Mercurial > octave
annotate doc/interpreter/splineimages.m @ 31246:43a6be589387
doc: New documentation for memoization techniques (bug #60860)
vectorize.texi: New section on memoization
octave.texi: List new section
| author | Arun Giridhar <arungiridhar@gmail.com> |
|---|---|
| date | Thu, 29 Sep 2022 20:31:52 -0400 |
| parents | 796f54d4ddbf |
| children | 597f3ee61a48 |
| rev | line source |
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1 ######################################################################## |
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2 ## |
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3 ## Copyright (C) 2012-2022 The Octave Project Developers |
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4 ## |
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5 ## See the file COPYRIGHT.md in the top-level directory of this |
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6 ## distribution or <https://octave.org/copyright/>. |
| 14509 | 7 ## |
| 8 ## This file is part of Octave. | |
| 9 ## | |
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10 ## Octave is free software: you can redistribute it and/or modify it |
| 14509 | 11 ## under the terms of the GNU General Public License as published by |
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12 ## the Free Software Foundation, either version 3 of the License, or |
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13 ## (at your option) any later version. |
| 14509 | 14 ## |
| 15 ## Octave is distributed in the hope that it will be useful, but | |
| 16 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
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17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 ## GNU General Public License for more details. |
| 14509 | 19 ## |
| 20 ## You should have received a copy of the GNU General Public License | |
| 21 ## along with Octave; see the file COPYING. If not, see | |
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22 ## <https://www.gnu.org/licenses/>. |
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23 ## |
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24 ######################################################################## |
| 14509 | 25 |
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26 function splineimages (d, nm, typ) |
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27 |
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28 if (strcmp (typ, "txt")) |
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29 image_as_txt (d, nm); |
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30 return; |
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31 endif |
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32 |
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33 set_graphics_toolkit (); |
| 14509 | 34 set_print_size (); |
| 35 hide_output (); | |
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36 outfile = fullfile (d, [nm "." typ]); |
| 14509 | 37 if (strcmp (typ, "png")) |
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38 set (groot, "defaulttextfontname", "*"); |
| 14509 | 39 endif |
| 40 if (strcmp (typ, "eps")) | |
| 41 d_typ = "-depsc2"; | |
| 42 else | |
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43 d_typ = ["-d" typ]; |
| 14509 | 44 endif |
| 45 | |
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46 if (strcmp (nm, "splinefit1")) ## Breaks and Pieces |
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47 rand ("state", 1); |
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48 randn ("state", 1); |
| 14509 | 49 x = 2 * pi * rand (1, 200); |
| 50 y = sin (x) + sin (2 * x) + 0.2 * randn (size (x)); | |
| 51 ## Uniform breaks | |
| 52 breaks = linspace (0, 2 * pi, 41); ## 41 breaks, 40 pieces | |
| 53 pp1 = splinefit (x, y, breaks); | |
| 54 ## Breaks interpolated from data | |
| 55 pp2 = splinefit (x, y, 10); ## 11 breaks, 10 pieces | |
| 56 ## Plot | |
| 57 xx = linspace (0, 2 * pi, 400); | |
| 58 y1 = ppval (pp1, xx); | |
| 59 y2 = ppval (pp2, xx); | |
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60 plot (x, y, ".", xx, [y1; y2]); |
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61 axis tight; |
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62 ylim ([-2.5 2.5]); |
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63 legend ("data", "41 breaks, 40 pieces", "11 breaks, 10 pieces"); |
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64 print (outfile, d_typ); |
| 14509 | 65 elseif (strcmp (nm, "splinefit2")) ## Spline orders |
| 66 ## Data (200 points) | |
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67 rand ("state", 1); |
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68 randn ("state", 1); |
| 14509 | 69 x = 2 * pi * rand (1, 200); |
| 70 y = sin (x) + sin (2 * x) + 0.1 * randn (size (x)); | |
| 71 ## Splines | |
| 72 pp1 = splinefit (x, y, 8, "order", 0); ## Piecewise constant | |
| 73 pp2 = splinefit (x, y, 8, "order", 1); ## Piecewise linear | |
| 74 pp3 = splinefit (x, y, 8, "order", 2); ## Piecewise quadratic | |
