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    1:       SUBROUTINE DPOTRI( UPLO, N, A, LDA, INFO )
    2: *
    3: *  -- LAPACK routine (version 3.2) --
    4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    6: *     November 2006
    7: *
    8: *     .. Scalar Arguments ..
    9:       CHARACTER          UPLO
   10:       INTEGER            INFO, LDA, N
   11: *     ..
   12: *     .. Array Arguments ..
   13:       DOUBLE PRECISION   A( LDA, * )
   14: *     ..
   15: *
   16: *  Purpose
   17: *  =======
   18: *
   19: *  DPOTRI computes the inverse of a real symmetric positive definite
   20: *  matrix A using the Cholesky factorization A = U**T*U or A = L*L**T
   21: *  computed by DPOTRF.
   22: *
   23: *  Arguments
   24: *  =========
   25: *
   26: *  UPLO    (input) CHARACTER*1
   27: *          = 'U':  Upper triangle of A is stored;
   28: *          = 'L':  Lower triangle of A is stored.
   29: *
   30: *  N       (input) INTEGER
   31: *          The order of the matrix A.  N >= 0.
   32: *
   33: *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
   34: *          On entry, the triangular factor U or L from the Cholesky
   35: *          factorization A = U**T*U or A = L*L**T, as computed by
   36: *          DPOTRF.
   37: *          On exit, the upper or lower triangle of the (symmetric)
   38: *          inverse of A, overwriting the input factor U or L.
   39: *
   40: *  LDA     (input) INTEGER
   41: *          The leading dimension of the array A.  LDA >= max(1,N).
   42: *
   43: *  INFO    (output) INTEGER
   44: *          = 0:  successful exit
   45: *          < 0:  if INFO = -i, the i-th argument had an illegal value
   46: *          > 0:  if INFO = i, the (i,i) element of the factor U or L is
   47: *                zero, and the inverse could not be computed.
   48: *
   49: *  =====================================================================
   50: *
   51: *     .. External Functions ..
   52:       LOGICAL            LSAME
   53:       EXTERNAL           LSAME
   54: *     ..
   55: *     .. External Subroutines ..
   56:       EXTERNAL           DLAUUM, DTRTRI, XERBLA
   57: *     ..
   58: *     .. Intrinsic Functions ..
   59:       INTRINSIC          MAX
   60: *     ..
   61: *     .. Executable Statements ..
   62: *
   63: *     Test the input parameters.
   64: *
   65:       INFO = 0
   66:       IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
   67:          INFO = -1
   68:       ELSE IF( N.LT.0 ) THEN
   69:          INFO = -2
   70:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
   71:          INFO = -4
   72:       END IF
   73:       IF( INFO.NE.0 ) THEN
   74:          CALL XERBLA( 'DPOTRI', -INFO )
   75:          RETURN
   76:       END IF
   77: *
   78: *     Quick return if possible
   79: *
   80:       IF( N.EQ.0 )
   81:      $   RETURN
   82: *
   83: *     Invert the triangular Cholesky factor U or L.
   84: *
   85:       CALL DTRTRI( UPLO, 'Non-unit', N, A, LDA, INFO )
   86:       IF( INFO.GT.0 )
   87:      $   RETURN
   88: *
   89: *     Form inv(U)*inv(U)' or inv(L)'*inv(L).
   90: *
   91:       CALL DLAUUM( UPLO, N, A, LDA, INFO )
   92: *
   93:       RETURN
   94: *
   95: *     End of DPOTRI
   96: *
   97:       END