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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.distribution;
+
+import org.apache.commons.math3.exception.NumberIsTooLargeException;
+import org.apache.commons.math3.exception.NumberIsTooSmallException;
+import org.apache.commons.math3.exception.OutOfRangeException;
+import org.apache.commons.math3.exception.util.LocalizedFormats;
+import org.apache.commons.math3.random.RandomGenerator;
+import org.apache.commons.math3.random.Well19937c;
+import org.apache.commons.math3.util.FastMath;
+
+/**
+ * Implementation of the triangular real distribution.
+ *
+ * @see <a href="http://en.wikipedia.org/wiki/Triangular_distribution">Triangular distribution
+ * (Wikipedia)</a>
+ * @since 3.0
+ */
+public class TriangularDistribution extends AbstractRealDistribution {
+ /** Serializable version identifier. */
+ private static final long serialVersionUID = 20120112L;
+
+ /** Lower limit of this distribution (inclusive). */
+ private final double a;
+
+ /** Upper limit of this distribution (inclusive). */
+ private final double b;
+
+ /** Mode of this distribution. */
+ private final double c;
+
+ /** Inverse cumulative probability accuracy. */
+ private final double solverAbsoluteAccuracy;
+
+ /**
+ * Creates a triangular real distribution using the given lower limit, upper limit, and mode.
+ *
+ * <p><b>Note:</b> this constructor will implicitly create an instance of {@link Well19937c} as
+ * random generator to be used for sampling only (see {@link #sample()} and {@link
+ * #sample(int)}). In case no sampling is needed for the created distribution, it is advised to
+ * pass {@code null} as random generator via the appropriate constructors to avoid the
+ * additional initialisation overhead.
+ *
+ * @param a Lower limit of this distribution (inclusive).
+ * @param b Upper limit of this distribution (inclusive).
+ * @param c Mode of this distribution.
+ * @throws NumberIsTooLargeException if {@code a >= b} or if {@code c > b}.
+ * @throws NumberIsTooSmallException if {@code c < a}.
+ */
+ public TriangularDistribution(double a, double c, double b)
+ throws NumberIsTooLargeException, NumberIsTooSmallException {
+ this(new Well19937c(), a, c, b);
+ }
+
+ /**
+ * Creates a triangular distribution.
+ *
+ * @param rng Random number generator.
+ * @param a Lower limit of this distribution (inclusive).
+ * @param b Upper limit of this distribution (inclusive).
+ * @param c Mode of this distribution.
+ * @throws NumberIsTooLargeException if {@code a >= b} or if {@code c > b}.
+ * @throws NumberIsTooSmallException if {@code c < a}.
+ * @since 3.1
+ */
+ public TriangularDistribution(RandomGenerator rng, double a, double c, double b)
+ throws NumberIsTooLargeException, NumberIsTooSmallException {
+ super(rng);
+
+ if (a >= b) {
+ throw new NumberIsTooLargeException(
+ LocalizedFormats.LOWER_BOUND_NOT_BELOW_UPPER_BOUND, a, b, false);
+ }
+ if (c < a) {
+ throw new NumberIsTooSmallException(LocalizedFormats.NUMBER_TOO_SMALL, c, a, true);
+ }
+ if (c > b) {
+ throw new NumberIsTooLargeException(LocalizedFormats.NUMBER_TOO_LARGE, c, b, true);
+ }
+
+ this.a = a;
+ this.c = c;
+ this.b = b;
+ solverAbsoluteAccuracy = FastMath.max(FastMath.ulp(a), FastMath.ulp(b));
+ }
+
+ /**
+ * Returns the mode {@code c} of this distribution.
+ *
+ * @return the mode {@code c} of this distribution
+ */
+ public double getMode() {
+ return c;
+ }
+
+ /**
+ * {@inheritDoc}
+ *
+ * <p>For this distribution, the returned value is not really meaningful, since exact formulas
+ * are implemented for the computation of the {@link #inverseCumulativeProbability(double)} (no
+ * solver is invoked).
+ *
+ * <p>For lower limit {@code a} and upper limit {@code b}, the current implementation returns
+ * {@code max(ulp(a), ulp(b)}.
