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NAME

       PDPOCON  -  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 PDPOTRF

SYNOPSIS

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

           CHARACTER       UPLO

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

           DOUBLE          PRECISION ANORM, RCOND

           INTEGER         DESCA( * ), IWORK( * )

           DOUBLE          PRECISION A( * ), WORK( * )

PURPOSE

       PDPOCON 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 PDPOTRF.

       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) DOUBLE PRECISION 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 PDPOTRF.

       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
               The    1-norm   (or   infinity-norm)   of   the   symmetric   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) DOUBLE PRECISION 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.