/usr/share/octave/packages/octgpr-1.2.0/demo_octgpr.m is in octave-octgpr 1.2.0-3build1.
This file is owned by root:root, with mode 0o644.
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%
% Author: Jaroslav Hajek <highegg@gmail.com>
%
% This file is part of OctGPR.
%
% OctGPR 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 3 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 software; see the file COPYING. If not, see
% <http://www.gnu.org/licenses/>.
%
% -*- texinfo -*-
% @deftypefn {Function File} demo_octgpr (1, nsamp = 150)
% @deftypefnx {Function File} demo_octgpr (2, ncnt = 20, npt = 500)
% @deftypefnx {Function File} demo_octgpr (3, ncnt = 50, nsamp = 500)
% OctGPR package demo function.
% First argument selects available demos:
%
% @itemize
% @item 1. GPR regression demo @*
% A function is sampled (with small noise), then reconstructed using GPR
% regression. @var{nsamp} specifies the number of samples.
% @seealso{gpr_train, gpr_predict}
% @item 2. RBF centers selection demo @*
% Radial basis centers are selected amongst random points.
% @var{ncnt} specifies number of centers, @var{npt} number of points.
% @item 2. PGP regression demo @*
% A function is densely sampled (with small noise),
% radial basis centers are selected, then the function is reconstructed
% using PGP regression. @var{nsamp} specifies the number of samples,
% @var{ncnt} specifies number of centers.
% @end itemize
% @end deftypefn
function demo_octgpr (number, varargin)
global prntfmt = '';
if (nargin < 1)
print_usage ();
elseif (ischar (number))
prntfmt = number;
elseif (isscalar (number))
figure ();
if (! isempty (prntfmt))
figure (gcf, "visible", "off");
endif
switch (number)
case 1
demo_octgpr1 (varargin{:})
case 2
demo_octgpr2 (varargin{:})
case 3
demo_octgpr3 (varargin{:})
otherwise
error ("demo_octgpr: invalid demo number")
endswitch
else
print_usage ();
endif
endfunction
function demo_octgpr_pause (idemo, iplot)
global prntfmt;
if (isempty (prntfmt))
pause;
else
print (sprintf (prntfmt, idemo, iplot));
fflush (stdout);
endif
endfunction
% define the test function (the well-known matlab "peaks" plus some sines)
function z = testfun1 (x, y)
z = 4 + 3 * (1-x).^2 .* exp(-(x.^2) - (y+1).^2) ...
+ 10 * (x/5 - x.^3 - y.^5) .* exp(-x.^2 - y.^2) ...
- 1/3 * exp(-(x+1).^2 - y.^2) ...
+ 2*sin (x + y + 1e-1*x.*y);
endfunction
function demo_octgpr1 (nsamp = 150)
global prntfmt;
tit = "a peaked surface";
disp (tit);
% create the mesh onto which to interpolate
t = linspace (-3, 3, 50);
[xi,yi] = meshgrid (t, t);
% evaluate
zi = testfun1 (xi, yi);
zimax = max (vec (zi)); zimin = min (vec (zi));
subplot (2, 2, 1);
mesh (xi, yi, zi);
title (tit);
subplot (2, 2, 3);
contourf (xi, yi, zi, 20);
demo_octgpr_pause (1, 1);
tit = sprintf ("sampled at %d random points", nsamp);
disp (tit);
% create random samples
xs = rand (nsamp,1); ys = rand (nsamp,1);
xs = 6*xs-3; ys = 6*ys - 3;
% evaluate at random samples
zs = testfun1 (xs, ys);
xys = [xs ys];
subplot (2, 2, 2);
plot3 (xs, ys, zs, ".+");
title (tit);
subplot (2, 2, 3);
hold on
plot (xs, ys, "+6");
hold off
subplot (2, 2, 4);
plot (xs, ys, ".+");
demo_octgpr_pause (1, 2);
tit = "GPR model with heuristic hypers";
disp (tit);
ths = 1 ./ std (xys);
