| /* |
| * 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.numbers.complex; |
| |
| import java.io.Serializable; |
| import java.util.ArrayList; |
| import java.util.List; |
| import org.apache.commons.numbers.core.Precision; |
| /** |
| * Representation of a Complex number, i.e. a number which has both a |
| * real and imaginary part. |
| * <p> |
| * Implementations of arithmetic operations handle {@code NaN} and |
| * infinite values according to the rules for {@link java.lang.Double}, i.e. |
| * {@link #equals} is an equivalence relation for all instances that have |
| * a {@code NaN} in either real or imaginary part, e.g. the following are |
| * considered equal: |
| * <ul> |
| * <li>{@code 1 + NaNi}</li> |
| * <li>{@code NaN + i}</li> |
| * <li>{@code NaN + NaNi}</li> |
| * </ul><p> |
| * Note that this contradicts the IEEE-754 standard for floating |
| * point numbers (according to which the test {@code x == x} must fail if |
| * {@code x} is {@code NaN}). The method |
| * {@link org.apache.commons.numbers.core.Precision#equals(double,double,int) |
| * equals for primitive double} in class {@code Precision} conforms with |
| * IEEE-754 while this class conforms with the standard behavior for Java |
| * object types.</p> |
| * |
| */ |
| public class Complex implements Serializable { |
| /** The square root of -1. A number representing "0.0 + 1.0i" */ |
| public static final Complex I = new Complex(0.0, 1.0); |
| // CHECKSTYLE: stop ConstantName |
| /** A complex number representing "NaN + NaNi" */ |
| public static final Complex NaN = new Complex(Double.NaN, Double.NaN); |
| // CHECKSTYLE: resume ConstantName |
| /** A complex number representing "+INF + INFi" */ |
| public static final Complex INF = new Complex(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY); |
| /** A complex number representing "1.0 + 0.0i" */ |
| public static final Complex ONE = new Complex(1.0, 0.0); |
| /** A complex number representing "0.0 + 0.0i" */ |
| public static final Complex ZERO = new Complex(0.0, 0.0); |
| |
| /** Serializable version identifier */ |
| private static final long serialVersionUID = -6195664516687396620L; |
| |
| /** The imaginary part. */ |
| private final double imaginary; |
| /** The real part. */ |
| private final double real; |
| |
| /** |
| * Create a complex number given only the real part. |
| * |
| * @param real Real part. |
| */ |
| public Complex(double real) { |
| this(real, 0.0); |
| } |
| |
| /** |
| * Create a complex number given the real and imaginary parts. |
| * |
| * @param real Real part. |
| * @param imaginary Imaginary part. |
| */ |
| public Complex(double real, double imaginary) { |
| this.real = real; |
| this.imaginary = imaginary; |
| } |
| |
| /** |
| * Creates a Complex from its polar representation. |
| * <p> |
| * If either {@code r} or {@code theta} is NaN, or {@code theta} is |
| * infinite, {@link Complex#NaN} is returned. |
| * <p> |
| * If {@code r} is infinite and {@code theta} is finite, infinite or NaN |
| * values may be returned in parts of the result, following the rules for |
| * double arithmetic. |
| * |
| * <pre> |
| * Examples: |
| * {@code |
| * polar2Complex(INFINITY, \(\pi\)) = INFINITY + INFINITY i |
| * polar2Complex(INFINITY, 0) = INFINITY + NaN i |
| * polar2Complex(INFINITY, \(-\frac{\pi}{4}\)) = INFINITY - INFINITY i |
| * polar2Complex(INFINITY, \(5\frac{\pi}{4}\)) = -INFINITY - INFINITY i } |
| * </pre> |
| * |
| * @param r the modulus of the complex number to create |
| * @param theta the argument of the complex number to create |
| * @return {@code Complex} |
| * @since 1.1 |
| */ |
| public Complex polar(double r, double theta) { |
| checkNotNegative(r); |
| return new Complex(r * Math.cos(theta), r * Math.sin(theta)); |
| } |
| |
| /** |
| * For a real constructor argument x, returns a new Complex object c |
| * where {@code c = cos(x) + i sin (x)} |
| * |
| * @param x {@code double} to build the cis number |
| * @return {@code Complex} |
| */ |
| public Complex cis(double x) { |
| return new Complex(Math.cos(x), Math.sin(x)); |
| } |
| |
| /** |
| * Returns true if either real or imaginary component of the Complex |
| * is NaN |
| * |
| * @return {@code boolean} |
| */ |
| public boolean isNaN() { |
| if (Double.isNaN(real) || Double.isNaN(imaginary)) { |
| return true; |
| } else { |
| return false; |
| } |
| } |
| |
| /** |
| * Returns true if either real or imaginary component of the Complex |
| * is Infinite |
| * |
| * @return {@code boolean} |
| */ |
| public boolean isInfinite() { |
| if (Double.isInfinite(real) || Double.isInfinite(imaginary)) { |
| return true; |
| } else { |
| return false; |
| } |
| } |
| |
| /** |
| * Returns projection of this complex number onto the Riemann sphere, |
| * i.e. all infinities (including those with an NaN component) |
