK.  LIWORK >= max(1,10*N).
   *>
   *>          If LIWORK = -1, then a workspace query is assumed; the
   *>          routine only calculates the optimal sizes of the WORK, RWORK
   *>          and IWORK arrays, returns these values as the first entries
   *>          of the WORK, RWORK and IWORK arrays, and no error message
   *>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>          = 0:  successful exit
   *>          < 0:  if INFO = -i, the i-th argument had an illegal value
   *>          > 0:  Internal error
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee
   *> \author Univ. of California Berkeley
   *> \author Univ. of Colorado Denver
   *> \author NAG Ltd.
   *
   *> \ingroup complex16HEeigen
   *
   *> \par Contributors:
   *  ==================
   *>
   *>     Inderjit Dhillon, IBM Almaden, USA \n
   *>     Osni Marques, LBNL/NERSC, USA \n
   *>     Ken Stanley, Computer Science Division, University of
   *>       California at Berkeley, USA \n
   *>     Jason Riedy, Computer Science Division, University of
   *>       California at Berkeley, USA \n
   *>
   *  =====================================================================
       SUBROUTINE ZHEEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,        SUBROUTINE ZHEEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
      $                   ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK,       $                   ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK,
      $                   RWORK, LRWORK, IWORK, LIWORK, INFO )       $                   RWORK, LRWORK, IWORK, LIWORK, INFO )
 *  *
 *  -- LAPACK driver routine (version 3.2.2) --  *  -- LAPACK driver routine --
 *  -- 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..--
 *     June 2010  
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          JOBZ, RANGE, UPLO        CHARACTER          JOBZ, RANGE, UPLO
Line 19 Line 371
       COMPLEX*16         A( LDA, * ), WORK( * ), Z( LDZ, * )        COMPLEX*16         A( LDA, * ), WORK( * ), Z( LDZ, * )
 *     ..  *     ..
 *  *
 *  Purpose  *  =====================================================================
 *  =======  
 *  
 *  ZHEEVR computes selected eigenvalues and, optionally, eigenvectors  
 *  of a complex Hermitian matrix A.  Eigenvalues and eigenvectors can  
 *  be selected by specifying either a range of values or a range of  
 *  indices for the desired eigenvalues.  
 *  
 *  ZHEEVR first reduces the matrix A to tridiagonal form T with a call  
 *  to ZHETRD.  Then, whenever possible, ZHEEVR calls ZSTEMR to compute  
 *  eigenspectrum using Relatively Robust Representations.  ZSTEMR  
 *  computes eigenvalues by the dqds algorithm, while orthogonal  
 *  eigenvectors are computed from various "good" L D L^T representations  
 *  (also known as Relatively Robust Representations). Gram-Schmidt  
 *  orthogonalization is avoided as far as possible. More specifically,  
 *  the various steps of the algorithm are as follows.  
 *  
 *  For each unreduced block (submatrix) of T,  
 *     (a) Compute T - sigma I  = L D L^T, so that L and D  
 *         define all the wanted eigenvalues to high relative accuracy.  
 *         This means that small relative changes in the entries of D and L  
 *         cause only small relative changes in the eigenvalues and  
 *         eigenvectors. The standard (unfactored) representation of the  
 *         tridiagonal matrix T does not have this property in general.  
 *     (b) Compute the eigenvalues to suitable accuracy.  
 *         If the eigenvectors are desired, the algorithm attains full  
 *         accuracy of the computed eigenvalues only right before  
 *         the corresponding vectors have to be computed, see steps c) and d).  
 *     (c) For each cluster of close eigenvalues, select a new  
 *         shift close to the cluster, find a new factorization, and refine  
 *         the shifted eigenvalues to suitable accuracy.  
 *     (d) For each eigenvalue with a large enough relative separation compute  
 *         the corresponding eigenvector by forming a rank revealing twisted  
 *         factorization. Go back to (c) for any clusters that remain.  
 *  
 *  The desired accuracy of the output can be specified by the input  
 *  parameter ABSTOL.  
