SemiVariance.java
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
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package org.apache.commons.math4.legacy.stat.descriptive.moment;
import org.apache.commons.math4.legacy.exception.MathIllegalArgumentException;
import org.apache.commons.math4.legacy.exception.NullArgumentException;
import org.apache.commons.math4.legacy.stat.descriptive.AbstractUnivariateStatistic;
import org.apache.commons.math4.legacy.core.MathArrays;
/**
* <p>Computes the semivariance of a set of values with respect to a given cutoff value.
* We define the <i>downside semivariance</i> of a set of values <code>x</code>
* against the <i>cutoff value</i> <code>cutoff</code> to be <br>
* <code>Σ (x[i] - target)<sup>2</sup> / df</code> <br>
* where the sum is taken over all <code>i</code> such that {@code x[i] < cutoff}
* and <code>df</code> is the length of <code>x</code> (non-bias-corrected) or
* one less than this number (bias corrected). The <i>upside semivariance</i>
* is defined similarly, with the sum taken over values of <code>x</code> that
* exceed the cutoff value.</p>
*
* <p>The cutoff value defaults to the mean, bias correction defaults to <code>true</code>
* and the "variance direction" (upside or downside) defaults to downside. The variance direction
* and bias correction may be set using property setters or their values can provided as
* parameters to {@link #evaluate(double[], double, Direction, boolean, int, int)}.</p>
*
* <p>If the input array is null, <code>evaluate</code> methods throw
* <code>IllegalArgumentException.</code> If the array has length 1, <code>0</code>
* is returned, regardless of the value of the <code>cutoff.</code>
*
* <p><strong>Note that this class is not intended to be threadsafe.</strong> If
* multiple threads access an instance of this class concurrently, and one or
* more of these threads invoke property setters, external synchronization must
* be provided to ensure correct results.</p>
*
* @since 2.1
*/
public class SemiVariance extends AbstractUnivariateStatistic {
/**
* The UPSIDE Direction is used to specify that the observations above the
* cutoff point will be used to calculate SemiVariance.
*/
public static final Direction UPSIDE_VARIANCE = Direction.UPSIDE;
/**
* The DOWNSIDE Direction is used to specify that the observations below.
* the cutoff point will be used to calculate SemiVariance
*/
public static final Direction DOWNSIDE_VARIANCE = Direction.DOWNSIDE;
/**
* Determines whether or not bias correction is applied when computing the
* value of the statistic. True means that bias is corrected.
*/
private boolean biasCorrected = true;
/**
* Determines whether to calculate downside or upside SemiVariance.
*/
private Direction varianceDirection = Direction.DOWNSIDE;
/**
* Constructs a SemiVariance with default (true) <code>biasCorrected</code>
* property and default (Downside) <code>varianceDirection</code> property.
*/
public SemiVariance() {
}
/**
* Constructs a SemiVariance with the specified <code>biasCorrected</code>
* property and default (Downside) <code>varianceDirection</code> property.
*
* @param biasCorrected setting for bias correction - true means
* bias will be corrected and is equivalent to using the "no arg"
* constructor
*/
public SemiVariance(final boolean biasCorrected) {
this.biasCorrected = biasCorrected;
}
/**
* Constructs a SemiVariance with the specified <code>Direction</code> property.
* and default (true) <code>biasCorrected</code> property
*
* @param direction setting for the direction of the SemiVariance
* to calculate
*/
public SemiVariance(final Direction direction) {
this.varianceDirection = direction;
}
/**
* Constructs a SemiVariance with the specified <code>isBiasCorrected</code>
* property and the specified <code>Direction</code> property.
*
* @param corrected setting for bias correction - true means
* bias will be corrected and is equivalent to using the "no arg"
* constructor
*
* @param direction setting for the direction of the SemiVariance
* to calculate
*/
public SemiVariance(final boolean corrected, final Direction direction) {
this.biasCorrected = corrected;
this.varianceDirection = direction;
}
/**
* Copy constructor, creates a new {@code SemiVariance} identical
* to the {@code original}.
*
* @param original the {@code SemiVariance} instance to copy
* @throws NullArgumentException if original is null
*/
public SemiVariance(final SemiVariance original) throws NullArgumentException {
copy(original, this);
}
/**
* {@inheritDoc}
*/
@Override
public SemiVariance copy() {
SemiVariance result = new SemiVariance();
// No try-catch or advertised exception because args are guaranteed non-null
copy(this, result);
return result;
}
/**
* Copies source to dest.
* <p>Neither source nor dest can be null.</p>
*
* @param source SemiVariance to copy
* @param dest SemiVariance to copy to
* @throws NullArgumentException if either source or dest is null
*/
public static void copy(final SemiVariance source, SemiVariance dest)
throws NullArgumentException {
NullArgumentException.check(source);
NullArgumentException.check(dest);
dest.biasCorrected = source.biasCorrected;
dest.varianceDirection = source.varianceDirection;
}
/**
* <p>Returns the {@link SemiVariance} of the designated values against the mean, using
* instance properties varianceDirection and biasCorrection.</p>
*
* <p>Returns <code>NaN</code> if the array is empty and throws
* <code>IllegalArgumentException</code> if the array is null.</p>
*
* @param values the input array
* @param start index of the first array element to include
* @param length the number of elements to include
* @return the SemiVariance
* @throws MathIllegalArgumentException if the parameters are not valid
*
*/
@Override
public double evaluate(final double[] values, final int start, final int length)
throws MathIllegalArgumentException {
double m = (new Mean()).evaluate(values, start, length);
return evaluate(values, m, varianceDirection, biasCorrected, 0, values.length);
}
/**
* This method calculates {@link SemiVariance} for the entire array against the mean, using
* the current value of the biasCorrection instance property.
