PSGETF2(3)    ScaLAPACK routine of NEC Numeric Library Collection   PSGETF2(3)



NAME
       PSGETF2  -  compute an LU factorization of a general M-by-N distributed
       matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) using  partial  pivoting  with
       row interchanges

SYNOPSIS
       SUBROUTINE PSGETF2( M, N, A, IA, JA, DESCA, IPIV, INFO )

           INTEGER         IA, INFO, JA, M, N

           INTEGER         DESCA( * ), IPIV( * )

           REAL            A( * )

PURPOSE
       PSGETF2  computes  an  LU factorization of a general M-by-N distributed
       matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) using  partial  pivoting  with
       row interchanges.  The factorization has the form sub( A ) = P * L * U,
       where P is a permutation matrix, L is lower triangular with unit diago-
       nal  elements  (lower  trapezoidal if m > n), and U is upper triangular
       (upper trapezoidal if m < n).

       This is the right-looking Parallel Level 2 BLAS version  of  the  algo-
       rithm.


       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 N <= NB_A-MOD(JA-1, NB_A) and square block decom-
       position ( MB_A = NB_A ).


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

       N       (global input) INTEGER
               The  number  of  columns  to be operated on, i.e. the number of
               columns of the distributed submatrix sub( A ).   NB_A-MOD(JA-1,
               NB_A) >= N >= 0.

       A       (local input/local output) 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  M-by-N
               distributed  matrix  sub( A ). On exit, this array contains the
               local pieces of the factors L and U from  the  factoriza-  tion
               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.

       INFO    (local 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,  and
               division  by zero will occur if it is used to solve a system of
               equations.



ScaLAPACK routine               31 October 2017                     PSGETF2(3)