GPM = gpr_train (xys, zs, ths, 1e-5);
zm = gpr_predict (GPM, [vec(xi) vec(yi)]);
zm = reshape (zm, size(zi));
zm = min (zm, zimax); zm = max (zm, zimin);
subplot (2, 2, 2);
mesh (xi, yi, zm);
title (tit);
subplot(2, 2, 4);
hold on
contourf (xi, yi, zm, 20);
plot (xs, ys, "+6");
hold off
demo_octgpr_pause (1, 3);
tit = "GPR model with MLE training";
disp (tit);
fflush (stdout);
GPM = gpr_train (xys, zs, ths, 1e-5, {"tol", 1e-5, "maxev", 400, "numin", 1e-8});
zm = gpr_predict (GPM, [vec(xi) vec(yi)]);
zm = reshape (zm, size (zi));
zm = min (zm, zimax); zm = max (zm, zimin);
subplot (2, 2, 2);
mesh (xi, yi, zm);
title (tit);
subplot(2, 2, 4);
hold on
contourf (xi, yi, zm, 20);
plot (xs, ys, "+6");
hold off
demo_octgpr_pause (1, 4);
close
endfunction
function demo_octgpr2 (ncnt = 50, npt = 500)
global prntfmt;
npt = ncnt*ceil (npt/ncnt);
U = rand (ncnt, 2);
cs = min (pdist2_mw (U, 2) + diag (Inf (ncnt, 1)));
X = repmat (U, npt/ncnt, 1) + repmat (cs', npt/ncnt, 2) .* randn (npt, 2);
disp ("slightly clustered random points")
plot (X(:,1), X(:,2), "+");
demo_octgpr_pause (2, 1);
[U, ur] = rbf_centers(X, ncnt);
fi = linspace (0, 2*pi, 20);
ncolors = rows (colormap);
hold on
for i = 1:rows (U)
xc = U(i,1) + ur(i) * cos (fi);
yc = U(i,2) + ur(i) * sin (fi);
line (xc, yc);
endfor
hold off
demo_octgpr_pause (2, 2);
close
endfunction
function demo_octgpr3 (ncnt = 100, nsamp = 1000)
global prntfmt;
tit = "a peaked surface";
disp (tit);
% create the mesh onto which to interpolate
t = linspace (-3, 3, 50);
[xi,yi] = meshgrid (t, t);
% evaluate
zi = testfun1 (xi, yi);
zimax = max (vec (zi)); zimin = min (vec (zi));
subplot (2, 2, 1);
mesh (xi, yi, zi);
title (tit);
subplot (2, 2, 3);
contourf (xi, yi, zi, 20);
demo_octgpr_pause (1, 1);
tit = sprintf ("sampled at %d random points, selected %d centers", nsamp, ncnt);
disp (tit);
% create random samples
xs = rand (nsamp,1); ys = rand (nsamp,1);
xs = 6*xs-3; ys = 6*ys - 3;
% evaluate at random samples
zs = testfun1 (xs, ys);
xys = [xs ys];
% select centers using k-means
xyc = rbf_centers (xys, ncnt);
xc = xyc(:,1); yc = xyc(:,2);
subplot (2, 2, 2);
plot3 (xs, ys, zs, ".+");
title (tit);
subplot (2, 2, 3);
hold on
plot (xs, ys, "+6");
hold off
subplot (2, 2, 4);
hold on
plot (xs, ys, "+");
plot (xc, yc, "o2");
hold off
demo_octgpr_pause (1, 2);
tit = "PGP model with heuristic hypers";
disp (tit);
ths = 1 ./ std (xyc);
GPM = pgp_train (xys, xyc, zs, ths, 1e-5);
zm = pgp_predict (GPM, [vec(xi) vec(yi)]);
zm = reshape (zm, size(zi));
zm = min (zm, zimax); zm = max (zm, zimin);
subplot (2, 2, 2);
mesh (xi, yi, zm);
title (tit);
subplot(2, 2, 4);
hold on
contourf (xi, yi, zm, 20);
plot (xs, ys, "+6");
plot (xc, yc, "o5");
hold off
demo_octgpr_pause (1, 3);
tit = "PGP model with MLE training";
disp (tit);
fflush (stdout);
GPM = pgp_train (xys, xyc, zs, ths, 1e-3, {"tol", 1e-5, "maxev", 400});
zm = pgp_predict (GPM, [vec(xi) vec(yi)]);
zm = reshape (zm, size (zi));
zm = min (zm, zimax); zm = max (zm, zimin);
subplot (2, 2, 2);
mesh (xi, yi, zm);
title (tit);
subplot(2, 2, 4);
hold on
contourf (xi, yi, zm, 20);
plot (xs, ys, "+6");
plot (xc, yc, "o5");
hold off
demo_octgpr_pause (1, 4);
close
endfunction
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