PDTRTRS(3) ScaLAPACK routine of NEC Numeric Library Collection PDTRTRS(3)
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 routine 31 October 2017 PDTRTRS(3)