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    1:       SUBROUTINE ZHPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK,
    2:      $                  INFO )
    3: *
    4: *  -- LAPACK driver routine (version 3.2) --
    5: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    6: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    7: *     November 2006
    8: *
    9: *     .. Scalar Arguments ..
   10:       CHARACTER          JOBZ, UPLO
   11:       INTEGER            INFO, LDZ, N
   12: *     ..
   13: *     .. Array Arguments ..
   14:       DOUBLE PRECISION   RWORK( * ), W( * )
   15:       COMPLEX*16         AP( * ), WORK( * ), Z( LDZ, * )
   16: *     ..
   17: *
   18: *  Purpose
   19: *  =======
   20: *
   21: *  ZHPEV computes all the eigenvalues and, optionally, eigenvectors of a
   22: *  complex Hermitian matrix in packed storage.
   23: *
   24: *  Arguments
   25: *  =========
   26: *
   27: *  JOBZ    (input) CHARACTER*1
   28: *          = 'N':  Compute eigenvalues only;
   29: *          = 'V':  Compute eigenvalues and eigenvectors.
   30: *
   31: *  UPLO    (input) CHARACTER*1
   32: *          = 'U':  Upper triangle of A is stored;
   33: *          = 'L':  Lower triangle of A is stored.
   34: *
   35: *  N       (input) INTEGER
   36: *          The order of the matrix A.  N >= 0.
   37: *
   38: *  AP      (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
   39: *          On entry, the upper or lower triangle of the Hermitian matrix
   40: *          A, packed columnwise in a linear array.  The j-th column of A
   41: *          is stored in the array AP as follows:
   42: *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
   43: *          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
   44: *
   45: *          On exit, AP is overwritten by values generated during the
   46: *          reduction to tridiagonal form.  If UPLO = 'U', the diagonal
   47: *          and first superdiagonal of the tridiagonal matrix T overwrite
   48: *          the corresponding elements of A, and if UPLO = 'L', the
   49: *          diagonal and first subdiagonal of T overwrite the
   50: *          corresponding elements of A.
   51: *
   52: *  W       (output) DOUBLE PRECISION array, dimension (N)
   53: *          If INFO = 0, the eigenvalues in ascending order.
   54: *
   55: *  Z       (output) COMPLEX*16 array, dimension (LDZ, N)
   56: *          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
   57: *          eigenvectors of the matrix A, with the i-th column of Z
   58: *          holding the eigenvector associated with W(i).
   59: *          If JOBZ = 'N', then Z is not referenced.
   60: *
   61: *  LDZ     (input) INTEGER
   62: *          The leading dimension of the array Z.  LDZ >= 1, and if
   63: *          JOBZ = 'V', LDZ >= max(1,N).
   64: *
   65: *  WORK    (workspace) COMPLEX*16 array, dimension (max(1, 2*N-1))
   66: *
   67: *  RWORK   (workspace) DOUBLE PRECISION array, dimension (max(1, 3*N-2))
   68: *
   69: *  INFO    (output) INTEGER
   70: *          = 0:  successful exit.
   71: *          < 0:  if INFO = -i, the i-th argument had an illegal value.
   72: *          > 0:  if INFO = i, the algorithm failed to converge; i
   73: *                off-diagonal elements of an intermediate tridiagonal
   74: *                form did not converge to zero.
   75: *
   76: *  =====================================================================
   77: *
   78: *     .. Parameters ..
   79:       DOUBLE PRECISION   ZERO, ONE
   80:       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
   81: *     ..
   82: *     .. Local Scalars ..
   83:       LOGICAL            WANTZ
   84:       INTEGER            IINFO, IMAX, INDE, INDRWK, INDTAU, INDWRK,
   85:      $                   ISCALE
   86:       DOUBLE PRECISION   ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
   87:      $                   SMLNUM
   88: *     ..
   89: *     .. External Functions ..
   90:       LOGICAL            LSAME
   91:       DOUBLE PRECISION   DLAMCH, ZLANHP
   92:       EXTERNAL           LSAME, DLAMCH, ZLANHP
   93: *     ..
   94: *     .. External Subroutines ..