+ */
+ @Override
+ protected double getSolverAbsoluteAccuracy() {
+ return solverAbsoluteAccuracy;
+ }
+
+ /**
+ * {@inheritDoc}
+ *
+ * <p>For lower limit {@code a}, upper limit {@code b} and mode {@code c}, the PDF is given by
+ *
+ * <ul>
+ * <li>{@code 2 * (x - a) / [(b - a) * (c - a)]} if {@code a <= x < c},
+ * <li>{@code 2 / (b - a)} if {@code x = c},
+ * <li>{@code 2 * (b - x) / [(b - a) * (b - c)]} if {@code c < x <= b},
+ * <li>{@code 0} otherwise.
+ * </ul>
+ */
+ public double density(double x) {
+ if (x < a) {
+ return 0;
+ }
+ if (a <= x && x < c) {
+ double divident = 2 * (x - a);
+ double divisor = (b - a) * (c - a);
+ return divident / divisor;
+ }
+ if (x == c) {
+ return 2 / (b - a);
+ }
+ if (c < x && x <= b) {
+ double divident = 2 * (b - x);
+ double divisor = (b - a) * (b - c);
+ return divident / divisor;
+ }
+ return 0;
+ }
+
+ /**
+ * {@inheritDoc}
+ *
+ * <p>For lower limit {@code a}, upper limit {@code b} and mode {@code c}, the CDF is given by
+ *
+ * <ul>
+ * <li>{@code 0} if {@code x < a},
+ * <li>{@code (x - a)^2 / [(b - a) * (c - a)]} if {@code a <= x < c},
+ * <li>{@code (c - a) / (b - a)} if {@code x = c},
+ * <li>{@code 1 - (b - x)^2 / [(b - a) * (b - c)]} if {@code c < x <= b},
+ * <li>{@code 1} if {@code x > b}.
+ * </ul>
+ */
+ public double cumulativeProbability(double x) {
+ if (x < a) {
+ return 0;
+ }
+ if (a <= x && x < c) {
+ double divident = (x - a) * (x - a);
+ double divisor = (b - a) * (c - a);
+ return divident / divisor;
+ }
+ if (x == c) {
+ return (c - a) / (b - a);
+ }
+ if (c < x && x <= b) {
+ double divident = (b - x) * (b - x);
+ double divisor = (b - a) * (b - c);
+ return 1 - (divident / divisor);
+ }
+ return 1;
+ }
+
+ /**
+ * {@inheritDoc}
+ *
+ * <p>For lower limit {@code a}, upper limit {@code b}, and mode {@code c}, the mean is {@code
+ * (a + b + c) / 3}.
+ */
+ public double getNumericalMean() {
+ return (a + b + c) / 3;
+ }
+
+ /**
+ * {@inheritDoc}
+ *
+ * <p>For lower limit {@code a}, upper limit {@code b}, and mode {@code c}, the variance is
+ * {@code (a^2 + b^2 + c^2 - a * b - a * c - b * c) / 18}.
+ */
+ public double getNumericalVariance() {
+ return (a * a + b * b + c * c - a * b - a * c - b * c) / 18;
+ }
+
+ /**
+ * {@inheritDoc}
+ *
+ * <p>The lower bound of the support is equal to the lower limit parameter {@code a} of the
+ * distribution.
+ *
+ * @return lower bound of the support
+ */
+ public double getSupportLowerBound() {
+ return a;
+ }
+
+ /**
+ * {@inheritDoc}
+ *
+ * <p>The upper bound of the support is equal to the upper limit parameter {@code b} of the
+ * distribution.
+ *
+ * @return upper bound of the support
+ */
+ public double getSupportUpperBound() {
+ return b;
+ }
+
+ /** {@inheritDoc} */
+ public boolean isSupportLowerBoundInclusive() {
+ return true;
+ }
+
+ /** {@inheritDoc} */
+ public boolean isSupportUpperBoundInclusive() {
+ return true;
+ }
+
+ /**
+ * {@inheritDoc}
+ *
+ * <p>The support of this distribution is connected.
+ *
+ * @return {@code true}
+ */
+ public boolean isSupportConnected() {
+ return true;
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public double inverseCumulativeProbability(double p) throws OutOfRangeException {
+ if (p < 0 || p > 1) {
+ throw new OutOfRangeException(p, 0, 1);
+ }
+ if (p == 0) {
+ return a;
+ }
+ if (p == 1) {
+ return b;
+ }
+ if (p < (c - a) / (b - a)) {
+ return a + FastMath.sqrt(p * (b - a) * (c - a));
+ }
+ return b - FastMath.sqrt((1 - p) * (b - a) * (b - c));
+ }
+}
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