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    1: *> \brief \b ZHBGV
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at
    6: *            http://www.netlib.org/lapack/explore-html/
    7: *
    8: *> \htmlonly
    9: *> Download ZHBGV + dependencies
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhbgv.f">
   11: *> [TGZ]</a>
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhbgv.f">
   13: *> [ZIP]</a>
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhbgv.f">
   15: *> [TXT]</a>
   16: *> \endhtmlonly
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE ZHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
   22: *                         LDZ, WORK, RWORK, INFO )
   23: *
   24: *       .. Scalar Arguments ..
   25: *       CHARACTER          JOBZ, UPLO
   26: *       INTEGER            INFO, KA, KB, LDAB, LDBB, LDZ, N
   27: *       ..
   28: *       .. Array Arguments ..
   29: *       DOUBLE PRECISION   RWORK( * ), W( * )
   30: *       COMPLEX*16         AB( LDAB, * ), BB( LDBB, * ), WORK( * ),
   31: *      $                   Z( LDZ, * )
   32: *       ..
   33: *
   34: *
   35: *> \par Purpose:
   36: *  =============
   37: *>
   38: *> \verbatim
   39: *>
   40: *> ZHBGV computes all the eigenvalues, and optionally, the eigenvectors
   41: *> of a complex generalized Hermitian-definite banded eigenproblem, of
   42: *> the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
   43: *> and banded, and B is also positive definite.
   44: *> \endverbatim
   45: *
   46: *  Arguments:
   47: *  ==========
   48: *
   49: *> \param[in] JOBZ
   50: *> \verbatim
   51: *>          JOBZ is CHARACTER*1
   52: *>          = 'N':  Compute eigenvalues only;
   53: *>          = 'V':  Compute eigenvalues and eigenvectors.
   54: *> \endverbatim
   55: *>
   56: *> \param[in] UPLO
   57: *> \verbatim
   58: *>          UPLO is CHARACTER*1
   59: *>          = 'U':  Upper triangles of A and B are stored;
   60: *>          = 'L':  Lower triangles of A and B are stored.
   61: *> \endverbatim
   62: *>
   63: *> \param[in] N
   64: *> \verbatim
   65: *>          N is INTEGER
   66: *>          The order of the matrices A and B.  N >= 0.
   67: *> \endverbatim
   68: *>
   69: *> \param[in] KA
   70: *> \verbatim
   71: *>          KA is INTEGER
   72: *>          The number of superdiagonals of the matrix A if UPLO = 'U',
   73: *>          or the number of subdiagonals if UPLO = 'L'. KA >= 0.
   74: *> \endverbatim
   75: *>
   76: *> \param[in] KB
   77: *> \verbatim
   78: *>          KB is INTEGER
   79: *>          The number of superdiagonals of the matrix B if UPLO = 'U',
   80: *>          or the number of subdiagonals if UPLO = 'L'. KB >= 0.
   81: *> \endverbatim
   82: *>
   83: *> \param[in,out] AB
   84: *> \verbatim
   85: *>          AB is COMPLEX*16 array, dimension (LDAB, N)
   86: *>          On entry, the upper or lower triangle of the Hermitian band
   87: *>          matrix A, stored in the first ka+1 rows of the array.  The
   88: *>          j-th column of A is stored in the j-th column of the array AB
   89: *>          as follows:
   90: *>          if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
   91: *>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka).
   92: *>
   93: *>          On exit, the contents of AB are destroyed.
   94: *> \endverbatim
   95: *>
   96: *> \param[in] LDAB
   97: *> \verbatim
   98: *>          LDAB is INTEGER
   99: *>          The leading dimension of the array AB.  LDAB >= KA+1.
  100: *> \endverbatim
  101: *>
  102: *> \param[in,out] BB
  103: *> \verbatim
  104: *>          BB is COMPLEX*16 array, dimension (LDBB, N)
  105: *>          On entry, the upper or lower triangle of the Hermitian band
  106: *>          matrix B, stored in the first kb+1 rows of the array.  The
  107: *>          j-th column of B is stored in the j-th column of the array BB
  108: *>          as follows:
  109: *>          if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
  110: *>          if UPLO = 'L', BB(1+i-j,j)    = B(i,j) for j<=i<=min(n,j+kb).
  111: *>
  112: *>          On exit, the factor S from the split Cholesky factorization
  113: *>          B = S**H*S, as returned by ZPBSTF.
  114: *> \endverbatim
  115: *>
  116: *> \param[in] LDBB
  117: *> \verbatim
  118: *>          LDBB is INTEGER
  119: *>          The leading dimension of the array BB.  LDBB >= KB+1.
  120: *> \endverbatim
  121: *>
  122: *> \param[out] W
  123: *> \verbatim
  124: *>          W is DOUBLE PRECISION array, dimension (N)
  125: *>          If INFO = 0, the eigenvalues in ascending order.
  126: *> \endverbatim
  127: *>
  128: *> \param[out] Z
  129: *> \verbatim
  130: *>          Z is COMPLEX*16 array, dimension (LDZ, N)
  131: *>          If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
  132: *>          eigenvectors, with the i-th column of Z holding the
  133: *>          eigenvector associated with W(i). The eigenvectors are
  134: *>          normalized so that Z**H*B*Z = I.
  135: *>          If JOBZ = 'N', then Z is not referenced.
  136: *> \endverbatim
  137: *>
  138: *> \param[in] LDZ
  139: *> \verbatim
  140: *>          LDZ is INTEGER
  141: *>          The leading dimension of the array Z.  LDZ >= 1, and if
  142: *>          JOBZ = 'V', LDZ >= N.
