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mo_mpi_stubs.f90
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!> \file mo_mpi_stubs.f90
!> \brief Module provides dummy functions for common MPI routines.
!> \details This module provides dummy functions for the most commonly called MPI routines.\n
!> Most of the stub routines do not do anything. In a few cases, where it makes sense,
!> they do some simple action or return a value that is appropriate for the serial processing case.\n
!> mo_mpi_stubs can be used as a convenience, when a real MPI implementation is not available,
!> and the user simply wants to test-compile a code. It may also be useful in those occasions\n
!> when a code has been so carefully written that it will still execute correctly on a single processor.\n
!>
!> The original code was provided by J. Burkardt who based the code on a similar package
!> supplied as part of the LAMMPS program.\n
!> Burkardt's code can be downloaded at http://people.sc.fsu.edu/~jburkardt/f_src/mpi_stubs/mpi_stubs.html.
!>
!> \authors LAMMPS project, John Burkardt (F90), Matthias Cuntz (JAMS)
!> \date March 2015
module mo_mpi_stubs
! This module part of the JAMS Fortran library.
! Written Matthias Cuntz, March 2015
! License
! -------
! This file is part of the JAMS Fortran package, distributed under the MIT License.
!
! Copyright (c) 2015 LAMMPS, John Burkardt, Matthias Cuntz - mc (at) macu (dot) de
!
! Permission is hereby granted, free of charge, to any person obtaining a copy
! of this software and associated documentation files (the "Software"), to deal
! in the Software without restriction, including without limitation the rights
! to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
! copies of the Software, and to permit persons to whom the Software is
! furnished to do so, subject to the following conditions:
!
! The above copyright notice and this permission notice shall be included in all
! copies or substantial portions of the Software.
!
! THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
! IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
! FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
! AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
! LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
! OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
! SOFTWARE.
use mo_kind, only: i4, i8, sp, dp
implicit none
integer(i4), parameter :: mpi_comm_world = 0
!
! Return values
integer(i4), parameter :: mpi_failure = 1
integer(i4), parameter :: mpi_success = 0
!
! recv message status
integer(i4), parameter :: mpi_status_size = 3
integer(i4), parameter :: mpi_source = 1
integer(i4), parameter :: mpi_tag = 2
integer(i4), parameter :: mpi_count = 3
!
! recv flags
integer(i4), parameter :: mpi_any_source = -1
integer(i4), parameter :: mpi_any_tag = -1
!
! data types and sizes
integer(i4), parameter :: mpi_integer = 1
integer(i4), parameter :: mpi_real = 2
integer(i4), parameter :: mpi_double_precision = 3
integer(i4), parameter :: mpi_logical = 4
integer(i4), parameter :: mpi_character = 5
!
! allreduce operations
integer(i4), parameter :: mpi_sum = 1
integer(i4), parameter :: mpi_max = 2
integer(i4), parameter :: mpi_min = 3
integer(i4), parameter :: mpi_product = 4
interface mpi_allgather
module procedure mpi_allgather_i4, mpi_allgather_sp, mpi_allgather_dp
end interface mpi_allgather
interface mpi_allgatherv
module procedure mpi_allgatherv_i4, mpi_allgatherv_sp, mpi_allgatherv_dp
end interface mpi_allgatherv
interface mpi_allreduce
module procedure mpi_allreduce_i4, mpi_allreduce_sp, mpi_allreduce_dp
end interface mpi_allreduce
interface mpi_reduce
module procedure mpi_reduce_0d_i4, mpi_reduce_1d_i4, mpi_reduce_sp, mpi_reduce_dp
end interface mpi_reduce
interface mpi_reduce_scatter
module procedure mpi_reduce_scatter_i4, mpi_reduce_scatter_sp, mpi_reduce_scatter_dp
end interface mpi_reduce_scatter
contains
subroutine mpi_abort( comm, errorcode, ierror )
!*****************************************************************************80
!
!! MPI_ABORT shuts down the processes in a given communicator.