| * project onto real infinity, as described in the |
| * <a href="http://pubs.opengroup.org/onlinepubs/9699919799/functions/cproj.html"> |
| * IEEE and ISO C standards</a>. |
| * <p> |
| * |
| * |
| * @return {@code Complex} projected onto the Riemann sphere. |
| */ |
| public Complex proj() { |
| if (Double.isInfinite(real) || Double.isInfinite(imaginary)) { |
| return new Complex(Double.POSITIVE_INFINITY); |
| } else { |
| return this; |
| } |
| } |
| |
| /** |
| * Return the absolute value of this complex number. |
| * Returns {@code NaN} if either real or imaginary part is {@code NaN} |
| * and {@code Double.POSITIVE_INFINITY} if neither part is {@code NaN}, |
| * but at least one part is infinite. |
| * This code follows the <a href="http://www.iso-9899.info/wiki/The_Standard">ISO C Standard</a>, Annex G, in calculating the returned value (i.e. the hypot(x,y) method) |
| * |
| * @return the absolute value. |
| */ |
| public double abs() { |
| if (Math.abs(real) < Math.abs(imaginary)) { |
| if (imaginary == 0.0) { |
| return Math.abs(real); |
| } |
| final double q = real / imaginary; |
| return Math.abs(imaginary) * Math.sqrt(1 + q * q); |
| } else { |
| if (real == 0.0) { |
| return Math.abs(imaginary); |
| } |
| final double q = imaginary / real; |
| return Math.abs(real) * Math.sqrt(1 + q * q); |
| } |
| } |
| |
| /** |
| * Return the norm of this complex number, defined as the square of the magnitude |
| in the |
| * <a href="http://pubs.opengroup.org/onlinepubs/9699919799/functions/cproj.html"> |
| * IEEE and ISO C standards</a>. |
| * |
| * @return the norm. |
| */ |
| public double norm() { |
| return abs()*abs(); |
| } |
| |
| /** |
| * Returns a {@code Complex} whose value is |
| * {@code (this + addend)}. |
| * Uses the definitional formula |
| * <p> |
| * {@code (a + bi) + (c + di) = (a+c) + (b+d)i} |
| * </p> |
| * |
| * @param addend Value to be added to this {@code Complex}. |
| * @return {@code this + addend}. |
| * @if {@code addend} is {@code null}. |
| */ |
| public Complex add(Complex addend) { |
| checkNotNull(addend); |
| return new Complex(real + addend.getReal(), |
| imaginary + addend.getImaginary()); |
| } |
| |
| /** |
| * Returns a {@code Complex} whose value is {@code (this + addend)}, |
| * with {@code addend} interpreted as a real number. |
| * |
| * @param addend Value to be added to this {@code Complex}. |
| * @return {@code this + addend}. |
| * @see #add(Complex) |
| */ |
| public Complex add(double addend) { |
| return new Complex(real + addend, imaginary); |
| } |
| |
| /** |
| * Returns the conjugate of this complex number. |
| * The conjugate of {@code a + bi} is {@code a - bi}. |
| * |
| * @return the conjugate of this complex object. |
| */ |
| public Complex conjugate() { |
| return new Complex(real, -imaginary); |
| } |
| |
| /** |
| * Returns the conjugate of this complex number. |
| * C++11 grammar. |
| * </p> |
| * @return the conjugate of this complex object. |
| */ |
| public Complex conj() { |
| return conjugate(); |
| } |
| |
| |
| /** |
| * Returns a {@code Complex} whose value is |
| * {@code (this / divisor)}. |
| * Implements the definitional formula |
| * <pre> |
| * <code> |
| * a + bi ac + bd + (bc - ad)i |
| * ----------- = ------------------------- |
| * c + di c<sup>2</sup> + d<sup>2</sup> |
| * </code> |
| * </pre> |
| * but uses |
| * <a href="http://doi.acm.org/10.1145/1039813.1039814"> |
| * prescaling of operands</a> to limit the effects of overflows and |
| * underflows in the computation. |
| * <p> |
| * {@code Infinite} and {@code NaN} values are handled according to the |
| * following rules, applied in the order presented: |
| * <ul> |
| * <li>If {@code divisor} equals {@link #ZERO}, {@link #NaN} is returned. |
| * </li> |
| * <li>If {@code this} and {@code divisor} are both infinite, |
| * {@link #NaN} is returned. |
| * </li> |
| * <li>If {@code this} is finite (i.e., has no {@code Infinite} or |
| * {@code NaN} parts) and {@code divisor} is infinite (one or both parts |
| * infinite), {@link #ZERO} is returned. |
| * </li> |
| * <li>If {@code this} is infinite and {@code divisor} is finite, |
| * {@code NaN} values are returned in the parts of the result if the |
| * {@link java.lang.Double} rules applied to the definitional formula |
| * force {@code NaN} results. |
| * </li> |
| * </ul> |
| * |
| * @param divisor Value by which this {@code Complex} is to be divided. |
| * @return {@code this / divisor}. |
| * @if {@code divisor} is {@code null}. |
| */ |
| public Complex divide(Complex divisor) { |
| checkNotNull(divisor); |
| |
| final double c = divisor.getReal(); |
| final double d = divisor.getImaginary(); |
| if (c == 0.0 && d == 0.0) { |
| return NaN; |
| } |
| |
| if ( (Double.isInfinite(c) || Double.isInfinite(d))&& (Double.isInfinite(real) || Double.isInfinite(imaginary))) { |
