PCGESV(3) ScaLAPACK routine of NEC Numeric Library Collection PCGESV(3)
NAME
PCGESV - compute the solution to a complex system of linear equations
sub( A ) * X = sub( B ),
SYNOPSIS
SUBROUTINE PCGESV( N, NRHS, A, IA, JA, DESCA, IPIV, B, IB, JB, DESCB,
INFO )
INTEGER IA, IB, INFO, JA, JB, N, NRHS
INTEGER DESCA( * ), DESCB( * ), IPIV( * )
COMPLEX A( * ), B( * )
PURPOSE
PCGESV computes the solution to a complex system of linear equations
sub( A ) * X = sub( B ), 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 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
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) COMPLEX 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) COMPLEX 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 dis-
tributed 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.
ScaLAPACK routine 31 October 2017 PCGESV(3)