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 08 February 2007
!
! Author:
!
! John Burkardt
!
! Reference:
!
! William Gropp, Ewing Lusk, Anthony Skjellum,
! Using MPI: Portable Parallel Programming with the
! Message-Passing Interface,
! Second Edition,
! MIT Press, 1999,
! ISBN: 0262571323.
!
! Parameters:
!
! Input, integer COMM, the MPI communicator.
!
! Input, integer ERRORCODE, the error code to be returned.
!
! Output, integer IERROR, is nonzero if an error occurred.
!
implicit none
integer(i4) :: comm
integer(i4) :: errorcode
integer(i4) :: ierror
ierror = MPI_SUCCESS
write ( *, '(a)' ) ' '
write ( *, '(a)' ) 'MPI_ABORT:'
write ( *, '(a,i12)' ) ' Shut down with error code = ', errorcode
stop
end subroutine mpi_abort
subroutine mpi_allgather_i4( data1, nsend, sendtype,data2, nrecv, recvtype, &
comm, ierror )
!*****************************************************************************80
!
!! MPI_ALLGATHER gathers data from all the processes in a communicator.
!
! Discussion:
!
! Copy values from DATA1 to DATA2.
!
! The data to be transferred can be integer, real, or double precision.
! In this routine, it is declared and documented as INTEGER type,
! but using the other types should generally not cause a problem.
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 05 February 2007
!
! Author:
!
! John Burkardt
!
! Reference:
!
! William Gropp, Ewing Lusk, Anthony Skjellum,
! Using MPI: Portable Parallel Programming with the
! Message-Passing Interface,
! Second Edition,
! MIT Press, 1999,
! ISBN: 0262571323.
!
! Parameters:
!
! Input, integer COMM, the MPI communicator.
!
! Output, integer IERROR, is nonzero if an error occurred.
!
implicit none
integer(i4) :: nsend
integer(i4) :: comm
integer(i4) :: data1(nsend)
integer(i4) :: data2(nsend)
integer(i4) :: ierror
integer(i4) :: nrecv
integer(i4) :: recvtype
integer(i4) :: sendtype
ierror = MPI_SUCCESS
if ( sendtype == mpi_integer ) then
call mpi_copy_integer ( data1, data2, nsend, ierror )
else
ierror = MPI_FAILURE
end if
return
end subroutine mpi_allgather_i4
subroutine mpi_allgather_sp( data1, nsend, sendtype,data2, nrecv, recvtype, &
comm, ierror )
!*****************************************************************************80
!
!! MPI_ALLGATHER gathers data from all the processes in a communicator.
!
! Discussion:
!
! Copy values from DATA1 to DATA2.
!
! The data to be transferred can be integer, real, or double precision.
! In this routine, it is declared and documented as INTEGER type,
! but using the other types should generally not cause a problem.
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 05 February 2007
!
! Author:
!
! John Burkardt
!
! Reference:
!
! William Gropp, Ewing Lusk, Anthony Skjellum,
! Using MPI: Portable Parallel Programming with the
! Message-Passing Interface,
! Second Edition,
! MIT Press, 1999,
! ISBN: 0262571323.
!
! Parameters:
!
! Input, integer COMM, the MPI communicator.
!
! Output, integer IERROR, is nonzero if an error occurred.
!
implicit none
integer(i4) :: nsend
integer(i4) :: comm
real(sp) :: data1(nsend)
real(sp) :: data2(nsend)
integer(i4) :: ierror
integer(i4) :: nrecv
integer(i4) :: recvtype
integer(i4) :: sendtype
ierror = MPI_SUCCESS
if ( sendtype == mpi_real ) then
call mpi_copy_real ( data1, data2, nsend, ierror )
else
ierror = MPI_FAILURE
end if
return
end subroutine mpi_allgather_sp
subroutine mpi_allgather_dp( data1, nsend, sendtype,data2, nrecv, recvtype, &
comm, ierror )
!*****************************************************************************80
!
