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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.