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[Octave-cvsupdate] SF.net SVN: octave:[8300] trunk/octave-forge/main
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From: <ad...@us...> - 2011-06-01 19:35:43
|
Revision: 8300
http://octave.svn.sourceforge.net/octave/?rev=8300&view=rev
Author: adb014
Date: 2011-06-01 19:35:33 +0000 (Wed, 01 Jun 2011)
Log Message:
-----------
Work in progress replacement for the galois field type in the communications package, using the Octave OOP functionality
Modified Paths:
--------------
trunk/octave-forge/main/gsl/doc/.ps
Added Paths:
-----------
trunk/octave-forge/main/galois/
trunk/octave-forge/main/galois/COPYING
trunk/octave-forge/main/galois/DESCRIPTION
trunk/octave-forge/main/galois/INDEX
trunk/octave-forge/main/galois/Makefile
trunk/octave-forge/main/galois/inst/
trunk/octave-forge/main/galois/inst/@gf/
trunk/octave-forge/main/galois/inst/@gf/all.m
trunk/octave-forge/main/galois/inst/@gf/and.m
trunk/octave-forge/main/galois/inst/@gf/any.m
trunk/octave-forge/main/galois/inst/@gf/conv.m
trunk/octave-forge/main/galois/inst/@gf/convmtx.m
trunk/octave-forge/main/galois/inst/@gf/ctranspose.m
trunk/octave-forge/main/galois/inst/@gf/deconv.m
trunk/octave-forge/main/galois/inst/@gf/dftmtx.m
trunk/octave-forge/main/galois/inst/@gf/diag.m
trunk/octave-forge/main/galois/inst/@gf/display.m
trunk/octave-forge/main/galois/inst/@gf/double.m
trunk/octave-forge/main/galois/inst/@gf/end.m
trunk/octave-forge/main/galois/inst/@gf/eq.m
trunk/octave-forge/main/galois/inst/@gf/exp.m
trunk/octave-forge/main/galois/inst/@gf/fft.m
trunk/octave-forge/main/galois/inst/@gf/filter.m
trunk/octave-forge/main/galois/inst/@gf/finite.m
trunk/octave-forge/main/galois/inst/@gf/ge.m
trunk/octave-forge/main/galois/inst/@gf/gf.m
trunk/octave-forge/main/galois/inst/@gf/gt.m
trunk/octave-forge/main/galois/inst/@gf/horzcat.m
trunk/octave-forge/main/galois/inst/@gf/ifft.m
trunk/octave-forge/main/galois/inst/@gf/isempty.m
trunk/octave-forge/main/galois/inst/@gf/isinf.m
trunk/octave-forge/main/galois/inst/@gf/isna.m
trunk/octave-forge/main/galois/inst/@gf/isnan.m
trunk/octave-forge/main/galois/inst/@gf/isprimitive.m
trunk/octave-forge/main/galois/inst/@gf/le.m
trunk/octave-forge/main/galois/inst/@gf/length.m
trunk/octave-forge/main/galois/inst/@gf/log.m
trunk/octave-forge/main/galois/inst/@gf/lt.m
trunk/octave-forge/main/galois/inst/@gf/minpol.m
trunk/octave-forge/main/galois/inst/@gf/minus.m
trunk/octave-forge/main/galois/inst/@gf/mtimes.m
trunk/octave-forge/main/galois/inst/@gf/ne.m
trunk/octave-forge/main/galois/inst/@gf/not.m
trunk/octave-forge/main/galois/inst/@gf/numel.m
trunk/octave-forge/main/galois/inst/@gf/or.m
trunk/octave-forge/main/galois/inst/@gf/plus.m
trunk/octave-forge/main/galois/inst/@gf/power.m
trunk/octave-forge/main/galois/inst/@gf/private/
trunk/octave-forge/main/galois/inst/@gf/private/cachefield.m
trunk/octave-forge/main/galois/inst/@gf/private/modn.m
trunk/octave-forge/main/galois/inst/@gf/private/promote_and_check.m
trunk/octave-forge/main/galois/inst/@gf/rdivide.m
trunk/octave-forge/main/galois/inst/@gf/reshape.m
trunk/octave-forge/main/galois/inst/@gf/roots.m
trunk/octave-forge/main/galois/inst/@gf/size.m
trunk/octave-forge/main/galois/inst/@gf/sqrt.m
trunk/octave-forge/main/galois/inst/@gf/subsasgn.m
trunk/octave-forge/main/galois/inst/@gf/subsindex.m
trunk/octave-forge/main/galois/inst/@gf/subsref.m
trunk/octave-forge/main/galois/inst/@gf/times.m
trunk/octave-forge/main/galois/inst/@gf/transpose.m
trunk/octave-forge/main/galois/inst/@gf/uminus.m
trunk/octave-forge/main/galois/inst/@gf/uplus.m
trunk/octave-forge/main/galois/inst/@gf/vertcat.m
trunk/octave-forge/main/galois/inst/convmtx.m
trunk/octave-forge/main/galois/inst/cosets.m
trunk/octave-forge/main/galois/inst/gftable.m
trunk/octave-forge/main/galois/inst/isgalois.m
trunk/octave-forge/main/galois/inst/rsdecof.m
trunk/octave-forge/main/galois/inst/rsencof.m
trunk/octave-forge/main/galois/inst/rsgenpoly.m
trunk/octave-forge/main/galois/src/
trunk/octave-forge/main/galois/src/Makefile
