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NAME

       PSPOCON  -  estimate  the  reciprocal  of  the condition number (in the
       1-norm) of a real symmetric positive definite distributed matrix  using
       the Cholesky factorization A = U**T*U or A = L*L**T computed by PSPOTRF

SYNOPSIS

       SUBROUTINE PSPOCON( UPLO, N, A, IA,  JA,  DESCA,  ANORM,  RCOND,  WORK,
                           LWORK, IWORK, LIWORK, INFO )

           CHARACTER       UPLO

           INTEGER         IA, INFO, JA, LIWORK, LWORK, N

           REAL            ANORM, RCOND

           INTEGER         DESCA( * ), IWORK( * )

           REAL            A( * ), WORK( * )

PURPOSE

       PSPOCON  estimates  the  reciprocal  of  the  condition  number (in the
       1-norm) of a real symmetric positive definite distributed matrix  using
       the  Cholesky  factorization  A  =  U**T*U  or  A  = L*L**T computed by
       PSPOTRF.

       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

       UPLO    (global input) CHARACTER
               Specifies whether the factor stored  in  A(IA:IA+N-1,JA:JA+N-1)
               is upper or lower triangular.
               = ’U’:  Upper triangular
               = ’L’:  Lower 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) REAL 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 or U from the
               Cholesky factorization A(IA:IA+N-1,JA:JA+N-1) = U’*U  or  L*L’,
               as computed by PSPOTRF.

       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) REAL
               The  1-norm  (or  infinity-norm)  of  the symmetric distributed
               matrix A(IA:IA+N-1,JA:JA+N-1).

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

               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.

       IWORK   (local workspace/local output) INTEGER array,
               dimension (LIWORK) On exit, IWORK(1) returns  the  minimal  and
               optimal LIWORK.

       LIWORK  (local or global input) INTEGER
               The  dimension  of  the array IWORK.  LIWORK is local input and
               must be at least LIWORK >= LOCr(N+MOD(IA-1,MB_A)).

               If LIWORK = -1, then LIWORK 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.