.TH P_Transpose 3 "10/23/2001" " " "ParLib 1.1"
.SH NAME
P_Transpose_init, P_Transpose_start, P_Transpose_end, P_Transpose_free \-  Perform nonblocking transposition
.SH SYNOPSIS
.nf
\fB#include "parlib.h"\fR

\fBint P_Transpose_init(\fR int ndims, int dim_source, int *lblks_source,
	int dim_dest, int *lblks_dest, int *stride, int *blklen,
	int *overlap, MPI_Datatype datatype, MPI_Comm comm, int period,
	Transposition *transp \fB);\fR
\fBint P_Transpose_start(\fR void *arr_source, void *arr_dest,
	Transposition *transp \fB);\fR
\fBint P_Transpose_end(\fR Transposition *transp \fB);\fR
\fBint P_Transpose_free(\fR Transposition *transp \fB);\fR
.fi

.SH ARGUMENTS
.PD 0
.TP
.B ndims
- number of dimensions of the arrays (positive integer)
.PD 1
.PD 0
.TP
.B arr_source
- address of the local part of the source array (choice)
.PD 1
.PD 0
.TP
.B dim_source
- decomposed dimension of array \fIarr_source\fR
.PD 1
.PD 0
.TP
.B lblks_source
- distribution of array \fIarr_source\fR
.PD 0
.TP
.B arr_dest
- address of the local part of the destination array (choice)
.PD 1
.PD 0
.TP
.B dim_dest
- decomposed dimension of array \fIarr_dest\fR
.PD 1
.PD 0
.TP
.B lblks_dest
- distribution of array \fIarr_dest\fR
.PD 1
.PD 0
.TP
.B stride, blklen
- parameters specifying dimensions of the arrays \fIarr_source\fR, \fIarr_dest\fR
and location of the communicated data within the arrays
.PD 1
.PD 0
.TP
.B overlap
- overlapping of the output array \fIarr_dest\fR
.PD 1
.PD 0
.TP
.B datatype
- data type of the arrays
.PD 1
.PD 0
.TP
.B comm
- communicator specifying the processor group
.PD 1
.PD 0
.TP
.B period
- true, if the overlapping is periodic, false otherwise (logical)
.PD 1
.PD 0
.TP
.B transp
- pointer to a \fITransposition\fR structure

.SH DESCRIPTION
.PD 0
The routine set performes a nonblocking transposition of array \fIarr_source\fR storing the result in array \fIarr_dest\fR.

.PD 0
\fBP_Transpose_init ()\fR builds data types required by the transposition.

Both arrays \fIarr_source\fR and \fIarr_dest\fR should have the same number of dimensions \fIndims\fR.
Array \fIarr_source\fR have to be distriduted in dimension \fIdim_source\fR while array \fIarr_dest\fR in dimension \fIdim_dest\fR.

The dimensions and the location of the communicated data within the arrays are specified by parameters \fIstride\fR, \fIblklen\fR, \fIlblks_source\fR and \fIlblks_dest\fR.
We assume all indexes to be ranged from 1 in this manual.

The arrays have the following dimensions:

.nf
           | regular dim | \fIdim_source\fR         | \fIdim_dest\fR
-----------|-------------|--------------------|-----------------
\fIarr_source\fR | \fIstride\fR(dim) | \fIblklen\fR(\fIdim_source\fR) | \fIstride\fR(\fIdim_dest\fR)
\fIarr_dest\fR   | \fIstride\fR(dim) | \fIstride\fR(\fIdim_source\fR) | \fIblklen\fR(\fIdim_dest\fR)
.fi

The following blocks of the arrays are communicated:

.nf
           | regular dim | \fIdim_source\fR          | \fIdim_dest\fR
-----------|-------------|---------------------|-------------------
\fIarr_source\fR |1:\fIblklen\fR(dim)|1:\fIlblks_source\fR(\fIiproc\fR)|1:\fBSUM\fR(\fIlblks_dest\fR)
\fIarr_dest\fR   |1:\fIblklen\fR(dim)|1:\fBSUM\fR(\fIlblks_source\fR)  |1:\fIlblks_dest\fR(\fIiproc\fR)
.fi

where the regular dimension is any dimension but \fIdim_source\fR and \fIdim_dest\fR, \fIiproc\fR is the processor number within the given group; \fBSUM\fR denotes the summation upon all processors of the group (e.g.,

.nf
   \fBSUM\fR(\fIlblks_source\fR)=SUM(\fIlblks_source\fR(i),i=1,\fInproc\fR)),
.fi

\fInproc\fR is the number of processors in the group.
These blocks should be augmented by overlapped regions, if overlapping is taking place.

.PD 1
.PD 0
\fBP_Transpose_start ()\fR starts the transposition.

