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## Copyright (C) 2012-2015 Ben Abbott, Jonas Lundgren
##
## This file is part of Octave.
##
## Octave 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.
##
## Octave 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 Octave; see the file COPYING. If not, see
## <http://www.gnu.org/licenses/>.
function splineimages (nm, typ)
graphics_toolkit ("gnuplot");
set_print_size ();
hide_output ();
if (strcmp (typ, "png"))
set (0, "defaulttextfontname", "*");
endif
if (strcmp (typ, "eps"))
d_typ = "-depsc2";
else
d_typ = ["-d" typ];
endif
if (strcmp (typ, "txt"))
image_as_txt (nm);
elseif (strcmp (nm, "splinefit1")) ## Breaks and Pieces
x = 2 * pi * rand (1, 200);
y = sin (x) + sin (2 * x) + 0.2 * randn (size (x));
## Uniform breaks
breaks = linspace (0, 2 * pi, 41); ## 41 breaks, 40 pieces
pp1 = splinefit (x, y, breaks);
## Breaks interpolated from data
pp2 = splinefit (x, y, 10); ## 11 breaks, 10 pieces
## Plot
xx = linspace (0, 2 * pi, 400);
y1 = ppval (pp1, xx);
y2 = ppval (pp2, xx);
plot (x, y, ".", xx, [y1; y2]);
axis tight;
ylim ([-2.5 2.5]);
legend ("data", "41 breaks, 40 pieces", "11 breaks, 10 pieces");
print ([nm "." typ], d_typ);
elseif (strcmp (nm, "splinefit2")) ## Spline orders
## Data (200 points)
x = 2 * pi * rand (1, 200);
y = sin (x) + sin (2 * x) + 0.1 * randn (size (x));
## Splines
pp1 = splinefit (x, y, 8, "order", 0); ## Piecewise constant
pp2 = splinefit (x, y, 8, "order", 1); ## Piecewise linear
pp3 = splinefit (x, y, 8, "order", 2); ## Piecewise quadratic
pp4 = splinefit (x, y, 8, "order", 3); ## Piecewise cubic
pp5 = splinefit (x, y, 8, "order", 4); ## Etc.
## Plot
xx = linspace (0, 2 * pi, 400);
y1 = ppval (pp1, xx);
y2 = ppval (pp2, xx);
y3 = ppval (pp3, xx);
y4 = ppval (pp4, xx);
y5 = ppval (pp5, xx);
plot (x, y, ".", xx, [y1; y2; y3; y4; y5]);
axis tight;
ylim ([-2.5 2.5]);
legend ({"data", "order 0", "order 1", "order 2", "order 3", "order 4"});
print ([nm, "." typ], d_typ);
elseif (strcmp (nm, "splinefit3"))
## Data (100 points)
x = 2 * pi * [0, (rand (1, 98)), 1];
y = sin (x) - cos (2 * x) + 0.2 * randn (size (x));
## No constraints
pp1 = splinefit (x, y, 10, "order", 5);
## Periodic boundaries
pp2 = splinefit (x, y, 10, "order", 5, "periodic", true);
## Plot
xx = linspace (0, 2 * pi, 400);
y1 = ppval (pp1, xx);
y2 = ppval (pp2, xx);
plot (x, y, ".", xx, [y1; y2]);
axis tight;
ylim ([-2 3]);
legend ({"data", "no constraints", "periodic"});
print ([nm "." typ], d_typ);
elseif (strcmp (nm, "splinefit4"))
## Data (200 points)
x = 2 * pi * rand (1, 200);
y = sin (2 * x) + 0.1 * randn (size (x));
## Breaks
breaks = linspace (0, 2 * pi, 10);
## Clamped endpoints, y = y" = 0
xc = [0, 0, 2*pi, 2*pi];
cc = [(eye (2)), (eye (2))];
con = struct ("xc", xc, "cc", cc);
pp1 = splinefit (x, y, breaks, "constraints", con);
## Hinged periodic endpoints, y = 0
con = struct ("xc", 0);
