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

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 )**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 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) 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, indicating that the submatrix is singular and the solutions X have not been computed.