Return to dpptrf.f CVS log

Up to [local] / rpl / lapack / lapack

Cohérence

    1: *> \brief \b DPPTRF
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at 
    6: *            http://www.netlib.org/lapack/explore-html/ 
    7: *
    8: *> \htmlonly
    9: *> Download DPPTRF + dependencies 
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpptrf.f"> 
   11: *> [TGZ]</a> 
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpptrf.f"> 
   13: *> [ZIP]</a> 
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpptrf.f"> 
   15: *> [TXT]</a>
   16: *> \endhtmlonly 
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE DPPTRF( UPLO, N, AP, INFO )
   22: * 
   23: *       .. Scalar Arguments ..
   24: *       CHARACTER          UPLO
   25: *       INTEGER            INFO, N
   26: *       ..
   27: *       .. Array Arguments ..
   28: *       DOUBLE PRECISION   AP( * )
   29: *       ..
   30: *  
   31: *
   32: *> \par Purpose:
   33: *  =============
   34: *>
   35: *> \verbatim
   36: *>
   37: *> DPPTRF computes the Cholesky factorization of a real symmetric
   38: *> positive definite matrix A stored in packed format.
   39: *>
   40: *> The factorization has the form
   41: *>    A = U**T * U,  if UPLO = 'U', or
   42: *>    A = L  * L**T,  if UPLO = 'L',
   43: *> where U is an upper triangular matrix and L is lower triangular.
   44: *> \endverbatim
   45: *
   46: *  Arguments:
   47: *  ==========
   48: *
   49: *> \param[in] UPLO
   50: *> \verbatim
   51: *>          UPLO is CHARACTER*1
   52: *>          = 'U':  Upper triangle of A is stored;
   53: *>          = 'L':  Lower triangle of A is stored.
   54: *> \endverbatim
   55: *>
   56: *> \param[in] N
   57: *> \verbatim
   58: *>          N is INTEGER
   59: *>          The order of the matrix A.  N >= 0.
   60: *> \endverbatim
   61: *>
   62: *> \param[in,out] AP
   63: *> \verbatim
   64: *>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
   65: *>          On entry, the upper or lower triangle of the symmetric matrix
   66: *>          A, packed columnwise in a linear array.  The j-th column of A
   67: *>          is stored in the array AP as follows:
   68: *>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
   69: *>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
   70: *>          See below for further details.
   71: *>
   72: *>          On exit, if INFO = 0, the triangular factor U or L from the
   73: *>          Cholesky factorization A = U**T*U or A = L*L**T, in the same
   74: *>          storage format as A.
   75: *> \endverbatim
   76: *>
   77: *> \param[out] INFO
   78: *> \verbatim
   79: *>          INFO is INTEGER
   80: *>          = 0:  successful exit
   81: *>          < 0:  if INFO = -i, the i-th argument had an illegal value
   82: *>          > 0:  if INFO = i, the leading minor of order i is not
   83: *>                positive definite, and the factorization could not be
   84: *>                completed.
   85: *> \endverbatim
   86: *
   87: *  Authors:
   88: *  ========
   89: *
   90: *> \author Univ. of Tennessee 
   91: *> \author Univ. of California Berkeley 
   92: *> \author Univ. of Colorado Denver 
   93: *> \author NAG Ltd. 
   94: *
   95: *> \date November 2011
   96: *
   97: *> \ingroup doubleOTHERcomputational
   98: *
   99: *> \par Further Details:
  100: *  =====================
  101: *>
  102: *> \verbatim
  103: *>
  104: *>  The packed storage scheme is illustrated by the following example
  105: *>  when N = 4, UPLO = 'U':
  106: *>
  107: *>  Two-dimensional storage of the symmetric matrix A:
  108: *>
  109: *>     a11 a12 a13 a14
  110: *>         a22 a23 a24
  111: *>             a33 a34     (aij = aji)
  112: *>                 a44
  113: *>
  114: *>  Packed storage of the upper triangle of A:
  115: *>
  116: *>  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
  117: *> \endverbatim
