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    1: *> \brief <b> ZHPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices</b>
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at
    6: *            http://www.netlib.org/lapack/explore-html/
    7: *
    8: *> \htmlonly
    9: *> Download ZHPEV + dependencies
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhpev.f">
   11: *> [TGZ]</a>
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhpev.f">
   13: *> [ZIP]</a>
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhpev.f">
   15: *> [TXT]</a>
   16: *> \endhtmlonly
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE ZHPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK,
   22: *                         INFO )
   23: *
   24: *       .. Scalar Arguments ..
   25: *       CHARACTER          JOBZ, UPLO
   26: *       INTEGER            INFO, LDZ, N
   27: *       ..
   28: *       .. Array Arguments ..
   29: *       DOUBLE PRECISION   RWORK( * ), W( * )
   30: *       COMPLEX*16         AP( * ), WORK( * ), Z( LDZ, * )
   31: *       ..
   32: *
   33: *
   34: *> \par Purpose:
   35: *  =============
   36: *>
   37: *> \verbatim
   38: *>
   39: *> ZHPEV computes all the eigenvalues and, optionally, eigenvectors of a
   40: *> complex Hermitian matrix in packed storage.
   41: *> \endverbatim
   42: *
   43: *  Arguments:
   44: *  ==========
   45: *
   46: *> \param[in] JOBZ
   47: *> \verbatim
   48: *>          JOBZ is CHARACTER*1
   49: *>          = 'N':  Compute eigenvalues only;
   50: *>          = 'V':  Compute eigenvalues and eigenvectors.
   51: *> \endverbatim
   52: *>
   53: *> \param[in] UPLO
   54: *> \verbatim
   55: *>          UPLO is CHARACTER*1
   56: *>          = 'U':  Upper triangle of A is stored;
   57: *>          = 'L':  Lower triangle of A is stored.
   58: *> \endverbatim
   59: *>
   60: *> \param[in] N
   61: *> \verbatim
   62: *>          N is INTEGER
   63: *>          The order of the matrix A.  N >= 0.
   64: *> \endverbatim
   65: *>
   66: *> \param[in,out] AP
   67: *> \verbatim
   68: *>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
   69: *>          On entry, the upper or lower triangle of the Hermitian matrix
   70: *>          A, packed columnwise in a linear array.  The j-th column of A
   71: *>          is stored in the array AP as follows:
   72: *>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
   73: *>          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
   74: *>
   75: *>          On exit, AP is overwritten by values generated during the
   76: *>          reduction to tridiagonal form.  If UPLO = 'U', the diagonal
   77: *>          and first superdiagonal of the tridiagonal matrix T overwrite
   78: *>          the corresponding elements of A, and if UPLO = 'L', the
   79: *>          diagonal and first subdiagonal of T overwrite the
   80: *>          corresponding elements of A.
   81: *> \endverbatim
   82: *>
   83: *> \param[out] W
   84: *> \verbatim
   85: *>          W is DOUBLE PRECISION array, dimension (N)
   86: *>          If INFO = 0, the eigenvalues in ascending order.
   87: *> \endverbatim
   88: *>
   89: *> \param[out] Z
   90: *> \verbatim
   91: *>          Z is COMPLEX*16 array, dimension (LDZ, N)
   92: *>          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
   93: *>          eigenvectors of the matrix A, with the i-th column of Z
   94: *>          holding the eigenvector associated with W(i).
   95: *>          If JOBZ = 'N', then Z is not referenced.
   96: *> \endverbatim
   97: *>
   98: *> \param[in] LDZ
   99: *> \verbatim
  100: *>          LDZ is INTEGER
  101: *>          The leading dimension of the array Z.  LDZ >= 1, and if
  102: *>          JOBZ = 'V', LDZ >= max(1,N).
  103: *> \endverbatim
  104: *>
  105: *> \param[out] WORK
  106: *> \verbatim
  107: *>          WORK is COMPLEX*16 array, dimension (max(1, 2*N-1))
  108: *> \endverbatim
  109: *>
  110: *> \param[out] RWORK
  111: *> \verbatim
  112: *>          RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2))
  113: *> \endverbatim
  114: *>
  115: *> \param[out] INFO
  116: *> \verbatim
  117: *>          INFO is INTEGER
  118: *>          = 0:  successful exit.
  119: *>          < 0:  if INFO = -i, the i-th argument had an illegal value.
  120: *>          > 0:  if INFO = i, the algorithm failed to converge; i
  121: *>                off-diagonal elements of an intermediate tridiagonal
  122: *>                form did not converge to zero.
  123: *> \endverbatim
  124: *
  125: *  Authors:
  126: *  ========
  127: *
  128: *> \author Univ. of Tennessee
  129: *> \author Univ. of California Berkeley
  130: *> \author Univ. of Colorado Denver
  131: *> \author NAG Ltd.
  132: *
  133: *> \date December 2016
  134: *
  135: *> \ingroup complex16OTHEReigen
  136: *
  137: *  =====================================================================
  138:       SUBROUTINE ZHPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK,
  139:      $                  INFO )
  140: *
  141: *  -- LAPACK driver routine (version 3.7.0) --
  142: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  143: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  144: *     December 2016
  145: *
  146: *     .. Scalar Arguments ..
