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Mise à jour de lapack vers la version 3.3.0.

    1:       SUBROUTINE ZHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
    2:      $                  LDZ, WORK, RWORK, 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, KA, KB, LDAB, LDBB, LDZ, N
   12: *     ..
   13: *     .. Array Arguments ..
   14:       DOUBLE PRECISION   RWORK( * ), W( * )
   15:       COMPLEX*16         AB( LDAB, * ), BB( LDBB, * ), WORK( * ),
   16:      $                   Z( LDZ, * )
   17: *     ..
   18: *
   19: *  Purpose
   20: *  =======
   21: *
   22: *  ZHBGV computes all the eigenvalues, and optionally, the eigenvectors
   23: *  of a complex generalized Hermitian-definite banded eigenproblem, of
   24: *  the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
   25: *  and banded, and B is also positive definite.
   26: *
   27: *  Arguments
   28: *  =========
   29: *
   30: *  JOBZ    (input) CHARACTER*1
   31: *          = 'N':  Compute eigenvalues only;
   32: *          = 'V':  Compute eigenvalues and eigenvectors.
   33: *
   34: *  UPLO    (input) CHARACTER*1
   35: *          = 'U':  Upper triangles of A and B are stored;
   36: *          = 'L':  Lower triangles of A and B are stored.
   37: *
   38: *  N       (input) INTEGER
   39: *          The order of the matrices A and B.  N >= 0.
   40: *
   41: *  KA      (input) INTEGER
   42: *          The number of superdiagonals of the matrix A if UPLO = 'U',
   43: *          or the number of subdiagonals if UPLO = 'L'. KA >= 0.
   44: *
   45: *  KB      (input) INTEGER
   46: *          The number of superdiagonals of the matrix B if UPLO = 'U',
   47: *          or the number of subdiagonals if UPLO = 'L'. KB >= 0.
   48: *
   49: *  AB      (input/output) COMPLEX*16 array, dimension (LDAB, N)
   50: *          On entry, the upper or lower triangle of the Hermitian band
   51: *          matrix A, stored in the first ka+1 rows of the array.  The
   52: *          j-th column of A is stored in the j-th column of the array AB
   53: *          as follows:
   54: *          if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
   55: *          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka).
   56: *
   57: *          On exit, the contents of AB are destroyed.
   58: *
   59: *  LDAB    (input) INTEGER
   60: *          The leading dimension of the array AB.  LDAB >= KA+1.
   61: *
   62: *  BB      (input/output) COMPLEX*16 array, dimension (LDBB, N)
   63: *          On entry, the upper or lower triangle of the Hermitian band
   64: *          matrix B, stored in the first kb+1 rows of the array.  The
   65: *          j-th column of B is stored in the j-th column of the array BB
   66: *          as follows:
   67: *          if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
   68: *          if UPLO = 'L', BB(1+i-j,j)    = B(i,j) for j<=i<=min(n,j+kb).
   69: *
   70: *          On exit, the factor S from the split Cholesky factorization
   71: *          B = S**H*S, as returned by ZPBSTF.
   72: *
   73: *  LDBB    (input) INTEGER
   74: *          The leading dimension of the array BB.  LDBB >= KB+1.
   75: *
   76: *  W       (output) DOUBLE PRECISION array, dimension (N)
   77: *          If INFO = 0, the eigenvalues in ascending order.
   78: *
   79: *  Z       (output) COMPLEX*16 array, dimension (LDZ, N)
   80: *          If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
   81: *          eigenvectors, with the i-th column of Z holding the
   82: *          eigenvector associated with W(i). The eigenvectors are
   83: *          normalized so that Z**H*B*Z = I.
   84: *          If JOBZ = 'N', then Z is not referenced.
   85: *
   86: *  LDZ     (input) INTEGER
   87: *          The leading dimension of the array Z.  LDZ >= 1, and if
   88: *          JOBZ = 'V', LDZ >= N.