| 75 pp4 = splinefit (x, y, 8, "order", 3); ## Piecewise cubic | |
| 76 pp5 = splinefit (x, y, 8, "order", 4); ## Etc. | |
| 77 ## Plot | |
| 78 xx = linspace (0, 2 * pi, 400); | |
| 79 y1 = ppval (pp1, xx); | |
| 80 y2 = ppval (pp2, xx); | |
| 81 y3 = ppval (pp3, xx); | |
| 82 y4 = ppval (pp4, xx); | |
| 83 y5 = ppval (pp5, xx); | |
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84 plot (x, y, ".", xx, [y1; y2; y3; y4; y5]); |
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85 axis tight; |
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86 ylim ([-2.5 2.5]); |
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87 legend ({"data", "order 0", "order 1", "order 2", "order 3", "order 4"}); |
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88 print (outfile, d_typ); |
| 14509 | 89 elseif (strcmp (nm, "splinefit3")) |
| 90 ## Data (100 points) | |
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91 rand ("state", 1); |
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92 randn ("state", 1); |
| 14509 | 93 x = 2 * pi * [0, (rand (1, 98)), 1]; |
| 94 y = sin (x) - cos (2 * x) + 0.2 * randn (size (x)); | |
| 95 ## No constraints | |
| 96 pp1 = splinefit (x, y, 10, "order", 5); | |
| 97 ## Periodic boundaries | |
| 98 pp2 = splinefit (x, y, 10, "order", 5, "periodic", true); | |
| 99 ## Plot | |
| 100 xx = linspace (0, 2 * pi, 400); | |
| 101 y1 = ppval (pp1, xx); | |
| 102 y2 = ppval (pp2, xx); | |
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103 plot (x, y, ".", xx, [y1; y2]); |
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104 axis tight; |
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105 ylim ([-2 3]); |
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106 legend ({"data", "no constraints", "periodic"}); |
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107 print (outfile, d_typ); |
| 14509 | 108 elseif (strcmp (nm, "splinefit4")) |
| 109 ## Data (200 points) | |
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110 rand ("state", 1); |
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111 randn ("state", 1); |
| 14509 | 112 x = 2 * pi * rand (1, 200); |
| 113 y = sin (2 * x) + 0.1 * randn (size (x)); | |
| 114 ## Breaks | |
| 115 breaks = linspace (0, 2 * pi, 10); | |
| 116 ## Clamped endpoints, y = y" = 0 | |
| 117 xc = [0, 0, 2*pi, 2*pi]; | |
| 118 cc = [(eye (2)), (eye (2))]; | |
| 119 con = struct ("xc", xc, "cc", cc); | |
| 120 pp1 = splinefit (x, y, breaks, "constraints", con); | |
| 121 ## Hinged periodic endpoints, y = 0 | |
| 122 con = struct ("xc", 0); | |
| 123 pp2 = splinefit (x, y, breaks, "constraints", con, "periodic", true); | |
| 124 ## Plot | |
| 125 xx = linspace (0, 2 * pi, 400); | |
| 126 y1 = ppval (pp1, xx); | |
| 127 y2 = ppval (pp2, xx); | |
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128 plot (x, y, ".", xx, [y1; y2]); |
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129 axis tight; |
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130 ylim ([-1.5 1.5]); |
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131 legend ({"data", "clamped", "hinged periodic"}); |
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132 print (outfile, d_typ); |
| 14509 | 133 elseif (strcmp (nm, "splinefit5")) |
| 134 ## Truncated data | |
| 135 x = [0, 1, 2, 4, 8, 16, 24, 40, 56, 72, 80] / 80; | |
| 136 y = [0, 28, 39, 53, 70, 86, 90, 79, 55, 22, 2] / 1000; | |
| 137 xy = [x; y]; | |
| 138 ## Curve length parameter | |
| 139 ds = sqrt (diff (x).^2 + diff (y).^2); | |
| 140 s = [0, cumsum(ds)]; | |
| 141 ## Constraints at s = 0: (x,y) = (0,0), (dx/ds,dy/ds) = (0,1) | |
| 142 con = struct ("xc", [0 0], "yc", [0 0; 0 1], "cc", eye (2)); | |
| 143 ## Fit a spline with 4 pieces | |
| 144 pp = splinefit (s, xy, 4, "constraints", con); | |
| 145 ## Plot | |
| 146 ss = linspace (0, s(end), 400); | |
| 147 xyfit = ppval (pp, ss); | |
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148 xyb = ppval (pp, pp.breaks); |
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149 plot (x, y, ".", xyfit(1,:), xyfit(2,:), "r", xyb(1,:), xyb(2,:), "ro"); |
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150 legend ({"data", "spline", "breaks"}); |
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151 axis tight; |
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152 ylim ([0 0.1]); |
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153 print (outfile, d_typ); |
| 14509 | 154 elseif (strcmp (nm, "splinefit6")) |
| 155 ## Data | |
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156 randn ("state", 1); |
| 14509 | 157 x = linspace (0, 2*pi, 200); |
| 158 y = sin (x) + sin (2 * x) + 0.05 * randn (size (x)); | |
| 159 ## Add outliers | |
| 160 x = [x, linspace(0,2*pi,60)]; | |
| 161 y = [y, -ones(1,60)]; | |
| 162 ## Fit splines with hinged conditions | |
| 163 con = struct ("xc", [0, 2*pi]); | |
| 164 pp1 = splinefit (x, y, 8, "constraints", con, "beta", 0.25); ## Robust fitting | |
| 165 pp2 = splinefit (x, y, 8, "constraints", con, "beta", 0.75); ## Robust fitting | |
