Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / econometrics-1.0.8 / kernel_density.m

diff --git a/octave_packages/econometrics-1.0.8/kernel_density.m b/octave_packages/econometrics-1.0.8/kernel_density.m
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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_density: multivariate kernel density estimator
+#
+# usage:
+#      dens = kernel_density(eval_points, data, bandwidth)
+#
+# inputs:
+#      eval_points: PxK matrix of points at which to calculate the density
+#      data: NxK matrix of data points
+#      bandwidth: positive scalar, the smoothing parameter. The fit
+#              is more smooth as the bandwidth increases.
+#      kernel (optional): string. Name of the kernel function. Default is
+#              Gaussian kernel.
+#      prewhiten bool (optional): default false. If true, rotate data
+#              using Choleski decomposition of inverse of covariance,
+#              to approximate independence after the transformation, which
+#              makes a product kernel a reasonable choice.
+#      do_cv: bool (optional). default false. If true, calculate leave-1-out
+#               density for cross validation
+#      computenodes: int (optional, default 0).
+#              Number of compute nodes for parallel evaluation
+#      debug: bool (optional, default false). show results on compute nodes if doing
+#              a parallel run
+# outputs:
+#      dens: Px1 vector: the fitted density value at each of the P evaluation points.
+#
+# References:
+# Wand, M.P. and Jones, M.C. (1995), 'Kernel smoothing'.
+# http://www.xplore-stat.de/ebooks/scripts/spm/html/spmhtmlframe73.html
+
+function z = kernel_density(eval_points, data, bandwidth, kernel, prewhiten, do_cv, computenodes, debug)
+
+       if nargin < 2; error("kernel_density: at least 2 arguments are required"); endif
+
+       n = rows(data);
+       k = columns(data);
+
+
+       # set defaults for optional args
+       if (nargin < 3) bandwidth = (n ^ (-1/(4+k))); endif     # bandwidth - see Li and Racine pg. 26
+       if (nargin < 4) kernel = "__kernel_normal"; endif # what kernel?
+       if (nargin < 5) prewhiten = false; endif        # automatic prewhitening?
+       if (nargin < 6) do_cv = false; endif            # ordinary or leave-1-out
+       if (nargin < 7) computenodes = 0; endif         # parallel?
+       if (nargin < 8) debug = false; endif;           # debug?
+
+       nn = rows(eval_points);
+       n = rows(data);
+       if prewhiten
+               H = bandwidth*chol(cov(data));
+       else
+               H = bandwidth;
+       endif
+
+       # Inverse bandwidth matrix H_inv
+       H_inv = inv(H);
+
+       # weight by inverse bandwidth matrix
+       eval_points = eval_points*H_inv;
+       data = data*H_inv;
+
+       # check if doing this parallel or serial
+       global PARALLEL NSLAVES NEWORLD NSLAVES TAG
+       PARALLEL = 0;
+
+       if computenodes > 0
+               PARALLEL = 1;
+               NSLAVES = computenodes;
+               LAM_Init(computenodes, debug);
+       endif
+
+       if !PARALLEL # ordinary serial version
+               points_per_node = nn; # do the all on this node
+               z = kernel_density_nodes(eval_points, data, do_cv, kernel, points_per_node, computenodes, debug);
+       else # parallel version
+               z = zeros(nn,1);
+               points_per_node = floor(nn/(NSLAVES + 1)); # number of obsns per slave
+               # The command that the slave nodes will execute
+               cmd=['z_on_node = kernel_density_nodes(eval_points, data, do_cv, kernel, points_per_node, computenodes, debug); ',...
+               'MPI_Send(z_on_node, 0, TAG, NEWORLD);'];
+
+               # send items to slaves
+
+               NumCmds_Send({"eval_points", "data", "do_cv", "kernel", "points_per_node", "computenodes", "debug","cmd"}, {eval_points, data, do_cv, kernel, points_per_node, computenodes, debug, cmd});
+
+               # evaluate last block on master while slaves are busy
+               z_on_node = kernel_density_nodes(eval_points, data, do_cv, kernel, points_per_node, computenodes, debug);
+               startblock = NSLAVES*points_per_node + 1;
+               endblock = nn;
+               z(startblock:endblock,:) = z(startblock:endblock,:) + z_on_node;
+
+               # collect slaves' results
+               z_on_node = zeros(points_per_node,1); # size may differ between master and compute nodes - reset here
+               for i = 1:NSLAVES
+                       MPI_Recv(z_on_node,i,TAG,NEWORLD);
+                       startblock = i*points_per_node - points_per_node + 1;
+                       endblock = i*points_per_node;
+                       z(startblock:endblock,:) = z(startblock:endblock,:) + z_on_node;
+               endfor
+
+               # clean up after parallel
+               LAM_Finalize;
+       endif
+       z = z*det(H_inv);
+endfunction