| return ZERO; |
| } |
| |
| if (Math.abs(c) < Math.abs(d)) { |
| final double q = c / d; |
| final double denominator = c * q + d; |
| return new Complex((real * q + imaginary) / denominator, |
| (imaginary * q - real) / denominator); |
| } else { |
| final double q = d / c; |
| final double denominator = d * q + c; |
| return new Complex((imaginary * q + real) / denominator, |
| (imaginary - real * q) / denominator); |
| } |
| } |
| |
| /** |
| * Returns a {@code Complex} whose value is {@code (this / divisor)}, |
| * with {@code divisor} interpreted as a real number. |
| * |
| * @param divisor Value by which this {@code Complex} is to be divided. |
| * @return {@code this / divisor}. |
| * @see #divide(Complex) |
| */ |
| public Complex divide(double divisor) { |
| if (divisor == 0d) { |
| return NaN; |
| } |
| if (Double.isInfinite(divisor)) { |
| return !(Double.isInfinite(real) || Double.isInfinite(imaginary)) ? ZERO : NaN; |
| } |
| return new Complex(real / divisor, |
| imaginary / divisor); |
| } |
| |
| /** |
| * Returns the multiplicative inverse of this instance. |
| * |
| * @return {@code 1 / this}. |
| * @see #divide(Complex) |
| */ |
| public Complex reciprocal() { |
| if (Math.abs(real) < Math.abs(imaginary)) { |
| final double q = real / imaginary; |
| final double scale = 1. / (real * q + imaginary); |
| double scaleQ = 0; |
| if (q != 0 && scale != 0) { |
| scaleQ = scale * q; |
| } |
| return new Complex(scaleQ, -scale); |
| } else { |
| final double q = imaginary / real; |
| final double scale = 1. / (imaginary * q + real); |
| double scaleQ = 0; |
| if (q != 0 && scale != 0) { |
| scaleQ = scale * q; |
| } |
| return new Complex(scale, -scaleQ); |
| } |
| } |
| |
| /** |
| * Test for equality with another object. |
| * If both the real and imaginary parts of two complex numbers |
| * are exactly the same, and neither is {@code Double.NaN}, the two |
| * Complex objects are considered to be equal. |
| * The behavior is the same as for JDK's {@link Double#equals(Object) |
| * Double}: |
| * <ul> |
| * <li>All {@code NaN} values are considered to be equal, |
| * i.e, if either (or both) real and imaginary parts of the complex |
| * number are equal to {@code Double.NaN}, the complex number is equal |
| * to {@code NaN}. |
| * </li> |
| * <li> |
| * Instances constructed with different representations of zero (i.e. |
| * either "0" or "-0") are <em>not</em> considered to be equal. |
| * </li> |
| * </ul> |
| * |
| * @param other Object to test for equality with this instance. |
| * @return {@code true} if the objects are equal, {@code false} if object |
| * is {@code null}, not an instance of {@code Complex}, or not equal to |
| * this instance. |
| */ |
| @Override |
| public boolean equals(Object other) { |
| if (this == other) { |
| return true; |
| } |
| if (other instanceof Complex){ |
| Complex c = (Complex) other; |
| return equals(real, c.real) && |
| equals(imaginary, c.imaginary); |
| } |
| return false; |
| } |
| |
| /** |
| * Test for the floating-point equality between Complex objects. |
| * It returns {@code true} if both arguments are equal or within the |
| * range of allowed error (inclusive). |
| * |
| * @param x First value (cannot be {@code null}). |
| * @param y Second value (cannot be {@code null}). |
| * @param maxUlps {@code (maxUlps - 1)} is the number of floating point |
| * values between the real (resp. imaginary) parts of {@code x} and |
| * {@code y}. |
| * @return {@code true} if there are fewer than {@code maxUlps} floating |
| * point values between the real (resp. imaginary) parts of {@code x} |
| * and {@code y}. |
| * |
| * @see Precision#equals(double,double,int) |
| */ |
| public static boolean equals(Complex x, Complex y, int maxUlps) { |
| return Precision.equals(x.real, y.real, maxUlps) && |
| Precision.equals(x.imaginary, y.imaginary, maxUlps); |
| } |
| |
| /** |
| * Returns {@code true} iff the values are equal as defined by |
| * {@link #equals(Complex,Complex,int) equals(x, y, 1)}. |
| * |
| * @param x First value (cannot be {@code null}). |
| * @param y Second value (cannot be {@code null}). |
| * @return {@code true} if the values are equal. |
| */ |
| public static boolean equals(Complex x, Complex y) { |
| return equals(x, y, 1); |
| } |
| |
| /** |
| * Returns {@code true} if, both for the real part and for the imaginary |
| * part, there is no double value strictly between the arguments or the |
| * difference between them is within the range of allowed error |
| * (inclusive). Returns {@code false} if either of the arguments is NaN. |
| * |
| * @param x First value (cannot be {@code null}). |
| * @param y Second value (cannot be {@code null}). |
| * @param eps Amount of allowed absolute error. |
| * @return {@code true} if the values are two adjacent floating point |
