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NAME

       PDGESV - compute the solution to a real system of linear equations   sub( A ) * X = sub( B
       ),

SYNOPSIS

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

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

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

           DOUBLE         PRECISION A( * ), B( * )

PURPOSE

       PDGESV computes the solution to a real system of linear equations

       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  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

       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) DOUBLE PRECISION 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) DOUBLE PRECISION 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 distributed 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.