 *  
 *  For more details, see DSTEMR's documentation and:  
 *  - Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representations  
 *    to compute orthogonal eigenvectors of symmetric tridiagonal matrices,"  
 *    Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004.  
 *  - Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors and  
 *    Relative Gaps," SIAM Journal on Matrix Analysis and Applications, Vol. 25,  
 *    2004.  Also LAPACK Working Note 154.  
 *  - Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric  
 *    tridiagonal eigenvalue/eigenvector problem",  
 *    Computer Science Division Technical Report No. UCB/CSD-97-971,  
 *    UC Berkeley, May 1997.  
 *  
 *  
 *  Note 1 : ZHEEVR calls ZSTEMR when the full spectrum is requested  
 *  on machines which conform to the ieee-754 floating point standard.  
 *  ZHEEVR calls DSTEBZ and ZSTEIN on non-ieee machines and  
 *  when partial spectrum requests are made.  
 *  
 *  Normal execution of ZSTEMR may create NaNs and infinities and  
 *  hence may abort due to a floating point exception in environments  
 *  which do not handle NaNs and infinities in the ieee standard default  
 *  manner.  
 *  
 *  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.  
 ********** For RANGE = 'V' or 'I' and IU - IL < N - 1, DSTEBZ and  
 ********** ZSTEIN are called  
 *  
 *  UPLO    (input) CHARACTER*1  
 *          = 'U':  Upper triangle of A is stored;  
 *          = 'L':  Lower triangle of A is stored.  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrix A.  N >= 0.  
 *  
 *  A       (input/output) COMPLEX*16 array, dimension (LDA, N)  
 *          On entry, the Hermitian matrix A.  If UPLO = 'U', the  
 *          leading N-by-N upper triangular part of A contains the  
 *          upper triangular part of the matrix A.  If UPLO = 'L',  
 *          the leading N-by-N lower triangular part of A contains  
 *          the lower triangular part of the matrix A.  
 *          On exit, the lower triangle (if UPLO='L') or the upper  
 *          triangle (if UPLO='U') of A, including the diagonal, is  
 *          destroyed.  
 *  
 *  LDA     (input) INTEGER  
 *          The leading dimension of the array A.  LDA >= max(1,N).  
 *  
 *  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; IL = 1 and IU = 0 if N = 0.  
 *          Not referenced if RANGE = 'A' or 'V'.  
 *  
 *  ABSTOL  (input) DOUBLE PRECISION  
 *          The absolute error tolerance for the eigenvalues.  
 *          An approximate eigenvalue is accepted as converged  
 *          when it is determined to lie in an interval [a,b]  
 *          of width less than or equal to  
 *  
 *                  ABSTOL + EPS *   max( |a|,|b| ) ,  
 *  
 *          where EPS is the machine precision.  If ABSTOL is less than  
 *          or equal to zero, then  EPS*|T|  will be used in its place,  
 *          where |T| is the 1-norm of the tridiagonal matrix obtained  
 *          by reducing A to tridiagonal form.  
 *  
 *          See "Computing Small Singular Values of Bidiagonal Matrices  
 *          with Guaranteed High Relative Accuracy," by Demmel and  
 *          Kahan, LAPACK Working Note #3.  
 *  
 *          If high relative accuracy is important, set ABSTOL to  
 *          DLAMCH( 'Safe minimum' ).  Doing so will guarantee that  
 *          eigenvalues are computed to high relative accuracy when  
 *          possible in future releases.  The current code does not  
 *          make any guarantees about high relative accuracy, but  
 *          furutre releases will. See J. Barlow and J. Demmel,  
 *          "Computing Accurate Eigensystems of Scaled Diagonally  
 *          Dominant Matrices", LAPACK Working Note #7, for a discussion  
 *          of which matrices define their eigenvalues to high relative  
 *          accuracy.  
 *  
 *  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', then if INFO = 0, the first M columns of Z  
 *          contain the orthonormal eigenvectors of the matrix A  
 *          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.  
 *  
 *  LDZ     (input) INTEGER  
 *          The leading dimension of the array Z.  LDZ >= 1, and if  
 *          JOBZ = 'V', 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 eigenvector  
 *          is nonzero only in elements ISUPPZ( 2*i-1 ) through  
 *          ISUPPZ( 2*i ).  