trunk/octave-forge/main/galois/src/__gfilter__.cc
trunk/octave-forge/main/galois/src/__gmtimes__.cc
trunk/octave-forge/main/galois/src/isprimitive.cc
trunk/octave-forge/main/galois/src/primpoly.cc
Added: trunk/octave-forge/main/galois/COPYING
===================================================================
--- trunk/octave-forge/main/galois/COPYING (rev 0)
+++ trunk/octave-forge/main/galois/COPYING 2011-06-01 19:35:33 UTC (rev 8300)
@@ -0,0 +1,337 @@
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Property changes on: trunk/octave-forge/main/galois/COPYING
___________________________________________________________________
Added: svn:executable
+ *
Added: trunk/octave-forge/main/galois/DESCRIPTION
===================================================================
--- trunk/octave-forge/main/galois/DESCRIPTION (rev 0)
+++ trunk/octave-forge/main/galois/DESCRIPTION 2011-06-01 19:35:33 UTC (rev 8300)
@@ -0,0 +1,12 @@
+Name: Galois Field
+Version: 0.0.1
+Date: 2008-11-14
+Author: David Bateman
+Maintainer: David Bateman
+Title: Galois Field Test Package
+Description: Test package for new implementation galois field code.
+Depends: octave (>= 3.4.0)
+Depends: signal (>= 1.0.0)
+Autoload: yes
+License: GPL version 2 or later
+Url: http://octave.sf.net
Property changes on: trunk/octave-forge/main/galois/DESCRIPTION
___________________________________________________________________
Added: svn:executable
+ *
Added: trunk/octave-forge/main/galois/INDEX
===================================================================
--- trunk/octave-forge/main/galois/INDEX (rev 0)
+++ trunk/octave-forge/main/galois/INDEX 2011-06-01 19:35:33 UTC (rev 8300)
@@ -0,0 +1,59 @@
+galois >> Galois
+Galois Fields of Even Characateristic
+ + - = Addition and subtraction in a Galois Field.
+ * / \ = Matrix multiplication and division of Galois arrays.
+ .* ./ .\ = Element by element multiplication and division of Galois arrays.
+ ** ^ = Matrix exponentiation of Galois arrays.
+ .** .^ = Element by element matrix exponentiation of Galois arrays.
+ ' .' = Matrix transpose of Galois arrays.
+ == ~= != > >= < <= = Logical operators on Galois arrays.
+ all
+ and
+ any
+ conv
+ convmtx
+ cosets
+ deconv
+ dftmtx
+ diag
+ exp
+ ge
+ gf
+ gt
+ fft
+ filter
+ ifft
+ inv
+ inverse
+ isempty
+ isequal
+ isgalois
+ isprimitive
+ le
+ length
+ log
+ lt
+ minpol
+ mtimes
+ or
+ power
+ reshape
+ roots
+ polyval
+ primpoly
+ size
+To be implemented
+ det
+ lu
+ rank
+ prod
+ sum
+ sumsq
+ ldivide
+ mldivide
+ mpower
+ mrdivide
+ bchdeco
+ bchenco
+ rsdec
+ rsenc
Added: trunk/octave-forge/main/galois/Makefile
===================================================================
--- trunk/octave-forge/main/galois/Makefile (rev 0)
+++ trunk/octave-forge/main/galois/Makefile 2011-06-01 19:35:33 UTC (rev 8300)
@@ -0,0 +1,29 @@
+sinclude ../../Makeconf
+
+
+PKG_FILES = COPYING DESCRIPTION INDEX $(wildcard src/*) \
+ $(wildcard inst/*)
+SUBDIRS = src
+
+.PHONY: $(SUBDIRS)
+
+pre-pkg::
+ @for _dir in $(SUBDIRS); do \
+ $(MAKE) -C $$_dir pre-pkg; \
+ done
+
+clean:
+ @for _dir in $(SUBDIRS); do \
+ $(MAKE) -C $$_dir $(MAKECMDGOALS); \
+ done
+
+build::
+ @for _dir in $(SUBDIRS); do \
+ $(MAKE) -C $$_dir all; \
+ done
+
+check:: build
+ @$(RM) __check__.m
+ @find . -name "*.m" -exec grep %\! {} \; -o -name "*.cc" -exec grep %\! {} \; >> __check__.m
+ @octave -q --eval 'addpath("./src"); addpath("./inst"); test("__check__","normal",stdout);'
+ @$(RM) __check__.m
Property changes on: trunk/octave-forge/main/galois/Makefile
___________________________________________________________________
Added: svn:executable
+ *
Added: trunk/octave-forge/main/galois/inst/@gf/all.m
===================================================================
--- trunk/octave-forge/main/galois/inst/@gf/all.m (rev 0)
+++ trunk/octave-forge/main/galois/inst/@gf/all.m 2011-06-01 19:35:33 UTC (rev 8300)
@@ -0,0 +1,27 @@
+## Copyright (C) 2011 David Bateman
+##
+## 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.
