Mercurial > octave
annotate doc/interpreter/splineimages.m @ 19717:606b05352351
Backout cset 59ad278cfb98, use gnuplot for building doc images.
Until OpenGL supports TeX we need to keep using gnuplot.
| author | Rik <rik@octave.org> |
|---|---|
| date | Sun, 15 Feb 2015 07:13:09 -0800 |
| parents | 1170c849952b |
| children | c3c1fb44f9b5 |
| rev | line source |
|---|---|
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maint: Update copyright notices for 2015.
John W. Eaton <jwe@octave.org>
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1 ## Copyright (C) 2012-2015 Ben Abbott, Jonas Lundgren |
| 14509 | 2 ## |
| 3 ## This file is part of Octave. | |
| 4 ## | |
| 5 ## Octave is free software; you can redistribute it and/or modify it | |
| 6 ## under the terms of the GNU General Public License as published by | |
| 7 ## the Free Software Foundation; either version 3 of the License, or (at | |
| 8 ## your option) any later version. | |
| 9 ## | |
| 10 ## Octave is distributed in the hope that it will be useful, but | |
| 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 13 ## General Public License for more details. | |
| 14 ## | |
| 15 ## You should have received a copy of the GNU General Public License | |
| 16 ## along with Octave; see the file COPYING. If not, see | |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 18 | |
| 19 function splineimages (nm, typ) | |
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Backout cset 59ad278cfb98, use gnuplot for building doc images.
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20 graphics_toolkit ("gnuplot"); |
| 14509 | 21 set_print_size (); |
| 22 hide_output (); | |
| 23 if (strcmp (typ, "png")) | |
| 24 set (0, "defaulttextfontname", "*"); | |
| 25 endif | |
| 26 if (strcmp (typ, "eps")) | |
| 27 d_typ = "-depsc2"; | |
| 28 else | |
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29 d_typ = ["-d" typ]; |
| 14509 | 30 endif |
| 31 | |
| 32 if (strcmp (typ, "txt")) | |
| 33 image_as_txt (nm); | |
| 34 elseif (strcmp (nm, "splinefit1")) ## Breaks and Pieces | |
| 35 x = 2 * pi * rand (1, 200); | |
| 36 y = sin (x) + sin (2 * x) + 0.2 * randn (size (x)); | |
| 37 ## Uniform breaks | |
| 38 breaks = linspace (0, 2 * pi, 41); ## 41 breaks, 40 pieces | |
| 39 pp1 = splinefit (x, y, breaks); | |
| 40 ## Breaks interpolated from data | |
| 41 pp2 = splinefit (x, y, 10); ## 11 breaks, 10 pieces | |
| 42 ## Plot | |
| 43 xx = linspace (0, 2 * pi, 400); | |
| 44 y1 = ppval (pp1, xx); | |
| 45 y2 = ppval (pp2, xx); | |
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46 plot (x, y, ".", xx, [y1; y2]); |
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47 axis tight; |
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48 ylim ([-2.5 2.5]); |
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49 legend ("data", "41 breaks, 40 pieces", "11 breaks, 10 pieces"); |
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50 print ([nm "." typ], d_typ); |
| 14509 | 51 elseif (strcmp (nm, "splinefit2")) ## Spline orders |
| 52 ## Data (200 points) | |
| 53 x = 2 * pi * rand (1, 200); | |
| 54 y = sin (x) + sin (2 * x) + 0.1 * randn (size (x)); | |
| 55 ## Splines | |
| 56 pp1 = splinefit (x, y, 8, "order", 0); ## Piecewise constant | |
| 57 pp2 = splinefit (x, y, 8, "order", 1); ## Piecewise linear | |
| 58 pp3 = splinefit (x, y, 8, "order", 2); ## Piecewise quadratic | |
| 59 pp4 = splinefit (x, y, 8, "order", 3); ## Piecewise cubic | |