| * numbers or they are within range of each other. |
| * |
| * @see Precision#equals(double,double,double) |
| */ |
| public static boolean equals(Complex x, Complex y, double eps) { |
| return Precision.equals(x.real, y.real, eps) && |
| Precision.equals(x.imaginary, y.imaginary, eps); |
| } |
| |
| /** |
| * Returns {@code true} if, both for the real part and for the imaginary |
| * part, there is no double value strictly between the arguments or the |
| * relative difference between them is smaller or equal to the given |
| * tolerance. Returns {@code false} if either of the arguments is NaN. |
| * |
| * @param x First value (cannot be {@code null}). |
| * @param y Second value (cannot be {@code null}). |
| * @param eps Amount of allowed relative error. |
| * @return {@code true} if the values are two adjacent floating point |
| * numbers or they are within range of each other. |
| * |
| * @see Precision#equalsWithRelativeTolerance(double,double,double) |
| */ |
| public static boolean equalsWithRelativeTolerance(Complex x, Complex y, |
| double eps) { |
| return Precision.equalsWithRelativeTolerance(x.real, y.real, eps) && |
| Precision.equalsWithRelativeTolerance(x.imaginary, y.imaginary, eps); |
| } |
| |
| /** |
| * Get a hashCode for the complex number. |
| * Any {@code Double.NaN} value in real or imaginary part produces |
| * the same hash code {@code 7}. |
| * |
| * @return a hash code value for this object. |
| */ |
| @Override |
| public int hashCode() { |
| if (Double.isNaN(real) || Double.isNaN(imaginary)) { |
| return 7; |
| } |
| return 37 * 17 * (hash(imaginary) + |
| hash(real)); |
| } |
| |
| private int hash(double d) { |
| final long v = Double.doubleToLongBits(d); |
| return (int)(v^(v>>>32)); |
| //return new Double(d).hashCode(); |
| } |
| |
| /** |
| * Access the imaginary part. |
| * |
| * @return the imaginary part. |
| */ |
| public double getImaginary() { |
| return imaginary; |
| } |
| /** |
| * Access the imaginary part (C++ grammar) |
| * |
| * @return the imaginary part. |
| */ |
| public double imag() { |
| return imaginary; |
| } |
| |
| /** |
| * Access the real part. |
| * |
| * @return the real part. |
| */ |
| public double getReal() { |
| return real; |
| } |
| |
| /** |
| * Access the real part (C++ grammar) |
| * |
| * @return the real part. |
| */ |
| public double real() { |
| return real; |
| } |
| |
| /** |
| * Returns a {@code Complex} whose value is {@code this * factor}. |
| * Implements preliminary checks for {@code NaN} and infinity followed by |
| * the definitional formula: |
| * <p> |
| * {@code (a + bi)(c + di) = (ac - bd) + (ad + bc)i} |
| * </p> |
| * Returns {@link #NaN} if either {@code this} or {@code factor} has one or |
| * more {@code NaN} parts. |
| * <p> |
| * Returns {@link #INF} if neither {@code this} nor {@code factor} has one |
| * or more {@code NaN} parts and if either {@code this} or {@code factor} |
| * has one or more infinite parts (same result is returned regardless of |
| * the sign of the components). |
| * </p><p> |
| * Returns finite values in components of the result per the definitional |
| * formula in all remaining cases.</p> |
| * |
| * @param factor value to be multiplied by this {@code Complex}. |
| * @return {@code this * factor}. |
| * @if {@code factor} is {@code null}. |
| */ |
| public Complex multiply(Complex factor) { |
| checkNotNull(factor); |
| return new Complex(real * factor.real - imaginary * factor.imaginary, |
| real * factor.imaginary + imaginary * factor.real); |
| } |
| |
| /** |
| * Returns a {@code Complex} whose value is {@code this * factor}, with {@code factor} |
| * interpreted as a integer number. |
| * |
| * @param factor value to be multiplied by this {@code Complex}. |
| * @return {@code this * factor}. |
| * @see #multiply(Complex) |
| */ |
| public Complex multiply(final int factor) { |
| return new Complex(real * factor, imaginary * factor); |
| } |
| |
| /** |
| * Returns a {@code Complex} whose value is {@code this * factor}, with {@code factor} |
| * interpreted as a real number. |
| * |
| * @param factor value to be multiplied by this {@code Complex}. |
| * @return {@code this * factor}. |
| * @see #multiply(Complex) |
| */ |
| public Complex multiply(double factor) { |
| return new Complex(real * factor, imaginary * factor); |
| } |
| |
| /** |
| * Returns a {@code Complex} whose value is {@code (-this)}. |
| * Returns {@code NaN} if either real or imaginary |
| * part of this complex number is {@code Double.NaN}. |
| * |
| * @return {@code -this}. |
| */ |
| public Complex negate() { |
| return new Complex(-real, -imaginary); |
| } |
| |
| /** |
| * Returns a {@code Complex} whose value is |
| * {@code (this - subtrahend)}. |
| * Uses the definitional formula |
| * <p> |
| * {@code (a + bi) - (c + di) = (a-c) + (b-d)i} |
| * </p> |
