annotate scripts/geometry/griddatan.m @ 28210:bb929d5a34cb

griddata.m: Added support for "v4" biharmonic spline interpolation method (bug #33539). * griddata.m: Add v4 method algorithm, documentation notes, and BIST tests. * griddatan.m: Updated method error messages and added BIST tests. * NEWS: Announce support for "v4" method in Matlab compatibility section.
author Nicholas R. Jankowski <jankowskin@asme.org>
date Thu, 09 Apr 2020 16:21:05 -0400
parents 2e6dc7e2b191
children 289882040316
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1 ########################################################################
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2 ##
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3 ## Copyright (C) 2007-2020 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
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6 ## distribution or <https://octave.org/copyright/>.
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7 ##
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8 ## This file is part of Octave.
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9 ##
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10 ## Octave is free software: you can redistribute it and/or modify it
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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.
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14 ##
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15 ## Octave is distributed in the hope that it will be useful, but
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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.
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19 ##
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20 ## You should have received a copy of the GNU General Public License
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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 ########################################################################
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25
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26 ## -*- texinfo -*-
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27 ## @deftypefn {} {@var{yi} =} griddatan (@var{x}, @var{y}, @var{xi})
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28 ## @deftypefnx {} {@var{yi} =} griddatan (@var{x}, @var{y}, @var{xi}, @var{method})
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29 ## @deftypefnx {} {@var{yi} =} griddatan (@var{x}, @var{y}, @var{xi}, @var{method}, @var{options})
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30 ##
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31 ## Generate a regular mesh from irregular data using interpolation.
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32 ##
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33 ## The function is defined by @code{@var{y} = f (@var{x})}.
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34 ## The interpolation points are all @var{xi}.
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35 ##
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36 ## The interpolation method can be @qcode{"nearest"} or @qcode{"linear"}.
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37 ## If method is omitted it defaults to @qcode{"linear"}.
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38 ##
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39 ## The optional argument @var{options} is passed directly to Qhull when
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40 ## computing the Delaunay triangulation used for interpolation. See
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41 ## @code{delaunayn} for information on the defaults and how to pass different
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42 ## values.
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43 ## @seealso{griddata, griddata3, delaunayn}
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44 ## @end deftypefn
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45
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46 function yi = griddatan (x, y, xi, method = "linear", varargin)
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47
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48 if (nargin < 3)
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49 print_usage ();
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50 endif
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51
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52 if (ischar (method))
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53 method = tolower (method);
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54 endif
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55
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56 [m, n] = size (x);
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57 [mi, ni] = size (xi);
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58
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59 if (n != ni || rows (y) != m || columns (y) != 1)
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60 error ("griddatan: dimensional mismatch");
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61 endif
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62
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63 ## triangulate data
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64 tri = delaunayn (x, varargin{:});
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65
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66 yi = NaN (mi, 1);
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67
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68 if (strcmp (method, "nearest"))
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69 ## search index of nearest point
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70 idx = dsearchn (x, tri, xi);
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71 valid = ! isnan (idx);
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72 yi(valid) = y(idx(valid));
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73
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74 elseif (strcmp (method, "linear"))
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75 ## search for every point the enclosing triangle
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76 [tri_list, bary_list] = tsearchn (x, tri, xi);
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77
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78 ## only keep the points within triangles.
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79 valid = ! isnan (tri_list);
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80 tri_list = tri_list(valid);
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81 bary_list = bary_list(valid, :);
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82 nr_t = rows (tri_list);
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83
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84 ## Use barycentric coordinate of point to calculate yi
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85 if (isscalar (tri_list))
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86 ## Special case required by orientation rules for vector/vector index.
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87 yi(valid) = sum (y(tri(tri_list,:)).' .* bary_list, 2);
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88 else
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89 yi(valid) = sum (y(tri(tri_list,:)) .* bary_list, 2);
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90 endif
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91
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92 elseif (any (strcmp (method, {"cubic", "v4"})))
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93 error ('griddata: "%s" METHOD only valid for 2-D inputs using "griddata"', method);
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94
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95 elseif (strcmp (method, "natural"))
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96 ## FIXME: implement missing interpolation method 'natural' for 3-D inputs.
