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Patches pour OS/2

    1:       SUBROUTINE DSBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
    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, KD, LDAB, LDZ, N
   12: *     ..
   13: *     .. Array Arguments ..
   14:       DOUBLE PRECISION   AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )
   15: *     ..
   16: *
   17: *  Purpose
   18: *  =======
   19: *
   20: *  DSBEV computes all the eigenvalues and, optionally, eigenvectors of
   21: *  a real symmetric band matrix A.
   22: *
   23: *  Arguments
   24: *  =========
   25: *
   26: *  JOBZ    (input) CHARACTER*1
   27: *          = 'N':  Compute eigenvalues only;
   28: *          = 'V':  Compute eigenvalues and eigenvectors.
   29: *
   30: *  UPLO    (input) CHARACTER*1
   31: *          = 'U':  Upper triangle of A is stored;
   32: *          = 'L':  Lower triangle of A is stored.
   33: *
   34: *  N       (input) INTEGER
   35: *          The order of the matrix A.  N >= 0.
   36: *
   37: *  KD      (input) INTEGER
   38: *          The number of superdiagonals of the matrix A if UPLO = 'U',
   39: *          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
   40: *
   41: *  AB      (input/output) DOUBLE PRECISION array, dimension (LDAB, N)
   42: *          On entry, the upper or lower triangle of the symmetric band
   43: *          matrix A, stored in the first KD+1 rows of the array.  The
   44: *          j-th column of A is stored in the j-th column of the array AB
   45: *          as follows:
   46: *          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
   47: *          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
   48: *
   49: *          On exit, AB is overwritten by values generated during the
   50: *          reduction to tridiagonal form.  If UPLO = 'U', the first
   51: *          superdiagonal and the diagonal of the tridiagonal matrix T
   52: *          are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
   53: *          the diagonal and first subdiagonal of T are returned in the
   54: *          first two rows of AB.
   55: *
   56: *  LDAB    (input) INTEGER
   57: *          The leading dimension of the array AB.  LDAB >= KD + 1.
   58: *
   59: *  W       (output) DOUBLE PRECISION array, dimension (N)
   60: *          If INFO = 0, the eigenvalues in ascending order.
   61: *
   62: *  Z       (output) DOUBLE PRECISION array, dimension (LDZ, N)
   63: *          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
   64: *          eigenvectors of the matrix A, with the i-th column of Z
   65: *          holding the eigenvector associated with W(i).
   66: *          If JOBZ = 'N', then Z is not referenced.
   67: *
   68: *  LDZ     (input) INTEGER
   69: *          The leading dimension of the array Z.  LDZ >= 1, and if
   70: *          JOBZ = 'V', LDZ >= max(1,N).
   71: *
   72: *  WORK    (workspace) DOUBLE PRECISION array, dimension (max(1,3*N-2))
   73: *
   74: *  INFO    (output) INTEGER
   75: *          = 0:  successful exit
   76: *          < 0:  if INFO = -i, the i-th argument had an illegal value
   77: *          > 0:  if INFO = i, the algorithm failed to converge; i
   78: *                off-diagonal elements of an intermediate tridiagonal
   79: *                form did not converge to zero.
   80: *
   81: *  =====================================================================
   82: *
   83: *     .. Parameters ..
   84:       DOUBLE PRECISION   ZERO, ONE
   85:       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
   86: *     ..
   87: *     .. Local Scalars ..
   88:       LOGICAL            LOWER, WANTZ
   89:       INTEGER            IINFO, IMAX, INDE, INDWRK, ISCALE
   90:       DOUBLE PRECISION   ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
   91:      $                   SMLNUM
   92: *     ..
   93: *     .. External Functions ..
   94:       LOGICAL            LSAME
   95:       DOUBLE PRECISION   DLAMCH, DLANSB
   96:       EXTERNAL           LSAME, DLAMCH, DLANSB
   97: *     ..
   98: *     .. External Subroutines ..
   99:       EXTERNAL           DLASCL, DSBTRD, DSCAL, DSTEQR, DSTERF, XERBLA
  100: *     ..