| 60 pp5 = splinefit (x, y, 8, "order", 4); ## Etc. | |
| 61 ## Plot | |
| 62 xx = linspace (0, 2 * pi, 400); | |
| 63 y1 = ppval (pp1, xx); | |
| 64 y2 = ppval (pp2, xx); | |
| 65 y3 = ppval (pp3, xx); | |
| 66 y4 = ppval (pp4, xx); | |
| 67 y5 = ppval (pp5, xx); | |
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68 plot (x, y, ".", xx, [y1; y2; y3; y4; y5]); |
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69 axis tight; |
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70 ylim ([-2.5 2.5]); |
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71 legend ({"data", "order 0", "order 1", "order 2", "order 3", "order 4"}); |
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72 print ([nm, "." typ], d_typ); |
| 14509 | 73 elseif (strcmp (nm, "splinefit3")) |
| 74 ## Data (100 points) | |
| 75 x = 2 * pi * [0, (rand (1, 98)), 1]; | |
| 76 y = sin (x) - cos (2 * x) + 0.2 * randn (size (x)); | |
| 77 ## No constraints | |
| 78 pp1 = splinefit (x, y, 10, "order", 5); | |
| 79 ## Periodic boundaries | |
| 80 pp2 = splinefit (x, y, 10, "order", 5, "periodic", true); | |
| 81 ## Plot | |
| 82 xx = linspace (0, 2 * pi, 400); | |
| 83 y1 = ppval (pp1, xx); | |
| 84 y2 = ppval (pp2, xx); | |
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85 plot (x, y, ".", xx, [y1; y2]); |
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86 axis tight; |
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87 ylim ([-2 3]); |
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88 legend ({"data", "no constraints", "periodic"}); |
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89 print ([nm "." typ], d_typ); |
| 14509 | 90 elseif (strcmp (nm, "splinefit4")) |
| 91 ## Data (200 points) | |
| 92 x = 2 * pi * rand (1, 200); | |
| 93 y = sin (2 * x) + 0.1 * randn (size (x)); | |
| 94 ## Breaks | |
| 95 breaks = linspace (0, 2 * pi, 10); | |
| 96 ## Clamped endpoints, y = y" = 0 | |
| 97 xc = [0, 0, 2*pi, 2*pi]; | |
| 98 cc = [(eye (2)), (eye (2))]; | |
| 99 con = struct ("xc", xc, "cc", cc); | |
| 100 pp1 = splinefit (x, y, breaks, "constraints", con); | |
| 101 ## Hinged periodic endpoints, y = 0 | |
| 102 con = struct ("xc", 0); | |
| 103 pp2 = splinefit (x, y, breaks, "constraints", con, "periodic", true); | |
| 104 ## Plot | |
| 105 xx = linspace (0, 2 * pi, 400); | |
| 106 y1 = ppval (pp1, xx); | |
| 107 y2 = ppval (pp2, xx); | |
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108 plot (x, y, ".", xx, [y1; y2]); |
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109 axis tight; |
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110 ylim ([-1.5 1.5]); |
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111 legend({"data", "clamped", "hinged periodic"}); |
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112 print ([nm "." typ], d_typ); |
| 14509 | 113 elseif (strcmp (nm, "splinefit5")) |
| 114 ## Truncated data | |
| 115 x = [0, 1, 2, 4, 8, 16, 24, 40, 56, 72, 80] / 80; | |
| 116 y = [0, 28, 39, 53, 70, 86, 90, 79, 55, 22, 2] / 1000; | |
| 117 xy = [x; y]; | |
| 118 ## Curve length parameter | |
| 119 ds = sqrt (diff (x).^2 + diff (y).^2); | |
| 120 s = [0, cumsum(ds)]; | |
| 121 ## Constraints at s = 0: (x,y) = (0,0), (dx/ds,dy/ds) = (0,1) | |
| 122 con = struct ("xc", [0 0], "yc", [0 0; 0 1], "cc", eye (2)); | |
| 123 ## Fit a spline with 4 pieces | |
| 124 pp = splinefit (s, xy, 4, "constraints", con); | |
| 125 ## Plot | |
| 126 ss = linspace (0, s(end), 400); | |
| 127 xyfit = ppval (pp, ss); | |
