.TH PSTRTI2 l "12 May 1997" "LAPACK version 1.5" "LAPACK routine (version 1.5)"
.SH NAME
PSTRTI2 - compute the inverse of a real upper or lower triangular block matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1)
.SH SYNOPSIS
.TP 20
SUBROUTINE PSTRTI2(
UPLO, DIAG, N, A, IA, JA, DESCA, INFO )
.TP 20
.ti +4
CHARACTER
DIAG, UPLO
.TP 20
.ti +4
INTEGER
IA, INFO, JA, N
.TP 20
.ti +4
INTEGER
DESCA( * )
.TP 20
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REAL
A( * )
.SH PURPOSE
PSTRTI2 computes the inverse of a real upper or lower triangular
block matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1). This matrix should be
contained in one and only one process memory space (local operation).

Notes
.br
=====
.br

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.
.br

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".
.br

NOTATION        STORED IN      EXPLANATION
.br
--------------- -------------- --------------------------------------
DTYPE_A(global) DESCA( DTYPE_ )The descriptor type.  In this case,
                               DTYPE_A = 1.
.br
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.
.br
M_A    (global) DESCA( M_ )    The number of rows in the global
                               array A.
.br
N_A    (global) DESCA( N_ )    The number of columns in the global
                               array A.
.br
MB_A   (global) DESCA( MB_ )   The blocking factor used to distribute
                               the rows of the array.
.br
NB_A   (global) DESCA( NB_ )   The blocking factor used to distribute
                               the columns of the array.
.br
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.
.br
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.
.br
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.
.br
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.
.br
The values of LOCr() and LOCc() may be determined via a call to the
ScaLAPACK tool function, NUMROC:
.br
        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:
.br
        LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
.br
        LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
.br

.SH ARGUMENTS
.TP 8
UPLO    (global input) CHARACTER*1
= 'U':  sub( A ) is upper triangular;
.br
= 'L':  sub( A ) is lower triangular.
.TP 8
DIAG    (global input) CHARACTER*1
.br
= 'N':  sub( A ) is non-unit triangular
.br
= 'U':  sub( A ) is unit triangular
.TP 8
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.
.TP 8
A       (local input/local output) REAL pointer into the
local memory to an array of dimension (LLD_A,LOCc(JA+N-1)),
this array contains the local pieces of the triangular matrix
sub( A ). If UPLO = 'U', the leading N-by-N upper triangular
part of the matrix sub( A ) contains the upper triangular
matrix, and the strictly lower triangular part of sub( A )
is not referenced.  If UPLO = 'L', the leading N-by-N lower
triangular part of the matrix sub( A ) contains the lower
triangular matrix, and the strictly upper triangular part
of sub( A ) is not referenced. If DIAG = 'U', the diagonal
elements of sub( A ) are also not referenced and are assumed
to be 1.  On exit, the (triangular) inverse of the original
matrix, in the same storage format.
.TP 8
IA      (global input) INTEGER
The row index in the global array A indicating the first
row of sub( A ).
.TP 8
JA      (global input) INTEGER
The column index in the global array A indicating the
first column of sub( A ).
.TP 8
DESCA   (global and local input) INTEGER array of dimension DLEN_.
The array descriptor for the distributed matrix A.
.TP 8
INFO    (local output) INTEGER
= 0:  successful exit
.br
< 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.
