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# 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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