Mercurial > octave
view scripts/geometry/griddatan.m @ 30564:796f54d4ddbf stable
update Octave Project Developers copyright for the new year
In files that have the "Octave Project Developers" copyright notice,
update for 2021.
In all .txi and .texi files except gpl.txi and gpl.texi in the
doc/liboctave and doc/interpreter directories, change the copyright
to "Octave Project Developers", the same as used for other source
files. Update copyright notices for 2022 (not done since 2019). For
gpl.txi and gpl.texi, change the copyright notice to be "Free Software
Foundation, Inc." and leave the date at 2007 only because this file
only contains the text of the GPL, not anything created by the Octave
Project Developers.
Add Paul Thomas to contributors.in.
author | John W. Eaton <jwe@octave.org> |
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date | Tue, 28 Dec 2021 18:22:40 -0500 |
parents | 7854d5752dd2 |
children | 597f3ee61a48 |
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######################################################################## ## ## Copyright (C) 2007-2022 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this ## distribution or <https://octave.org/copyright/>. ## ## 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 ## <https://www.gnu.org/licenses/>. ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {@var{yi} =} griddatan (@var{x}, @var{y}, @var{xi}) ## @deftypefnx {} {@var{yi} =} griddatan (@var{x}, @var{y}, @var{xi}, @var{method}) ## @deftypefnx {} {@var{yi} =} griddatan (@var{x}, @var{y}, @var{xi}, @var{method}, @var{options}) ## ## Interpolate irregular source data @var{x}, @var{y} at points specified by ## @var{xi}. ## ## The input @var{x} is an MxN matrix representing M points in an N-dimensional ## space. The input @var{y} is a single-valued column vector (Mx1) ## representing a function evaluated at the points @var{x}, i.e., ## @code{@var{y} = fcn (@var{x})}. The input @var{xi} is a list of points ## for which the function output @var{yi} should be approximated through ## interpolation. @var{xi} must have the same number of columns (@var{N}) ## as @var{x} so that the dimensionality matches. ## ## The optional input interpolation @var{method} can be @qcode{"nearest"} or ## @qcode{"linear"}. When the method is @qcode{"nearest"}, the output @var{yi} ## will be the closest point in the original data @var{x} to the query point ## @var{xi}. When the method is @qcode{"linear"}, the output @var{yi} will ## be a linear interpolation between the two closest points in the original ## source data. If @var{method} is omitted or empty, it defaults to ## @qcode{"linear"}. ## ## The optional argument @var{options} is passed directly to Qhull when ## computing the Delaunay triangulation used for interpolation. See ## @code{delaunayn} for information on the defaults and how to pass different ## values. ## ## Example ## ## @example ## @group ## ## Evaluate sombrero() function at irregular data points ## x = 16*gallery ("uniformdata", [200,1], 1) - 8; ## y = 16*gallery ("uniformdata", [200,1], 11) - 8; ## z = sin (sqrt (x.^2 + y.^2)) ./ sqrt (x.^2 + y.^2); ## ## Create a regular grid and interpolate data ## [xi, yi] = ndgrid (linspace (-8, 8, 50)); ## zi = griddatan ([x, y], z, [xi(:), yi(:)]); ## zi = reshape (zi, size (xi)); ## ## Plot results ## clf (); ## plot3 (x, y, z, "or"); ## hold on ## surf (xi, yi, zi); ## legend ("Original Data", "Interpolated Data"); ## @end group ## @end example ## ## Programming Notes: If the input is complex the real and imaginary parts ## are interpolated separately. Interpolation is based on a Delaunay ## triangulation and any query values outside the convex