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NAME

       PCTRCON  -  estimate  the  reciprocal  of  the  condition  number  of a
       triangular distributed matrix  A(IA:IA+N-1,JA:JA+N-1),  in  either  the
       1-norm or the infinity-norm

SYNOPSIS

       SUBROUTINE PCTRCON( NORM, UPLO, DIAG, N, A, IA, JA, DESCA, RCOND, WORK,
                           LWORK, RWORK, LRWORK, INFO )

           CHARACTER       DIAG, NORM, UPLO

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

           REAL            RCOND

           INTEGER         DESCA( * )

           REAL            RWORK( * )

           COMPLEX         A( * ), WORK( * )

PURPOSE

       PCTRCON  estimates  the  reciprocal  of  the  condition  number  of   a
       triangular  distributed  matrix  A(IA:IA+N-1,JA:JA+N-1),  in either the
       1-norm or the infinity-norm.

       The norm of A(IA:IA+N-1,JA:JA+N-1)  is  computed  and  an  estimate  is
       obtained  for norm(inv(A(IA:IA+N-1,JA:JA+N-1))), then 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.

       UPLO    (global input) CHARACTER
               = ’U’:  A(IA:IA+N-1,JA:JA+N-1) is upper triangular;
               = ’L’:  A(IA:IA+N-1,JA:JA+N-1) is lower triangular.

       DIAG    (global input) CHARACTER
               = ’N’:  A(IA:IA+N-1,JA:JA+N-1) is non-unit triangular;
               = ’U’:  A(IA:IA+N-1,JA:JA+N-1) is unit triangular.

       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 pointer into the local memory
               to  an  array  of dimension ( LLD_A, LOCc(JA+N-1) ). This array
               contains the local pieces of the triangular distributed  matrix
               A(IA:IA+N-1,JA:JA+N-1). If UPLO = ’U’, the leading N-by-N upper
               triangular part of this distributed matrix con- tains the upper
               triangular  matrix,  and  its strictly lower triangular part is
               not referenced.  If  UPLO  =  ’L’,  the  leading  N-by-N  lower
               triangular  part  of  this ditributed matrix contains the lower
               triangular matrix, and the strictly upper  triangular  part  is
               not  referenced.  If  DIAG  =  ’U’,  the  diagonal  elements of
               A(IA:IA+N-1,JA:JA+N-1) are also not referenced and are  assumed
               to be 1.

       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.

       RCOND   (global output) REAL
               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 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(P-1,Q),LOCc(N+MOD(JA-1,NB_A)) + NB_A*CEIL(Q-1,P))
               ).

               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 >= 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.