ComplexUtils.java

/*
 * 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
 *
 *      https://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.
 */

/*
 * This is not the original file distributed by the Apache Software Foundation
 * It has been modified by the Hipparchus project
 */

package org.hipparchus.complex;

import org.hipparchus.CalculusFieldElement;
import org.hipparchus.exception.LocalizedCoreFormats;
import org.hipparchus.exception.MathIllegalArgumentException;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.FieldSinCos;
import org.hipparchus.util.SinCos;

/**
 * Static implementations of common {@link Complex} utilities functions.
 */
public class ComplexUtils {

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

    /**
     * Creates a complex number from the given polar representation.
     * <p>
     * The value returned is <code>r&middot;e<sup>i&middot;theta</sup></code>,
     * computed as <code>r&middot;cos(theta) + r&middot;sin(theta)i</code>
     * </p>
     * <p>
     * If either <code>r</code> or <code>theta</code> is NaN, or
     * <code>theta</code> is infinite, {@link Complex#NaN} is returned.
     * </p>
     * <p>
     * If <code>r</code> is infinite and <code>theta</code> is finite,
     * infinite or NaN values may be returned in parts of the result, following
     * the rules for double arithmetic.</p>
     * <pre>
     * Examples:
     * <code>
     * polar2Complex(INFINITY, &pi;/4) = INFINITY + INFINITY i
     * polar2Complex(INFINITY, 0) = INFINITY + NaN i
     * polar2Complex(INFINITY, -&pi;/4) = INFINITY - INFINITY i
     * polar2Complex(INFINITY, 5&pi;/4) = -INFINITY - INFINITY i </code>
     * </pre>
     *
     * @param r the modulus of the complex number to create
     * @param theta  the argument of the complex number to create
     * @return <code>r&middot;e<sup>i&middot;theta</sup></code>
     * @throws MathIllegalArgumentException if {@code r} is negative.
     */
    public static Complex polar2Complex(double r, double theta) throws MathIllegalArgumentException {
        if (r < 0) {
            throw new MathIllegalArgumentException(
                  LocalizedCoreFormats.NEGATIVE_COMPLEX_MODULE, r);
        }
        final SinCos sc = FastMath.sinCos(theta);
        return new Complex(r * sc.cos(), r * sc.sin());
    }

    /**
     * Creates a complex number from the given polar representation.
     * <p>
     * The value returned is <code>r&middot;e<sup>i&middot;theta</sup></code>,
     * computed as <code>r&middot;cos(theta) + r&middot;sin(theta)i</code>
     * </p>
     * <p>
     * If either <code>r</code> or <code>theta</code> is NaN, or
     * <code>theta</code> is infinite, {@link Complex#NaN} is returned.
     * </p>
     * <p>
     * If <code>r</code> is infinite and <code>theta</code> is finite,
     * infinite or NaN values may be returned in parts of the result, following
     * the rules for double arithmetic.
     * </p>
     * <pre>
     * Examples:
     * <code>
     * polar2Complex(INFINITY, &pi;/4) = INFINITY + INFINITY i
     * polar2Complex(INFINITY, 0) = INFINITY + NaN i
     * polar2Complex(INFINITY, -&pi;/4) = INFINITY - INFINITY i
     * polar2Complex(INFINITY, 5&pi;/4) = -INFINITY - INFINITY i </code>
     * </pre>
     *
     * @param r the modulus of the complex number to create
     * @param theta  the argument of the complex number to create
     * @param <T> type of the field elements
     * @return <code>r&middot;e<sup>i&middot;theta</sup></code>
     * @throws MathIllegalArgumentException if {@code r} is negative.
     * @since 2.0
     */
    public static <T extends CalculusFieldElement<T>> FieldComplex<T> polar2Complex(T r, T theta) throws MathIllegalArgumentException {
        if (r.getReal() < 0) {
            throw new MathIllegalArgumentException(
                  LocalizedCoreFormats.NEGATIVE_COMPLEX_MODULE, r);
        }
        final FieldSinCos<T> sc = FastMath.sinCos(theta);
        return new FieldComplex<>(r.multiply(sc.cos()), r.multiply(sc.sin()));
    }

    /**
     * Convert an array of primitive doubles to an array of {@code Complex} objects.
     *
     * @param real Array of numbers to be converted to their {@code Complex} equivalent.
     * @return an array of {@code Complex} objects.
     */
    public static Complex[] convertToComplex(double[] real) {
        final Complex[] c = new Complex[real.length];
        for (int i = 0; i < real.length; i++) {
            c[i] = new Complex(real[i], 0);
        }

        return c;
    }

}