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