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Cohérence Lapack.

    1: *> \brief \b DPTTRF
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at 
    6: *            http://www.netlib.org/lapack/explore-html/ 
    7: *
    8: *> \htmlonly
    9: *> Download DPTTRF + dependencies 
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpttrf.f"> 
   11: *> [TGZ]</a> 
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpttrf.f"> 
   13: *> [ZIP]</a> 
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpttrf.f"> 
   15: *> [TXT]</a>
   16: *> \endhtmlonly 
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE DPTTRF( N, D, E, INFO )
   22: * 
   23: *       .. Scalar Arguments ..
   24: *       INTEGER            INFO, N
   25: *       ..
   26: *       .. Array Arguments ..
   27: *       DOUBLE PRECISION   D( * ), E( * )
   28: *       ..
   29: *  
   30: *
   31: *> \par Purpose:
   32: *  =============
   33: *>
   34: *> \verbatim
   35: *>
   36: *> DPTTRF computes the L*D*L**T factorization of a real symmetric
   37: *> positive definite tridiagonal matrix A.  The factorization may also
   38: *> be regarded as having the form A = U**T*D*U.
   39: *> \endverbatim
   40: *
   41: *  Arguments:
   42: *  ==========
   43: *
   44: *> \param[in] N
   45: *> \verbatim
   46: *>          N is INTEGER
   47: *>          The order of the matrix A.  N >= 0.
   48: *> \endverbatim
   49: *>
   50: *> \param[in,out] D
   51: *> \verbatim
   52: *>          D is DOUBLE PRECISION array, dimension (N)
   53: *>          On entry, the n diagonal elements of the tridiagonal matrix
   54: *>          A.  On exit, the n diagonal elements of the diagonal matrix
   55: *>          D from the L*D*L**T factorization of A.
   56: *> \endverbatim
   57: *>
   58: *> \param[in,out] E
   59: *> \verbatim
   60: *>          E is DOUBLE PRECISION array, dimension (N-1)
   61: *>          On entry, the (n-1) subdiagonal elements of the tridiagonal
   62: *>          matrix A.  On exit, the (n-1) subdiagonal elements of the
   63: *>          unit bidiagonal factor L from the L*D*L**T factorization of A.
   64: *>          E can also be regarded as the superdiagonal of the unit
   65: *>          bidiagonal factor U from the U**T*D*U factorization of A.
   66: *> \endverbatim
   67: *>
   68: *> \param[out] INFO
   69: *> \verbatim
   70: *>          INFO is INTEGER
   71: *>          = 0: successful exit
   72: *>          < 0: if INFO = -k, the k-th argument had an illegal value
   73: *>          > 0: if INFO = k, the leading minor of order k is not
   74: *>               positive definite; if k < N, the factorization could not
   75: *>               be completed, while if k = N, the factorization was
   76: *>               completed, but D(N) <= 0.
   77: *> \endverbatim
   78: *
   79: *  Authors:
   80: *  ========
   81: *
   82: *> \author Univ. of Tennessee 
   83: *> \author Univ. of California Berkeley 
   84: *> \author Univ. of Colorado Denver 
   85: *> \author NAG Ltd. 
   86: *
   87: *> \date September 2012
   88: *
   89: *> \ingroup doublePTcomputational
   90: *
   91: *  =====================================================================
   92:       SUBROUTINE DPTTRF( N, D, E, INFO )
   93: *
   94: *  -- LAPACK computational routine (version 3.4.2) --
   95: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
   96: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
   97: *     September 2012
   98: *
   99: *     .. Scalar Arguments ..
  100:       INTEGER            INFO, N
  101: *     ..
  102: *     .. Array Arguments ..
  103:       DOUBLE PRECISION   D( * ), E( * )
  104: *     ..
  105: *
  106: *  =====================================================================
  107: *
  108: *     .. Parameters ..
  109:       DOUBLE PRECISION   ZERO
  110:       PARAMETER          ( ZERO = 0.0D+0 )
  111: *     ..
  112: *     .. Local Scalars ..
  113:       INTEGER            I, I4
  114:       DOUBLE PRECISION   EI
  115: *     ..
  116: *     .. External Subroutines ..
  117:       EXTERNAL           XERBLA
  118: *     ..
  119: *     .. Intrinsic Functions ..
  120:       INTRINSIC          MOD
  121: *     ..
  122: *     .. Executable Statements ..
  123: *
  124: *     Test the input parameters.
  125: *
  126:       INFO = 0
  127:       IF( N.LT.0 ) THEN
  128:          INFO = -1
  129:          CALL XERBLA( 'DPTTRF', -INFO )
  130:          RETURN
  131:       END IF
  132: *
  133: *     Quick return if possible
  134: *
  135:       IF( N.EQ.0 )
  136:      $   RETURN
  137: *
  138: *     Compute the L*D*L**T (or U**T*D*U) factorization of A.
  139: *
  140:       I4 = MOD( N-1, 4 )
  141:       DO 10 I = 1, I4
  142:          IF( D( I ).LE.ZERO ) THEN
  143:             INFO = I
  144:             GO TO 30
  145:          END IF
  146:          EI = E( I )
  147:          E( I ) = EI / D( I )
  148:          D( I+1 ) = D( I+1 ) - E( I )*EI
  149:    10 CONTINUE
  150: *
  151:       DO 20 I = I4 + 1, N - 4, 4
  152: *
  153: *        Drop out of the loop if d(i) <= 0: the matrix is not positive
  154: *        definite.
  155: *
  156:          IF( D( I ).LE.ZERO ) THEN
  157:             INFO = I
  158:             GO TO 30
  159:          END IF
  160: *
  161: *        Solve for e(i) and d(i+1).
  162: *
  163:          EI = E( I )
  164:          E( I ) = EI / D( I )
  165:          D( I+1 ) = D( I+1 ) - E( I )*EI
  166: *
  167:          IF( D( I+1 ).LE.ZERO ) THEN
  168:             INFO = I + 1
  169:             GO TO 30
  170:          END IF
  171: *
  172: *        Solve for e(i+1) and d(i+2).
  173: *
  174:          EI = E( I+1 )
  175:          E( I+1 ) = EI / D( I+1 )
  176:          D( I+2 ) = D( I+2 ) - E( I+1 )*EI
  177: *
  178:          IF( D( I+2 ).LE.ZERO ) THEN
  179:             INFO = I + 2
  180:             GO TO 30
  181:          END IF
  182: *
  183: *        Solve for e(i+2) and d(i+3).
  184: *
  185:          EI = E( I+2 )
  186:          E( I+2 ) = EI / D( I+2 )
  187:          D( I+3 ) = D( I+3 ) - E( I+2 )*EI
  188: *
  189:          IF( D( I+3 ).LE.ZERO ) THEN
  190:             INFO = I + 3
  191:             GO TO 30
  192:          END IF
  193: *
  194: *        Solve for e(i+3) and d(i+4).
  195: *
  196:          EI = E( I+3 )
  197:          E( I+3 ) = EI / D( I+3 )
  198:          D( I+4 ) = D( I+4 ) - E( I+3 )*EI
  199:    20 CONTINUE
  200: *
  201: *     Check d(n) for positive definiteness.
  202: *
  203:       IF( D( N ).LE.ZERO )
  204:      $   INFO = N
  205: *
  206:    30 CONTINUE
  207:       RETURN
  208: *
  209: *     End of DPTTRF
  210: *
  211:       END