In the next section, we will assume that the first index of the arrays \fIarr_source\fR and \fIarr_dest\fR corresponds to dimension \fIdim_source\fR while the second to dimension \fIdim_dest\fR. Then the transposition algorithm can be outlined as follows. 

Processor \fIiproc\fR sends

.nf
   \fIarr_source\fR(1:\fIlblks_source\fR(\fIiproc\fR),
              \fIjb\fR(\fIjproc\fR)-overlap(1):\fIje\fR(\fIjproc\fR)+overlap(2))
.fi

to every processor \fIjproc\fR of the group (including himself) and receives

.nf
   \fIarr_dest\fR(\fIib\fR(\fIjproc\fR):\fIie\fR(\fIjproc\fR),
            1-overlap(1):\fIlblks_dest\fR(\fIiproc\fR)+overlap(2))
.fi

In the nonperiodic case (\fIperiod\fR is false), \fIoverlap\fR(1) is counted for 0, if \fIiproc\fR is equal to 1 as well as \fIoverlap\fR(2), if \fIiproc\fR is equal to \fInproc\fR.
Starting and ending indexes \fIib\fR, \fIie\fR, \fIjb\fR, \fIje\fR are calculated as follows

.nf
   \fIib\fR(1)=1; \fIib\fR(i+1)=\fIib\fR(i)+\fIlblks_dest\fR(i),i=1,...,\fInproc\fR-1;
   \fIie\fR(\fInproc\fR)=\fBSUM\fR(\fIlblks_dest\fR);
      \fIie\fR(i-1)=\fIie\fR(i)-\fIlblks_dest\fR(i),i=\fInproc\fR,...,2;
.fi

.nf
   \fIjb\fR(1)=1; \fIjb\fR(j+1)=\fIjb\fR(j)+\fIlblks_source\fR(j),j=1,...,\fInproc\fR-1;
   \fIje\fR(\fInproc\fR)=\fBSUM\fR(\fIlblks_source\fR);
      \fIje\fR(j-1)=\fIje\fR(j)-\fIlblks_source\fR(j),j=\fInproc\fR,...,2.
.fi

\fBP_Transpose_end ()\fR waits untill the transposition will be completed.

\fBP_Transpose_free ()\fR deallocate data types allocated by \fBP_Transpose_init\fR.

.SH NOTES
Transposition with overlapping is equiualent to transposition widthout overlapping and subsequent interprocessor boundary exchange applied to the resultant array \fIarr_dest\fR.

.SH NOTES FOR FORTRAN
All INM ParLib routines in Fortran have an additional argument
.I ierr
at the end of the argument list.
.I ierr
is an integer and has the same meaning as the return value of the routine
in C.  In Fortran, INM ParLib routines are subroutines, and are invoked with the
.I call
statement.

All INM ParLib objects (e.g., \fIBExchange\fR, \fITransposition\fR) are \fIINTEGER\fR arrays of size \fIHANDLE_SIZE\fR in Fortran.
The parameter \fIHANDLE_SIZE\fR is defined in 'parlibf.h' which is recommended to be included in Fortran code beforehand.

.SH ERRORS
\fBP_Transpose_init\fR returns the following error codes:
.RS 3
.TP
.PD 0
.TP 3
.B 0
- No error; the routine completed successfully.
.TP
.B 1
- Number of dimensions \fIndims\fR is less than 2.
.TP
.B 2
- \fIdim_source\fR is out of range [1,\fIndims\fR].
.TP
.B 3
- \fIdim_dest\fR is out of range [1,\fIndims\fR].
.TP
.B 4
- \fIdim_source\fR and \fIdim_dest\fR coincide.
.TP
.B 5
- Nonpositive array dimension.
.TP
.B 6
- Negative overlapping.
.TP
.B 7
- \fIblklen\fR exceeds \fIstride\fR.
.TP
.B 8
- \fIlblks_source\fR(\fIiproc\fR) exceeds \fIblklen\fR(\fIdim_source\fR).
.TP
.B 9
- \fIlblks_dest\fR(\fIiproc\fR) exceeds \fIblklen\fR(\fIdim_dest\fR).
.TP
.B 10
- \fBSUM\fR(\fIlblks_source\fR) exceeds \fIstride\fR(\fIdim_source\fR).
.TP
.B 11
- \fBSUM\fR(\fIlblks_dest\fR) exceeds \fIstride\fR(\fIdim_dest\fR).
.TP
.B 12
- \fIoverlap\fR(1) exceeds \fIlblks_dest\fR(1).
.TP
.B 13
- \fIoverlap\fR(2) exceeds \fIlblks_dest\fR(\fInproc\fR).
.TP
.B 14
- \fIlblks_source\fR is nonpositive.
.TP
.B 15
- \fIlblks_dest\fR is nonpositive.

.SH SEE ALSO
\fBP_Transpose\fR(3)

.SH AUTHOR
Val N. Gloukhov, gluhoff@inm.ras.ru