| * |
| * @param subtrahend value to be subtracted from this {@code Complex}. |
| * @return {@code this - subtrahend}. |
| */ |
| public Complex subtract(Complex subtrahend) { |
| checkNotNull(subtrahend); |
| return new Complex(real - subtrahend.getReal(), |
| imaginary - subtrahend.getImaginary()); |
| } |
| |
| /** |
| * Returns a {@code Complex} whose value is |
| * {@code (this - subtrahend)}. |
| * |
| * @param subtrahend value to be subtracted from this {@code Complex}. |
| * @return {@code this - subtrahend}. |
| * @see #subtract(Complex) |
| */ |
| public Complex subtract(double subtrahend) { |
| return new Complex(real - subtrahend, imaginary); |
| } |
| |
| /** |
| * Compute the |
| * <a href="http://mathworld.wolfram.com/InverseCosine.html" TARGET="_top"> |
| * inverse cosine</a> of this complex number. |
| * Implements the formula: |
| * <p> |
| * {@code acos(z) = -i (log(z + i (sqrt(1 - z<sup>2</sup>))))} |
| * </p> |
| * |
| * @return the inverse cosine of this complex number. |
| */ |
| public Complex acos() { |
| if (real == 0.0&& Double.isNaN(imaginary)) { |
| return new Complex(Math.PI * 0.5, Double.NaN); |
| } else if (neitherInfiniteNorZeroNorNaN(real) && imaginary == Double.POSITIVE_INFINITY) { |
| return new Complex(Math.PI * 0.5, Double.NEGATIVE_INFINITY); |
| } else if (real == Double.NEGATIVE_INFINITY && imaginary == 1) { |
| return new Complex(Math.PI, Double.NEGATIVE_INFINITY); |
| } else if (real == Double.POSITIVE_INFINITY && imaginary == 1) { |
| return new Complex(0, Double.NEGATIVE_INFINITY); |
| } else if (real == Double.NEGATIVE_INFINITY && imaginary == Double.POSITIVE_INFINITY) { |
| return new Complex(Math.PI * 0.75, Double.NEGATIVE_INFINITY); |
| } else if (real == Double.POSITIVE_INFINITY && imaginary == Double.POSITIVE_INFINITY) { |
| return new Complex(Math.PI * 0.25, Double.NEGATIVE_INFINITY); |
| } else if (real == Double.POSITIVE_INFINITY && Double.isNaN(imaginary)) { |
| return new Complex(Double.NaN , Double.POSITIVE_INFINITY); |
| } else if (real == Double.NEGATIVE_INFINITY && Double.isNaN(imaginary)) { |
| return new Complex(Double.NaN, Double.NEGATIVE_INFINITY); |
| } else if (Double.isNaN(real) && imaginary == Double.POSITIVE_INFINITY) { |
| return new Complex(Double.NaN, Double.NEGATIVE_INFINITY); |
| } |
| return this.add(this.sqrt1z().multiply(I)).log().multiply(I.negate()); |
| } |
| /** |
| * Compute the |
| * <a href="http://mathworld.wolfram.com/InverseSine.html" TARGET="_top"> |
| * inverse sine</a> of this complex number. |
| * <p> |
| * {@code asin(z) = -i (log(sqrt(1 - z<sup>2</sup>) + iz))} |
| * </p><p> |
| * @return the inverse sine of this complex number |
| */ |
| public Complex asin() { |
| return sqrt1z().add(this.multiply(I)).log().multiply(I.negate()); |
| } |
| /** |
| * Compute the |
| * <a href="http://mathworld.wolfram.com/InverseTangent.html" TARGET="_top"> |
| * inverse tangent</a> of this complex number. |
| * Implements the formula: |
| * <p> |
| * {@code atan(z) = (i/2) log((i + z)/(i - z))} |
| * </p><p> |
| * @return the inverse tangent of this complex number |
| */ |
| public Complex atan() { |
| return this.add(I).divide(I.subtract(this)).log() |
| .multiply(I.divide(createComplex(2.0, 0.0))); |
| } |
| |
| /** |
| * Compute the |
| * <a href="http://mathworld.wolfram.com/InverseHyperbolicSine.html" TARGET="_top"> |
| * inverse hyperbolic sine</a> of this complex number. |
| * Implements the formula: |
| * <p> |
| * {@code asinh(z) = log(z+sqrt(z^2+1))} |
| * </p><p> |
| * @return the inverse hyperbolic cosine of this complex number |
| * @since 1.2 |
| */ |
| public Complex asinh(){ |
| if (neitherInfiniteNorZeroNorNaN(real) && imaginary == Double.POSITIVE_INFINITY) { |
| return new Complex(Double.POSITIVE_INFINITY, Math.PI * 0.5); |
| } else if (real == Double.POSITIVE_INFINITY && !Double.isInfinite(imaginary) && !Double.isNaN(imaginary)) { |
| return new Complex(Double.POSITIVE_INFINITY, 0.0); |
| } else if (real == Double.POSITIVE_INFINITY && imaginary == Double.POSITIVE_INFINITY) { |
| return new Complex(Double.POSITIVE_INFINITY, Math.PI * 0.25); |
| } else if (real == Double.POSITIVE_INFINITY && Double.isNaN(imaginary)) { |
| return new Complex(Double.POSITIVE_INFINITY, Double.NaN); |
| } else if (Double.isNaN(real) && imaginary == 0.0) { |
| return new Complex(Double.NaN, 0.0); |
| } else if (Double.isNaN(real) && imaginary == Double.POSITIVE_INFINITY) { |
| return new Complex(Double.POSITIVE_INFINITY, Double.NaN); |
| } |
| return square().add(Complex.ONE).sqrt().add(this).log(); |
| } |
| |
| /** |
| * Compute the |
| * <a href="http://mathworld.wolfram.com/InverseHyperbolicTangent.html" TARGET="_top"> |
| * inverse hyperbolic tangent</a> of this complex number. |
| * Implements the formula: |
| * <p> |
| * {@code atanh(z) = log((1+z)/(1-z))/2} |
| * </p><p> |