!! MPI_ALLGATHER gathers data from all the processes in a communicator.
!
! Discussion:
!
! Copy values from DATA1 to DATA2.
!
! The data to be transferred can be integer, real, or double precision.
! In this routine, it is declared and documented as INTEGER type,
! but using the other types should generally not cause a problem.
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 05 February 2007
!
! Author:
!
! John Burkardt
!
! Reference:
!
! William Gropp, Ewing Lusk, Anthony Skjellum,
! Using MPI: Portable Parallel Programming with the
! Message-Passing Interface,
! Second Edition,
! MIT Press, 1999,
! ISBN: 0262571323.
!
! Parameters:
!
! Input, integer COMM, the MPI communicator.
!
! Output, integer IERROR, is nonzero if an error occurred.
!
implicit none
integer(i4) :: nsend
integer(i4) :: comm
real(dp) :: data1(nsend)
real(dp) :: data2(nsend)
integer(i4) :: ierror
integer(i4) :: nrecv
integer(i4) :: recvtype
integer(i4) :: sendtype
ierror = MPI_SUCCESS
if ( sendtype == mpi_double_precision ) then
call mpi_copy_double_precision ( data1, data2, nsend, ierror )
else
ierror = MPI_FAILURE
end if
return
end subroutine mpi_allgather_dp
subroutine mpi_allgatherv_i4( data1, nsend, sendtype, data2, nrecv, ndispls, &
recvtype, comm, ierror )
!*****************************************************************************80
!
!! MPI_ALLGATHERV gathers data from all the processes in a communicator.
!
! Discussion:
!
! Copy values from DATA1 to DATA2.
!
! The data to be transferred can be integer, real, or double precision.
! In this routine, it is declared and documented as INTEGER type,
! but using the other types should generally not cause a problem.
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 05 February 2007
!
! Author:
!
! John Burkardt
!
! Reference:
!
! William Gropp, Ewing Lusk, Anthony Skjellum,
! Using MPI: Portable Parallel Programming with the
! Message-Passing Interface,
! Second Edition,
! MIT Press, 1999,
! ISBN: 0262571323.
!
! Parameters:
!
! Input, integer COMM, the MPI communicator.
!
! Output, integer IERROR, is nonzero if an error occurred.
!
implicit none
integer(i4) :: nsend
integer(i4) :: comm
integer(i4) :: data1(nsend)
integer(i4) :: data2(nsend)
integer(i4) :: ierror
integer(i4) :: ndispls
integer(i4) :: nrecv
integer(i4) :: recvtype
integer(i4) :: sendtype
ierror = MPI_SUCCESS
if ( sendtype == mpi_integer ) then
call mpi_copy_integer ( data1, data2, nsend, ierror )
else
ierror = MPI_FAILURE
end if
return
end subroutine mpi_allgatherv_i4
subroutine mpi_allgatherv_sp( data1, nsend, sendtype, data2, nrecv, ndispls, &
recvtype, comm, ierror )
!*****************************************************************************80
!
!! MPI_ALLGATHERV gathers data from all the processes in a communicator.
!
! Discussion:
!
! Copy values from DATA1 to DATA2.
!
! The data to be transferred can be integer, real, or double precision.
! In this routine, it is declared and documented as INTEGER type,
! but using the other types should generally not cause a problem.
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 05 February 2007
!
! Author:
!
! John Burkardt
!
! Reference:
!
! William Gropp, Ewing Lusk, Anthony Skjellum,
! Using MPI: Portable Parallel Programming with the
! Message-Passing Interface,
! Second Edition,
! MIT Press, 1999,
! ISBN: 0262571323.
!
! Parameters:
!
! Input, integer COMM, the MPI communicator.
!
! Output, integer IERROR, is nonzero if an error occurred.