+##
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with this program; If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} all (@var{x}, @var{dim})
+## For a Galois array @var{x}, return true if all of the elements along the
+## dimension @var{dim} are non-zero.
+## @end deftypefn
+
+function y = all (g, varargin)
+ y = all (g._x, varargin{:});
+endfunction
+
+%!assert (all (gf (0:3, 2)), false)
+%!assert (all (gf (ones(1,4), 2)), true)
Added: trunk/octave-forge/main/galois/inst/@gf/and.m
===================================================================
--- trunk/octave-forge/main/galois/inst/@gf/and.m (rev 0)
+++ trunk/octave-forge/main/galois/inst/@gf/and.m 2011-06-01 19:35:33 UTC (rev 8300)
@@ -0,0 +1,28 @@
+## Copyright (C) 2011 David Bateman
+##
+## 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.
+##
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with this program; If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} gt (@var{a}, @var{b})
+## Element-by-element logical and operator for Galois arrays.
+## @end deftypefn
+
+function y = and (a, b)
+ [a, b] = promote_and_check (a, b);
+ y = a._x & b._x;
+endfunction
+
+%!assert(gf(1) & gf(1), true)
+%!assert(gf(0) & gf(1), false)
+%!assert(gf(0) & gf(0), false)
Added: trunk/octave-forge/main/galois/inst/@gf/any.m
===================================================================
--- trunk/octave-forge/main/galois/inst/@gf/any.m (rev 0)
+++ trunk/octave-forge/main/galois/inst/@gf/any.m 2011-06-01 19:35:33 UTC (rev 8300)
@@ -0,0 +1,27 @@
+## Copyright (C) 2011 David Bateman
+##
+## 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.
+##
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with this program; If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} any (@var{x}, @var{dim})
+## For a Galois array @var{x}, return true if any of the elements along the
+## dimension @var{dim} are non-zero.
+## @end deftypefn
+
+function y = any (g, varargin)
+ y = any (g._x, varargin{:});
+endfunction
+
+%!assert (any (gf (0:3, 2)), true)
+%!assert (any (gf (zeros(1,4), 2)), false)
Added: trunk/octave-forge/main/galois/inst/@gf/conv.m
===================================================================
--- trunk/octave-forge/main/galois/inst/@gf/conv.m (rev 0)
+++ trunk/octave-forge/main/galois/inst/@gf/conv.m 2011-06-01 19:35:33 UTC (rev 8300)
@@ -0,0 +1,90 @@
+## Copyright (C) 2011 David Bateman
+##
+## 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.
+##
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with this program; If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} conv (@var{a}, @var{b})
+## Convolve two Galois vectors.
+##
+## @code{y = conv (a, b)} returns a vector of length equal to
+## @code{length (a) + length (b) - 1}.
+## If @var{a} and @var{b} are polynomial coefficient vectors, @code{conv}
+## returns the coefficients of the product polynomial.
+## @end deftypefn
+## @seealso{deconv}
+
+function y = conv (a, b)
+
+ if (nargin != 2)
+ usage ("conv(a, b)");
+ endif
+
+ if (!isgalois (a) && !isgalois (b))
+ error("conv: at least one argument must be a galois variable");
+ elseif (!isgalois (a))
+ a = gf(a, b._m, b._prim_poly);
+ elseif (!isgalois (b))
+ b = gf(b, a._m, a._prim_poly);
+ elseif (a._m != b._m && a._prim_poly != b._prim_poly)
+ error("conv: both vectors must be in the same galois field");
+ endif
+
+ if (min(size(a)) > 1 || min(size(b)) > 1)
+ error("conv: both arguments must be vectors");
+ endif
+
+ la = length (a);
+ lb = length (b);
+
+ ly = la + lb - 1;
+
+ ## Ensure that both vectors are row vectors.
+ if (rows (a) > 1)
+ a = reshape (a, 1, la);
+ endif
+ if (rows (b) > 1)
+ b = reshape (b, 1, lb);
+ endif
+
+ ## Use the shortest vector as the coefficent vector to filter.
