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 * The ASF licenses this file to You under the Apache License, Version 2.0
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 *      http://www.apache.org/licenses/LICENSE-2.0
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package org.apache.commons.math3.optimization.univariate;

import java.util.Arrays;
import java.util.Comparator;

import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.exception.MathIllegalStateException;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.random.RandomGenerator;
import org.apache.commons.math3.optimization.GoalType;
import org.apache.commons.math3.optimization.ConvergenceChecker;

Special implementation of the UnivariateOptimizer interface adding multi-start features to an existing optimizer. This class wraps a classical optimizer to use it several times in turn with different starting points in order to avoid being trapped into a local extremum when looking for a global one. 
Type parameters:
<FUNC> – Type of the objective function to be optimized.
Deprecated:
As of 3.1 (to be removed in 4.0).
Since:
3.0/**
 * Special implementation of the {@link UnivariateOptimizer} interface
 * adding multi-start features to an existing optimizer.
 *
 * This class wraps a classical optimizer to use it several times in
 * turn with different starting points in order to avoid being trapped
 * into a local extremum when looking for a global one.
 *
 * @param <FUNC> Type of the objective function to be optimized.
 *
 * @deprecated As of 3.1 (to be removed in 4.0).
 * @since 3.0
 */
@Deprecated
public class UnivariateMultiStartOptimizer<FUNC extends UnivariateFunction>
    implements BaseUnivariateOptimizer<FUNC> {
    
Underlying classical optimizer. /** Underlying classical optimizer. */
    private final BaseUnivariateOptimizer<FUNC> optimizer;
    
Maximal number of evaluations allowed. /** Maximal number of evaluations allowed. */
    private int maxEvaluations;
    
Number of evaluations already performed for all starts. /** Number of evaluations already performed for all starts. */
    private int totalEvaluations;
    
Number of starts to go. /** Number of starts to go. */
    private int starts;
    
Random generator for multi-start. /** Random generator for multi-start. */
    private RandomGenerator generator;
    
Found optima. /** Found optima. */
    private UnivariatePointValuePair[] optima;

    
Create a multi-start optimizer from a single-start optimizer.
Params:
optimizer – Single-start optimizer to wrap.
starts – Number of starts to perform. If starts == 1, the optimize methods will return the same solution as optimizer would.
generator – Random generator to use for restarts.
Throws:
NullArgumentException – if optimizer or generator is null.
NotStrictlyPositiveException – if starts < 1./**
     * Create a multi-start optimizer from a single-start optimizer.
     *
     * @param optimizer Single-start optimizer to wrap.
     * @param starts Number of starts to perform. If {@code starts == 1},
     * the {@code optimize} methods will return the same solution as
     * {@code optimizer} would.
     * @param generator Random generator to use for restarts.
     * @throws NullArgumentException if {@code optimizer} or {@code generator}
     * is {@code null}.
     * @throws NotStrictlyPositiveException if {@code starts < 1}.
     */
    public UnivariateMultiStartOptimizer(final BaseUnivariateOptimizer<FUNC> optimizer,
                                             final int starts,
                                             final RandomGenerator generator) {
        if (optimizer == null ||
                generator == null) {
                throw new NullArgumentException();
        }
        if (starts < 1) {
            throw new NotStrictlyPositiveException(starts);
        }

        this.optimizer = optimizer;
        this.starts = starts;
        this.generator = generator;
    }

    
{@inheritDoc}
/**
     * {@inheritDoc}
     */
    public ConvergenceChecker<UnivariatePointValuePair> getConvergenceChecker() {
        return optimizer.getConvergenceChecker();
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public int getMaxEvaluations() {
        return maxEvaluations;
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public int getEvaluations() {
        return totalEvaluations;
    }

