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package de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator;
/*
This file is part of ELKI:
Environment for Developing KDD-Applications Supported by Index-Structures
Copyright (C) 2013
Ludwig-Maximilians-Universität München
Lehr- und Forschungseinheit für Datenbanksysteme
ELKI Development Team
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Affero General Public License as published by
the Free Software Foundation, either version 3 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 Affero General Public License for more details.
You should have received a copy of the GNU Affero General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
import de.lmu.ifi.dbs.elki.math.statistics.distribution.Distribution;
import de.lmu.ifi.dbs.elki.utilities.datastructures.QuickSelect;
import de.lmu.ifi.dbs.elki.utilities.datastructures.arraylike.NumberArrayAdapter;
/**
* Abstract base class for estimators based on the median and MAD.
*
* @author Erich Schubert
*
* @param <D> Distribution to generate.
*/
public abstract class AbstractLogMADEstimator<D extends Distribution> implements LogMADDistributionEstimator<D> {
/**
* Constructor.
*/
public AbstractLogMADEstimator() {
super();
}
@Override
public abstract D estimateFromLogMedianMAD(double median, double mad, double shift);
@Override
public <A> D estimate(A data, NumberArrayAdapter<?, A> adapter) {
// TODO: detect pre-sorted data?
final int len = adapter.size(data);
double min = AbstractLogMOMEstimator.min(data, adapter, 0., 1e-10);
// Modifiable copy:
double[] x = new double[len];
for (int i = 0; i < len; i++) {
final double val = adapter.getDouble(data, i) - min;
x[i] = val > 0. ? Math.log(val) : Double.NEGATIVE_INFINITY;
if (Double.isNaN(x[i])) {
throw new ArithmeticException("NaN value.");
}
}
double median = QuickSelect.median(x);
double mad = computeMAD(x, median);
return estimateFromLogMedianMAD(median, mad, min);
}
/**
* Compute the median absolute deviation from median.
*
* @param x Input data <b>will be modified</b>
* @param median Median value.
* @return Median absolute deviation from median.
*/
public static double computeMAD(double[] x, double median) {
// Compute deviations:
for (int i = 0; i < x.length; i++) {
x[i] = Math.abs(x[i] - median);
}
double mad = QuickSelect.median(x);
// Fallback if we have more than 50% ties to next largest.
if (!(mad > 0.)) {
double min = Double.POSITIVE_INFINITY;
for (double xi : x) {
if (xi > 0. && xi < min) {
min = xi;
}
}
if (min < Double.POSITIVE_INFINITY) {
mad = min;
} else {
mad = 1.0; // Maybe all constant. No real value.
}
}
return mad;
}
@Override
public String toString() {
return this.getClass().getSimpleName();
}
}
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