PDPOSV(3) MathKeisan ScaLAPACK routine PDPOSV(3)
NAME
PDPOSV - compute the solution to a real system of linear equations
sub( A ) * X = sub( B ),
SYNOPSIS
SUBROUTINE PDPOSV( UPLO, N, NRHS, A, IA, JA, DESCA, B, IB, JB, DESCB,
INFO )
CHARACTER UPLO
INTEGER IA, IB, INFO, JA, JB, N, NRHS
INTEGER DESCA( * ), DESCB( * )
DOUBLE PRECISION A( * ), B( * )
PURPOSE
PDPOSV computes the solution to a real system of linear equations sub(
A ) * X = sub( B ), where sub( A ) denotes A(IA:IA+N-1,JA:JA+N-1) and
is an N-by-N symmetric distributed positive definite matrix and X and
sub( B ) denoting B(IB:IB+N-1,JB:JB+NRHS-1) are N-by-NRHS distributed
matrices.
The Cholesky decomposition is used to factor sub( A ) as
sub( A ) = U**T * U, if UPLO = 'U', or
sub( A ) = L * L**T, if UPLO = 'L',
where U is an upper triangular matrix and L is a lower triangular
matrix. The factored form of sub( A ) is then used to solve the system
of equations.
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
UPLO (global input) CHARACTER
= 'U': Upper triangle of sub( A ) is stored;
= 'L': Lower triangle of sub( A ) is stored.
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( B ). NRHS >= 0.
A (local input/local output) DOUBLE PRECISION pointer into the
local memory to an array of dimension (LLD_A, LOCc(JA+N-1)).
On entry, this array contains the local pieces of the N-by-N
symmetric distributed matrix sub( A ) to be factored. If UPLO
= 'U', the leading N-by-N upper triangular part of sub( A )
contains the upper triangular part of the matrix, and its
strictly lower triangular part is not referenced. If UPLO =
'L', the leading N-by-N lower triangular part of sub( A ) con-
tains the lower triangular part of the distribu- ted matrix,
and its strictly upper triangular part is not referenced. On
exit, if INFO = 0, this array contains the local pieces of the
factor U or L from the Cholesky factori- zation sub( A ) =
U**T*U or L*L**T.
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,LOC(JB+NRHS-1)).
On entry, the local pieces of the right hand sides distribu-
ted matrix sub( B ). On exit, if INFO = 0, sub( B ) is over-
written with 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, the leading minor of order K,
A(IA:IA+K-1,JA:JA+K-1) is not positive definite, and the fac-
torization could not be completed, and the solution has not
been computed.
ScaLAPACK version 1.7 13 August 2001 PDPOSV(3)