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The Apache Commons Math project is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang.

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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.complex;

import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.util.FastMath;

/**
 * Static implementations of common
 * {@link org.apache.commons.math3.complex.Complex} utilities functions.
 *
 * @version $Id: ComplexUtils.java 1244107 2012-02-14 16:17:55Z erans $
 */
public class ComplexUtils {

    /**
     * Default constructor.
     */
    private ComplexUtils() {
        super();
    }

    /**
     * Creates a complex number from the given polar representation.
     * 
     * The value returned is r·e^i·theta,
     * computed as r·cos(theta) + r·sin(theta)i
     * 
     * If either r or theta is NaN, or
     * theta is infinite, {@link Complex#NaN} is returned.
     * 
     * If r is infinite and theta is finite,
     * infinite or NaN values may be returned in parts of the result, following
     * the rules for double arithmetic.
     * Examples:
     * 
     * polar2Complex(INFINITY, π/4) = INFINITY + INFINITY i
     * polar2Complex(INFINITY, 0) = INFINITY + NaN i
     * polar2Complex(INFINITY, -π/4) = INFINITY - INFINITY i
     * polar2Complex(INFINITY, 5π/4) = -INFINITY - INFINITY i 

     *
     * @param r the modulus of the complex number to create
     * @param theta  the argument of the complex number to create
     * @return r·e^i·theta
     * @throws MathIllegalArgumentException  if r is negative
     * @since 1.1
     */
    public static Complex polar2Complex(double r, double theta) {
        if (r < 0) {
            throw new MathIllegalArgumentException(
                  LocalizedFormats.NEGATIVE_COMPLEX_MODULE, r);
        }
        return new Complex(r * FastMath.cos(theta), r * FastMath.sin(theta));
    }

}