+ if (la < lb)
+ if (ly > lb)
+ ## Can't concatenate galois variables like this yet
+ ## x = [b, (zeros (1, ly - lb))];
+ x = gf([b, (zeros (1, ly - lb))], b._m, b._prim_poly);
+ else
+ x = b;
+ endif
+ y = filter (a, 1, x);
+ else
+ if(ly > la)
+ ## Can't concatenate galois variables like this yet
+ ## x = [a, (zeros (1, ly - la))];
+ x = gf([a, (zeros (1, ly - la))], a._m, a._prim_poly);
+ else
+ x = a;
+ endif
+ y = filter (b, 1, x);
+ endif
+
+endfunction
+
+%!test
+%! poly1 = gf([2,4,5,1],3);
+%! poly2 = gf([1,2],3);
+%! mulpoly = conv(poly1, poly2); ## multiplication
+%! poly3 = [poly,remd] = deconv(mulpoly, poly2);
+%! assert (isequal(poly1,poly3))
+%! assert (!any (remd))
+
Added: trunk/octave-forge/main/galois/inst/@gf/convmtx.m
===================================================================
--- trunk/octave-forge/main/galois/inst/@gf/convmtx.m (rev 0)
+++ trunk/octave-forge/main/galois/inst/@gf/convmtx.m 2011-06-01 19:35:33 UTC (rev 8300)
@@ -0,0 +1,57 @@
+## Copyright (C) 2011 David Bateman
+##
+## 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.
+##
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with this program; If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} convmtx (@var{a}, @var{n})
+##
+## Create matrix to perform repeated convolutions with the same vector
+## in a Galois Field. If @var{a} is a column vector and @var{x} is a
+## column vector of length @var{n}, in a Galois Field then
+##
+## @code{convmtx(@var{a}, @var{n}) * @var{x}}
+##
+## gives the convolution of of @var{a} and @var{x} and is the
+## same as @code{conv(@var{a}, @var{x})}. The difference is if
+## many vectors are to be convolved with the same vector, then
+## this technique is possibly faster.
+##
+## Similarly, if @var{a} is a row vector and @var{x} is a row
+## vector of length @var{n}, then
+##
+## @code{@var{x} * convmtx(@var{a}, @var{n})}
+##
+## is the same as @code{conv(@var{x}, @var{a})}.
+## @end deftypefn
+## @seealso{conv}
+
+function b = convmtx (a, n)
+
+ if (!isgalois (a))
+ error("convmtx: argument must be a galois variable");
+ endif
+
+ b = gf(convmtx(a._x, n), a._m, a._prim_poly);
+endfunction
+
+%!test
+%! grow = gf (0:7, 3);
+%! b = gf([1,0,0,1,0,1,0,1],3);
+%! a = gf([1,0,1,1],3);
+%! x = gf([1,zeros(1,99)],3);
+%! y1 = conv(grow+1, grow);
+%! y2 = grow * convmtx(grow+1, length(grow));
+%! assert (all(y1 == y2));
+
+
Added: trunk/octave-forge/main/galois/inst/@gf/ctranspose.m
===================================================================
--- trunk/octave-forge/main/galois/inst/@gf/ctranspose.m (rev 0)
+++ trunk/octave-forge/main/galois/inst/@gf/ctranspose.m 2011-06-01 19:35:33 UTC (rev 8300)
@@ -0,0 +1,28 @@
+## Copyright (C) 2011 David Bateman
+##
+## 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.
+##
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with this program; If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} all (@var{x}, @var{dim})
+## Return the complex conjugate transpose of the Galois array @var{x}.
+## This function is equivalent to @code{x'}.
+## @end deftypefn
+
+function y = ctranspose (g);
+ y = g;
+ y._x = g._x ';
+endfunction
+
+%!assert(ctranspose(gf(0:3,3)),gf([0:3]',3))
+%!assert(gf(0:3,3)',gf([0:3]',3))
Added: trunk/octave-forge/main/galois/inst/@gf/deconv.m
===================================================================
--- trunk/octave-forge/main/galois/inst/@gf/deconv.m (rev 0)
+++ trunk/octave-forge/main/galois/inst/@gf/deconv.m 2011-06-01 19:35:33 UTC (rev 8300)
@@ -0,0 +1,80 @@
+## Copyright (C) 2011 David Bateman
+##
+## 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.
+##
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with this program; If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} deconv (@var{y}, @var{a})
+## Deconvolve two Galois vectors.
+##
+## @code{[b, r] = deconv (y, a)} solves for @var{b} and @var{r} such that
+## @code{y = gconv (a, b) + r}.
+##
+## If @var{y} and @var{a} are polynomial coefficient vectors, @var{b} will
+## contain the coefficients of the polynomial quotient and @var{r} will be
+## a remander polynomial of lowest order.
+## @end deftypefn
+## @seealso{gconv,deconv,conv}
+
+function [b, r] = deconv (y, a)
+
+
+ if (nargin != 2)
+ usage ("deconv(a, b)");
+ endif
+
+ if (!isgalois (y) && !isgalois (a))
+ error("deconv: at least one argument must be a galois variable");
+ elseif (!isgalois (y))
+ y = gf(y, a._m, a._prim_poly);
+ elseif (!isgalois (a))
+ a = gf(a, y._m, y._prim_poly);
+ elseif (a._m != y._m && a._prim_poly != y._prim_poly)
+ error("deconv: both vectors must be in the same galois field");
+ endif
+
+ if (min(size(a)) > 1 || min(size(y)) > 1)
+ error("deconv: both arguments must be vectors");
+ endif
+
+ la = length (a);
+ ly = length (y);
+
+ lb = ly - la + 1;
+
+ ## Ensure that both vectors are row vectors.