hull of the input ## points will return @code{NaN}. For 2-D and 3-D data additional ## interpolation methods are available by using the @code{griddata} function. ## @seealso{griddata, griddata3, delaunayn} ## @end deftypefn function yi = griddatan (x, y, xi, method = "linear", varargin) if (nargin < 3) print_usage (); endif [m, n] = size (x); [mi, ni] = size (xi); if (m < n + 1) error ("griddatan: number of points in X (rows of X) must be greater than dimensionality of data + 1 (columns of X + 1)"); endif if (! iscolumn (y) || rows (y) != m) error ("griddatan: Y must be a column vector with the same number of points (rows) as X"); endif if (n != ni) error ("griddatan: dimension of query data XI (columns) must match X"); endif if (nargin > 3) if (isempty (method)) method = "linear"; elseif (! ischar (method)) error ("griddatan: METHOD must be a string"); else method = tolower (method); endif if (strcmp (method, "linear") || strcmp (method, "nearest")) ## Do nothing, these are implemented methods elseif (strcmp (method, "v4")) error ('griddatan: "%s" METHOD is available for 2-D inputs by using "griddata"', method); elseif (any (strcmp (method, {"cubic", "natural"}))) ## FIXME: Remove when griddata.m supports these methods. error ('griddatan: "%s" interpolation METHOD not yet implemented', method); else error ('griddatan: unknown interpolation METHOD: "%s"', method); endif endif ## triangulate data tri = delaunayn (x, varargin{:}); yi = NaN (mi, 1); if (strcmp (method, "linear")) ## search for every point the enclosing triangle [tri_list, bary_list] = tsearchn (x, tri, xi); ## only keep the points within triangles. valid = ! isnan (tri_list); tri_list = tri_list(valid); bary_list = bary_list(valid, :); nr_t = rows (tri_list); ## Use barycentric coordinate of point to calculate yi if (isscalar (tri_list)) ## Special case required by orientation rules for vector/vector index. yi(valid) = sum (y(tri(tri_list,:)).' .* bary_list, 2); else yi(valid) = sum (y(tri(tri_list,:)) .* bary_list, 2); endif else ## search index of nearest point idx = dsearchn (x, tri, xi); valid = ! isnan (idx); yi(valid) = y(idx(valid)); endif endfunction %!testif HAVE_QHULL %! [xx,yy] = meshgrid (linspace (-1,1,32)); %! xi = [xx(:), yy(:)]; %! x = 2*rand (100,2) - 1; %! x = [x;1,1;1,-1;-1,-1;-1,1]; %! y = sin (2 * sum (x.^2,2)); %! zz = griddatan (x,y,xi, "linear"); %! zz2 = griddata (x(:,1),x(:,2),y,xi(:,1),xi(:,2), "linear"); %! assert (zz, zz2, 1e-10); %!testif HAVE_QHULL %! [xx,yy] = meshgrid (linspace (-1,1,32)); %! xi = [xx(:), yy(:)]; %! x = 2*rand (100,2) - 1; %! x = [x;1,1;1,-1;-1,-1;-1,1]; %! y = sin (2*sum (x.^2,2)); %! zz = griddatan (x,y,xi, "nearest"); %! zz2 = griddata (x(:,1),x(:,2),y,xi(:,1),xi(:,2), "nearest"); %! assert (zz, zz2, 1e-10); %!testif HAVE_QHULL <*56515> %! x = [ 0, 0; 1, 1; 0, 1; 1, 0 ]; %! y = [ 1; 2; 3; 4 ]; %! xi = [ .5, .5 ]; %! yi = griddatan (x, y, xi); ## Test input validation %!error <Invalid call> griddatan () %!error <Invalid call> griddatan (1) %!error <Invalid call> griddatan (1,2) %!error <number of points in X> griddatan (1,2,3) %!error <Y must be a column vector> griddatan ([1;2],[3,4], 1) %!error <Y must .* same number of points .* as X> griddatan ([1;2],[3;4;5], 1) %!error <dimension of .* XI .* must match X> griddatan ([1;2],[3;4], [1, 2]) %!error <METHOD must be a string> griddatan ([1;2],[3;4], 1, 5) %!error <"v4" METHOD is available for 2-D> griddatan ([1;2],[3;4], 1, "v4") %!error <"cubic" .* not yet implemented> griddatan ([1;2],[3;4], 1, "cubic") %!error <"natural" .* not yet implemented> griddatan ([1;2],[3;4], 1, "natural") %!error <unknown .* METHOD: "foobar"> griddatan ([1;2],[3;4], 1, "foobar")