PZPOTRS

# PZPOTRS

Section: LAPACK routine (version 1.5) (l) Updated: 12 May 1997
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## NAME

PZPOTRS - solve a system of linear equations sub( A ) * X = sub( B ) A(IA:IA+N-1,JA:JA+N-1)*X = B(IB:IB+N-1,JB:JB+NRHS-1)

## SYNOPSIS

SUBROUTINE PZPOTRS(
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( * )

COMPLEX*16 A( * ), B( * )

## PURPOSE

PZPOTRS solves a system of linear equations

where sub( A ) denotes A(IA:IA+N-1,JA:JA+N-1) and is a N-by-N hermitian positive definite distributed matrix using the Cholesky factorization sub( A ) = U**H*U or L*L**H computed by PZPOTRF. sub( B ) denotes the distributed matrix B(IB:IB+N-1,JB:JB+NRHS-1).

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

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) COMPLEX*16 pointer into local memory to
an array of dimension (LLD_A, LOCc(JA+N-1)). On entry, this array contains the factors L or U from the Cholesky facto- rization sub( A ) = L*L**H or U**H*U, as computed by PZPOTRF.
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) COMPLEX*16 pointer into the
local memory to an array of local dimension (LLD_B,LOCc(JB+NRHS-1)). On entry, this array contains the the local pieces of the right hand sides sub( B ). On exit, this array contains the local pieces of 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.

## Index

NAME
SYNOPSIS
PURPOSE
ARGUMENTS

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