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128 xyb = ppval (pp, pp.breaks); |
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129 plot (x, y, ".", xyfit(1,:), xyfit(2,:), "r", xyb(1,:), xyb(2,:), "ro"); |
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130 legend ({"data", "spline", "breaks"}); |
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131 axis tight; |
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132 ylim ([0 0.1]); |
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133 print ([nm "." typ], d_typ); |
| 14509 | 134 elseif (strcmp (nm, "splinefit6")) |
| 135 ## Data | |
| 136 x = linspace (0, 2*pi, 200); | |
| 137 y = sin (x) + sin (2 * x) + 0.05 * randn (size (x)); | |
| 138 ## Add outliers | |
| 139 x = [x, linspace(0,2*pi,60)]; | |
| 140 y = [y, -ones(1,60)]; | |
| 141 ## Fit splines with hinged conditions | |
| 142 con = struct ("xc", [0, 2*pi]); | |
| 143 pp1 = splinefit (x, y, 8, "constraints", con, "beta", 0.25); ## Robust fitting | |
| 144 pp2 = splinefit (x, y, 8, "constraints", con, "beta", 0.75); ## Robust fitting | |
| 145 pp3 = splinefit (x, y, 8, "constraints", con); ## No robust fitting | |
| 146 ## Plot | |
| 147 xx = linspace (0, 2*pi, 400); | |
| 148 y1 = ppval (pp1, xx); | |
| 149 y2 = ppval (pp2, xx); | |
| 150 y3 = ppval (pp3, xx); | |
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151 plot (x, y, ".", xx, [y1; y2; y3]); |
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152 legend ({"data with outliers","robust, beta = 0.25", ... |
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153 "robust, beta = 0.75", "no robust fitting"}); |
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154 axis tight; |
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155 ylim ([-2 2]); |
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156 print ([nm "." typ], d_typ); |
| 14509 | 157 endif |
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158 hide_output (); |
| 14509 | 159 endfunction |
| 160 | |
| 161 function set_print_size () | |
| 162 image_size = [5.0, 3.5]; # in inches, 16:9 format | |
| 163 border = 0; # For postscript use 50/72 | |
| 164 set (0, "defaultfigurepapertype", "<custom>"); | |
| 165 set (0, "defaultfigurepaperorientation", "landscape"); | |
| 166 set (0, "defaultfigurepapersize", image_size + 2*border); | |
| 167 set (0, "defaultfigurepaperposition", [border, border, image_size]); | |
| 168 endfunction | |
| 169 | |
| 170 ## Use this function before plotting commands and after every call to | |
| 171 ## print since print() resets output to stdout (unfortunately, gnpulot | |
| 172 ## can't pop output as it can the terminal type). | |
| 173 function hide_output () | |
| 174 f = figure (1); | |
| 175 set (f, "visible", "off"); | |
| 176 endfunction | |
| 177 | |
| 178 ## generate something for the texinfo @image command to process | |
| 179 function image_as_txt(nm) | |
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180 fid = fopen (sprintf ("%s.txt", nm), "wt"); |
| 14509 | 181 fputs (fid, "\n"); |
| 182 fputs (fid, "+---------------------------------+\n"); | |
| 183 fputs (fid, "| Image unavailable in text mode. |\n"); | |
| 184 fputs (fid, "+---------------------------------+\n"); | |
| 185 fclose (fid); | |
| 186 endfunction | |
| 187 | |
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188 |
| 14509 | 189 %!demo |
| 190 %! for s = 1:6 | |
| 191 %! splineimages (sprintf ("splinefit##d", s), "pdf") | |
| 192 %! endfor | |
| 193 |