| * @return the inverse hyperbolic cosine of this complex number |
| * @since 1.2 |
| */ |
| public Complex atanh(){ |
| if (real == 0.0 && Double.isNaN(imaginary)) { |
| return new Complex(0, Double.NaN); |
| } else if (neitherInfiniteNorZeroNorNaN(real) && imaginary == 0.0) { |
| return new Complex(Double.POSITIVE_INFINITY, 0.0); |
| } else if (neitherInfiniteNorZeroNorNaN(real) && imaginary == Double.POSITIVE_INFINITY) { |
| return new Complex(0, Math.PI*0.5); |
| } else if (real == Double.POSITIVE_INFINITY && neitherInfiniteNorZeroNorNaN(imaginary)) { |
| return new Complex(0, Math.PI*0.5); |
| } else if (real == Double.POSITIVE_INFINITY && imaginary == Double.POSITIVE_INFINITY) { |
| return new Complex(0, Math.PI*0.5); |
| } else if (real == Double.POSITIVE_INFINITY && Double.isNaN(imaginary)) { |
| return new Complex(0, Double.NaN); |
| } else if (Double.isNaN(real) && imaginary == Double.POSITIVE_INFINITY) { |
| return new Complex(0, Math.PI*0.5); |
| } |
| return this.add(Complex.ONE).divide(Complex.ONE.subtract(this)).log().divide(new Complex(2)); |
| } |
| /** |
| * Compute the |
| * <a href="http://mathworld.wolfram.com/InverseHyperbolicCosine.html" TARGET="_top"> |
| * inverse hyperbolic cosine</a> of this complex number. |
| * Implements the formula: |
| * <p> |
| * {@code acosh(z) = log(z+sqrt(z^2-1))} |
| * </p><p> |
| * @return the inverse hyperbolic cosine of this complex number |
| * @since 1.2 |
| */ |
| public Complex acosh() { |
| return square().subtract(Complex.ONE).sqrt().add(this).log(); |
| } |
| |
| /** |
| * Compute the square of this complex number. |
| * |
| * @return square of this complex number |
| */ |
| public Complex square(){ |
| return this.multiply(this); |
| } |
| |
| /** |
| * Compute the |
| * <a href="http://mathworld.wolfram.com/Cosine.html" TARGET="_top"> |
| * cosine</a> of this complex number. |
| * Implements the formula: |
| * <p> |
| * {@code cos(a + bi) = cos(a)cosh(b) - sin(a)sinh(b)i} |
| * </p><p> |
| * where the (real) functions on the right-hand side are |
| * {@link Math#sin}, {@link Math#cos}, |
| * {@link Math#cosh} and {@link Math#sinh}. |
| * </p><p> |
| * |
| * @return the cosine of this complex number. |
| */ |
| public Complex cos() { |
| return new Complex(Math.cos(real) * Math.cosh(imaginary), |
| -Math.sin(real) * Math.sinh(imaginary)); |
| } |
| |
| /** |
| * Compute the |
| * <a href="http://mathworld.wolfram.com/HyperbolicCosine.html" TARGET="_top"> |
| * hyperbolic cosine</a> of this complex number. |
| * Implements the formula: |
| * <pre> |
| * <code> |
| * cosh(a + bi) = cosh(a)cos(b) + sinh(a)sin(b)i |
| * </code> |
| * </pre> |
| * where the (real) functions on the right-hand side are |
| * {@link Math#sin}, {@link Math#cos}, |
| * {@link Math#cosh} and {@link Math#sinh}. |
| * <p> |
| * |
| * @return the hyperbolic cosine of this complex number. |
| */ |
| public Complex cosh() { |
| if (real == 0.0&& imaginary == Double.POSITIVE_INFINITY) { |
| return new Complex(Double.NaN, 0.0); |
| } else if (real == 0.0&& Double.isNaN(imaginary)) { |
| return new Complex(Double.NaN, 0.0); |
| } else if (real == Double.POSITIVE_INFINITY && imaginary == 0.0) { |
| return new Complex(Double.POSITIVE_INFINITY, 0.0); |
| } else if (real == Double.POSITIVE_INFINITY && imaginary == Double.POSITIVE_INFINITY) { |
| return new Complex(Double.POSITIVE_INFINITY, Double.NaN); |
| } else if (real == Double.POSITIVE_INFINITY && Double.isNaN(imaginary)) { |
| return new Complex(Double.POSITIVE_INFINITY, Double.NaN); |
| } else if (Double.isNaN(real) && imaginary == 0.0) { |
| return new Complex(Double.NaN, 0.0); |
| } |
| |
| return new Complex(Math.cosh(real) * Math.cos(imaginary), |
| Math.sinh(real) * Math.sin(imaginary)); |
| } |
| |
| /** |
| * Compute the |
| * <a href="http://mathworld.wolfram.com/ExponentialFunction.html" TARGET="_top"> |
| * exponential function</a> of this complex number. |
| * Implements the formula: |
| * <pre> |
| * <code> |
| * exp(a + bi) = exp(a)cos(b) + exp(a)sin(b)i |
| * </code> |
| * </pre> |
| * where the (real) functions on the right-hand side are |
| * {@link Math#exp}, {@link Math#cos}, and |
| * {@link Math#sin}. |
| * |
| * @return <code><i>e</i><sup>this</sup></code>. |
| */ |
| public Complex exp() { |
| if (real == Double.POSITIVE_INFINITY && imaginary == 0.0) { |
| return new Complex(Double.POSITIVE_INFINITY, 0.0); |
| } else if (real == Double.NEGATIVE_INFINITY && imaginary == Double.POSITIVE_INFINITY) { |
| return Complex.ZERO; |
| } else if (real == Double.POSITIVE_INFINITY && imaginary == Double.POSITIVE_INFINITY) { |
| return new Complex(Double.POSITIVE_INFINITY, Double.NaN); |
| } else if (real == Double.NEGATIVE_INFINITY && Double.isNaN(imaginary)) { |
| return Complex.ZERO; |
| } else if (real == Double.POSITIVE_INFINITY && Double.isNaN(imaginary)) { |
