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+/*
+ * 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.
+ */
+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 <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. */
+    public static final int TRAPEZOID_MAX_ITERATIONS_COUNT = 64;
+
+    /** Intermediate result. */
+    private double s;
+
+    /**
+     * 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.
+     * @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 {@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 <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} */
+    @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();
+        }
+
+    }
+
+}