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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.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/RombergIntegration.html">
+ * Romberg Algorithm</a> for integration of real univariate functions. For
+ * reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X,
+ * chapter 3.
+ * <p>
+ * Romberg integration employs k successive refinements of the trapezoid
+ * rule to remove error terms less than order O(N^(-2k)). Simpson's rule
+ * is a special case of k = 2.</p>
+ *
+ * @since 1.2
+ */
+public class RombergIntegrator extends BaseAbstractUnivariateIntegrator {
+
+    /** Maximal number of iterations for Romberg. */
+    public static final int ROMBERG_MAX_ITERATIONS_COUNT = 32;
+
+    /**
+     * Build a Romberg 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 #ROMBERG_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 #ROMBERG_MAX_ITERATIONS_COUNT}
+     */
+    public RombergIntegrator(final double relativeAccuracy,
+                             final double absoluteAccuracy,
+                             final int minimalIterationCount,
+                             final int maximalIterationCount)
+        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
+        super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
+        if (maximalIterationCount > ROMBERG_MAX_ITERATIONS_COUNT) {
+            throw new NumberIsTooLargeException(maximalIterationCount,
+                                                ROMBERG_MAX_ITERATIONS_COUNT, false);
+        }
+    }
+
+    /**
+     * Build a Romberg 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 #ROMBERG_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 #ROMBERG_MAX_ITERATIONS_COUNT}
+     */
+    public RombergIntegrator(final int minimalIterationCount,
+                             final int maximalIterationCount)
+        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
+        super(minimalIterationCount, maximalIterationCount);
+        if (maximalIterationCount > ROMBERG_MAX_ITERATIONS_COUNT) {
+            throw new NumberIsTooLargeException(maximalIterationCount,
+                                                ROMBERG_MAX_ITERATIONS_COUNT, false);
+        }
+    }
+
+    /**
+     * Construct a Romberg integrator with default settings
+     * (max iteration count set to {@link #ROMBERG_MAX_ITERATIONS_COUNT})
+     */
+    public RombergIntegrator() {
+        super(DEFAULT_MIN_ITERATIONS_COUNT, ROMBERG_MAX_ITERATIONS_COUNT);
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    protected double doIntegrate()
+        throws TooManyEvaluationsException, MaxCountExceededException {
+
+        final int m = getMaximalIterationCount() + 1;
+        double previousRow[] = new double[m];
+        double currentRow[]  = new double[m];
+
+        TrapezoidIntegrator qtrap = new TrapezoidIntegrator();
+        currentRow[0] = qtrap.stage(this, 0);
+        incrementCount();
+        double olds = currentRow[0];
+        while (true) {
+
+            final int i = getIterations();
+
+            // switch rows
+            final double[] tmpRow = previousRow;
+            previousRow = currentRow;
+            currentRow = tmpRow;
+
+            currentRow[0] = qtrap.stage(this, i);
+            incrementCount();
+            for (int j = 1; j <= i; j++) {
+                // Richardson extrapolation coefficient
+                final double r = (1L << (2 * j)) - 1;
+                final double tIJm1 = currentRow[j - 1];
+                currentRow[j] = tIJm1 + (tIJm1 - previousRow[j - 1]) / r;
+            }
+            final double s = currentRow[i];
+            if (i >= getMinimalIterationCount()) {
+                final double delta  = FastMath.abs(s - olds);
+                final double rLimit = getRelativeAccuracy() * (FastMath.abs(olds) + FastMath.abs(s)) * 0.5;
+                if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) {
+                    return s;
+                }
+            }
+            olds = s;
+        }
+
+    }
+
+}