   89: *
   90: *  WORK    (workspace) COMPLEX*16 array, dimension (N)
   91: *
   92: *  RWORK   (workspace) DOUBLE PRECISION array, dimension (3*N)
   93: *
   94: *  INFO    (output) INTEGER
   95: *          = 0:  successful exit
   96: *          < 0:  if INFO = -i, the i-th argument had an illegal value
   97: *          > 0:  if INFO = i, and i is:
   98: *             <= N:  the algorithm failed to converge:
   99: *                    i off-diagonal elements of an intermediate
  100: *                    tridiagonal form did not converge to zero;
  101: *             > N:   if INFO = N + i, for 1 <= i <= N, then ZPBSTF
  102: *                    returned INFO = i: B is not positive definite.
  103: *                    The factorization of B could not be completed and
  104: *                    no eigenvalues or eigenvectors were computed.
  105: *
  106: *  =====================================================================
  107: *
  108: *     .. Local Scalars ..
  109:       LOGICAL            UPPER, WANTZ
  110:       CHARACTER          VECT
  111:       INTEGER            IINFO, INDE, INDWRK
  112: *     ..
  113: *     .. External Functions ..
  114:       LOGICAL            LSAME
  115:       EXTERNAL           LSAME
  116: *     ..
  117: *     .. External Subroutines ..
  118:       EXTERNAL           DSTERF, XERBLA, ZHBGST, ZHBTRD, ZPBSTF, ZSTEQR
  119: *     ..
  120: *     .. Executable Statements ..
  121: *
  122: *     Test the input parameters.
  123: *
  124:       WANTZ = LSAME( JOBZ, 'V' )
  125:       UPPER = LSAME( UPLO, 'U' )
  126: *
  127:       INFO = 0
  128:       IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
  129:          INFO = -1
  130:       ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
  131:          INFO = -2
  132:       ELSE IF( N.LT.0 ) THEN
  133:          INFO = -3
  134:       ELSE IF( KA.LT.0 ) THEN
  135:          INFO = -4
  136:       ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN
  137:          INFO = -5
  138:       ELSE IF( LDAB.LT.KA+1 ) THEN
  139:          INFO = -7
  140:       ELSE IF( LDBB.LT.KB+1 ) THEN
  141:          INFO = -9
  142:       ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
  143:          INFO = -12
  144:       END IF
  145:       IF( INFO.NE.0 ) THEN
  146:          CALL XERBLA( 'ZHBGV ', -INFO )
  147:          RETURN
  148:       END IF
  149: *
  150: *     Quick return if possible
  151: *
  152:       IF( N.EQ.0 )
  153:      $   RETURN
  154: *
  155: *     Form a split Cholesky factorization of B.
  156: *
  157:       CALL ZPBSTF( UPLO, N, KB, BB, LDBB, INFO )
  158:       IF( INFO.NE.0 ) THEN
  159:          INFO = N + INFO
  160:          RETURN
  161:       END IF
  162: *
  163: *     Transform problem to standard eigenvalue problem.
  164: *
  165:       INDE = 1
  166:       INDWRK = INDE + N
  167:       CALL ZHBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ,
  168:      $             WORK, RWORK( INDWRK ), IINFO )
  169: *
  170: *     Reduce to tridiagonal form.
  171: *
  172:       IF( WANTZ ) THEN
  173:          VECT = 'U'
  174:       ELSE
  175:          VECT = 'N'
  176:       END IF
  177:       CALL ZHBTRD( VECT, UPLO, N, KA, AB, LDAB, W, RWORK( INDE ), Z,
  178:      $             LDZ, WORK, IINFO )
  179: *
  180: *     For eigenvalues only, call DSTERF.  For eigenvectors, call ZSTEQR.
  181: *
  182:       IF( .NOT.WANTZ ) THEN
  183:          CALL DSTERF( N, W, RWORK( INDE ), INFO )
  184:       ELSE
  185:          CALL ZSTEQR( JOBZ, N, W, RWORK( INDE ), Z, LDZ,
  186:      $                RWORK( INDWRK ), INFO )
  187:       END IF
  188:       RETURN
  189: *
  190: *     End of ZHBGV
  191: *
  192:       END