pp2 = splinefit (x, y, breaks, "constraints", con, "periodic", true);
## Plot
xx = linspace (0, 2 * pi, 400);
y1 = ppval (pp1, xx);
y2 = ppval (pp2, xx);
plot (x, y, ".", xx, [y1; y2]);
axis tight;
ylim ([-1.5 1.5]);
legend({"data", "clamped", "hinged periodic"});
print ([nm "." typ], d_typ);
elseif (strcmp (nm, "splinefit5"))
## Truncated data
x = [0, 1, 2, 4, 8, 16, 24, 40, 56, 72, 80] / 80;
y = [0, 28, 39, 53, 70, 86, 90, 79, 55, 22, 2] / 1000;
xy = [x; y];
## Curve length parameter
ds = sqrt (diff (x).^2 + diff (y).^2);
s = [0, cumsum(ds)];
## Constraints at s = 0: (x,y) = (0,0), (dx/ds,dy/ds) = (0,1)
con = struct ("xc", [0 0], "yc", [0 0; 0 1], "cc", eye (2));
## Fit a spline with 4 pieces
pp = splinefit (s, xy, 4, "constraints", con);
## Plot
ss = linspace (0, s(end), 400);
xyfit = ppval (pp, ss);
xyb = ppval (pp, pp.breaks);
plot (x, y, ".", xyfit(1,:), xyfit(2,:), "r", xyb(1,:), xyb(2,:), "ro");
legend ({"data", "spline", "breaks"});
axis tight;
ylim ([0 0.1]);
print ([nm "." typ], d_typ);
elseif (strcmp (nm, "splinefit6"))
## Data
x = linspace (0, 2*pi, 200);
y = sin (x) + sin (2 * x) + 0.05 * randn (size (x));
## Add outliers
x = [x, linspace(0,2*pi,60)];
y = [y, -ones(1,60)];
## Fit splines with hinged conditions
con = struct ("xc", [0, 2*pi]);
pp1 = splinefit (x, y, 8, "constraints", con, "beta", 0.25); ## Robust fitting
pp2 = splinefit (x, y, 8, "constraints", con, "beta", 0.75); ## Robust fitting
pp3 = splinefit (x, y, 8, "constraints", con); ## No robust fitting
## Plot
xx = linspace (0, 2*pi, 400);
y1 = ppval (pp1, xx);
y2 = ppval (pp2, xx);
y3 = ppval (pp3, xx);
plot (x, y, ".", xx, [y1; y2; y3]);
legend ({"data with outliers","robust, beta = 0.25", ...
"robust, beta = 0.75", "no robust fitting"});
axis tight;
ylim ([-2 2]);
print ([nm "." typ], d_typ);
endif
hide_output ();
endfunction
function set_print_size ()
image_size = [5.0, 3.5]; # in inches, 16:9 format
border = 0; # For postscript use 50/72
set (0, "defaultfigurepapertype", "<custom>");
set (0, "defaultfigurepaperorientation", "landscape");
set (0, "defaultfigurepapersize", image_size + 2*border);
set (0, "defaultfigurepaperposition", [border, border, image_size]);
endfunction
## Use this function before plotting commands and after every call to
## print since print() resets output to stdout (unfortunately, gnpulot
## can't pop output as it can the terminal type).
function hide_output ()
f = figure (1);
set (f, "visible", "off");
endfunction
## generate something for the texinfo @image command to process
function image_as_txt(nm)
fid = fopen (sprintf ("%s.txt", nm), "wt");
fputs (fid, "\n");
fputs (fid, "+---------------------------------+\n");
fputs (fid, "| Image unavailable in text mode. |\n");
fputs (fid, "+---------------------------------+\n");
fclose (fid);
endfunction
%!demo
%! for s = 1:6
%! splineimages (sprintf ("splinefit##d", s), "pdf")
%! endfor
|