+ if (rows (a) > 1)
+ a = reshape (a, 1, la);
+ endif
+ if (rows (y) > 1)
+ y = reshape (y, 1, ly);
+ endif
+
+ if (ly > la)
+ b = filter (y, a, [1, (zeros (1, ly - la))]);
+ elseif (ly == la)
+ b = filter (y, a, 1);
+ else
+ b = gf(0, y._m, y._prim_poly);
+ endif
+
+ lc = la + length (b) - 1;
+ if (ly == lc)
+ r = y - conv (a, b);
+ else
+ ## Can't concatenate galois variables like this yet
+ ## r = [(zeros (1, lc - ly)), y] - conv (a, b);
+ r = gf([(zeros (1, lc - ly)), y], y._m, y._prim_poly) - conv (a, b);
+ endif
+
+endfunction
Added: trunk/octave-forge/main/galois/inst/@gf/dftmtx.m
===================================================================
--- trunk/octave-forge/main/galois/inst/@gf/dftmtx.m (rev 0)
+++ trunk/octave-forge/main/galois/inst/@gf/dftmtx.m 2011-06-01 19:35:33 UTC (rev 8300)
@@ -0,0 +1,83 @@
+## Copyright (C) 2011 David Bateman
+##
+## 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.
+##
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with this program; If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{d} = } dftmtx (@var{a})
+##
+## Form a matrix, that can be used to perform Fourier transforms in
+## a Galois Field.
+##
+## Given that @var{a} is an element of the Galois Field GF(2^m), and
+## that the minimum value for @var{k} for which @code{@var{a} ^ @var{k}}
+## is equal to one is @code{2^m - 1}, then this function produces a
+## @var{k}-by-@var{k} matrix representing the discrete Fourier transform
+## over a Galois Field with respect to @var{a}. The Fourier transform of
+## a column vector is then given by @code{dftmtx(@var{a}) * @var{x}}.
+##
+## The inverse Fourier transform is given by @code{dftmtx(1/@var{a})}
+## @end deftypefn
+
+function d = dftmtx(a)
+
+ if (nargin != 1)
+ error ("usage: d = dftmtx (a)");
+ endif
+
+ if (!isgalois(a))
+ error("dftmtx: argument must be a galois variable");
+ endif
+
+ m = a._m;
+ prim = a._prim_poly;
+ n = 2^a._m - 1;
+ if (n > 255)
+ error ([ "dftmtx: argument must be in Galois Field GF(2^m), where" ...
+ " m is not greater than 8"]);
+ endif
+
+ if (length(a) ~= 1)
+ error ("dftmtx: argument must be a scalar");
+ endif
+
+ mp = minpol(a);
+ if ((mp(1) ~= 1) || !isprimitive(mp))
+ error("dftmtx: argument must be a primitive nth root of unity");
+ endif
+
+ step = log(a);
+ step = step._x;
+ row = exp(gf([0:n-1], m, prim));
+ d = gf(zeros(n,n),m, prim);
+ for i=1:n;
+ d(i,:) = row .^ mod(step*(i-1),n);
+ end
+
+endfunction
+
+%!test
+%! m = 3;
+%! n = 2.^m - 1;
+%! alph = gf(2,m);
+%! x = gf(floor(2^m*rand(n,1)),m);
+%! fm = dftmtx(alph);
+%! ifm = dftmtx(1/alph);
+%! y0 = fft(x);
+%! y1 = fm * x;
+%! assert(all (y0 == y1))
+%! z0 = gifft(y0);
+%! z1 = ifm * y1;
+%! assert(all (z0 == x))
+%! assert(all (z1 == x))
+
Added: trunk/octave-forge/main/galois/inst/@gf/diag.m
===================================================================
--- trunk/octave-forge/main/galois/inst/@gf/diag.m (rev 0)
+++ trunk/octave-forge/main/galois/inst/@gf/diag.m 2011-06-01 19:35:33 UTC (rev 8300)
@@ -0,0 +1,53 @@
+## Copyright (C) 2011 David Bateman
+##
+## 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.
+##
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with this program; If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} diag (@var{v}, @var{k})
+## Return a diagonal matrix with Galois vector @var{v} on diagonal @var{k}.
