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package org.apache.commons.math3.analysis.integration.gauss;

import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.NonMonotonicSequenceException;
import org.apache.commons.math3.util.MathArrays;
import org.apache.commons.math3.util.Pair;

Class that implements the Gaussian rule for integrating a weighted function. 
Since:
3.1/**
 * Class that implements the Gaussian rule for
 * {@link #integrate(UnivariateFunction) integrating} a weighted
 * function.
 *
 * @since 3.1
 */
public class GaussIntegrator {
    
Nodes. /** Nodes. */
    private final double[] points;
    
Nodes weights. /** Nodes weights. */
    private final double[] weights;

    
Creates an integrator from the given points and weights. The integration interval is defined by the first and last value of points which must be sorted in increasing order. 
Params:
points – Integration points.
weights – Weights of the corresponding integration nodes.
Throws:
NonMonotonicSequenceException – if the points are not sorted in increasing order.
DimensionMismatchException – if points and weights don't have the same length/**
     * Creates an integrator from the given {@code points} and {@code weights}.
     * The integration interval is defined by the first and last value of
     * {@code points} which must be sorted in increasing order.
     *
     * @param points Integration points.
     * @param weights Weights of the corresponding integration nodes.
     * @throws NonMonotonicSequenceException if the {@code points} are not
     * sorted in increasing order.
     * @throws DimensionMismatchException if points and weights don't have the same length
     */
    public GaussIntegrator(double[] points,
                           double[] weights)
        throws NonMonotonicSequenceException, DimensionMismatchException {
        if (points.length != weights.length) {
            throw new DimensionMismatchException(points.length,
                                                 weights.length);
        }

        MathArrays.checkOrder(points, MathArrays.OrderDirection.INCREASING, true, true);

        this.points = points.clone();
        this.weights = weights.clone();
    }

    
Creates an integrator from the given pair of points (first element of
the pair) and weights (second element of the pair.
Params:
pointsAndWeights – Integration points and corresponding weights.
Throws:
NonMonotonicSequenceException – if the points are not sorted in increasing order.
See Also:
GaussIntegrator(double[], double[])/**
     * Creates an integrator from the given pair of points (first element of
     * the pair) and weights (second element of the pair.
     *
     * @param pointsAndWeights Integration points and corresponding weights.
     * @throws NonMonotonicSequenceException if the {@code points} are not
     * sorted in increasing order.
     *
     * @see #GaussIntegrator(double[], double[])
     */
    public GaussIntegrator(Pair<double[], double[]> pointsAndWeights)
        throws NonMonotonicSequenceException {
        this(pointsAndWeights.getFirst(), pointsAndWeights.getSecond());
    }

    
Returns an estimate of the integral of f(x) * w(x), where w is a weight function that depends on the actual flavor of the Gauss integration scheme. The algorithm uses the points and associated weights, as passed to the constructor. 
Params:
f – Function to integrate.
Returns:
the integral of the weighted function./**
     * Returns an estimate of the integral of {@code f(x) * w(x)},
     * where {@code w} is a weight function that depends on the actual
     * flavor of the Gauss integration scheme.
     * The algorithm uses the points and associated weights, as passed
     * to the {@link #GaussIntegrator(double[],double[]) constructor}.
     *
     * @param f Function to integrate.
     * @return the integral of the weighted function.
     */
    public double integrate(UnivariateFunction f) {
        double s = 0;
        double c = 0;
        for (int i = 0; i < points.length; i++) {
            final double x = points[i];
            final double w = weights[i];
            final double y = w * f.value(x) - c;
            final double t = s + y;
            c = (t - s) - y;
            s = t;
        }
        return s;
    }

    
Returns:
the order of the integration rule (the number of integration
points)./**
     * @return the order of the integration rule (the number of integration
     * points).
     */
    public int getNumberOfPoints() {
        return points.length;
    }

    
Gets the integration point at the given index.
The index must be in the valid range but no check is performed.
Params:
index – index of the integration point
Returns:
the integration point./**
     * Gets the integration point at the given index.
     * The index must be in the valid range but no check is performed.
     * @param index index of the integration point
     * @return the integration point.
     */
    public double getPoint(int index) {
        return points[index];
    }

    
Gets the weight of the integration point at the given index.
The index must be in the valid range but no check is performed.
Params:
index – index of the integration point
Returns:
the weight./**
     * Gets the weight of the integration point at the given index.
     * The index must be in the valid range but no check is performed.
     * @param index index of the integration point
     * @return the weight.
     */
    public double getWeight(int index) {
        return weights[index];
    }
}