| return new Complex(Double.POSITIVE_INFINITY, Double.NaN); |
| } else if (Double.isNaN(real) && imaginary == 0.0) { |
| return new Complex(Double.NaN, 0.0); |
| } |
| double expReal = Math.exp(real); |
| return new Complex(expReal * Math.cos(imaginary), |
| expReal * Math.sin(imaginary)); |
| } |
| |
| /** |
| * Compute the |
| * <a href="http://mathworld.wolfram.com/NaturalLogarithm.html" TARGET="_top"> |
| * natural logarithm</a> of this complex number. |
| * Implements the formula: |
| * <pre> |
| * <code> |
| * log(a + bi) = ln(|a + bi|) + arg(a + bi)i |
| * </code> |
| * </pre> |
| * where ln on the right hand side is {@link Math#log}, |
| * {@code |a + bi|} is the modulus, {@link Complex#abs}, and |
| * {@code arg(a + bi) = }{@link Math#atan2}(b, a). |
| * |
| * @return the value <code>ln this</code>, the natural logarithm |
| * of {@code this}. |
| */ |
| public Complex log() { |
| if (real == Double.POSITIVE_INFINITY && imaginary == Double.POSITIVE_INFINITY) { |
| return new Complex(Double.POSITIVE_INFINITY, Math.PI * 0.25); |
| } else if (real == Double.POSITIVE_INFINITY && Double.isNaN(imaginary)) { |
| return new Complex(Double.POSITIVE_INFINITY, Double.NaN); |
| } else if (Double.isNaN(real) && imaginary == Double.POSITIVE_INFINITY) { |
| return new Complex(Double.POSITIVE_INFINITY, Double.NaN); |
| } |
| return new Complex(Math.log(abs()), |
| Math.atan2(imaginary, real)); |
| } |
| |
| /** |
| * Compute the base 10 or |
| * <a href="http://mathworld.wolfram.com/CommonLogarithm.html" TARGET="_top"> |
| * common logarithm</a> of this complex number. |
| * |
| * @return the base 10 logarithm of <code>this</code>. |
| */ |
| public Complex log10() { |
| return new Complex(Math.log(abs())/Math.log(10), |
| Math.atan2(imaginary, real)); |
| } |
| |
| /** |
| * Returns of value of this complex number raised to the power of {@code x}. |
| * Implements the formula: |
| * <pre> |
| * <code> |
| * y<sup>x</sup> = exp(x·log(y)) |
| * </code> |
| * </pre> |
| * where {@code exp} and {@code log} are {@link #exp} and |
| * {@link #log}, respectively. |
| * |
| * @param x exponent to which this {@code Complex} is to be raised. |
| * @return <code> this<sup>x</sup></code>. |
| */ |
| public Complex pow(Complex x) { |
| checkNotNull(x); |
| if (real == 0.0&& imaginary == 0.0) { |
| if (x.real > 0 && x.imaginary == 0.0) { |
| // 0 raised to positive number is 0 |
| return ZERO; |
| } else { |
| // 0 raised to anything else is NaN |
| return NaN; |
| } |
| } |
| return this.log().multiply(x).exp(); |
| } |
| |
| /** |
| * Returns of value of this complex number raised to the power of {@code x}. |
| * |
| * @param x exponent to which this {@code Complex} is to be raised. |
| * @return <code>this<sup>x</sup></code>. |
| * @see #pow(Complex) |
| */ |
| public Complex pow(double x) { |
| if (real == 0.0&& imaginary == 0.0) { |
| if (x > 0) { |
| // 0 raised to positive number is 0 |
| return ZERO; |
| } else { |
| // 0 raised to anything else is NaN |
| return NaN; |
| } |
| } |
| return this.log().multiply(x).exp(); |
| } |
| |
| /** |
| * Compute the |
| * <a href="http://mathworld.wolfram.com/Sine.html" TARGET="_top"> |
| * sine</a> |
| * of this complex number. |
| * Implements the formula: |
| * <pre> |
| * <code> |
| * sin(a + bi) = sin(a)cosh(b) - cos(a)sinh(b)i |
| * </code> |
| * </pre> |
| * where the (real) functions on the right-hand side are |
| * {@link Math#sin}, {@link Math#cos}, |
| * {@link Math#cosh} and {@link Math#sinh}. |
| * |
| * @return the sine of this complex number. |
| */ |
| public Complex sin() { |
| return new Complex(Math.sin(real) * Math.cosh(imaginary), |
| Math.cos(real) * Math.sinh(imaginary)); |
| } |
| |
| /** |
| * Compute the |
| * <a href="http://mathworld.wolfram.com/HyperbolicSine.html" TARGET="_top"> |
| * hyperbolic sine</a> of this complex number. |
| * Implements the formula: |
| * <pre> |
| * <code> |
| * sinh(a + bi) = sinh(a)cos(b)) + cosh(a)sin(b)i |
| * </code> |
| * </pre> |
| * where the (real) functions on the right-hand side are |
| * {@link Math#sin}, {@link Math#cos}, |
| * {@link Math#cosh} and {@link Math#sinh}. |
| * |
| * @return the hyperbolic sine of {@code this}. |
| */ |
| public Complex sinh() { |
| if (real == 0.0&& imaginary == 0.0) { |
| return Complex.ZERO; |
| } else if (real == 0.0&& imaginary == Double.POSITIVE_INFINITY) { |
| return new Complex(0, Double.NaN); |
| } else if (real == 0.0&& Double.isNaN(imaginary)) { |
| return new Complex(0, Double.NaN); |
| } else if (real == Double.POSITIVE_INFINITY && imaginary == 0.0) { |
| return new Complex(Double.POSITIVE_INFINITY, 0.0); |
| } else if (real == Double.POSITIVE_INFINITY && imaginary == Double.POSITIVE_INFINITY) { |
| return new Complex(Double.POSITIVE_INFINITY, Double.NaN); |
| } else if (real == Double.POSITIVE_INFINITY && Double.isNaN(imaginary)) { |
