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    1: *> \brief \b DPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (unblocked algorithm).
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at
    6: *            http://www.netlib.org/lapack/explore-html/
    7: *
    8: *> \htmlonly
    9: *> Download DPOTF2 + dependencies
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpotf2.f">
   11: *> [TGZ]</a>
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpotf2.f">
   13: *> [ZIP]</a>
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpotf2.f">
   15: *> [TXT]</a>
   16: *> \endhtmlonly
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE DPOTF2( UPLO, N, A, LDA, INFO )
   22: *
   23: *       .. Scalar Arguments ..
   24: *       CHARACTER          UPLO
   25: *       INTEGER            INFO, LDA, N
   26: *       ..
   27: *       .. Array Arguments ..
   28: *       DOUBLE PRECISION   A( LDA, * )
   29: *       ..
   30: *
   31: *
   32: *> \par Purpose:
   33: *  =============
   34: *>
   35: *> \verbatim
   36: *>
   37: *> DPOTF2 computes the Cholesky factorization of a real symmetric
   38: *> positive definite matrix A.
   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: *>
   45: *> This is the unblocked version of the algorithm, calling Level 2 BLAS.
   46: *> \endverbatim
   47: *
   48: *  Arguments:
   49: *  ==========
   50: *
   51: *> \param[in] UPLO
   52: *> \verbatim
   53: *>          UPLO is CHARACTER*1
   54: *>          Specifies whether the upper or lower triangular part of the
   55: *>          symmetric matrix A is stored.
   56: *>          = 'U':  Upper triangular
   57: *>          = 'L':  Lower triangular
   58: *> \endverbatim
   59: *>
   60: *> \param[in] N
   61: *> \verbatim
   62: *>          N is INTEGER
   63: *>          The order of the matrix A.  N >= 0.
   64: *> \endverbatim
   65: *>
   66: *> \param[in,out] A
   67: *> \verbatim
   68: *>          A is DOUBLE PRECISION array, dimension (LDA,N)
   69: *>          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
   70: *>          n by n upper triangular part of A contains the upper
   71: *>          triangular part of the matrix A, and the strictly lower
   72: *>          triangular part of A is not referenced.  If UPLO = 'L', the
   73: *>          leading n by n lower triangular part of A contains the lower
   74: *>          triangular part of the matrix A, and the strictly upper
   75: *>          triangular part of A is not referenced.
   76: *>
   77: *>          On exit, if INFO = 0, the factor U or L from the Cholesky
   78: *>          factorization A = U**T *U  or A = L*L**T.
   79: *> \endverbatim
   80: *>
   81: *> \param[in] LDA
   82: *> \verbatim
   83: *>          LDA is INTEGER
   84: *>          The leading dimension of the array A.  LDA >= max(1,N).
   85: *> \endverbatim
   86: *>
   87: *> \param[out] INFO
   88: *> \verbatim
   89: *>          INFO is INTEGER
   90: *>          = 0: successful exit
   91: *>          < 0: if INFO = -k, the k-th argument had an illegal value
   92: *>          > 0: if INFO = k, the leading minor of order k is not
   93: *>               positive definite, and the factorization could not be
   94: *>               completed.
   95: *> \endverbatim
   96: *
   97: *  Authors:
   98: *  ========
   99: *
  100: *> \author Univ. of Tennessee
  101: *> \author Univ. of California Berkeley
  102: *> \author Univ. of Colorado Denver
  103: *> \author NAG Ltd.
  104: *
  105: *> \ingroup doublePOcomputational
  106: *
  107: *  =====================================================================
  108:       SUBROUTINE DPOTF2( UPLO, N, A, LDA, INFO )
  109: *
  110: *  -- LAPACK computational routine --
  111: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  112: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  113: *
  114: *     .. Scalar Arguments ..
  115:       CHARACTER          UPLO
  116:       INTEGER            INFO, LDA, N
  117: *     ..
  118: *     .. Array Arguments ..
  119:       DOUBLE PRECISION   A( LDA, * )
  120: *     ..