  147:       CHARACTER          JOBZ, UPLO
  148:       INTEGER            INFO, LDZ, N
  149: *     ..
  150: *     .. Array Arguments ..
  151:       DOUBLE PRECISION   RWORK( * ), W( * )
  152:       COMPLEX*16         AP( * ), WORK( * ), Z( LDZ, * )
  153: *     ..
  154: *
  155: *  =====================================================================
  156: *
  157: *     .. Parameters ..
  158:       DOUBLE PRECISION   ZERO, ONE
  159:       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
  160: *     ..
  161: *     .. Local Scalars ..
  162:       LOGICAL            WANTZ
  163:       INTEGER            IINFO, IMAX, INDE, INDRWK, INDTAU, INDWRK,
  164:      $                   ISCALE
  165:       DOUBLE PRECISION   ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
  166:      $                   SMLNUM
  167: *     ..
  168: *     .. External Functions ..
  169:       LOGICAL            LSAME
  170:       DOUBLE PRECISION   DLAMCH, ZLANHP
  171:       EXTERNAL           LSAME, DLAMCH, ZLANHP
  172: *     ..
  173: *     .. External Subroutines ..
  174:       EXTERNAL           DSCAL, DSTERF, XERBLA, ZDSCAL, ZHPTRD, ZSTEQR,
  175:      $                   ZUPGTR
  176: *     ..
  177: *     .. Intrinsic Functions ..
  178:       INTRINSIC          SQRT
  179: *     ..
  180: *     .. Executable Statements ..
  181: *
  182: *     Test the input parameters.
  183: *
  184:       WANTZ = LSAME( JOBZ, 'V' )
  185: *
  186:       INFO = 0
  187:       IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
  188:          INFO = -1
  189:       ELSE IF( .NOT.( LSAME( UPLO, 'L' ) .OR. LSAME( UPLO, 'U' ) ) )
  190:      $          THEN
  191:          INFO = -2
  192:       ELSE IF( N.LT.0 ) THEN
  193:          INFO = -3
  194:       ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
  195:          INFO = -7
  196:       END IF
  197: *
  198:       IF( INFO.NE.0 ) THEN
  199:          CALL XERBLA( 'ZHPEV ', -INFO )
  200:          RETURN
  201:       END IF
  202: *
  203: *     Quick return if possible
  204: *
  205:       IF( N.EQ.0 )
  206:      $   RETURN
  207: *
  208:       IF( N.EQ.1 ) THEN
  209:          W( 1 ) = AP( 1 )
  210:          RWORK( 1 ) = 1
  211:          IF( WANTZ )
  212:      $      Z( 1, 1 ) = ONE
  213:          RETURN
  214:       END IF
  215: *
  216: *     Get machine constants.
  217: *
  218:       SAFMIN = DLAMCH( 'Safe minimum' )
  219:       EPS = DLAMCH( 'Precision' )
  220:       SMLNUM = SAFMIN / EPS
  221:       BIGNUM = ONE / SMLNUM
  222:       RMIN = SQRT( SMLNUM )
  223:       RMAX = SQRT( BIGNUM )
  224: *
  225: *     Scale matrix to allowable range, if necessary.
  226: *
  227:       ANRM = ZLANHP( 'M', UPLO, N, AP, RWORK )
  228:       ISCALE = 0
  229:       IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
  230:          ISCALE = 1
  231:          SIGMA = RMIN / ANRM
  232:       ELSE IF( ANRM.GT.RMAX ) THEN
  233:          ISCALE = 1
  234:          SIGMA = RMAX / ANRM
  235:       END IF
  236:       IF( ISCALE.EQ.1 ) THEN
  237:          CALL ZDSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 )
  238:       END IF
  239: *
  240: *     Call ZHPTRD to reduce Hermitian packed matrix to tridiagonal form.
  241: *
  242:       INDE = 1
  243:       INDTAU = 1
  244:       CALL ZHPTRD( UPLO, N, AP, W, RWORK( INDE ), WORK( INDTAU ),
  245:      $             IINFO )
  246: *
  247: *     For eigenvalues only, call DSTERF.  For eigenvectors, first call
  248: *     ZUPGTR to generate the orthogonal matrix, then call ZSTEQR.
  249: *
  250:       IF( .NOT.WANTZ ) THEN
  251:          CALL DSTERF( N, W, RWORK( INDE ), INFO )
  252:       ELSE
  253:          INDWRK = INDTAU + N
  254:          CALL ZUPGTR( UPLO, N, AP, WORK( INDTAU ), Z, LDZ,
  255:      $                WORK( INDWRK ), IINFO )
  256:          INDRWK = INDE + N
  257:          CALL ZSTEQR( JOBZ, N, W, RWORK( INDE ), Z, LDZ,
  258:      $                RWORK( INDRWK ), INFO )
  259:       END IF
  260: *
  261: *     If matrix was scaled, then rescale eigenvalues appropriately.
  262: *
  263:       IF( ISCALE.EQ.1 ) THEN
  264:          IF( INFO.EQ.0 ) THEN
  265:             IMAX = N
  266:          ELSE
  267:             IMAX = INFO - 1
  268:          END IF
  269:          CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
  270:       END IF
  271: *
  272:       RETURN
  273: *
  274: *     End of ZHPEV
  275: *
  276:       END