   95:       EXTERNAL           DSCAL, DSTERF, XERBLA, ZDSCAL, ZHPTRD, ZSTEQR,
   96:      $                   ZUPGTR
   97: *     ..
   98: *     .. Intrinsic Functions ..
   99:       INTRINSIC          SQRT
  100: *     ..
  101: *     .. Executable Statements ..
  102: *
  103: *     Test the input parameters.
  104: *
  105:       WANTZ = LSAME( JOBZ, 'V' )
  106: *
  107:       INFO = 0
  108:       IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
  109:          INFO = -1
  110:       ELSE IF( .NOT.( LSAME( UPLO, 'L' ) .OR. LSAME( UPLO, 'U' ) ) )
  111:      $          THEN
  112:          INFO = -2
  113:       ELSE IF( N.LT.0 ) THEN
  114:          INFO = -3
  115:       ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
  116:          INFO = -7
  117:       END IF
  118: *
  119:       IF( INFO.NE.0 ) THEN
  120:          CALL XERBLA( 'ZHPEV ', -INFO )
  121:          RETURN
  122:       END IF
  123: *
  124: *     Quick return if possible
  125: *
  126:       IF( N.EQ.0 )
  127:      $   RETURN
  128: *
  129:       IF( N.EQ.1 ) THEN
  130:          W( 1 ) = AP( 1 )
  131:          RWORK( 1 ) = 1
  132:          IF( WANTZ )
  133:      $      Z( 1, 1 ) = ONE
  134:          RETURN
  135:       END IF
  136: *
  137: *     Get machine constants.
  138: *
  139:       SAFMIN = DLAMCH( 'Safe minimum' )
  140:       EPS = DLAMCH( 'Precision' )
  141:       SMLNUM = SAFMIN / EPS
  142:       BIGNUM = ONE / SMLNUM
  143:       RMIN = SQRT( SMLNUM )
  144:       RMAX = SQRT( BIGNUM )
  145: *
  146: *     Scale matrix to allowable range, if necessary.
  147: *
  148:       ANRM = ZLANHP( 'M', UPLO, N, AP, RWORK )
  149:       ISCALE = 0
  150:       IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
  151:          ISCALE = 1
  152:          SIGMA = RMIN / ANRM
  153:       ELSE IF( ANRM.GT.RMAX ) THEN
  154:          ISCALE = 1
  155:          SIGMA = RMAX / ANRM
  156:       END IF
  157:       IF( ISCALE.EQ.1 ) THEN
  158:          CALL ZDSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 )
  159:       END IF
  160: *
  161: *     Call ZHPTRD to reduce Hermitian packed matrix to tridiagonal form.
  162: *
  163:       INDE = 1
  164:       INDTAU = 1
  165:       CALL ZHPTRD( UPLO, N, AP, W, RWORK( INDE ), WORK( INDTAU ),
  166:      $             IINFO )
  167: *
  168: *     For eigenvalues only, call DSTERF.  For eigenvectors, first call
  169: *     ZUPGTR to generate the orthogonal matrix, then call ZSTEQR.
  170: *
  171:       IF( .NOT.WANTZ ) THEN
  172:          CALL DSTERF( N, W, RWORK( INDE ), INFO )
  173:       ELSE
  174:          INDWRK = INDTAU + N
  175:          CALL ZUPGTR( UPLO, N, AP, WORK( INDTAU ), Z, LDZ,
  176:      $                WORK( INDWRK ), IINFO )
  177:          INDRWK = INDE + N
  178:          CALL ZSTEQR( JOBZ, N, W, RWORK( INDE ), Z, LDZ,
  179:      $                RWORK( INDRWK ), INFO )
  180:       END IF
  181: *
  182: *     If matrix was scaled, then rescale eigenvalues appropriately.
  183: *
  184:       IF( ISCALE.EQ.1 ) THEN
  185:          IF( INFO.EQ.0 ) THEN
  186:             IMAX = N
  187:          ELSE
  188:             IMAX = INFO - 1
  189:          END IF
  190:          CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
  191:       END IF
  192: *
  193:       RETURN
  194: *
  195: *     End of ZHPEV
  196: *
  197:       END