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version 1.1, 2010/01/26 15:22:45 version 1.17, 2023/08/07 08:39:22
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   *> \brief <b> ZHBEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices</b>
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at
   *            http://www.netlib.org/lapack/explore-html/
   *
   *> \htmlonly
   *> Download ZHBEVD + dependencies
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhbevd.f">
   *> [TGZ]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhbevd.f">
   *> [ZIP]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhbevd.f">
   *> [TXT]</a>
   *> \endhtmlonly
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZHBEVD( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
   *                          LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
   *
   *       .. Scalar Arguments ..
   *       CHARACTER          JOBZ, UPLO
   *       INTEGER            INFO, KD, LDAB, LDZ, LIWORK, LRWORK, LWORK, N
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            IWORK( * )
   *       DOUBLE PRECISION   RWORK( * ), W( * )
   *       COMPLEX*16         AB( LDAB, * ), WORK( * ), Z( LDZ, * )
   *       ..
   *
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZHBEVD computes all the eigenvalues and, optionally, eigenvectors of
   *> a complex Hermitian band matrix A.  If eigenvectors are desired, it
   *> uses a divide and conquer algorithm.
   *>
   *> The divide and conquer algorithm 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.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] JOBZ
   *> \verbatim
   *>          JOBZ is CHARACTER*1
   *>          = 'N':  Compute eigenvalues only;
   *>          = 'V':  Compute eigenvalues and eigenvectors.
   *> \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] KD
   *> \verbatim
   *>          KD is INTEGER
   *>          The number of superdiagonals of the matrix A if UPLO = 'U',
   *>          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
   *> \endverbatim
   *>
   *> \param[in,out] AB
   *> \verbatim
   *>          AB is COMPLEX*16 array, dimension (LDAB, N)
   *>          On entry, the upper or lower triangle of the Hermitian band
   *>          matrix A, stored in the first KD+1 rows of the array.  The
   *>          j-th column of A is stored in the j-th column of the array AB
   *>          as follows:
   *>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
   *>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
   *>
   *>          On exit, AB is overwritten by values generated during the
   *>          reduction to tridiagonal form.  If UPLO = 'U', the first
   *>          superdiagonal and the diagonal of the tridiagonal matrix T
   *>          are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
   *>          the diagonal and first subdiagonal of T are returned in the
   *>          first two rows of AB.
   *> \endverbatim
   *>
   *> \param[in] LDAB
   *> \verbatim
   *>          LDAB is INTEGER
   *>          The leading dimension of the array AB.  LDAB >= KD + 1.
   *> \endverbatim
   *>
   *> \param[out] W
   *> \verbatim
   *>          W is DOUBLE PRECISION array, dimension (N)
   *>          If INFO = 0, the eigenvalues in ascending order.
   *> \endverbatim
   *>
   *> \param[out] Z
   *> \verbatim
   *>          Z is COMPLEX*16 array, dimension (LDZ, N)
   *>          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
   *>          eigenvectors of the matrix A, with the i-th column of Z
   *>          holding the eigenvector associated with W(i).
   *>          If JOBZ = 'N', then Z is not referenced.
   *> \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] 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 dimension of the array WORK.
   *>          If N <= 1,               LWORK must be at least 1.
   *>          If JOBZ = 'N' and N > 1, LWORK must be at least N.
   *>          If JOBZ = 'V' and N > 1, LWORK must be at least 2*N**2.
   *>
   *>          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 (LRWORK)
   *>          On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
   *> \endverbatim
   *>
   *> \param[in] LRWORK
   *> \verbatim
   *>          LRWORK is INTEGER
   *>          The dimension of array RWORK.
   *>          If N <= 1,               LRWORK must be at least 1.
   *>          If JOBZ = 'N' and N > 1, LRWORK must be at least N.
   *>          If JOBZ = 'V' and N > 1, LRWORK must be at least
   *>                        1 + 5*N + 2*N**2.
   *>
   *>          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 LIWORK.
   *> \endverbatim
   *>
   *> \param[in] LIWORK
   *> \verbatim
   *>          LIWORK is INTEGER
   *>          The dimension of array IWORK.
   *>          If JOBZ = 'N' or N <= 1, LIWORK must be at least 1.
   *>          If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*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:  if INFO = i, the algorithm failed to converge; i
   *>                off-diagonal elements of an intermediate tridiagonal
   *>                form did not converge to zero.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee
   *> \author Univ. of California Berkeley
   *> \author Univ. of Colorado Denver
   *> \author NAG Ltd.