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97 error ('griddatan: "natural" interpolation METHOD not yet implemented');
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98
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99 else
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100 error ('griddatan: unknown interpolation METHOD: "%s"', method);
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101 endif
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102
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103 endfunction
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104
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105
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106 %!testif HAVE_QHULL
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107 %! [xx,yy] = meshgrid (linspace (-1,1,32));
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108 %! xi = [xx(:), yy(:)];
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109 %! x = 2*rand (100,2) - 1;
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110 %! x = [x;1,1;1,-1;-1,-1;-1,1];
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111 %! y = sin (2 * sum (x.^2,2));
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112 %! zz = griddatan (x,y,xi,"linear");
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113 %! zz2 = griddata (x(:,1),x(:,2),y,xi(:,1),xi(:,2),"linear");
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114 %! assert (zz, zz2, 1e-10);
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115
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116 %!testif HAVE_QHULL
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117 %! [xx,yy] = meshgrid (linspace (-1,1,32));
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118 %! xi = [xx(:), yy(:)];
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119 %! x = 2*rand (100,2) - 1;
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120 %! x = [x;1,1;1,-1;-1,-1;-1,1];
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121 %! y = sin (2*sum (x.^2,2));
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122 %! zz = griddatan (x,y,xi,"nearest");
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123 %! zz2 = griddata (x(:,1),x(:,2),y,xi(:,1),xi(:,2),"nearest");
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124 %! assert (zz, zz2, 1e-10);
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125
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126 %!testif HAVE_QHULL <*56515>
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127 %! x = [ 0, 0; 1, 1; 0, 1; 1, 0 ];
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128 %! y = [ 1; 2; 3; 4 ];
3f354ef16400 griddatan.m: Allow a single query point as input (bug #45542, bug #56515).
Rik <rik@octave.org>
parents: 27239
diff changeset
129 %! xi = [ .5, .5 ];
3f354ef16400 griddatan.m: Allow a single query point as input (bug #45542, bug #56515).
Rik <rik@octave.org>
parents: 27239
diff changeset
130 %! yi = griddatan (x, y, xi);
28210
bb929d5a34cb griddata.m: Added support for "v4" biharmonic spline interpolation method (bug #33539).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 28027
diff changeset
131
bb929d5a34cb griddata.m: Added support for "v4" biharmonic spline interpolation method (bug #33539).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 28027
diff changeset
132 ## Test input validation
bb929d5a34cb griddata.m: Added support for "v4" biharmonic spline interpolation method (bug #33539).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 28027
diff changeset
133 %!error griddatan ()
bb929d5a34cb griddata.m: Added support for "v4" biharmonic spline interpolation method (bug #33539).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 28027
diff changeset
134 %!error griddatan (1)
bb929d5a34cb griddata.m: Added support for "v4" biharmonic spline interpolation method (bug #33539).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 28027
diff changeset
135 %!error griddatan (1,2)
bb929d5a34cb griddata.m: Added support for "v4" biharmonic spline interpolation method (bug #33539).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 28027
diff changeset
136 %!error griddatan (1,2,3)
bb929d5a34cb griddata.m: Added support for "v4" biharmonic spline interpolation method (bug #33539).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 28027
diff changeset
137 %!error <OPTIONS argument must be a string> griddatan (1,2,3,4,5)
bb929d5a34cb griddata.m: Added support for "v4" biharmonic spline interpolation method (bug #33539).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 28027
diff changeset
138 %!error <unknown interpolation METHOD> griddatan (1,2,3,4)
bb929d5a34cb griddata.m: Added support for "v4" biharmonic spline interpolation method (bug #33539).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 28027
diff changeset
139 %!#error <"v4" METHOD only valid for 2-D inputs>
bb929d5a34cb griddata.m: Added support for "v4" biharmonic spline interpolation method (bug #33539).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 28027
diff changeset
140 %! griddatan (ones(2,2,2), 2*ones(2,2,2), 3, "v4")
bb929d5a34cb griddata.m: Added support for "v4" biharmonic spline interpolation method (bug #33539).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 28027
diff changeset
141 %!error <"cubic" METHOD only valid for> griddatan (1, 2, 3, "cubic")
bb929d5a34cb griddata.m: Added support for "v4" biharmonic spline interpolation method (bug #33539).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 28027
diff changeset
142 %!error <"natural" .* not yet implemented> griddatan (1, 2, 3, "natural")
bb929d5a34cb griddata.m: Added support for "v4" biharmonic spline interpolation method (bug #33539).
Nicholas R. Jankowski <jankowskin@asme.org>
parents: 28027
diff changeset
143 %!error <unknown interpolation METHOD: "foobar"> griddatan (1, 2, 3, "foobar")