+## The second argument is optional. If it is positive, the vector is placed on
+## the @var{k}-th super-diagonal. If it is negative, it is placed on the
+## @var{-k}-th sub-diagonal. The default value of @var{k} is 0, and the
+## vector is placed on the main diagonal. For example,
+##
+## @example
+## diag (gf([1, 2, 3],2), 1)
+## ans =
+## GF(2^2) array. Primitive Polynomial = D^2+D+1 (decimal 7)
+##
+## Array elements =
+##
+## 0 1 0 0
+## 0 0 2 0
+## 0 0 0 3
+## 0 0 0 0
+## @end example
+## @end deftypefn
+
+function y = diag (g, varargin)
+ y = g;
+ y._x = diag (y._x, varargin{:});
+endfunction
+
+%!assert(diag(gf([1; 2; 3], 3)), gf([1, 0, 0; 0, 2, 0; 0, 0, 3], 3));
+%!assert(diag (gf([1; 2; 3], 3), 1), gf([0, 1, 0, 0; 0, 0, 2, 0; 0, 0, 0, 3; 0, 0, 0, 0], 3));
+%!assert(diag (gf([1; 2; 3], 3), 2), gf([0, 0, 1, 0, 0; 0, 0, 0, 2, 0; 0, 0, 0, 0, 3; 0, 0, 0, 0, 0; 0, 0, 0, 0, 0], 3));
+%!assert(diag (gf([1; 2; 3], 3),-1), gf([0, 0, 0, 0; 1, 0, 0, 0; 0, 2, 0, 0; 0, 0, 3, 0], 3));
+%!assert(diag (gf([1; 2; 3], 3),-2), gf([0, 0, 0, 0, 0; 0, 0, 0, 0, 0; 1, 0, 0, 0, 0; 0, 2, 0, 0, 0; 0, 0, 3, 0, 0], 3));
+%!assert(diag (gf([1, 0, 0; 0, 2, 0; 0, 0, 3], 3)), gf([1; 2; 3], 3));
+%!assert(diag (gf([0, 1, 0, 0; 0, 0, 2, 0; 0, 0, 0, 3; 0, 0, 0, 0], 3), 1), gf([1; 2; 3],3));
+%!assert(diag (gf([0, 0, 0, 0; 1, 0, 0, 0; 0, 2, 0, 0; 0, 0, 3, 0], 3), -1), gf([1; 2; 3], 3));
+%!assert(diag (gf(ones(1, 0), 3), 2), gf(zeros (2), 3));
+%!assert(diag (gf(1:3, 3), 4, 2), gf([1, 0; 0, 2; 0, 0; 0, 0], 3));
+
Added: trunk/octave-forge/main/galois/inst/@gf/display.m
===================================================================
--- trunk/octave-forge/main/galois/inst/@gf/display.m (rev 0)
+++ trunk/octave-forge/main/galois/inst/@gf/display.m 2011-06-01 19:35:33 UTC (rev 8300)
@@ -0,0 +1,60 @@
+## Copyright (C) 2011 David Bateman
+##
+## 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.
+##
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with this program; If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} display (@var{g})
+## Displays a Galois array.
+## @end deftypefn
+
+function display (g)
+
+ if (!isempty (inputname(1)))
+ fprintf("%s = \n",inputname(1));
+ endif
+ if (g._m == 1)
+ fprintf ("GF(2) array.");
+ else
+ fprintf ("GF(2^%d) array. Primitive Polynomial = ", g._m);
+ p = g._prim_poly;
+ m = g._m;
+ first = true;
+ for i = m + 1 : -1 : 1
+ if (bitget (p, i) != 0)
+ if (i > 1)
+ if (first)
+ first = false;
+ fprintf("D")
+ else
+ fprintf("+D")
+ endif
+ if (i != 2)
+ fprintf("^%d", i - 1);
+ endif
+ else
+ if (first)
+ first = false;
+ fprintf("1");
+ else
+ fprintf("+1");
+ endif
+ endif
+ endif
+ endfor
+ fprintf (" (decimal %d)", p);
+ endif
+ fprintf("\n\nArray elements = \n\n");
+ disp (g._x);
+ fprintf("\n");
+endfunction
Added: trunk/octave-forge/main/galois/inst/@gf/double.m
===================================================================
--- trunk/octave-forge/main/galois/inst/@gf/double.m (rev 0)
+++ trunk/octave-forge/main/galois/inst/@gf/double.m 2011-06-01 19:35:33 UTC (rev 8300)
@@ -0,0 +1,23 @@
+## Copyright (C) 2011 David Bateman
+##
+## 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.
+##
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with this program; If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} double (@var{g})
+## Convert a Galois array to a double array.
+## @end deftypefn
+
+function x = double (g)
+ x = double (g._x);
+endfunction
Added: trunk/octave-forge/main/galois/inst/@gf/end.m
===================================================================
--- trunk/octave-forge/main/galois/inst/@gf/end.m (rev 0)
+++ trunk/octave-forge/main/galois/inst/@gf/end.m 2011-06-01 19:35:33 UTC (rev 8300)
@@ -0,0 +1,34 @@
+## Copyright (C) 2011 David Bateman
+##
+## 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.
