PZGETRI(l)						   LAPACK routine (version 1.5) 						PZGETRI(l)

NAME

       PZGETRI - compute the inverse of a distributed matrix using the LU factorization computed by PZGETRF

SYNOPSIS

       SUBROUTINE PZGETRI( N, A, IA, JA, DESCA, IPIV, WORK, LWORK, IWORK, LIWORK, INFO )

	   INTEGER	   IA, INFO, JA, LIWORK, LWORK, N

	   INTEGER	   DESCA( * ), IPIV( * ), IWORK( * )

	   COMPLEX*16	   A( * ), WORK( * )

PURPOSE

       PZGETRI	computes  the  inverse of a distributed matrix using the LU factorization computed by PZGETRF. This method inverts U and then com-
       putes the inverse of sub( A ) = A(IA:IA+N-1,JA:JA+N-1) denoted InvA by solving the system InvA*L = inv(U) for InvA.

       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  col-
       umn.
       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

       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) COMPLEX*16 pointer into the
	       local memory to an array of dimension (LLD_A,LOCc(JA+N-1)).  On entry, the local pieces of the L and U obtained by  the	factoriza-
	       tion  sub(  A ) = P*L*U computed by PZGETRF. On exit, if INFO = 0, sub( A ) contains the inverse of the original distributed matrix
	       sub( A ).

       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.

       IPIV    (local input) INTEGER array, dimension LOCr(M_A)+MB_A
	       keeps track of the pivoting information. IPIV(i) is the global row index the local row i was swapped with.  This array is  tied	to
	       the distributed matrix A.

       WORK    (local workspace/local output) COMPLEX*16 array,
	       dimension (LWORK) On exit, WORK(1) returns the minimal and optimal LWORK.

       LWORK   (local or global input) INTEGER
	       The  dimension  of  the array WORK.  LWORK is local input and must be at least LWORK = LOCr(N+MOD(IA-1,MB_A))*NB_A. WORK is used to
	       keep a copy of at most an entire column block of sub( A ).

	       If LWORK = -1, then LWORK is global input and a workspace query is assumed; the routine only calculates	the  minimum  and  optimal
	       size for all work arrays. Each of these values is returned in the first entry of the corresponding work array, and no error message
	       is issued by PXERBLA.

       IWORK   (local workspace/local output) INTEGER array,
	       dimension (LIWORK) On exit, IWORK(1) returns the minimal and optimal LIWORK.

       LIWORK  (local or global input) INTEGER
	       The dimension of the array IWORK used as workspace for physically transposing the pivots.  LIWORK is local input  and  must  be	at
	       least  if  NPROW  ==  NPCOL then LIWORK = LOCc( N_A + MOD(JA-1, NB_A) ) + NB_A, else LIWORK =  LOCc( N_A + MOD(JA-1, NB_A) ) + MAX(
	       CEIL(CEIL(LOCr(M_A)/MB_A)/(LCM/NPROW)), NB_A ) where LCM is the least common multiple  of  process  rows  and  columns  (NPROW  and
	       NPCOL).	end if

	       If  LIWORK  = -1, then LIWORK is global input and a workspace query is assumed; the routine only calculates the minimum and optimal
	       size for all work arrays. Each of these values is returned in the first entry of the corresponding work array, and no error message
	       is issued by PXERBLA.

       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 = K, U(IA+K-1,IA+K-1) is exactly zero; the matrix is  singular  and
	       its inverse could not be computed.

LAPACK version 1.5						    12 May 1997 							PZGETRI(l)