  118: *>
  119: *  =====================================================================
  120:       SUBROUTINE DPPTRF( UPLO, N, AP, INFO )
  121: *
  122: *  -- LAPACK computational routine (version 3.4.0) --
  123: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  124: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  125: *     November 2011
  126: *
  127: *     .. Scalar Arguments ..
  128:       CHARACTER          UPLO
  129:       INTEGER            INFO, N
  130: *     ..
  131: *     .. Array Arguments ..
  132:       DOUBLE PRECISION   AP( * )
  133: *     ..
  134: *
  135: *  =====================================================================
  136: *
  137: *     .. Parameters ..
  138:       DOUBLE PRECISION   ONE, ZERO
  139:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
  140: *     ..
  141: *     .. Local Scalars ..
  142:       LOGICAL            UPPER
  143:       INTEGER            J, JC, JJ
  144:       DOUBLE PRECISION   AJJ
  145: *     ..
  146: *     .. External Functions ..
  147:       LOGICAL            LSAME
  148:       DOUBLE PRECISION   DDOT
  149:       EXTERNAL           LSAME, DDOT
  150: *     ..
  151: *     .. External Subroutines ..
  152:       EXTERNAL           DSCAL, DSPR, DTPSV, XERBLA
  153: *     ..
  154: *     .. Intrinsic Functions ..
  155:       INTRINSIC          SQRT
  156: *     ..
  157: *     .. Executable Statements ..
  158: *
  159: *     Test the input parameters.
  160: *
  161:       INFO = 0
  162:       UPPER = LSAME( UPLO, 'U' )
  163:       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
  164:          INFO = -1
  165:       ELSE IF( N.LT.0 ) THEN
  166:          INFO = -2
  167:       END IF
  168:       IF( INFO.NE.0 ) THEN
  169:          CALL XERBLA( 'DPPTRF', -INFO )
  170:          RETURN
  171:       END IF
  172: *
  173: *     Quick return if possible
  174: *
  175:       IF( N.EQ.0 )
  176:      $   RETURN
  177: *
  178:       IF( UPPER ) THEN
  179: *
  180: *        Compute the Cholesky factorization A = U**T*U.
  181: *
  182:          JJ = 0
  183:          DO 10 J = 1, N
  184:             JC = JJ + 1
  185:             JJ = JJ + J
  186: *
  187: *           Compute elements 1:J-1 of column J.
  188: *
  189:             IF( J.GT.1 )
  190:      $         CALL DTPSV( 'Upper', 'Transpose', 'Non-unit', J-1, AP,
  191:      $                     AP( JC ), 1 )
  192: *
  193: *           Compute U(J,J) and test for non-positive-definiteness.
  194: *
  195:             AJJ = AP( JJ ) - DDOT( J-1, AP( JC ), 1, AP( JC ), 1 )
  196:             IF( AJJ.LE.ZERO ) THEN
  197:                AP( JJ ) = AJJ
  198:                GO TO 30
  199:             END IF
  200:             AP( JJ ) = SQRT( AJJ )
  201:    10    CONTINUE
  202:       ELSE
  203: *
  204: *        Compute the Cholesky factorization A = L*L**T.
  205: *
  206:          JJ = 1
  207:          DO 20 J = 1, N
  208: *
  209: *           Compute L(J,J) and test for non-positive-definiteness.
  210: *
  211:             AJJ = AP( JJ )
  212:             IF( AJJ.LE.ZERO ) THEN
  213:                AP( JJ ) = AJJ
  214:                GO TO 30
  215:             END IF
  216:             AJJ = SQRT( AJJ )
  217:             AP( JJ ) = AJJ
  218: *
  219: *           Compute elements J+1:N of column J and update the trailing
  220: *           submatrix.
  221: *
  222:             IF( J.LT.N ) THEN
  223:                CALL DSCAL( N-J, ONE / AJJ, AP( JJ+1 ), 1 )
  224:                CALL DSPR( 'Lower', N-J, -ONE, AP( JJ+1 ), 1,
  225:      $                    AP( JJ+N-J+1 ) )
  226:                JJ = JJ + N - J + 1
  227:             END IF
  228:    20    CONTINUE
  229:       END IF
  230:       GO TO 40
  231: *
  232:    30 CONTINUE
  233:       INFO = J
  234: *
  235:    40 CONTINUE
  236:       RETURN
  237: *
  238: *     End of DPPTRF
  239: *
  240:       END