NAME
PSGESV - compute the solution to a real system of linear equations
sub( A ) * X = sub( B ),
SYNOPSIS
SUBROUTINE PSGESV( N, NRHS, A, IA, JA, DESCA, IPIV, B, IB, JB, DESCB,
INFO )
INTEGER IA, IB, INFO, JA, JB, N, NRHS
INTEGER DESCA( * ), DESCB( * ), IPIV( * )
REAL A( * ), B( * )
PURPOSE
PSGESV computes the solution to a real system of linear equations
where sub( A ) = A(IA:IA+N-1,JA:JA+N-1) is an N-by-N distributed matrix
and X and sub( B ) = B(IB:IB+N-1,JB:JB+NRHS-1) are N-by-NRHS
distributed matrices.
The LU decomposition with partial pivoting and row interchanges is used
to factor sub( A ) as sub( A ) = P * L * U, where P is a permu- tation
matrix, L is unit lower triangular, and U is upper triangular. L and U
are stored in sub( A ). The factored form of sub( A ) is then used to
solve the system of equations sub( A ) * X = sub( B ).
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
This routine requires square block decomposition ( MB_A = NB_A ).
ARGUMENTS
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 submatrix sub( A ). NRHS >= 0.
A (local input/local output) REAL pointer into the
local memory to an array of dimension (LLD_A,LOCc(JA+N-1)). On
entry, the local pieces of the N-by-N distributed matrix sub( A
) to be factored. On exit, this array contains the local pieces
of the factors L and U from the factorization sub( A ) = P*L*U;
the unit diagonal elements of L are not stored.
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.
IPIV (local output) INTEGER array, dimension ( LOCr(M_A)+MB_A )
This array contains the pivoting information. IPIV(i) -> The
global row local row i was swapped with. This array is tied to
the distributed matrix A.
B (local input/local output) REAL pointer into the
local memory to an array of dimension (LLD_B,LOCc(JB+NRHS-1)).
On entry, the right hand side distributed matrix sub( B ). On
exit, if INFO = 0, sub( B ) is overwritten by the solution
distributed 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 (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, U(IA+K-1,JA+K-1) is exactly zero. The factorization
has been completed, but the factor U is exactly singular, so
the solution could not be computed.