+##
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with this program; If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} end (@var{obj}, @var{ind}, @var{num})
+## Return the @code{end} index of a Galois array.
+## @end deftypefn
+
+function r = end (obj, index_pos, num_indices)
+ dv = size (obj._x);
+ for i = (num_indices + 1) : length (dv)
+ dv(num_indices) *= dv(i);
+ endfor
+ if (index_pos <= length (dv))
+ r = dv (index_pos);
+ else
+ r = 1;
+ endif
+endfunction
+
+%!assert(gf(0:7,3)(end), gf(7,3))
+%!assert(gf([0, 1; 2, 3], 3)(end, 1:2), gf ([2, 3], 3))
Added: trunk/octave-forge/main/galois/inst/@gf/eq.m
===================================================================
--- trunk/octave-forge/main/galois/inst/@gf/eq.m (rev 0)
+++ trunk/octave-forge/main/galois/inst/@gf/eq.m 2011-06-01 19:35:33 UTC (rev 8300)
@@ -0,0 +1,27 @@
+## Copyright (C) 2011 David Bateman
+##
+## 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.
+##
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with this program; If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} eq (@var{a}, @var{b})
+## Equivalence operator for Galois arrays.
+## @end deftypefn
+
+function y = eq (a, b)
+ [a, b] = promote_and_check (a, b);
+ y = a._x == b._x;
+endfunction
+
+%!assert(gf(1) == gf(1), true)
+%!assert(gf(0) == gf(1), false)
Added: trunk/octave-forge/main/galois/inst/@gf/exp.m
===================================================================
--- trunk/octave-forge/main/galois/inst/@gf/exp.m (rev 0)
+++ trunk/octave-forge/main/galois/inst/@gf/exp.m 2011-06-01 19:35:33 UTC (rev 8300)
@@ -0,0 +1,30 @@
+## Copyright (C) 2011 David Bateman
+##
+## 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.
+##
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with this program; If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} exp (@var{x})
+## Compute the anti-logarithm for each element of @var{x} for a Galois
+## array.
+## @end deftypefn
+
+function y = exp (g)
+ if (any (g._x == g._n))
+ warning ("exp: exp of 2^m-1 undefined in galois field");
+ endif
+ y = g;
+ y._x = reshape (g._alpha_to (g._x + 1), size(g._x));
+endfunction
+
+%!assert(exp(gf(0:7,3)),gf([1, 2, 4, 3, 6, 7, 5, 0], 3))
Added: trunk/octave-forge/main/galois/inst/@gf/fft.m
===================================================================
--- trunk/octave-forge/main/galois/inst/@gf/fft.m (rev 0)
+++ trunk/octave-forge/main/galois/inst/@gf/fft.m 2011-06-01 19:35:33 UTC (rev 8300)
@@ -0,0 +1,50 @@
+## Copyright (C) 2011 David Bateman
+##
+## 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.
+##
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with this program; If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} fft (@var{x})
+##
+## If @var{x} is a column vector, finds the FFT over the primitive element
+## of the Galois Field of @var{x}. If @var{x} is in the Galois Field
+## GF(2^@var{m}), then @var{x} must have @code{2^@var{m} - 1} elements.
+## @end deftypefn
+
+function y = fft(x)
+
+ if (nargin != 1)
+ error ("usage: y = fft (x)");
+ endif
+
+ if (!isgalois(x))
+ error("fft: argument must be a galois variable");
+ endif
+
+ n = g._n;
+ if (n > 255)
+ error ([ "fft: argument must be in Galois Field GF(2^m), where", ...
+ " m is not greater than 8"]);
+ endif
+
+ alph = gf(2, x._m, x._prim_poly);
+ [nr, nc] = size(x);
+ if ((nc == 1) && (nr == n))
+ y = dftmtx(alph) * x;
+ elseif ((nc == n) && (nr == 1))
+ y = (dftmtx(alph) * x')';
+ else
+ error ("fft: argument must be a vector in GF(2^m) of length 2^m-1");
+ endif
+
+endfunction
Added: trunk/octave-forge/main/galois/inst/@gf/filter.m
===================================================================
--- trunk/octave-forge/main/galois/inst/@gf/filter.m (rev 0)
+++ trunk/octave-forge/main/galois/inst/@gf/filter.m 2011-06-01 19:35:33 UTC (rev 8300)
@@ -0,0 +1,131 @@
+## Copyright (C) 2011 David Bateman
+##
+## 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.
+##
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with this program; If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {y =} filter (@var{b}, @var{a}, @var{x})
+## @deftypefnx {Function File} {[@var{y}, @var{sf}] =} filter (@var{b}, @var{a}, @var{x}, @var{si})
+##
+## Digital filtering of vectors in a Galois Field. Returns the solution to
+## the following linear, time-invariant difference equation over a Galois
+## Field:
+## @iftex
+## @tex
+## $$
+## \\sum_{k=0}^N a_{k+1} y_{n-k} = \\sum_{k=0}^M b_{k+1} x_{n-k}, \\qquad
+## 1 \\le n \\le P
+## $$
+## @end tex
+## @end iftex
+## @ifinfo
+##
+## @smallexample
+## N M
+## SUM a(k+1) y(n-k) = SUM b(k+1) x(n-k) for 1<=n<=length(x)
+## k=0 k=0
+## @end smallexample
+## @end ifinfo
+##
+## @noindent
+## where
+## @ifinfo
+## N=length(a)-1 and M=length(b)-1.
