PSPOTRI - compute 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

- SUBROUTINE PSPOTRI(
- UPLO, N, A, IA, JA, DESCA, INFO )

CHARACTER UPLO INTEGER IA, INFO, JA, N INTEGER DESCA( * ) REAL A( * )

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

- 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.