  101: *     .. Intrinsic Functions ..
  102:       INTRINSIC          SQRT
  103: *     ..
  104: *     .. Executable Statements ..
  105: *
  106: *     Test the input parameters.
  107: *
  108:       WANTZ = LSAME( JOBZ, 'V' )
  109:       LOWER = LSAME( UPLO, 'L' )
  110: *
  111:       INFO = 0
  112:       IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
  113:          INFO = -1
  114:       ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
  115:          INFO = -2
  116:       ELSE IF( N.LT.0 ) THEN
  117:          INFO = -3
  118:       ELSE IF( KD.LT.0 ) THEN
  119:          INFO = -4
  120:       ELSE IF( LDAB.LT.KD+1 ) THEN
  121:          INFO = -6
  122:       ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
  123:          INFO = -9
  124:       END IF
  125: *
  126:       IF( INFO.NE.0 ) THEN
  127:          CALL XERBLA( 'DSBEV ', -INFO )
  128:          RETURN
  129:       END IF
  130: *
  131: *     Quick return if possible
  132: *
  133:       IF( N.EQ.0 )
  134:      $   RETURN
  135: *
  136:       IF( N.EQ.1 ) THEN
  137:          IF( LOWER ) THEN
  138:             W( 1 ) = AB( 1, 1 )
  139:          ELSE
  140:             W( 1 ) = AB( KD+1, 1 )
  141:          END IF
  142:          IF( WANTZ )
  143:      $      Z( 1, 1 ) = ONE
  144:          RETURN
  145:       END IF
  146: *
  147: *     Get machine constants.
  148: *
  149:       SAFMIN = DLAMCH( 'Safe minimum' )
  150:       EPS = DLAMCH( 'Precision' )
  151:       SMLNUM = SAFMIN / EPS
  152:       BIGNUM = ONE / SMLNUM
  153:       RMIN = SQRT( SMLNUM )
  154:       RMAX = SQRT( BIGNUM )
  155: *
  156: *     Scale matrix to allowable range, if necessary.
  157: *
  158:       ANRM = DLANSB( 'M', UPLO, N, KD, AB, LDAB, WORK )
  159:       ISCALE = 0
  160:       IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
  161:          ISCALE = 1
  162:          SIGMA = RMIN / ANRM
  163:       ELSE IF( ANRM.GT.RMAX ) THEN
  164:          ISCALE = 1
  165:          SIGMA = RMAX / ANRM
  166:       END IF
  167:       IF( ISCALE.EQ.1 ) THEN
  168:          IF( LOWER ) THEN
  169:             CALL DLASCL( 'B', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
  170:          ELSE
  171:             CALL DLASCL( 'Q', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
  172:          END IF
  173:       END IF
  174: *
  175: *     Call DSBTRD to reduce symmetric band matrix to tridiagonal form.
  176: *
  177:       INDE = 1
  178:       INDWRK = INDE + N
  179:       CALL DSBTRD( JOBZ, UPLO, N, KD, AB, LDAB, W, WORK( INDE ), Z, LDZ,
  180:      $             WORK( INDWRK ), IINFO )
  181: *
  182: *     For eigenvalues only, call DSTERF.  For eigenvectors, call SSTEQR.
  183: *
  184:       IF( .NOT.WANTZ ) THEN
  185:          CALL DSTERF( N, W, WORK( INDE ), INFO )
  186:       ELSE
  187:          CALL DSTEQR( JOBZ, N, W, WORK( INDE ), Z, LDZ, WORK( INDWRK ),
  188:      $                INFO )
  189:       END IF
  190: *
  191: *     If matrix was scaled, then rescale eigenvalues appropriately.
  192: *
  193:       IF( ISCALE.EQ.1 ) THEN
  194:          IF( INFO.EQ.0 ) THEN
  195:             IMAX = N
  196:          ELSE
  197:             IMAX = INFO - 1
  198:          END IF
  199:          CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
  200:       END IF
  201: *
  202:       RETURN
  203: *
  204: *     End of DSBEV
  205: *
  206:       END