  143: *> \endverbatim
  144: *>
  145: *> \param[out] WORK
  146: *> \verbatim
  147: *>          WORK is COMPLEX*16 array, dimension (N)
  148: *> \endverbatim
  149: *>
  150: *> \param[out] RWORK
  151: *> \verbatim
  152: *>          RWORK is DOUBLE PRECISION array, dimension (3*N)
  153: *> \endverbatim
  154: *>
  155: *> \param[out] INFO
  156: *> \verbatim
  157: *>          INFO is INTEGER
  158: *>          = 0:  successful exit
  159: *>          < 0:  if INFO = -i, the i-th argument had an illegal value
  160: *>          > 0:  if INFO = i, and i is:
  161: *>             <= N:  the algorithm failed to converge:
  162: *>                    i off-diagonal elements of an intermediate
  163: *>                    tridiagonal form did not converge to zero;
  164: *>             > N:   if INFO = N + i, for 1 <= i <= N, then ZPBSTF
  165: *>                    returned INFO = i: B is not positive definite.
  166: *>                    The factorization of B could not be completed and
  167: *>                    no eigenvalues or eigenvectors were computed.
  168: *> \endverbatim
  169: *
  170: *  Authors:
  171: *  ========
  172: *
  173: *> \author Univ. of Tennessee
  174: *> \author Univ. of California Berkeley
  175: *> \author Univ. of Colorado Denver
  176: *> \author NAG Ltd.
  177: *
  178: *> \date December 2016
  179: *
  180: *> \ingroup complex16OTHEReigen
  181: *
  182: *  =====================================================================
  183:       SUBROUTINE ZHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
  184:      $                  LDZ, WORK, RWORK, INFO )
  185: *
  186: *  -- LAPACK driver routine (version 3.7.0) --
  187: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  188: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  189: *     December 2016
  190: *
  191: *     .. Scalar Arguments ..
  192:       CHARACTER          JOBZ, UPLO
  193:       INTEGER            INFO, KA, KB, LDAB, LDBB, LDZ, N
  194: *     ..
  195: *     .. Array Arguments ..
  196:       DOUBLE PRECISION   RWORK( * ), W( * )
  197:       COMPLEX*16         AB( LDAB, * ), BB( LDBB, * ), WORK( * ),
  198:      $                   Z( LDZ, * )
  199: *     ..
  200: *
  201: *  =====================================================================
  202: *
  203: *     .. Local Scalars ..
  204:       LOGICAL            UPPER, WANTZ
  205:       CHARACTER          VECT
  206:       INTEGER            IINFO, INDE, INDWRK
  207: *     ..
  208: *     .. External Functions ..
  209:       LOGICAL            LSAME
  210:       EXTERNAL           LSAME
  211: *     ..
  212: *     .. External Subroutines ..
  213:       EXTERNAL           DSTERF, XERBLA, ZHBGST, ZHBTRD, ZPBSTF, ZSTEQR
  214: *     ..
  215: *     .. Executable Statements ..
  216: *
  217: *     Test the input parameters.
  218: *
  219:       WANTZ = LSAME( JOBZ, 'V' )
  220:       UPPER = LSAME( UPLO, 'U' )
  221: *
  222:       INFO = 0
  223:       IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
  224:          INFO = -1
  225:       ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
  226:          INFO = -2
  227:       ELSE IF( N.LT.0 ) THEN
  228:          INFO = -3
  229:       ELSE IF( KA.LT.0 ) THEN
  230:          INFO = -4
  231:       ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN
  232:          INFO = -5
  233:       ELSE IF( LDAB.LT.KA+1 ) THEN
  234:          INFO = -7
  235:       ELSE IF( LDBB.LT.KB+1 ) THEN
  236:          INFO = -9
  237:       ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
  238:          INFO = -12
  239:       END IF
  240:       IF( INFO.NE.0 ) THEN
  241:          CALL XERBLA( 'ZHBGV ', -INFO )
  242:          RETURN
  243:       END IF
  244: *
  245: *     Quick return if possible
  246: *
  247:       IF( N.EQ.0 )
  248:      $   RETURN
  249: *
  250: *     Form a split Cholesky factorization of B.
  251: *
  252:       CALL ZPBSTF( UPLO, N, KB, BB, LDBB, INFO )
  253:       IF( INFO.NE.0 ) THEN
  254:          INFO = N + INFO
  255:          RETURN
  256:       END IF
  257: *
  258: *     Transform problem to standard eigenvalue problem.
  259: *
  260:       INDE = 1
  261:       INDWRK = INDE + N
  262:       CALL ZHBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ,
  263:      $             WORK, RWORK( INDWRK ), IINFO )
  264: *
  265: *     Reduce to tridiagonal form.
  266: *
  267:       IF( WANTZ ) THEN
  268:          VECT = 'U'
  269:       ELSE
  270:          VECT = 'N'
  271:       END IF
  272:       CALL ZHBTRD( VECT, UPLO, N, KA, AB, LDAB, W, RWORK( INDE ), Z,
  273:      $             LDZ, WORK, IINFO )
  274: *
  275: *     For eigenvalues only, call DSTERF.  For eigenvectors, call ZSTEQR.
  276: *
  277:       IF( .NOT.WANTZ ) THEN
  278:          CALL DSTERF( N, W, RWORK( INDE ), INFO )
  279:       ELSE
  280:          CALL ZSTEQR( JOBZ, N, W, RWORK( INDE ), Z, LDZ,
  281:      $                RWORK( INDWRK ), INFO )
  282:       END IF
  283:       RETURN
  284: *
  285: *     End of ZHBGV
  286: *
  287:       END