| 166 pp3 = splinefit (x, y, 8, "constraints", con); ## No robust fitting | |
| 167 ## Plot | |
| 168 xx = linspace (0, 2*pi, 400); | |
| 169 y1 = ppval (pp1, xx); | |
| 170 y2 = ppval (pp2, xx); | |
| 171 y3 = ppval (pp3, xx); | |
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172 plot (x, y, ".", xx, [y1; y2; y3]); |
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173 legend ({"data with outliers","robust, beta = 0.25", ... |
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174 "robust, beta = 0.75", "no robust fitting"}); |
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175 axis tight; |
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176 ylim ([-2 2]); |
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177 print (outfile, d_typ); |
| 14509 | 178 endif |
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179 hide_output (); |
| 14509 | 180 endfunction |
| 181 | |
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182 ## This function no longer sets the graphics toolkit; That is now done |
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183 ## automatically by C++ code which will ordinarily choose 'qt', but might |
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184 ## choose gnuplot on older systems. Only a complete lack of plotting is a |
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185 ## problem. |
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186 function set_graphics_toolkit () |
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187 if (isempty (available_graphics_toolkits ())) |
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188 error ("no graphics toolkit available for plotting"); |
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189 elseif (strcmp ("qt", graphics_toolkit ()) |
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190 && __have_feature__ ("QT_OFFSCREEN")) |
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191 ## Use qt with QOffscreenSurface for plot |
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192 elseif (! strcmp ("gnuplot", graphics_toolkit ())) |
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193 if (! any (strcmp ("gnuplot", available_graphics_toolkits ()))) |
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194 error ("no graphics toolkit available for offscreen plotting"); |
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195 else |
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196 graphics_toolkit ("gnuplot"); |
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197 endif |
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198 endif |
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199 endfunction |
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200 |
| 14509 | 201 function set_print_size () |
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202 image_size = [5.0, 3.5]; # in inches, 16:9 format |
| 14509 | 203 border = 0; # For postscript use 50/72 |
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204 set (groot, "defaultfigurepapertype", "<custom>"); |
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205 set (groot, "defaultfigurepaperorientation", "landscape"); |
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206 set (groot, "defaultfigurepapersize", image_size + 2*border); |
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207 set (groot, "defaultfigurepaperposition", [border, border, image_size]); |
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208 ## FIXME: Required until listener for legend exists (bug #39697) |
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209 set (groot, "defaultfigureposition", [ 72*[border, border, image_size] ]); |
| 14509 | 210 endfunction |
| 211 | |
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212 ## Use this function before plotting commands and after every call to print |
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213 ## since print() resets output to stdout (unfortunately, gnuplot can't pop |
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214 ## output as it can the terminal type). |
| 14509 | 215 function hide_output () |
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216 hf = figure (1, "visible", "off"); |
| 14509 | 217 endfunction |
| 218 | |
| 219 ## generate something for the texinfo @image command to process | |
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220 function image_as_txt (d, nm) |
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221 fid = fopen (fullfile (d, [nm ".txt"]), "wt"); |
| 14509 | 222 fputs (fid, "\n"); |
| 223 fputs (fid, "+---------------------------------+\n"); | |
| 224 fputs (fid, "| Image unavailable in text mode. |\n"); | |
| 225 fputs (fid, "+---------------------------------+\n"); | |
| 226 fclose (fid); | |
| 227 endfunction | |
| 228 | |
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229 |
| 14509 | 230 %!demo |
| 231 %! for s = 1:6 | |
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232 %! splineimages (sprintf ("splinefit##d", s), "pdf"); |
| 14509 | 233 %! endfor |