SUBROUTINE PSPOTRI( UPLO, N, A, IA, JA, DESCA, INFO )
*
*  -- ScaLAPACK routine (version 1.7) --
*     University of Tennessee, Knoxville, Oak Ridge National Laboratory,
*     and University of California, Berkeley.
*     May 1, 1997
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            IA, INFO, JA, N
*     ..
*     .. Array Arguments ..
      INTEGER            DESCA( * )
      REAL               A( * )
*     ..
*
*  Purpose
*  =======
*
*  PSPOTRI computes the inverse of a real symmetric positive definite
*  distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1) using the
*  Cholesky factorization sub( A ) = U**T*U or L*L**T computed by
*  PSPOTRF.
*
*  Notes
*  =====
*
*  Each global data object is described by an associated description
*  vector.  This vector stores the information required to establish
*  the mapping between an object element and its corresponding process
*  and memory location.
*
*  Let A be a generic term for any 2D block cyclicly distributed array.
*  Such a global array has an associated description vector DESCA.
*  In the following comments, the character _ should be read as
*  "of the global array".
*
*  NOTATION        STORED IN      EXPLANATION
*  --------------- -------------- --------------------------------------
*  DTYPE_A(global) DESCA( DTYPE_ )The descriptor type.  In this case,
*                                 DTYPE_A = 1.
*  CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
*                                 the BLACS process grid A is distribu-
*                                 ted over. The context itself is glo-
*                                 bal, but the handle (the integer
*                                 value) may vary.
*  M_A    (global) DESCA( M_ )    The number of rows in the global
*                                 array A.
*  N_A    (global) DESCA( N_ )    The number of columns in the global
*                                 array A.
*  MB_A   (global) DESCA( MB_ )   The blocking factor used to distribute
*                                 the rows of the array.
*  NB_A   (global) DESCA( NB_ )   The blocking factor used to distribute
*                                 the columns of the array.
*  RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
*                                 row of the array A is distributed.
*  CSRC_A (global) DESCA( CSRC_ ) The process column over which the
*                                 first column of the array A is
*                                 distributed.
*  LLD_A  (local)  DESCA( LLD_ )  The leading dimension of the local
*                                 array.  LLD_A >= MAX(1,LOCr(M_A)).
*
*  Let K be the number of rows or columns of a distributed matrix,
*  and assume that its process grid has dimension p x q.
*  LOCr( K ) denotes the number of elements of K that a process
*  would receive if K were distributed over the p processes of its
*  process column.
*  Similarly, LOCc( K ) denotes the number of elements of K that a
*  process would receive if K were distributed over the q processes of
*  its process row.
*  The values of LOCr() and LOCc() may be determined via a call to the
*  ScaLAPACK tool function, NUMROC:
*          LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
*          LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
*  An upper bound for these quantities may be computed by:
*          LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
*          LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
*
*  Arguments
*  =========
*
*  UPLO    (global input) CHARACTER*1
*          = 'U':  Upper triangle of sub( A ) is stored;
*          = 'L':  Lower triangle of sub( A ) is stored.
*
*  N       (global input) INTEGER
*          The number of rows and columns to be operated on, i.e. the
*          order of the distributed submatrix sub( A ). N >= 0.
*
*  A       (local input/local output) REAL pointer into the
*          local memory to an array of dimension (LLD_A, LOCc(JA+N-1)).
*          On entry, the local pieces of the triangular factor U or L
*          from the Cholesky factorization of the distributed matrix
*          sub( A ) = U**T*U or  L*L**T, as computed by PSPOTRF.
*          On exit, the local pieces of the upper or lower triangle of
*          the (symmetric) inverse of sub( A ), overwriting the input
*          factor U or L.
*
*  IA      (global input) INTEGER
*          The row index in the global array A indicating the first
*          row of sub( A ).
*
*  JA      (global input) INTEGER
*          The column index in the global array A indicating the
*          first column of sub( A ).
*
*  DESCA   (global and local input) INTEGER array of dimension DLEN_.
*          The array descriptor for the distributed matrix A.
*
*  INFO    (global output) INTEGER
*          = 0:  successful exit
*          < 0:  If the i-th argument is an array and the j-entry had
*                an illegal value, then INFO = -(i*100+j), if the i-th
*                argument is a scalar and had an illegal value, then
*                INFO = -i.
*          > 0:  If INFO = i, the (i,i) element of the factor U or L is
*                zero, and the inverse could not be computed.
*
*  =====================================================================
*
*     .. Parameters ..
      INTEGER            BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
     $                   LLD_, MB_, M_, NB_, N_, RSRC_
      PARAMETER          ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1,
     $                     CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6,
     $                     RSRC_ = 7, CSRC_ = 8, LLD_ = 9 )
*     ..
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            ICOFF, ICTXT, IROFF, MYCOL, MYROW, NPCOL, NPROW
*     ..
*     .. Local Arrays ..
      INTEGER            IDUM1( 1 ), IDUM2( 1 )
*     ..
*     .. External Subroutines ..
      EXTERNAL           BLACS_GRIDINFO, CHK1MAT, PCHK1MAT, PSLAUUM,
     $                   PSTRTRI, PXERBLA
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ICHAR, MOD
*     ..
*     .. Executable Statements ..
*
*     Get grid parameters
*
      ICTXT = DESCA( CTXT_ )
      CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
*
*     Test the input parameters
*
      INFO = 0
      IF( NPROW.EQ.-1 ) THEN
         INFO = -(600+CTXT_)
      ELSE
         UPPER = LSAME( UPLO, 'U' )
         CALL CHK1MAT( N, 2, N, 2, IA, JA, DESCA, 6, INFO )
         IF( INFO.NE.0 ) THEN
            IROFF = MOD( IA-1, DESCA( MB_ ) )
            ICOFF = MOD( JA-1, DESCA( NB_ ) )
            IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
               INFO = -1
            ELSE IF( IROFF.NE.ICOFF .OR. IROFF.NE.0 ) THEN
               INFO = -5
            ELSE IF( DESCA( MB_ ).NE.DESCA( NB_ ) ) THEN
               INFO = -(600+NB_)
            END IF
         END IF
*
         IF( UPPER ) THEN
            IDUM1( 1 ) = ICHAR( 'U' )
         ELSE
            IDUM1( 1 ) = ICHAR( 'L' )
         END IF
         IDUM2( 1 ) = 1
         CALL PCHK1MAT( N, 2, N, 2, IA, JA, DESCA, 6, 1, IDUM1, IDUM2,
     $                  INFO )
      END IF
*
      IF( INFO.NE.0 ) THEN
         CALL PXERBLA( ICTXT, 'PSPOTRI', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 )
     $   RETURN
*
*     Invert the triangular Cholesky factor U or L.
*
      CALL PSTRTRI( UPLO, 'Non-unit', N, A, IA, JA, DESCA, INFO )
*
      IF( INFO.GT.0 )
     $   RETURN
*
*     Form inv(U)*inv(U)' or inv(L)'*inv(L).
*
      CALL PSLAUUM( UPLO, N, A, IA, JA, DESCA )
*
      RETURN
*
*     End of PSPOTRI
*
      END