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package org.broadinstitute.hellbender.utils;
import org.apache.commons.math3.optim.MaxEval;
import org.apache.commons.math3.optim.nonlinear.scalar.GoalType;
import org.apache.commons.math3.optim.univariate.BrentOptimizer;
import org.apache.commons.math3.optim.univariate.SearchInterval;
import org.apache.commons.math3.optim.univariate.UnivariateObjectiveFunction;
import org.apache.commons.math3.optim.univariate.UnivariatePointValuePair;
import java.util.function.DoubleUnaryOperator;
import java.util.function.Function;
/**
* Created by davidben on 4/27/16.
*/
public final class OptimizationUtils {
protected static final MaxEval DEFAULT_MAX_EVAL = new MaxEval(1000);
private static final double DEFAULT_RELATIVE_TOLERANCE = 0.001;
private static final double DEFAULT_ABSOLUTE_TOLERANCE = 0.001;
protected static final BrentOptimizer DEFAULT_OPTIMIZER = new BrentOptimizer(DEFAULT_RELATIVE_TOLERANCE, DEFAULT_ABSOLUTE_TOLERANCE);;
private static final double DEFAULT_EPSILON_FOR_NUMERIC_DERIVATIVES = 1.0e-5;
private static final double DEFAULT_DERIVATIVE_THRESHOLD = 1.0e-8;
private OptimizationUtils() { }
public static double argmax(final Function function, final double min, final double max, final double guess) {
return max(function, min, max, guess).getPoint();
}
public static UnivariatePointValuePair max(final Function function, final double min, final double max, final double guess) {
final SearchInterval interval = new SearchInterval(min, max, guess);
return DEFAULT_OPTIMIZER.optimize(new UnivariateObjectiveFunction(function::apply), GoalType.MAXIMIZE, interval, DEFAULT_MAX_EVAL);
}
public static UnivariatePointValuePair max(final DoubleUnaryOperator function, final double min, final double max, final double guess,
final double relativeTolerance, final double absoluteTolerance, final int maxEvaluations) {
final BrentOptimizer optimizer = new BrentOptimizer(relativeTolerance, absoluteTolerance);
final SearchInterval interval = new SearchInterval(min, max, guess);
return optimizer.optimize(new UnivariateObjectiveFunction(function::applyAsDouble), GoalType.MAXIMIZE, interval, new MaxEval(maxEvaluations));
}
/**
* One iteration of Newton's method for univariate optimization (i.e. not repeated until convergence)
* @param function the function to maximize
* @param min minimum allowable value
* @param max maximum allowable value
* @param guess current guess
* @param epsilon infinitesimal for numerical first and second derivatives
* @param derivativeThreshold first derivative below which current guess is considered stationary
*/
public static double singleNewtonArgmaxUpdate(final Function function, final double min, final double max,
final double guess, final double epsilon, final double derivativeThreshold) {
final double fx = function.apply(guess);
final double fxPlusEps = function.apply(guess + epsilon);
final double fxMinusEps = function.apply(guess - epsilon);
final double secondDerivative = (fxPlusEps + fxMinusEps - 2 * fx) / (epsilon * epsilon);
final double firstDerivative = (fxPlusEps - fxMinusEps)/(2*epsilon);
final double argmax = guess - firstDerivative / secondDerivative;
if (Math.abs(firstDerivative) < derivativeThreshold) {
return guess;
}
return argmax < min ? min : (argmax > max ? max : argmax);
}
public static double singleNewtonArgmaxUpdate(final Function function, final double min, final double max, final double guess) {
return singleNewtonArgmaxUpdate(function, min, max, guess, DEFAULT_EPSILON_FOR_NUMERIC_DERIVATIVES, DEFAULT_DERIVATIVE_THRESHOLD);
}
}
