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

import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.MaxCountExceededException;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.exception.TooManyEvaluationsException;
import org.apache.commons.math3.util.FastMath;

Implements the 
Trapezoid Rule for integration of real univariate functions. For
reference, see Introduction to Numerical Analysis, ISBN 038795452X,
chapter 3.

The function should be integrable.
Since:
1.2/**
 * Implements the <a href="http://mathworld.wolfram.com/TrapezoidalRule.html">
 * Trapezoid Rule</a> for integration of real univariate functions. For
 * reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X,
 * chapter 3.
 * <p>
 * The function should be integrable.</p>
 *
 * @since 1.2
 */
public class TrapezoidIntegrator extends BaseAbstractUnivariateIntegrator {

    
Maximum number of iterations for trapezoid. /** Maximum number of iterations for trapezoid. */
    public static final int TRAPEZOID_MAX_ITERATIONS_COUNT = 64;

    
Intermediate result. /** Intermediate result. */
    private double s;

    
Build a trapezoid integrator with given accuracies and iterations counts.
Params:
relativeAccuracy – relative accuracy of the result
absoluteAccuracy – absolute accuracy of the result
minimalIterationCount – minimum number of iterations
maximalIterationCount – maximum number of iterations (must be less than or equal to TRAPEZOID_MAX_ITERATIONS_COUNT
Throws:
NotStrictlyPositiveException – if minimal number of iterations
is not strictly positive
NumberIsTooSmallException – if maximal number of iterations
is lesser than or equal to the minimal number of iterations
NumberIsTooLargeException – if maximal number of iterations is greater than TRAPEZOID_MAX_ITERATIONS_COUNT/**
     * Build a trapezoid integrator with given accuracies and iterations counts.
     * @param relativeAccuracy relative accuracy of the result
     * @param absoluteAccuracy absolute accuracy of the result
     * @param minimalIterationCount minimum number of iterations
     * @param maximalIterationCount maximum number of iterations
     * (must be less than or equal to {@link #TRAPEZOID_MAX_ITERATIONS_COUNT}
     * @exception NotStrictlyPositiveException if minimal number of iterations
     * is not strictly positive
     * @exception NumberIsTooSmallException if maximal number of iterations
     * is lesser than or equal to the minimal number of iterations
     * @exception NumberIsTooLargeException if maximal number of iterations
     * is greater than {@link #TRAPEZOID_MAX_ITERATIONS_COUNT}
     */
    public TrapezoidIntegrator(final double relativeAccuracy,
                               final double absoluteAccuracy,
                               final int minimalIterationCount,
                               final int maximalIterationCount)
        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
        super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
        if (maximalIterationCount > TRAPEZOID_MAX_ITERATIONS_COUNT) {
            throw new NumberIsTooLargeException(maximalIterationCount,
                                                TRAPEZOID_MAX_ITERATIONS_COUNT, false);
        }
    }

    
Build a trapezoid integrator with given iteration counts.
Params:
minimalIterationCount – minimum number of iterations
maximalIterationCount – maximum number of iterations (must be less than or equal to TRAPEZOID_MAX_ITERATIONS_COUNT
Throws:
NotStrictlyPositiveException – if minimal number of iterations
is not strictly positive
NumberIsTooSmallException – if maximal number of iterations
is lesser than or equal to the minimal number of iterations
NumberIsTooLargeException – if maximal number of iterations is greater than TRAPEZOID_MAX_ITERATIONS_COUNT/**
     * Build a trapezoid integrator with given iteration counts.
     * @param minimalIterationCount minimum number of iterations
     * @param maximalIterationCount maximum number of iterations
     * (must be less than or equal to {@link #TRAPEZOID_MAX_ITERATIONS_COUNT}
     * @exception NotStrictlyPositiveException if minimal number of iterations
     * is not strictly positive
     * @exception NumberIsTooSmallException if maximal number of iterations
     * is lesser than or equal to the minimal number of iterations
     * @exception NumberIsTooLargeException if maximal number of iterations
     * is greater than {@link #TRAPEZOID_MAX_ITERATIONS_COUNT}
     */
    public TrapezoidIntegrator(final int minimalIterationCount,
                               final int maximalIterationCount)
        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
        super(minimalIterationCount, maximalIterationCount);
        if (maximalIterationCount > TRAPEZOID_MAX_ITERATIONS_COUNT) {
            throw new NumberIsTooLargeException(maximalIterationCount,
                                                TRAPEZOID_MAX_ITERATIONS_COUNT, false);
        }
    }

