PDTRTRS(l) ) PDTRTRS(l)NAME
PDTRTRS - solve a triangular system of the form sub( A ) * X = sub( B
) or sub( A )**T * X = sub( B ),
SYNOPSIS
SUBROUTINE PDTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, IA, JA, DESCA, B,
IB, JB, DESCB, INFO )
CHARACTER DIAG, TRANS, UPLO
INTEGER IA, IB, INFO, JA, JB, N, NRHS
INTEGER DESCA( * ), DESCB( * )
DOUBLE PRECISION A( * ), B( * )
PURPOSE
PDTRTRS solves a triangular system of the form sub( A ) * X = sub( B )
or sub( A )**T * X = sub( B ), where sub( A ) denotes
A(IA:IA+N-1,JA:JA+N-1) and is a triangular distributed matrix of order
N, and B(IB:IB+N-1,JB:JB+NRHS-1) is an N-by-NRHS distributed matrix
denoted by sub( B ). A check is made to verify that sub( A ) is nonsin‐
gular.
Notes
=====
Each global data object is described by an associated description vec‐
tor. This vector stores the information required to establish the map‐
ping 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
UPLO (global input) CHARACTER
= 'U': sub( A ) is upper triangular;
= 'L': sub( A ) is lower triangular.
TRANS (global input) CHARACTER
Specifies the form of the system of equations:
= 'N': Solve sub( A ) * X = sub( B ) (No transpose)
= 'T': Solve sub( A )**T * X = sub( B ) (Transpose)
= 'C': Solve sub( A )**T * X = sub( B ) (Transpose)
DIAG (global input) CHARACTER
= 'N': sub( A ) is non-unit triangular;
= 'U': sub( A ) is 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.
NRHS (global input) INTEGER
The number of right hand sides, i.e., the number of columns of
the distributed matrix sub( B ). NRHS >= 0.
A (local input) DOUBLE PRECISION pointer into the local memory
to an array of dimension (LLD_A,LOCc(JA+N-1) ). This array con‐
tains the local pieces of the distributed triangular matrix
sub( A ). If UPLO = 'U', the leading N-by-N upper triangular
part of 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 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.
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.
B (local input/local output) DOUBLE PRECISION pointer into the
local memory to an array of dimension (LLD_B,LOCc(JB+NRHS-1)).
On entry, this array contains the local pieces of the right
hand side distributed matrix sub( B ). On exit, if INFO = 0,
sub( B ) is overwritten by the solution matrix X.
IB (global input) INTEGER
The row index in the global array B indicating the first row of
sub( B ).
JB (global input) INTEGER
The column index in the global array B indicating the first
column of sub( B ).
DESCB (global and local input) INTEGER array of dimension DLEN_.
The array descriptor for the distributed matrix B.
INFO (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-th diagonal element of sub( A ) is zero, indi‐
cating that the submatrix is singular and the solutions X have
not been computed.
ScaLAPACK version 1.7 13 August 2001 PDTRTRS(l)
