PDTRCON(3)    ScaLAPACK routine of NEC Numeric Library Collection   PDTRCON(3)



NAME
       PDTRCON  - estimates the reciprocal of the condition number of a trian-
       gular distributed matrix A(IA:IA+N-1,JA:JA+N-1), in either  the  1-norm
       or the infinity-norm

SYNOPSIS
       SUBROUTINE PDTRCON( NORM, UPLO, DIAG, N, A, IA, JA, DESCA, RCOND, WORK,
                           LWORK, IWORK, LIWORK, INFO )

           CHARACTER       DIAG, NORM, UPLO

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

           DOUBLE          PRECISION RCOND

           INTEGER         DESCA( * ), IWORK( * )

           DOUBLE          PRECISION A( * ), WORK( * )

PURPOSE
       PDTRCON estimates the reciprocal of the condition number of a  triangu-
       lar  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  vec-
       tor.  This vector stores the information required to establish the map-
       ping 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  col-
       umn.
       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) DOUBLE PRECISION 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 trian-
               gular  part of this ditributed matrix contains the lower trian-
               gular 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) 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,  dimen-
       sion (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)) + LOCc(N+MOD(JA-1,NB_A))
               + MAX( 2, MAX( NB_A*MAX( 1, CEIL(NPROW-1,NPCOL) ),
                              LOCc(N+MOD(JA-1,NB_A)) +
                              NB_A*MAX( 1, 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.



ScaLAPACK routine               31 October 2017                     PDTRCON(3)