annotate libinterp/corefcn/tsearch.cc @ 27919:1891570abac8

update Octave Project Developers copyright for the new year In files that have the "Octave Project Developers" copyright notice, update for 2020.
author John W. Eaton <jwe@octave.org>
date Mon, 06 Jan 2020 22:29:51 -0500
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1 /*
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2
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1891570abac8 update Octave Project Developers copyright for the new year
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3 Copyright (C) 2002-2020 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 distribution
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6 or <https://octave.org/COPYRIGHT.html/>.
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7
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8
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9 This file is part of Octave.
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10
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11 Octave is free software: you can redistribute it and/or modify it
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12 under the terms of the GNU General Public License as published by
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13 the Free Software Foundation, either version 3 of the License, or
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14 (at your option) any later version.
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15
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16 Octave is distributed in the hope that it will be useful, but
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17 WITHOUT ANY WARRANTY; without even the implied warranty of
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18 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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19 GNU General Public License for more details.
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20
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21 You should have received a copy of the GNU General Public License
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22 along with Octave; see the file COPYING. If not, see
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23 <https://www.gnu.org/licenses/>.
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24
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25 */
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26
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27 // Author: Andreas Stahel <Andreas.Stahel@hta-bi.bfh.ch>
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28
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29 #if defined (HAVE_CONFIG_H)
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30 # include "config.h"
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31 #endif
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32
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33 #include <cmath>
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34
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35 #include "lo-ieee.h"
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36
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37 #include "defun.h"
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38 #include "error.h"
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39 #include "ovl.h"
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40
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41 inline double max (double a, double b, double c)
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42 {
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43 if (a < b)
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44 return (b < c ? c : b);
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45 else
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46 return (a < c ? c : a);
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47 }
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48
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49 inline double min (double a, double b, double c)
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50 {
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51 if (a > b)
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52 return (b > c ? c : b);
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53 else
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54 return (a > c ? c : a);
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55 }
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56
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57 #define REF(x,k,i) x(static_cast<octave_idx_type> (elem((k), (i))) - 1)
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58
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59 // for large data set the algorithm is very slow
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60 // one should presort (how?) either the elements of the points of evaluation
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61 // to cut down the time needed to decide which triangle contains the
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62 // given point
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63
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64 // e.g., build up a neighbouring triangle structure and use a simplex-like
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65 // method to traverse it
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66
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67 DEFUN (tsearch, args, ,
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68 doc: /* -*- texinfo -*-
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69 @deftypefn {} {@var{idx} =} tsearch (@var{x}, @var{y}, @var{t}, @var{xi}, @var{yi})
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70 Search for the enclosing Delaunay convex hull.
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71
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72 For @code{@var{t} = delaunay (@var{x}, @var{y})}, finds the index in @var{t}
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73 containing the points @code{(@var{xi}, @var{yi})}. For points outside the
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74 convex hull, @var{idx} is NaN.
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75 @seealso{delaunay, delaunayn}
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76 @end deftypefn */)
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77 {
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78 if (args.length () != 5)
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79 print_usage ();
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80
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81 const double eps = 1.0e-12;
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82
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83 const ColumnVector x (args(0).vector_value ());
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84 const ColumnVector y (args(1).vector_value ());
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85 const Matrix elem (args(2).matrix_value ());
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86 const ColumnVector xi (args(3).vector_value ());
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87 const ColumnVector yi (args(4).vector_value ());
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88
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89 const octave_idx_type nelem = elem.rows ();
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90
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91 ColumnVector minx (nelem);
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92 ColumnVector maxx (nelem);
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93 ColumnVector miny (nelem);
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94 ColumnVector maxy (nelem);
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95 for (octave_idx_type k = 0; k < nelem; k++)
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96 {
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97 minx(k) = min (REF (x, k, 0), REF (x, k, 1), REF (x, k, 2)) - eps;
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98 maxx(k) = max (REF (x, k, 0), REF (x, k, 1), REF (x, k, 2)) + eps;
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99 miny(k) = min (REF (y, k, 0), REF (y, k, 1), REF (y, k, 2)) - eps;
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100 maxy(k) = max (REF (y, k, 0), REF (y, k, 1), REF (y, k, 2)) + eps;
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101 }
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102
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103 const octave_idx_type np = xi.numel ();
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104 ColumnVector values (np);
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105
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106 double x0, y0, a11, a12, a21, a22, det;
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107 x0 = y0 = 0.0;
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108 a11 = a12 = a21 = a22 = 0.0;
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109 det = 0.0;
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110
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111 octave_idx_type k = nelem; // k is a counter of elements
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112 for (octave_idx_type kp = 0; kp < np; kp++)
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113 {
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114 const double xt = xi(kp);
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115 const double yt = yi(kp);
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116
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117 // check if last triangle contains the next point
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118 if (k < nelem)
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119 {
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120 const double dx1 = xt - x0;
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121 const double dx2 = yt - y0;
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122 const double c1 = (a22 * dx1 - a21 * dx2) / det;
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123 const double c2 = (-a12 * dx1 + a11 * dx2) / det;
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124 if (c1 >= -eps && c2 >= -eps && (c1 + c2) <= (1 + eps))
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125 {
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126 values(kp) = double(k+1);
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127 continue;
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128 }
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129 }
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130
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131 // it doesn't, so go through all elements
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132 for (k = 0; k < nelem; k++)
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133 {
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134 octave_quit ();
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135
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136 if (xt >= minx(k) && xt <= maxx(k) && yt >= miny(k) && yt <= maxy(k))
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137 {
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138 // element inside the minimum rectangle: examine it closely
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139 x0 = REF (x, k, 0);
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140 y0 = REF (y, k, 0);
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141 a11 = REF (x, k, 1) - x0;
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142 a12 = REF (y, k, 1) - y0;
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143 a21 = REF (x, k, 2) - x0;
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144 a22 = REF (y, k, 2) - y0;
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145 det = a11 * a22 - a21 * a12;
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146
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147 // solve the system
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148 const double dx1 = xt - x0;
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149 const double dx2 = yt - y0;
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150 const double c1 = (a22 * dx1 - a21 * dx2) / det;
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151 const double c2 = (-a12 * dx1 + a11 * dx2) / det;
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152 if ((c1 >= -eps) && (c2 >= -eps) && ((c1 + c2) <= (1 + eps)))
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153 {
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154 values(kp) = double(k+1);
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155 break;
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156 }
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157 } //endif # examine this element closely
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158 } //endfor # each element
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159
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160 if (k == nelem)
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161 values(kp) = lo_ieee_nan_value ();
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162
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163 } //endfor # kp
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164
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165 return ovl (values);
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166 }
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167
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168 /*
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169 %!shared x, y, tri
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170 %! x = [-1;-1;1];
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171 %! y = [-1;1;-1];
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172 %! tri = [1, 2, 3];
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173 %!assert (tsearch (x,y,tri,-1,-1), 1)
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174 %!assert (tsearch (x,y,tri, 1,-1), 1)
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175 %!assert (tsearch (x,y,tri,-1, 1), 1)
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176 %!assert (tsearch (x,y,tri,-1/3, -1/3), 1)
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177 %!assert (tsearch (x,y,tri, 1, 1), NaN)
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178
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179 %!error tsearch ()
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180 */