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    1: *> \brief \b DPOTRI
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at 
    6: *            http://www.netlib.org/lapack/explore-html/ 
    7: *
    8: *> \htmlonly
    9: *> Download DPOTRI + dependencies 
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpotri.f"> 
   11: *> [TGZ]</a> 
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpotri.f"> 
   13: *> [ZIP]</a> 
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpotri.f"> 
   15: *> [TXT]</a>
   16: *> \endhtmlonly 
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE DPOTRI( 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: *> DPOTRI computes the inverse of a real symmetric positive definite
   38: *> matrix A using the Cholesky factorization A = U**T*U or A = L*L**T
   39: *> computed by DPOTRF.
   40: *> \endverbatim
   41: *
   42: *  Arguments:
   43: *  ==========
   44: *
   45: *> \param[in] UPLO
   46: *> \verbatim
   47: *>          UPLO is CHARACTER*1
   48: *>          = 'U':  Upper triangle of A is stored;
   49: *>          = 'L':  Lower triangle of A is stored.
   50: *> \endverbatim
   51: *>
   52: *> \param[in] N
   53: *> \verbatim
   54: *>          N is INTEGER
   55: *>          The order of the matrix A.  N >= 0.
   56: *> \endverbatim
   57: *>
   58: *> \param[in,out] A
   59: *> \verbatim
   60: *>          A is DOUBLE PRECISION array, dimension (LDA,N)
   61: *>          On entry, the triangular factor U or L from the Cholesky
   62: *>          factorization A = U**T*U or A = L*L**T, as computed by
   63: *>          DPOTRF.
   64: *>          On exit, the upper or lower triangle of the (symmetric)
   65: *>          inverse of A, overwriting the input factor U or L.
   66: *> \endverbatim
   67: *>
   68: *> \param[in] LDA
   69: *> \verbatim
   70: *>          LDA is INTEGER
   71: *>          The leading dimension of the array A.  LDA >= max(1,N).
   72: *> \endverbatim
   73: *>
   74: *> \param[out] INFO
   75: *> \verbatim
   76: *>          INFO is INTEGER
   77: *>          = 0:  successful exit
   78: *>          < 0:  if INFO = -i, the i-th argument had an illegal value
   79: *>          > 0:  if INFO = i, the (i,i) element of the factor U or L is
   80: *>                zero, and the inverse could not be computed.
   81: *> \endverbatim
   82: *
   83: *  Authors:
   84: *  ========
   85: *
   86: *> \author Univ. of Tennessee 
   87: *> \author Univ. of California Berkeley 
   88: *> \author Univ. of Colorado Denver 
   89: *> \author NAG Ltd. 
   90: *
   91: *> \date November 2011
   92: *
   93: *> \ingroup doublePOcomputational
   94: *
   95: *  =====================================================================
   96:       SUBROUTINE DPOTRI( UPLO, N, A, LDA, INFO )
   97: *
   98: *  -- LAPACK computational routine (version 3.4.0) --
   99: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  100: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  101: *     November 2011
  102: *
  103: *     .. Scalar Arguments ..
  104:       CHARACTER          UPLO
  105:       INTEGER            INFO, LDA, N
  106: *     ..
  107: *     .. Array Arguments ..
  108:       DOUBLE PRECISION   A( LDA, * )
  109: *     ..
  110: *
  111: *  =====================================================================
  112: *
  113: *     .. External Functions ..
  114:       LOGICAL            LSAME
  115:       EXTERNAL           LSAME
  116: *     ..
  117: *     .. External Subroutines ..
  118:       EXTERNAL           DLAUUM, DTRTRI, XERBLA
  119: *     ..
  120: *     .. Intrinsic Functions ..
  121:       INTRINSIC          MAX
  122: *     ..
  123: *     .. Executable Statements ..
  124: *
  125: *     Test the input parameters.
  126: *
  127:       INFO = 0
  128:       IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
  129:          INFO = -1
  130:       ELSE IF( N.LT.0 ) THEN
  131:          INFO = -2
  132:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
  133:          INFO = -4
  134:       END IF
  135:       IF( INFO.NE.0 ) THEN
  136:          CALL XERBLA( 'DPOTRI', -INFO )
  137:          RETURN
  138:       END IF
  139: *
  140: *     Quick return if possible
  141: *
  142:       IF( N.EQ.0 )
  143:      $   RETURN
  144: *
  145: *     Invert the triangular Cholesky factor U or L.
  146: *
  147:       CALL DTRTRI( UPLO, 'Non-unit', N, A, LDA, INFO )
  148:       IF( INFO.GT.0 )
  149:      $   RETURN
  150: *
  151: *     Form inv(U) * inv(U)**T or inv(L)**T * inv(L).
  152: *
  153:       CALL DLAUUM( UPLO, N, A, LDA, INFO )
  154: *
  155:       RETURN
  156: *
  157: *     End of DPOTRI
  158: *
  159:       END