NAME
PDPOTF2 - compute the Cholesky factorization of a real symmetric
positive definite distributed matrix sub( A )=A(IA:IA+N-1,JA:JA+N-1)
SYNOPSIS
SUBROUTINE PDPOTF2( UPLO, N, A, IA, JA, DESCA, INFO )
CHARACTER UPLO
INTEGER IA, INFO, JA, N
INTEGER DESCA( * )
DOUBLE PRECISION A( * )
PURPOSE
PDPOTF2 computes the Cholesky factorization of a real symmetric
positive definite distributed matrix sub( A )=A(IA:IA+N-1,JA:JA+N-1).
The factorization has the form
sub( A ) = U’ * U , if UPLO = ’U’, or
sub( A ) = L * L’, if UPLO = ’L’,
where U is an upper triangular matrix and L is lower triangular.
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 N <= NB_A-MOD(JA-1, NB_A) and 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.
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 )
contains the lower triangular part of the distribu- ted matrix,
and its strictly upper triangular part is not referenced. On
exit, if UPLO = ’U’, the upper triangular part of the
distributed matrix contains the Cholesky factor U, if UPLO =
’L’, the lower triangular part of the distribu- ted matrix
contains the Cholesky factor L.
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.
INFO (local 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
factorization could not be completed.