*
* @param values the input array
* @param direction the {@link Direction} of the semivariance
* @return the SemiVariance
* @throws MathIllegalArgumentException if values is null
*
*/
public double evaluate(final double[] values, Direction direction)
throws MathIllegalArgumentException {
double m = (new Mean()).evaluate(values);
return evaluate(values, m, direction, biasCorrected, 0, values.length);
}
/**
* <p>Returns the {@link SemiVariance} of the designated values against the cutoff, using
* instance properties variancDirection and biasCorrection.</p>
*
* <p>Returns <code>NaN</code> if the array is empty and throws
* <code>MathIllegalArgumentException</code> if the array is null.</p>
*
* @param values the input array
* @param cutoff the reference point
* @return the SemiVariance
* @throws MathIllegalArgumentException if values is null
*/
public double evaluate(final double[] values, final double cutoff)
throws MathIllegalArgumentException {
return evaluate(values, cutoff, varianceDirection, biasCorrected, 0, values.length);
}
/**
* <p>Returns the {@link SemiVariance} of the designated values against the cutoff in the
* given direction, using the current value of the biasCorrection instance property.</p>
*
* <p>Returns <code>NaN</code> if the array is empty and throws
* <code>MathIllegalArgumentException</code> if the array is null.</p>
*
* @param values the input array
* @param cutoff the reference point
* @param direction the {@link Direction} of the semivariance
* @return the SemiVariance
* @throws MathIllegalArgumentException if values is null
*/
public double evaluate(final double[] values, final double cutoff, final Direction direction)
throws MathIllegalArgumentException {
return evaluate(values, cutoff, direction, biasCorrected, 0, values.length);
}
/**
* <p>Returns the {@link SemiVariance} of the designated values against the cutoff
* in the given direction with the provided bias correction.</p>
*
* <p>Returns <code>NaN</code> if the array is empty and throws
* <code>IllegalArgumentException</code> if the array is null.</p>
*
* @param values the input array
* @param cutoff the reference point
* @param direction the {@link Direction} of the semivariance
* @param corrected the BiasCorrection flag
* @param start index of the first array element to include
* @param length the number of elements to include
* @return the SemiVariance
* @throws MathIllegalArgumentException if the parameters are not valid
*
*/
public double evaluate (final double[] values, final double cutoff, final Direction direction,
final boolean corrected, final int start, final int length)
throws MathIllegalArgumentException {
MathArrays.verifyValues(values, start, length);
if (values.length == 0) {
return Double.NaN;
} else {
if (values.length == 1) {
return 0.0;
} else {
final boolean booleanDirection = direction.getDirection();
double dev = 0.0;
double sumsq = 0.0;
for (int i = start; i < length; i++) {
if ((values[i] > cutoff) == booleanDirection) {
dev = values[i] - cutoff;
sumsq += dev * dev;
}
}
if (corrected) {
return sumsq / (length - 1.0);
} else {
return sumsq / length;
}
}
}
}
/**
* Returns true iff biasCorrected property is set to true.
*
* @return the value of biasCorrected.
*/
public boolean isBiasCorrected() {
return biasCorrected;
}
/**
* Sets the biasCorrected property.
*
* @param biasCorrected new biasCorrected property value
*/
public void setBiasCorrected(boolean biasCorrected) {
this.biasCorrected = biasCorrected;
}
/**
* Returns the varianceDirection property.
*
* @return the varianceDirection
*/
public Direction getVarianceDirection () {
return varianceDirection;
}
/**
* Sets the variance direction.
*
* @param varianceDirection the direction of the semivariance
*/
public void setVarianceDirection(Direction varianceDirection) {
this.varianceDirection = varianceDirection;
}
/**
* The direction of the semivariance - either upside or downside. The direction
* is represented by boolean, with true corresponding to UPSIDE semivariance.
*/
public enum Direction {
/**
* The UPSIDE Direction is used to specify that the observations above the.
* cutoff point will be used to calculate SemiVariance
*/
UPSIDE (true),
/**
* The DOWNSIDE Direction is used to specify that the observations below.
* the cutoff point will be used to calculate SemiVariance
*/
DOWNSIDE (false);
/**
* boolean value UPSIDE <-> true.
*/
private boolean direction;
/**
* Create a Direction with the given value.
*
* @param b boolean value representing the Direction. True corresponds to UPSIDE.
*/
Direction (boolean b) {
direction = b;
}
/**
* Returns the value of this Direction. True corresponds to UPSIDE.
*
* @return true if direction is UPSIDE; false otherwise
*/
boolean getDirection () {
return direction;
}
}
}