    
Get all the optima found during the last call to optimize. The optimizer stores all the optima found during a set of restarts. The optimize method returns the best point only. This method returns all the points found at the end of each starts, including the best one already returned by the optimize method. 
 The returned array as one element for each start as specified in the constructor. It is ordered with the results from the runs that did converge first, sorted from best to worst objective value (i.e in ascending order if minimizing and in descending order if maximizing), followed by null elements corresponding to the runs that did not converge. This means all elements will be null if the optimize method did throw an exception. This also means that if the first element is not null, it is the best point found across all starts. 
Throws:
MathIllegalStateException – if optimize has not been called.
Returns:
an array containing the optima./**
     * Get all the optima found during the last call to {@link
     * #optimize(int,UnivariateFunction,GoalType,double,double) optimize}.
     * The optimizer stores all the optima found during a set of
     * restarts. The {@link #optimize(int,UnivariateFunction,GoalType,double,double) optimize}
     * method returns the best point only. This method returns all the points
     * found at the end of each starts, including the best one already
     * returned by the {@link #optimize(int,UnivariateFunction,GoalType,double,double) optimize}
     * method.
     * <br/>
     * The returned array as one element for each start as specified
     * in the constructor. It is ordered with the results from the
     * runs that did converge first, sorted from best to worst
     * objective value (i.e in ascending order if minimizing and in
     * descending order if maximizing), followed by {@code null} elements
     * corresponding to the runs that did not converge. This means all
     * elements will be {@code null} if the {@link
     * #optimize(int,UnivariateFunction,GoalType,double,double) optimize}
     * method did throw an exception.
     * This also means that if the first element is not {@code null}, it is
     * the best point found across all starts.
     *
     * @return an array containing the optima.
     * @throws MathIllegalStateException if {@link
     * #optimize(int,UnivariateFunction,GoalType,double,double) optimize}
     * has not been called.
     */
    public UnivariatePointValuePair[] getOptima() {
        if (optima == null) {
            throw new MathIllegalStateException(LocalizedFormats.NO_OPTIMUM_COMPUTED_YET);
        }
        return optima.clone();
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public UnivariatePointValuePair optimize(int maxEval, final FUNC f,
                                                 final GoalType goal,
                                                 final double min, final double max) {
        return optimize(maxEval, f, goal, min, max, min + 0.5 * (max - min));
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public UnivariatePointValuePair optimize(int maxEval, final FUNC f,
                                                 final GoalType goal,
                                                 final double min, final double max,
                                                 final double startValue) {
        RuntimeException lastException = null;
        optima = new UnivariatePointValuePair[starts];
        totalEvaluations = 0;

        // Multi-start loop.
        for (int i = 0; i < starts; ++i) {
            // CHECKSTYLE: stop IllegalCatch
            try {
                final double s = (i == 0) ? startValue : min + generator.nextDouble() * (max - min);
                optima[i] = optimizer.optimize(maxEval - totalEvaluations, f, goal, min, max, s);
            } catch (RuntimeException mue) {
                lastException = mue;
                optima[i] = null;
            }
            // CHECKSTYLE: resume IllegalCatch

            totalEvaluations += optimizer.getEvaluations();
        }

        sortPairs(goal);

        if (optima[0] == null) {
            throw lastException; // cannot be null if starts >=1
        }

        // Return the point with the best objective function value.
        return optima[0];
    }

    
Sort the optima from best to worst, followed by null elements. 
Params:
goal – Goal type./**
     * Sort the optima from best to worst, followed by {@code null} elements.
     *
     * @param goal Goal type.
     */
    private void sortPairs(final GoalType goal) {
        Arrays.sort(optima, new Comparator<UnivariatePointValuePair>() {
                
{@inheritDoc} /** {@inheritDoc} */
                public int compare(final UnivariatePointValuePair o1,
                                   final UnivariatePointValuePair o2) {
                    if (o1 == null) {
                        return (o2 == null) ? 0 : 1;
                    } else if (o2 == null) {
                        return -1;
                    }
                    final double v1 = o1.getValue();
                    final double v2 = o2.getValue();
                    return (goal == GoalType.MINIMIZE) ?
                        Double.compare(v1, v2) : Double.compare(v2, v1);
                }
            });
    }
}