  121: *
  122: *  =====================================================================
  123: *
  124: *     .. Parameters ..
  125:       DOUBLE PRECISION   ONE, ZERO
  126:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
  127: *     ..
  128: *     .. Local Scalars ..
  129:       LOGICAL            UPPER
  130:       INTEGER            J
  131:       DOUBLE PRECISION   AJJ
  132: *     ..
  133: *     .. External Functions ..
  134:       LOGICAL            LSAME, DISNAN
  135:       DOUBLE PRECISION   DDOT
  136:       EXTERNAL           LSAME, DDOT, DISNAN
  137: *     ..
  138: *     .. External Subroutines ..
  139:       EXTERNAL           DGEMV, DSCAL, XERBLA
  140: *     ..
  141: *     .. Intrinsic Functions ..
  142:       INTRINSIC          MAX, SQRT
  143: *     ..
  144: *     .. Executable Statements ..
  145: *
  146: *     Test the input parameters.
  147: *
  148:       INFO = 0
  149:       UPPER = LSAME( UPLO, 'U' )
  150:       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
  151:          INFO = -1
  152:       ELSE IF( N.LT.0 ) THEN
  153:          INFO = -2
  154:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
  155:          INFO = -4
  156:       END IF
  157:       IF( INFO.NE.0 ) THEN
  158:          CALL XERBLA( 'DPOTF2', -INFO )
  159:          RETURN
  160:       END IF
  161: *
  162: *     Quick return if possible
  163: *
  164:       IF( N.EQ.0 )
  165:      $   RETURN
  166: *
  167:       IF( UPPER ) THEN
  168: *
  169: *        Compute the Cholesky factorization A = U**T *U.
  170: *
  171:          DO 10 J = 1, N
  172: *
  173: *           Compute U(J,J) and test for non-positive-definiteness.
  174: *
  175:             AJJ = A( J, J ) - DDOT( J-1, A( 1, J ), 1, A( 1, J ), 1 )
  176:             IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN
  177:                A( J, J ) = AJJ
  178:                GO TO 30
  179:             END IF
  180:             AJJ = SQRT( AJJ )
  181:             A( J, J ) = AJJ
  182: *
  183: *           Compute elements J+1:N of row J.
  184: *
  185:             IF( J.LT.N ) THEN
  186:                CALL DGEMV( 'Transpose', J-1, N-J, -ONE, A( 1, J+1 ),
  187:      $                     LDA, A( 1, J ), 1, ONE, A( J, J+1 ), LDA )
  188:                CALL DSCAL( N-J, ONE / AJJ, A( J, J+1 ), LDA )
  189:             END IF
  190:    10    CONTINUE
  191:       ELSE
  192: *
  193: *        Compute the Cholesky factorization A = L*L**T.
  194: *
  195:          DO 20 J = 1, N
  196: *
  197: *           Compute L(J,J) and test for non-positive-definiteness.
  198: *
  199:             AJJ = A( J, J ) - DDOT( J-1, A( J, 1 ), LDA, A( J, 1 ),
  200:      $            LDA )
  201:             IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN
  202:                A( J, J ) = AJJ
  203:                GO TO 30
  204:             END IF
  205:             AJJ = SQRT( AJJ )
  206:             A( J, J ) = AJJ
  207: *
  208: *           Compute elements J+1:N of column J.
  209: *
  210:             IF( J.LT.N ) THEN
  211:                CALL DGEMV( 'No transpose', N-J, J-1, -ONE, A( J+1, 1 ),
  212:      $                     LDA, A( J, 1 ), LDA, ONE, A( J+1, J ), 1 )
  213:                CALL DSCAL( N-J, ONE / AJJ, A( J+1, J ), 1 )
  214:             END IF
  215:    20    CONTINUE
  216:       END IF
  217:       GO TO 40
  218: *
  219:    30 CONTINUE
  220:       INFO = J
  221: *
  222:    40 CONTINUE
  223:       RETURN
  224: *
  225: *     End of DPOTF2
  226: *
  227:       END