Provided by: scalapack-doc_1.5-11_all bug

NAME

       PZGERFS - improve the computed solution to a system of linear equations and provides error
       bounds and backward error estimates for the solutions

SYNOPSIS

       SUBROUTINE PZGERFS( 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( * )

           DOUBLE          PRECISION BERR( * ), FERR( * ), RWORK( * )

           COMPLEX*16      A( * ), AF( * ), B( * ), WORK( * ), X( * )

PURPOSE

       PZGERFS 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*16 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*16 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 PZGETRF.

       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  PZGETRF.  IPIV(i)  ->
               The global row local row i was swapped with. This array is tied to the distributed
               matrix A.

       B       (local input) COMPLEX*16 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*16 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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*16 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) DOUBLE PRECISION 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.