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NAME

       PZGECON - estimate the reciprocal of the condition number of a general distributed complex
       matrix A(IA:IA+N-1,JA:JA+N-1), in either the 1-norm or the  infinity-norm,  using  the  LU
       factorization computed by PZGETRF

SYNOPSIS

       SUBROUTINE PZGECON( NORM,  N,  A, IA, JA, DESCA, ANORM, RCOND, WORK, LWORK, RWORK, LRWORK,
                           INFO )

           CHARACTER       NORM

           INTEGER         IA, INFO, JA, LRWORK, LWORK, N

           DOUBLE          PRECISION ANORM, RCOND

           INTEGER         DESCA( * )

           DOUBLE          PRECISION RWORK( * )

           COMPLEX*16      A( * ), WORK( * )

PURPOSE

       PZGECON estimates the reciprocal of the condition number of a general distributed  complex
       matrix  A(IA:IA+N-1,JA:JA+N-1),  in  either  the 1-norm or the infinity-norm, using the LU
       factorization computed by PZGETRF.

       An estimate is obtained for norm(inv(A(IA:IA+N-1,JA:JA+N-1))), and the reciprocal  of  the
       condition number is computed as
                  RCOND = 1 / ( norm( A(IA:IA+N-1,JA:JA+N-1)      ) *
                                norm( inv(A(IA:IA+N-1,JA:JA+N-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

ARGUMENTS

       NORM    (global input) CHARACTER
               Specifies whether the 1-norm  condition  number  or  the  infinity-norm  condition
               number is required:
               = '1' or 'O':  1-norm
               = 'I':         Infinity-norm

       N       (global input) INTEGER
               The order of the distributed matrix A(IA:IA+N-1,JA:JA+N-1).  N >= 0.

       A       (local input) COMPLEX*16 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   factors   L   and   U   from   the   factorization
               A(IA:IA+N-1,JA:JA+N-1) = P*L*U; the unit diagonal elements of L are not stored.

       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.

       ANORM   (global input) DOUBLE PRECISION
               If   NORM   =   '1'  or  'O',  the  1-norm  of  the  original  distributed  matrix
               A(IA:IA+N-1,JA:JA+N-1).   If  NORM  =  'I',  the  infinity-norm  of  the  original
               distributed matrix A(IA:IA+N-1,JA:JA+N-1).

       RCOND   (global output) DOUBLE PRECISION
               The   reciprocal   of   the   condition   number   of   the   distributed   matrix
               A(IA:IA+N-1,JA:JA+N-1), computed as
               RCOND = 1 / ( norm( A(IA:IA+N-1,JA:JA+N-1)      ) *
               norm( inv(A(IA:IA+N-1,JA:JA+N-1)) ) ).

       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))            +            MAX(            2,
               MAX(NB_A*CEIL(NPROW-1,NPCOL),LOCc(N+MOD(JA-1,NB_A)) + NB_A*CEIL(NPCOL-1,NPROW)) ).

               LOCr and LOCc values can be computed using the  ScaLAPACK  tool  function  NUMROC;
               NPROW and NPCOL can be determined by calling the subroutine BLACS_GRIDINFO.

               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 >= 2*LOCc(N+MOD(JA-1,NB_A)).

               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.