!
implicit none
integer(i4) :: nsend
integer(i4) :: comm
real(sp) :: data1(nsend)
real(sp) :: data2(nsend)
integer(i4) :: ierror
integer(i4) :: ndispls
integer(i4) :: nrecv
integer(i4) :: recvtype
integer(i4) :: sendtype
ierror = MPI_SUCCESS
if ( sendtype == mpi_real ) then
call mpi_copy_real ( data1, data2, nsend, ierror )
else
ierror = MPI_FAILURE
end if
return
end subroutine mpi_allgatherv_sp
subroutine mpi_allgatherv_dp( data1, nsend, sendtype, data2, nrecv, ndispls, &
recvtype, comm, ierror )
!*****************************************************************************80
!
!! MPI_ALLGATHERV gathers data from all the processes in a communicator.
!
! Discussion:
!
! Copy values from DATA1 to DATA2.
!
! The data to be transferred can be integer, real, or double precision.
! In this routine, it is declared and documented as INTEGER type,
! but using the other types should generally not cause a problem.
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 05 February 2007
!
! Author:
!
! John Burkardt
!
! Reference:
!
! William Gropp, Ewing Lusk, Anthony Skjellum,
! Using MPI: Portable Parallel Programming with the
! Message-Passing Interface,
! Second Edition,
! MIT Press, 1999,
! ISBN: 0262571323.
!
! Parameters:
!
! Input, integer COMM, the MPI communicator.
!
! Output, integer IERROR, is nonzero if an error occurred.
!
implicit none
integer(i4) :: nsend
integer(i4) :: comm
real(dp) :: data1(nsend)
real(dp) :: data2(nsend)
integer(i4) :: ierror
integer(i4) :: ndispls
integer(i4) :: nrecv
integer(i4) :: recvtype
integer(i4) :: sendtype
ierror = MPI_SUCCESS
if ( sendtype == mpi_double_precision ) then
call mpi_copy_double_precision ( data1, data2, nsend, ierror )
else
ierror = MPI_FAILURE
end if
return
end subroutine mpi_allgatherv_dp
subroutine mpi_allreduce_i4( data1, data2, n, datatype, operation, comm, ierror )
!*****************************************************************************80
!
!! MPI_ALLREDUCE carries out a reduction operation.
!
! Discussion:
!
! The reduction operations are MAXIMUM, MINIMUM, PRODUCT and SUM.
!
! The data to be transferred can be integer, real, or double precision.
! In this routine, it is declared and documented as INTEGER type,
! but using the other types should generally not cause a problem.
!
! Thanks to Simppa Akaslompolo for correcting this routine!
! 12 January 2012.
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 12 January 2012
!
! Author:
!
! John Burkardt
!
! Reference:
!
! William Gropp, Ewing Lusk, Anthony Skjellum,
! Using MPI: Portable Parallel Programming with the
! Message-Passing Interface,
! Second Edition,
! MIT Press, 1999,
! ISBN: 0262571323.
!
! Parameters:
!
! Input, DATATYPE DATA1(N), the data to be processed.
!
! Output, DATATYPE DATA2(N), the value of the reduction operation.
!
! Input, integer N, the number of items in DATA1.
!
! Input, integer DATATYPE, indicates the datatype of DATA1 and DATA2.
!
! Input, integer OPERATION, should have the value of one of the symbolic
! constants MPI_MAX, MPI_MIN, MPI_PRODUCT or MPI_SUM.
!
! Input, integer COMM, the MPI communicator.
!
! Output, integer IERROR, is nonzero if an error occurred.
!
implicit none
integer(i4) :: n
integer(i4) :: comm
integer(i4) :: data1(n)
integer(i4) :: data2(n)
integer(i4) :: datatype
integer(i4) :: ierror
integer(i4) :: operation
ierror = MPI_SUCCESS
if ( datatype == mpi_integer ) then
call mpi_reduce_integer ( data1, data2, n, operation, ierror )
else
ierror = MPI_FAILURE
end if
return
end subroutine mpi_allreduce_i4
subroutine mpi_allreduce_sp( data1, data2, n, datatype, operation, comm, ierror )
!*****************************************************************************80
!