    
Construct a trapezoid integrator with default settings. (max iteration count set to TRAPEZOID_MAX_ITERATIONS_COUNT) /**
     * Construct a trapezoid integrator with default settings.
     * (max iteration count set to {@link #TRAPEZOID_MAX_ITERATIONS_COUNT})
     */
    public TrapezoidIntegrator() {
        super(DEFAULT_MIN_ITERATIONS_COUNT, TRAPEZOID_MAX_ITERATIONS_COUNT);
    }

    
Compute the n-th stage integral of trapezoid rule. This function
should only be called by API integrate() in the package.
To save time it does not verify arguments - caller does.

The interval is divided equally into 2^n sections rather than an
arbitrary m sections because this configuration can best utilize the
already computed values.
Params:
baseIntegrator – integrator holding integration parameters
n – the stage of 1/2 refinement, n = 0 is no refinement
Throws:
TooManyEvaluationsException – if the maximal number of evaluations
is exceeded.
Returns:
the value of n-th stage integral/**
     * Compute the n-th stage integral of trapezoid rule. This function
     * should only be called by API <code>integrate()</code> in the package.
     * To save time it does not verify arguments - caller does.
     * <p>
     * The interval is divided equally into 2^n sections rather than an
     * arbitrary m sections because this configuration can best utilize the
     * already computed values.</p>
     *
     * @param baseIntegrator integrator holding integration parameters
     * @param n the stage of 1/2 refinement, n = 0 is no refinement
     * @return the value of n-th stage integral
     * @throws TooManyEvaluationsException if the maximal number of evaluations
     * is exceeded.
     */
    double stage(final BaseAbstractUnivariateIntegrator baseIntegrator, final int n)
        throws TooManyEvaluationsException {

        if (n == 0) {
            final double max = baseIntegrator.getMax();
            final double min = baseIntegrator.getMin();
            s = 0.5 * (max - min) *
                      (baseIntegrator.computeObjectiveValue(min) +
                       baseIntegrator.computeObjectiveValue(max));
            return s;
        } else {
            final long np = 1L << (n-1);           // number of new points in this stage
            double sum = 0;
            final double max = baseIntegrator.getMax();
            final double min = baseIntegrator.getMin();
            // spacing between adjacent new points
            final double spacing = (max - min) / np;
            double x = min + 0.5 * spacing;    // the first new point
            for (long i = 0; i < np; i++) {
                sum += baseIntegrator.computeObjectiveValue(x);
                x += spacing;
            }
            // add the new sum to previously calculated result
            s = 0.5 * (s + sum * spacing);
            return s;
        }
    }

    
{@inheritDoc} /** {@inheritDoc} */
    @Override
    protected double doIntegrate()
        throws MathIllegalArgumentException, TooManyEvaluationsException, MaxCountExceededException {

        double oldt = stage(this, 0);
        incrementCount();
        while (true) {
            final int i = getIterations();
            final double t = stage(this, i);
            if (i >= getMinimalIterationCount()) {
                final double delta = FastMath.abs(t - oldt);
                final double rLimit =
                    getRelativeAccuracy() * (FastMath.abs(oldt) + FastMath.abs(t)) * 0.5;
                if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) {
                    return t;
                }
            }
            oldt = t;
            incrementCount();
        }

    }

}