Provided by: scalapack-doc_1.5-10_all 
NAME
PCGERFS - improve the computed solution to a system of linear equations and provides error bounds and
backward error estimates for the solutions
SYNOPSIS
SUBROUTINE PCGERFS( TRANS, N, NRHS, A, IA, JA, DESCA, AF, IAF, JAF, DESCAF, IPIV, B, IB, JB, DESCB, X,
IX, JX, DESCX, FERR, BERR, WORK, LWORK, RWORK, LRWORK, INFO )
CHARACTER TRANS
INTEGER IA, IAF, IB, IX, INFO, JA, JAF, JB, JX, LRWORK, LWORK, N, NRHS
INTEGER DESCA( * ), DESCAF( * ), DESCB( * ), DESCX( * ), IPIV( * )
REAL BERR( * ), FERR( * ), RWORK( * )
COMPLEX A( * ), AF( * ), B( * ), WORK( * ), X( * )
PURPOSE
PCGERFS improves the computed solution to a system of linear equations and provides error bounds and
backward error estimates for the solutions.
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
In the following comments, sub( A ), sub( X ) and sub( B ) denote respectively A(IA:IA+N-1,JA:JA+N-1),
X(IX:IX+N-1,JX:JX+NRHS-1) and B(IB:IB+N-1,JB:JB+NRHS-1).
ARGUMENTS
TRANS (global input) CHARACTER*1
Specifies the form of the system of equations. = 'N': sub( A ) * sub( X ) = sub( B )
(No transpose)
= 'T': sub( A )**T * sub( X ) = sub( B ) (Transpose)
= 'C': sub( A )**H * sub( X ) = sub( B ) (Conjugate transpose)
N (global input) INTEGER
The order of the matrix sub( A ). N >= 0.
NRHS (global input) INTEGER
The number of right hand sides, i.e., the number of columns of the matrices sub( B ) and sub( X
). NRHS >= 0.
A (local input) COMPLEX pointer into the local
memory to an array of local dimension (LLD_A,LOCc(JA+N-1)). This array contains the local pieces
of the distributed matrix sub( A ).
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.
AF (local input) COMPLEX pointer into the local
memory to an array of local dimension (LLD_AF,LOCc(JA+N-1)). This array contains the local
pieces of the distributed factors of the matrix sub( A ) = P * L * U as computed by PCGETRF.
IAF (global input) INTEGER
The row index in the global array AF indicating the first row of sub( AF ).
JAF (global input) INTEGER
The column index in the global array AF indicating the first column of sub( AF ).
DESCAF (global and local input) INTEGER array of dimension DLEN_.
The array descriptor for the distributed matrix AF.
IPIV (local input) INTEGER array of dimension LOCr(M_AF)+MB_AF.
This array contains the pivoting information as computed by PCGETRF. IPIV(i) -> The global row
local row i was swapped with. This array is tied to the distributed matrix A.
B (local input) COMPLEX pointer into the local
memory to an array of local dimension (LLD_B,LOCc(JB+NRHS-1)). This array contains the local
pieces of the distributed matrix of right hand sides sub( B ).
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.
X (local input and output) COMPLEX pointer into the
local memory to an array of local dimension (LLD_X,LOCc(JX+NRHS-1)). On entry, this array
contains the local pieces of the distributed matrix solution sub( X ). On exit, the improved
solution vectors.
IX (global input) INTEGER
The row index in the global array X indicating the first row of sub( X ).
JX (global input) INTEGER
The column index in the global array X indicating the first column of sub( X ).
DESCX (global and local input) INTEGER array of dimension DLEN_.
The array descriptor for the distributed matrix X.
FERR (local output) REAL array of local dimension
LOCc(JB+NRHS-1). The estimated forward error bound for each solution vector of sub( X ). If
XTRUE is the true solution corresponding to sub( X ), FERR is an estimated upper bound for the
magnitude of the largest element in (sub( X ) - XTRUE) divided by the magnitude of the largest
element in sub( X ). The estimate is as reliable as the estimate for RCOND, and is almost always
a slight overestimate of the true error. This array is tied to the distributed matrix X.
BERR (local output) REAL array of local dimension
LOCc(JB+NRHS-1). The componentwise relative backward error of each solution vector (i.e., the
smallest re- lative change in any entry of sub( A ) or sub( B ) that makes sub( X ) an exact
solution). This array is tied to the distributed matrix X.
WORK (local workspace/local output) COMPLEX array,
dimension (LWORK) On exit, WORK(1) returns the minimal and optimal LWORK.
LWORK (local or global input) INTEGER
The dimension of the array WORK. LWORK is local input and must be at least LWORK >= 2*LOCr( N +
MOD(IA-1,MB_A) )
If LWORK = -1, then LWORK is global input and a workspace query is assumed; the routine only
calculates the minimum and optimal size for all work arrays. Each of these values is returned in
the first entry of the corresponding work array, and no error message is issued by PXERBLA.
RWORK (local workspace/local output) REAL array,
dimension (LRWORK) On exit, RWORK(1) returns the minimal and optimal LRWORK.
LRWORK (local or global input) INTEGER
The dimension of the array RWORK. LRWORK is local input and must be at least LRWORK >= LOCr( N +
MOD(IB-1,MB_B) ).
If LRWORK = -1, then LRWORK is global input and a workspace query is assumed; the routine only
calculates the minimum and optimal size for all work arrays. Each of these values is returned in
the first entry of the corresponding work array, and no error message is issued by PXERBLA.
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.
PARAMETERS
ITMAX is the maximum number of steps of iterative refinement.
Notes =====
This routine temporarily returns when N <= 1.
The distributed submatrices op( A ) and op( AF ) (respectively sub( X ) and sub( B ) ) should be
distributed the same way on the same processes. These conditions ensure that sub( A ) and sub( AF )
(resp. sub( X ) and sub( B ) ) are "perfectly" aligned.
Moreover, this routine requires the distributed submatrices sub( A ), sub( AF ), sub( X ), and sub( B )
to be aligned on a block boundary, i.e., if f(x,y) = MOD( x-1, y ): f( IA, DESCA( MB_ ) ) = f( JA, DESCA(
NB_ ) ) = 0, f( IAF, DESCAF( MB_ ) ) = f( JAF, DESCAF( NB_ ) ) = 0, f( IB, DESCB( MB_ ) ) = f( JB, DESCB(
NB_ ) ) = 0, and f( IX, DESCX( MB_ ) ) = f( JX, DESCX( NB_ ) ) = 0.