!! MPI_ALLREDUCE carries out a reduction operation.
!
! Discussion:
!
! The reduction operations are MAXIMUM, MINIMUM, PRODUCT and SUM.
!
! The data to be transferred can be integer, real, or double precision.
! In this routine, it is declared and documented as INTEGER type,
! but using the other types should generally not cause a problem.
!
! Thanks to Simppa Akaslompolo for correcting this routine!
! 12 January 2012.
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 12 January 2012
!
! Author:
!
! John Burkardt
!
! Reference:
!
! William Gropp, Ewing Lusk, Anthony Skjellum,
! Using MPI: Portable Parallel Programming with the
! Message-Passing Interface,
! Second Edition,
! MIT Press, 1999,
! ISBN: 0262571323.
!
! Parameters:
!
! Input, DATATYPE DATA1(N), the data to be processed.
!
! Output, DATATYPE DATA2(N), the value of the reduction operation.
!
! Input, integer N, the number of items in DATA1.
!
! Input, integer DATATYPE, indicates the datatype of DATA1 and DATA2.
!
! Input, integer OPERATION, should have the value of one of the symbolic
! constants MPI_MAX, MPI_MIN, MPI_PRODUCT or MPI_SUM.
!
! Input, integer COMM, the MPI communicator.
!
! Output, integer IERROR, is nonzero if an error occurred.
!
implicit none
integer(i4) :: n
integer(i4) :: comm
real(sp) :: data1(n)
real(sp) :: data2(n)
integer(i4) :: datatype
integer(i4) :: ierror
integer(i4) :: operation
ierror = MPI_SUCCESS
if ( datatype == mpi_real ) then
call mpi_reduce_real ( data1, data2, n, operation, ierror )
else
ierror = MPI_FAILURE
end if
return
end subroutine mpi_allreduce_sp
subroutine mpi_allreduce_dp( data1, data2, n, datatype, operation, comm, ierror )
!*****************************************************************************80
!
!! MPI_ALLREDUCE carries out a reduction operation.
!
! Discussion:
!
! The reduction operations are MAXIMUM, MINIMUM, PRODUCT and SUM.
!
! The data to be transferred can be integer, real, or double precision.
! In this routine, it is declared and documented as INTEGER type,
! but using the other types should generally not cause a problem.
!
! Thanks to Simppa Akaslompolo for correcting this routine!
! 12 January 2012.
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 12 January 2012
!
! Author:
!
! John Burkardt
!
! Reference:
!
! William Gropp, Ewing Lusk, Anthony Skjellum,
! Using MPI: Portable Parallel Programming with the
! Message-Passing Interface,
! Second Edition,
! MIT Press, 1999,
! ISBN: 0262571323.
!
! Parameters:
!
! Input, DATATYPE DATA1(N), the data to be processed.
!
! Output, DATATYPE DATA2(N), the value of the reduction operation.
!
! Input, integer N, the number of items in DATA1.
!
! Input, integer DATATYPE, indicates the datatype of DATA1 and DATA2.
!
! Input, integer OPERATION, should have the value of one of the symbolic
! constants MPI_MAX, MPI_MIN, MPI_PRODUCT or MPI_SUM.
!
! Input, integer COMM, the MPI communicator.
!
! Output, integer IERROR, is nonzero if an error occurred.
!
implicit none
integer(i4) :: n
integer(i4) :: comm
real(dp) :: data1(n)
real(dp) :: data2(n)
integer(i4) :: datatype
integer(i4) :: ierror
integer(i4) :: operation
ierror = MPI_SUCCESS
if ( datatype == mpi_double_precision ) then
call mpi_reduce_double_precision ( data1, data2, n, operation, ierror )
else
ierror = MPI_FAILURE
end if
return
end subroutine mpi_allreduce_dp
subroutine mpi_barrier( comm, ierror )
!*****************************************************************************80
!
!! MPI_BARRIER forces processes within a communicator to wait together.
