Program beltrami version 0.1.4

Initial revision 2000-07-18; Last revision 2004-08-05

1  Download

2  File readme

beltrami --- Numerical solution of Beltrami equation


SUPPORTED ENVIRONMENTS

GNU/Linux/GMP or GNU/Linux

http://www.gnu.org    GNU/Linux 
http://www.mingw.org  MinGW --- Minimalist GNU For Windows
http://www.swox.com/gmp/ GNU Multiple Precision Library

COMPILATION

There are two variants of installation

1) No multiple precision (for poor men;). Enter 

make -f makefile.nomp (or gmake-f makefile.nomp) 

in the directory where sources reside.

2) With GNU Multiple Precision (GMP). Enter 'make' (or 'gmake') in the
directory where the sources reside. The compilation may fail if (a) GMP
library is not installed or (b) C++ wrapper <gmpxx.h> is not
installed. 

In both cases (a) and (b) download GMP library from the address above;

  ./configure --enable-cxx; make; make install

BRIEF INSTRUCTION

See algorithm description and an example in example/example.tex

License conditions are described in file LICENSE.txt

3  Usage and options summary

user@computer$ ./beltrami --help
Usage: beltrami [OPTIONS] FILE
Mandatory arguments to long options are mandatory for short options too
Default values are given in square brackets
  -o, --output=NAME    output results to NAME instead of standard output
  -i, --iterations=N   do N iterations [10]
  -a, --all-info=L     set verbose level to L [0]
  -d, --daripa         use Daripa's approach for computing operator T
  -k, --khmelev        use identity T=PDz to compute T
  -l, --lin-daripa     use linear approximation to compute T using [Daripa]
  -p, --precision=P    number of bits per number [54]
  -f, --fprecision=D   Set output format %.f
  -g, --gprecision=D   Set output format %.g
  -e, --eprecision=D   Set output format %.e
The following options are mutually exclusive (def --Rtransform)
  -T --Ttransform      do integral transform T (once)
  -P --Ptransform      do integral transform P (once)
  -S --Stransform      do transform S^N, where S=mu*(T+1)
  -R --Rtransform      do integral transform P S^N + I, I for identity
  -D --Dztransform     computes derivative f_z (in polar coordinates)
  -Z --Dzbartransform  computes derivative f_zbar (in polar coordinates)
  -M --Mutransform     computes Beltrami differential f_zbar/f_z
  -F --FFTtransform    do FFT transform
  -I --iFFTtransform   do inverse FFT transform
  -s --skipFFT         skip FFT before and after T and P transforms
The following long options allow to normalize solutions. 
  --zero_i=i0       If one of these four options is used, all of them
  --zero_j=j0          must be used. In that case h[i0][j0] will be set to 0
  --one_i=i1           and h[i1][j1] will be set to 1.
  --one_j=j1           You can shorten these options for --0i, --0j, --1i,--1j

  -q, --quiet          do not send any messages to stderr
  -h, --help           display this help and exit
  -m, --man            display complete description
  -v, --version        display version and exit

4  Description

user@computer$ ./beltrami --man
<Usage information from the previous section is omitted>


This program solves the Beltrami equation on finite plane, using
integration transforms T and P. It accepts on input the file
in the following format
M N
r[1]
...
r[M]
mu[0][0]
mu[1][0] mu[1][1] ... mu[1][N-1]
...
mu[M][0] mu[1][1] ... mu[M][N-1]

Integers M and N define the number of nodes in polar coordinates,
where M is the number of radiuses, and N is the number of nodes in
angular coordinates. All nodes of grid are equispaces in angular
direction. The number N *must* be the power of 2. In radial
coordinate, the radiuses must be defined (real numbers) r[1], ..., r[M].
By default r[0]=0.0.

The values of Beltrami differential should be given in the table,
following r[1..M]. In this table mu[i][j] corresponds to 
mu(r[i]*exp(2*Pi*j/N)). For r[0] only one value mu[0][0] must be given.

The example of the table follows:
4 8
0.1
0.2
0.3
0.4
(3,1)
(-0,1) (-3,1) (-0,1) (-3,1) (-7,5) (-4,1) (-7,5) (-4,1)
(-6,3) ( 7,1) (-6,3) ( 7,1) ( 1,2) (-2,4) ( 1,2) (-2,4)
(-6,3) ( 7,1) (-6,3) ( 7,1) ( 1,2) (-2,4) ( 1,2) (-2,4)
(-7,5) (-4,1) (-7,5) (-4,1) (-0,1) (-3,1) (-0,1) (-3,1)

EXIT CODES

The program exits with code 0, only in case it has done
what it was meant to do. In all other cases the exit code.
is non-zero. For example --help option exits with code
ERROR_HELP. The errors related to interaction with operating
system has code >=16. In future versions more exit codes
can be added, but the current exit code will remain as is.
  THE TABLE OF EXIT CODES:
   0 ERROR_OK
   1 ERROR_VERSION
   2 ERROR_HELP
   3 ERROR_DESCRIPTION
   4 ERROR_NO_ARGUMENT
   5 ERROR_WRONG_ARGUMENT
  16 ERROR_SERIOUS
  16 ERROR_INTERNAL
  17 ERROR_MALLOC
  18 ERROR_STAT_FILE
  19 ERROR_EMPTY_FILE
  20 ERROR_OPEN_FILE_READ
  21 ERROR_OPEN_FILE_WRITE
  22 ERROR_OPEN_FILE_TMP
  23 ERROR_WRITE_FILE
  24 ERROR_INPUT_FORMAT

5  Project revision history

2000-07-18

2004-01-24

2004-02-07

2004-02-08

2004-03-22

2004-03-23

2004-03-24

2004-03-26

2004-03-28

2004-03-29

2004-03-30

2004-03-31

2004-07-18

2004-08-05

6  License

Available at http://www.math.toronto.edu/dkhmelev/PROGS/

Author:

Dmitry V. Khmelev dkhmelev((at))math.toronto.edu [change ((at)) to @ in order to get proper address - antispam]

University of Toronto, Department of Mathematics, 100 St George Street, M5S 3G3 ON, Canada

LICENSING TERMS

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. You should obtain GNU GPL with file COPYING in this distribution.

Scientific results produced using the software provided shall acknowledge the use of this software. The proper reference is:

D. Khmelev, http://www.math.toronto.edu/dkhmelev/PROGS/

Moreover shall the author of the software be informed about the publication.

By using this program you agree to the licensing terms.

NO WARRANTY

BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM ÄS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.

IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR REDISTRIBUTE THE PROGRAM, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.