   *
   *> \ingroup complex16OTHEReigen
   *
   *  =====================================================================
       SUBROUTINE ZHBEVD( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,        SUBROUTINE ZHBEVD( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
      $                   LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )       $                   LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
 *  *
 *  -- LAPACK driver routine (version 3.2) --  *  -- 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..--
 *     November 2006  
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          JOBZ, UPLO        CHARACTER          JOBZ, UPLO
Line 16 Line 227
       COMPLEX*16         AB( LDAB, * ), WORK( * ), Z( LDZ, * )        COMPLEX*16         AB( LDAB, * ), WORK( * ), Z( LDZ, * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZHBEVD computes all the eigenvalues and, optionally, eigenvectors of  
 *  a complex Hermitian band matrix A.  If eigenvectors are desired, it  
 *  uses a divide and conquer algorithm.  
 *  
 *  The divide and conquer algorithm 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.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  JOBZ    (input) CHARACTER*1  
 *          = 'N':  Compute eigenvalues only;  
 *          = 'V':  Compute eigenvalues and eigenvectors.  
 *  
 *  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.  
 *  
 *  KD      (input) INTEGER  
 *          The number of superdiagonals of the matrix A if UPLO = 'U',  
 *          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.  
 *  
 *  AB      (input/output) COMPLEX*16 array, dimension (LDAB, N)  
 *          On entry, the upper or lower triangle of the Hermitian band  
 *          matrix A, stored in the first KD+1 rows of the array.  The  
 *          j-th column of A is stored in the j-th column of the array AB  
 *          as follows:  
 *          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;  
 *          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).  
 *  
 *          On exit, AB is overwritten by values generated during the  
 *          reduction to tridiagonal form.  If UPLO = 'U', the first  
 *          superdiagonal and the diagonal of the tridiagonal matrix T  
 *          are returned in rows KD and KD+1 of AB, and if UPLO = 'L',  
 *          the diagonal and first subdiagonal of T are returned in the  
 *          first two rows of AB.  
 *  
 *  LDAB    (input) INTEGER  
 *          The leading dimension of the array AB.  LDAB >= KD + 1.  
 *  
 *  W       (output) DOUBLE PRECISION array, dimension (N)  
 *          If INFO = 0, the eigenvalues in ascending order.  
 *  
 *  Z       (output) COMPLEX*16 array, dimension (LDZ, N)  
 *          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal  
 *          eigenvectors of the matrix A, with the i-th column of Z  
 *          holding the eigenvector associated with W(i).  
 *          If JOBZ = 'N', then Z is not referenced.  
 *  
 *  LDZ     (input) INTEGER  
 *          The leading dimension of the array Z.  LDZ >= 1, and if  
 *          JOBZ = 'V', LDZ >= max(1,N).  
 *  
 *  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 dimension of the array WORK.  
 *          If N <= 1,               LWORK must be at least 1.  
 *          If JOBZ = 'N' and N > 1, LWORK must be at least N.  
 *          If JOBZ = 'V' and N > 1, LWORK must be at least 2*N**2.  
 *  
 *          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 (LRWORK)  
 *          On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.  
 *  
 *  LRWORK  (input) INTEGER  
 *          The dimension of array RWORK.  
 *          If N <= 1,               LRWORK must be at least 1.  
 *          If JOBZ = 'N' and N > 1, LRWORK must be at least N.  
 *          If JOBZ = 'V' and N > 1, LRWORK must be at least  
 *                        1 + 5*N + 2*N**2.  
 *  
 *          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 LIWORK.  
 *  
 *  LIWORK  (input) INTEGER  
 *          The dimension of array IWORK.  
 *          If JOBZ = 'N' or N <= 1, LIWORK must be at least 1.  
 *          If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*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:  if INFO = i, the algorithm failed to converge; i  
 *                off-diagonal elements of an intermediate tridiagonal  
 *                form did not converge to zero.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Line 225 Line 320
      $   RETURN       $   RETURN
 *  *
       IF( N.EQ.1 ) THEN        IF( N.EQ.1 ) THEN
          W( 1 ) = AB( 1, 1 )           W( 1 ) = DBLE( AB( 1, 1 ) )
          IF( WANTZ )           IF( WANTZ )
      $      Z( 1, 1 ) = CONE       $      Z( 1, 1 ) = CONE
          RETURN           RETURN
Removed from v.1.1  
changed lines
  Added in v.1.17

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