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 05 February 2007
!
! Author:
!
! John Burkardt
!
! Reference:
!
! William Gropp, Ewing Lusk, Anthony Skjellum,
! Using MPI: Portable Parallel Programming with the
! Message-Passing Interface,
! Second Edition,
! MIT Press, 1999,
! ISBN: 0262571323.
!
! Parameters:
!
! Input, integer COMM, the MPI communicator.
!
! Output, integer IERROR, is nonzero if an error occurred.
!
implicit none
integer(i4) :: comm
integer(i4) :: ierror
ierror = MPI_SUCCESS
return
end subroutine mpi_barrier
subroutine mpi_bcast( data, n, datatype, node, comm, ierror )
!*****************************************************************************80
!
!! MPI_BCAST broadcasts data from one process to all others.
!
! Discussion:
!
! The data to be transferred can be integer, real, or double precision.
! In this routine, it is declared and documented as INTEGER type,
! but using the other types should generally not cause a problem.
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 05 February 2007
!
! Author:
!
! John Burkardt
!
! Reference:
!
! William Gropp, Ewing Lusk, Anthony Skjellum,
! Using MPI: Portable Parallel Programming with the
! Message-Passing Interface,
! Second Edition,
! MIT Press, 1999,
! ISBN: 0262571323.
!
! Parameters:
!
! Input, datatype DATA(N), the data to be broadcast.
!
! Input, integer N, the number of items of data.
!
! Input, integer DATATYPE, the MPI code for the datatype of the data.
!
! Input, integer NODE, the rank of the sending process within the
! given communicator.
!
! Input, integer COMM, the MPI communicator.
!
! Output, integer IERROR, is nonzero if an error occurred.
!
implicit none
integer(i4) :: n
integer(i4) :: comm
integer(i4) :: data(n)
integer(i4) :: datatype
integer(i4) :: ierror
integer(i4) :: node
ierror = MPI_SUCCESS
return
end subroutine mpi_bcast
subroutine mpi_bsend( data, n, datatype, iproc, itag, comm, ierror )
!*****************************************************************************80
!
!! MPI_BSEND sends data from one process to another, using buffering.
!
! Discussion:
!
! Warn against sending message to self, since no data copy is done.
!
! The data to be transferred can be integer, real, or double precision.
! In this routine, it is declared and documented as INTEGER type,
! but using the other types should generally not cause a problem.
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 06 February 2007
!
! Author:
!
! John Burkardt
!
! Reference:
!
! William Gropp, Ewing Lusk, Anthony Skjellum,
! Using MPI: Portable Parallel Programming with the
! Message-Passing Interface,
! Second Edition,
! MIT Press, 1999,
! ISBN: 0262571323.
!
! Parameters:
!
! Input, datatype DATA(N), the data to be sent.
!
! Input, integer N, the number of data items to send.
!
! Input, integer DATAYTPE, the MPI code for the datatype.
!
! Input, integer IPROC, the rank of the process within the communicator
! that is to receive the message.
!
! Input, integer ITAG, a tag for the message.
!
! Input, integer COMM, the MPI communicator.
!
! Output, integer IERROR, is nonzero if an error occurred.
!
implicit none
integer(i4) :: n
integer(i4) :: comm
integer(i4) :: data(n)
integer(i4) :: datatype
integer(i4) :: ierror
integer(i4) :: iproc
integer(i4) :: itag
ierror = MPI_FAILURE
write ( *, '(a)' ) ' '
write ( *, '(a)' ) 'MPI_BSEND - Error!'
write ( *, '(a)' ) ' Should not send message to self.'
return
end subroutine mpi_bsend
subroutine mpi_cart_create( comm, ndims, dims, periods, reorder, comm_cart, &
ierror )
!*****************************************************************************80
!
!! MPI_CART_CREATE creates a communicator for a Cartesian topology.
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 05 February 2007
!
! Author:
!
! John Burkardt
!
! Reference: