# Copyright (C) 2006 Michael Creel <michael.creel@uab.es> # # This program 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 2 of the License, or # (at your option) any later version. # # This program 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 this program; If not, see <http://www.gnu.org/licenses/>. # __kernel_epanechnikov: this function is for internal use by kernel_density # and kernel_regression # # multivariate spherical Epanechnikov kernel # input: PxK matrix - P data points, each of which is in R^K # output: Px1 vector, input matrix passed though the kernel # other multivariate kernel functions should follow this convention function z = __kernel_epanechnikov(z) K = columns(z); # Volume of d-dimensional unit sphere c = pi ^ (K/2) / gamma(K/2 + 1); # compute kernel z = sumsq(z, 2); z = ((1/2) / c * (K + 2) * (1 - z)) .* (z < 1); endfunction

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