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



NAME
       PCGESV  -  compute the solution to a complex system of linear equations
       sub( A ) * X = sub( B ),

SYNOPSIS
       SUBROUTINE PCGESV( N, NRHS, A, IA, JA, DESCA, IPIV, B, IB,  JB,  DESCB,
                          INFO )

           INTEGER        IA, IB, INFO, JA, JB, N, NRHS

           INTEGER        DESCA( * ), DESCB( * ), IPIV( * )

           COMPLEX        A( * ), B( * )

PURPOSE
       PCGESV  computes  the  solution to a complex system of linear equations
       sub( A ) * X = sub( B ), where sub( A ) = A(IA:IA+N-1,JA:JA+N-1) is  an
       N-by-N    distributed    matrix    and    X    and    sub(    B   )   =
       B(IB:IB+N-1,JB:JB+NRHS-1) are N-by-NRHS distributed matrices.

       The LU decomposition with partial pivoting and row interchanges is used
       to  factor sub( A ) as sub( A ) = P * L * U, where P is a permu- tation
       matrix, L is unit lower triangular, and U is upper triangular.  L and U
       are  stored  in sub( A ). The factored form of sub( A ) is then used to
       solve the system of equations sub( A ) * X = sub( B ).


       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

       This routine requires square block decomposition ( MB_A = NB_A ).


ARGUMENTS
       N       (global input) INTEGER
               The number of rows and columns to  be  operated  on,  i.e.  the
               order of the distributed submatrix sub( A ). N >= 0.

       NRHS    (global input) INTEGER
               The  number of right hand sides, i.e., the number of columns of
               the distributed submatrix sub( A ). NRHS >= 0.

       A       (local input/local output) COMPLEX pointer into the
               local memory to an array of dimension (LLD_A,LOCc(JA+N-1)).  On
               entry, the local pieces of the N-by-N distributed matrix sub( A
               ) to be factored. On exit, this array contains the local pieces
               of the factors L and U from the factorization sub( A ) = 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.

       IPIV    (local output) INTEGER array, dimension ( LOCr(M_A)+MB_A )
               This array contains the pivoting information.  IPIV(i)  ->  The
               global row local row i was swapped with.  This array is tied to
               the distributed matrix A.

       B       (local input/local output) COMPLEX pointer into the
               local memory to an array of dimension  (LLD_B,LOCc(JB+NRHS-1)).
               On  entry,  the right hand side distributed matrix sub( B ). On
               exit, if INFO = 0, sub( B ) is overwritten by the solution dis-
               tributed matrix X.

       IB      (global input) INTEGER
               The row index in the global array B indicating the first row of
               sub( B ).

       JB      (global input) INTEGER
               The column index in the global array  B  indicating  the  first
               column of sub( B ).

       DESCB   (global and local input) INTEGER array of dimension DLEN_.
               The array descriptor for the distributed matrix B.

       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.  > 0:  If
               INFO = K, U(IA+K-1,JA+K-1) is exactly zero.  The  factorization
               has  been  completed,  but the factor U is exactly singular, so
               the solution could not be computed.



ScaLAPACK routine               31 October 2017                      PCGESV(3)