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Man Pages


Manual Reference Pages  -  PCTRTRS (l)

NAME

PCTRTRS - solve a triangular system of the form sub( A ) * X = sub( B ) or sub( A )**T * X = sub( B ) or sub( A )**H * X = sub( B ),

CONTENTS

Synopsis
Purpose
Arguments

SYNOPSIS

SUBROUTINE PCTRTRS( 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( * )
    COMPLEX A( * ), B( * )

PURPOSE

PCTRTRS solves a triangular system of the form sub( A ) * X = sub( B ) or sub( A )**T * X = sub( B ) or sub( A )**H * 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 nonsingular.

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
  = ’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 )**H * X = sub( B ) (Conjugate 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) COMPLEX pointer into the local memory
  to an array of dimension (LLD_A,LOCc(JA+N-1) ). This array contains 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) COMPLEX 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, indicating that the submatrix is singular and the solutions X have not been computed.
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ScaLAPACK version 1.7 PCTRTRS (l) 13 August 2001

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