+## @end ifinfo
+## @iftex
+## @tex
+## $a \\in \\Re^{N-1}$, $b \\in \\Re^{M-1}$, and $x \\in \\Re^P$.
+## @end tex
+## @end iftex
+## An equivalent form of this equation is:
+## @iftex
+## @tex
+## $$
+## y_n = -\\sum_{k=1}^N c_{k+1} y_{n-k} + \\sum_{k=0}^M d_{k+1} x_{n-k}, \\qquad
+## 1 \\le n \\le P
+## $$
+## @end tex
+## @end iftex
+## @ifinfo
+##
+## @smallexample
+## N M
+## y(n) = - SUM c(k+1) y(n-k) + SUM d(k+1) x(n-k) for 1<=n<=length(x)
+## k=1 k=0
+## @end smallexample
+## @end ifinfo
+##
+## @noindent
+## where
+## @ifinfo
+## c = a/a(1) and d = b/a(1).
+## @end ifinfo
+## @iftex
+## @tex
+## $c = a/a_1$ and $d = b/a_1$.
+## @end tex
+## @end iftex
+##
+## If the fourth argument @var{si} is provided, it is taken as the
+## initial state of the system and the final state is returned as
+## @var{sf}. The state vector is a column vector whose length is
+## equal to the length of the longest coefficient vector minus one.
+## If @var{si} is not supplied, the initial state vector is set to all
+## zeros.
+## @end deftypefn
+
+function [y, sf] = filter (b, a, x, si)
+ if (nargin == 3)
+ [a, b, x] = promote_and_check (a, b, x);
+ if (rows(x) == 1)
+ si = gf (zeros (1, max (length (a), length (b)) - 1), a._m, a._prim_poly);
+ else
+ si = gf (zeros (max (length (a), length (b)) - 1, 1), a._m, a._prim_poly);
+ endif
+ elseif (nargin > 4)
+ [a, b, x, si] = promote_and_check (a, b, x, si);
+ else
+ print_usage();
+ endif
+
+ if (! (isvector (a) && isvector (b) && isvector (x) && isvector (si)))
+ error ("filter: arguments must be vectors")
+ endif
+
+ if (numel (a) > numel (b))
+ if (rows (b) == 1)
+ b = [b, zeros(1,numel(a)-numel(b))];
+ else
+ b = [b; zeros(numel(a)-numel(b)),1];
+ endif
+ elseif (numel (a) < numel (b))
+ if (rows (a) == 1)
+ a = [a, zeros(1,numel(b)-numel(a))];
+ else
+ a = [a; zeros(numel(b)-numel(a)),1];
+ endif
+ endif
+
+ [y, sf] = __gfilter__ (b._x, a._x, x._x, si._x, a._m, a._alpha_to, a._index_of);
+
+ sf = gf (sf, x._m, x._prim_poly);
+ y = gf (y, x._m, x._prim_poly);
+
+endfunction
+
+%!test
+%! b = gf([2, 0, 0, 1, 0, 2, 0, 1], 2);
+%! a = gf([2, 0, 1, 1], 2);
+%! x = gf([1, zeros(1,20)], 2);
+%! y = filter(b, a, x);
+%! assert(y, gf([1, 0, 3, 0, 2, 3, 1, 0, 1, 3, 3, 1, 0, 1, 3, 3, 1, 0, 1, 3, 3], 2))
Added: trunk/octave-forge/main/galois/inst/@gf/finite.m
===================================================================
--- trunk/octave-forge/main/galois/inst/@gf/finite.m (rev 0)
+++ trunk/octave-forge/main/galois/inst/@gf/finite.m 2011-06-01 19:35:33 UTC (rev 8300)
@@ -0,0 +1,24 @@
+## Copyright (C) 2011 David Bateman
+##
+## 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.
+##
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with this program; If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} finite (@var{x})
+## Returns a logical array of true values for a Galois Field as all
+## elements are finite.
+## @end deftypefn
+
+function y = finite (x)
+ y = true (size(x));
+endfunction
Added: trunk/octave-forge/main/galois/inst/@gf/ge.m
===================================================================
--- trunk/octave-forge/main/galois/inst/@gf/ge.m (rev 0)
+++ trunk/octave-forge/main/galois/inst/@gf/ge.m 2011-06-01 19:35:33 UTC (rev 8300)
@@ -0,0 +1,28 @@
+## Copyright (C) 2011 David Bateman
+##
+## 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.
+##
+## This ...
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