 ********** Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1  
 *  
 *  WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))  
 *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.  
 *  
 *  LWORK   (input) INTEGER  
 *          The length of the array WORK.  LWORK >= max(1,2*N).  
 *          For optimal efficiency, LWORK >= (NB+1)*N,  
 *          where NB is the max of the blocksize for ZHETRD and for  
 *          ZUNMTR as returned by ILAENV.  
 *  
 *          If LWORK = -1, then a workspace query is assumed; the routine  
 *          only calculates the optimal sizes of the WORK, RWORK and  
 *          IWORK arrays, returns these values as the first entries of  
 *          the WORK, RWORK and IWORK arrays, and no error message  
 *          related to LWORK or LRWORK or LIWORK is issued by XERBLA.  
 *  
 *  RWORK   (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LRWORK))  
 *          On exit, if INFO = 0, RWORK(1) returns the optimal  
 *          (and minimal) LRWORK.  
 *  
 * LRWORK   (input) INTEGER  
 *          The length of the array RWORK.  LRWORK >= max(1,24*N).  
 *  
 *          If LRWORK = -1, then a workspace query is assumed; the  
 *          routine only calculates the optimal sizes of the WORK, RWORK  
 *          and IWORK arrays, returns these values as the first entries  
 *          of the WORK, RWORK and IWORK arrays, and no error message  
 *          related to LWORK or LRWORK or LIWORK is issued by XERBLA.  
 *  
 *  IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))  
 *          On exit, if INFO = 0, IWORK(1) returns the optimal  
 *          (and minimal) LIWORK.  
 *  
 * LIWORK   (input) INTEGER  
 *          The dimension of the array IWORK.  LIWORK >= max(1,10*N).  
 *  
 *          If LIWORK = -1, then a workspace query is assumed; the  
 *          routine only calculates the optimal sizes of the WORK, RWORK  
 *          and IWORK arrays, returns these values as the first entries  
 *          of the WORK, RWORK and IWORK arrays, and no error message  
 *          related to LWORK or LRWORK or LIWORK is issued by XERBLA.  
 *  
 *  INFO    (output) INTEGER  
 *          = 0:  successful exit  
 *          < 0:  if INFO = -i, the i-th argument had an illegal value  
 *          > 0:  Internal error  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  Based on contributions by  
 *     Inderjit Dhillon, IBM Almaden, USA  
 *     Osni Marques, LBNL/NERSC, USA  
 *     Ken Stanley, Computer Science Division, University of  
 *       California at Berkeley, USA  
 *     Jason Riedy, Computer Science Division, University of  
 *       California at Berkeley, USA  
 *  
 * =====================================================================  
 *  *
 *     .. Parameters ..  *     .. Parameters ..
       DOUBLE PRECISION   ZERO, ONE, TWO        DOUBLE PRECISION   ZERO, ONE, TWO
Line 456 Line 585
 *     returns INFO > 0.  *     returns INFO > 0.
       INDIFL = INDISP + N        INDIFL = INDISP + N
 *     INDIWO is the offset of the remaining integer workspace.  *     INDIWO is the offset of the remaining integer workspace.
       INDIWO = INDISP + N        INDIWO = INDIFL + N
   
 *  *
 *     Call ZHETRD to reduce Hermitian matrix to tridiagonal form.  *     Call ZHETRD to reduce Hermitian matrix to tridiagonal form.
Line 494 Line 623
      $                   IWORK, LIWORK, INFO )       $                   IWORK, LIWORK, INFO )
 *  *
 *           Apply unitary matrix used in reduction to tridiagonal  *           Apply unitary matrix used in reduction to tridiagonal
 *           form to eigenvectors returned by ZSTEIN.  *           form to eigenvectors returned by ZSTEMR.
 *  *
             IF( WANTZ .AND. INFO.EQ.0 ) THEN              IF( WANTZ .AND. INFO.EQ.0 ) THEN
                INDWKN = INDWK                 INDWKN = INDWK
Removed from v.1.7  
changed lines
  Added in v.1.22

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