NAME
PDTRTRI - compute the inverse of a upper or lower triangular
distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1)
SYNOPSIS
SUBROUTINE PDTRTRI( UPLO, DIAG, N, A, IA, JA, DESCA, INFO )
CHARACTER DIAG, UPLO
INTEGER IA, INFO, JA, N
INTEGER DESCA( * )
DOUBLE PRECISION A( * )
PURPOSE
PDTRTRI computes the inverse of a upper or lower triangular distributed
matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1).
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
Specifies whether the distributed matrix sub( A ) is upper or
lower triangular:
= ’U’: Upper triangular,
= ’L’: Lower triangular.
DIAG (global input) CHARACTER
Specifies whether or not the distributed matrix sub( A ) is
unit triangular:
= ’N’: Non-unit triangular,
= ’U’: Unit triangular.
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) DOUBLE PRECISION pointer into the
local memory to an array of dimension (LLD_A,LOCc(JA+N-1)). On
entry, 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 to be inverted, 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. On exit, the
(triangular) inverse of the original matrix.
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 = K, A(IA+K-1,JA+K-1) is exactly zero. The triangular
matrix sub( A ) is singular and its inverse can not be
computed.