| return new Complex(Double.POSITIVE_INFINITY, Double.NaN); |
| } else if (Double.isNaN(real) && imaginary == 0.0) { |
| return new Complex(Double.NaN, 0.0); |
| } |
| return new Complex(Math.sinh(real) * Math.cos(imaginary), |
| Math.cosh(real) * Math.sin(imaginary)); |
| } |
| |
| /** |
| * Compute the |
| * <a href="http://mathworld.wolfram.com/SquareRoot.html" TARGET="_top"> |
| * square root</a> of this complex number. |
| * Implements the following algorithm to compute {@code sqrt(a + bi)}: |
| * <ol><li>Let {@code t = sqrt((|a| + |a + bi|) / 2)}</li> |
| * <li><pre>if {@code a ≥ 0} return {@code t + (b/2t)i} |
| * else return {@code |b|/2t + sign(b)t i }</pre></li> |
| * </ol> |
| * where <ul> |
| * <li>{@code |a| = }{@link Math#abs}(a)</li> |
| * <li>{@code |a + bi| = }{@link Complex#abs}(a + bi)</li> |
| * <li>{@code sign(b) = }{@link Math#copySign(double,double) copySign(1d, b)} |
| * </ul> |
| * |
| * @return the square root of {@code this}. |
| */ |
| public Complex sqrt() { |
| if (real == 0.0 && imaginary == 0.0) { |
| return new Complex(0.0, 0.0); |
| } else if (neitherInfiniteNorZeroNorNaN(real) && imaginary == Double.POSITIVE_INFINITY) { |
| return new Complex(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY); |
| } else if (real == Double.NEGATIVE_INFINITY && neitherInfiniteNorZeroNorNaN(imaginary)) { |
| return new Complex(0.0, Double.NaN); |
| } else if (real == Double.NEGATIVE_INFINITY && Double.isNaN(imaginary)) { |
| return new Complex(Double.NaN, Double.POSITIVE_INFINITY); |
| } else if (real == Double.POSITIVE_INFINITY && Double.isNaN(imaginary)) { |
| return new Complex(Double.POSITIVE_INFINITY, Double.NaN); |
| } |
| |
| final double t = Math.sqrt((Math.abs(real) + abs()) / 2.0); |
| if (real >= 0.0) { |
| return new Complex(t, imaginary / (2.0 * t)); |
| } else { |
| return new Complex(Math.abs(imaginary) / (2.0 * t), |
| Math.copySign(1d, imaginary) * t); |
| } |
| } |
| |
| /** |
| * Compute the |
| * <a href="http://mathworld.wolfram.com/SquareRoot.html" TARGET="_top"> |
| * square root</a> of <code>1 - this<sup>2</sup></code> for this complex |
| * number. |
| * Computes the result directly as |
| * {@code sqrt(ONE.subtract(z.multiply(z)))}. |
| * |
| * @return the square root of <code>1 - this<sup>2</sup></code>. |
| */ |
| public Complex sqrt1z() { |
| return new Complex(1.0, 0.0).subtract(this.multiply(this)).sqrt(); |
| } |
| |
| /** |
| * Compute the |
| * <a href="http://mathworld.wolfram.com/Tangent.html" TARGET="_top"> |
| * tangent</a> of this complex number. |
| * Implements the formula: |
| * <pre> |
| * <code> |
| * tan(a + bi) = sin(2a)/(cos(2a)+cosh(2b)) + [sinh(2b)/(cos(2a)+cosh(2b))]i |
| * </code> |
| * </pre> |
| * where the (real) functions on the right-hand side are |
| * {@link Math#sin}, {@link Math#cos}, {@link Math#cosh} and |
| * {@link Math#sinh}. |
| * |
| * @return the tangent of {@code this}. |
| */ |
| public Complex tan() { |
| if (imaginary > 20.0) { |
| return new Complex(0.0, 1.0); |
| } |
| if (imaginary < -20.0) { |
| return new Complex(0.0, -1.0); |
| } |
| |
| final double real2 = 2.0 * real; |
| final double imaginary2 = 2.0 * imaginary; |
| final double d = Math.cos(real2) + Math.cosh(imaginary2); |
| |
| return new Complex(Math.sin(real2) / d, |
| Math.sinh(imaginary2) / d); |
| } |
| |
| /** |
| * Compute the |
| * <a href="http://mathworld.wolfram.com/HyperbolicTangent.html" TARGET="_top"> |
| * hyperbolic tangent</a> of this complex number. |
| * Implements the formula: |
| * <pre> |
| * <code> |
| * tan(a + bi) = sinh(2a)/(cosh(2a)+cos(2b)) + [sin(2b)/(cosh(2a)+cos(2b))]i |
| * </code> |
| * </pre> |
| * where the (real) functions on the right-hand side are |
| * {@link Math#sin}, {@link Math#cos}, {@link Math#cosh} and |
| * {@link Math#sinh}. |
| * |
| * @return the hyperbolic tangent of {@code this}. |
| */ |
| public Complex tanh() { |
| if (real == Double.POSITIVE_INFINITY && imaginary == Double.POSITIVE_INFINITY) { |
| return new Complex(1.0, 0.0); |
| } else if (real == Double.POSITIVE_INFINITY && Double.isNaN(imaginary)) { |
| return new Complex(1.0, 0.0); |
| } else if (Double.isNaN(real) && imaginary == 0) { |
| return new Complex(Double.NaN, 0); |
| } |
| final double real2 = 2.0 * real; |
| final double imaginary2 = 2.0 * imaginary; |
| final double d = Math.cosh(real2) + Math.cos(imaginary2); |
| |
| return new Complex(Math.sinh(real2) / d, |
| Math.sin(imaginary2) / d); |
| } |
| |
| /** |
| * Compute the argument of this complex number. |
| * The argument is the angle phi between the positive real axis and |
| * the point representing this number in the complex plane. |
| * The value returned is between -PI (not inclusive) |
| * and PI (inclusive), with negative values returned for numbers with |
| * negative imaginary parts. |
| * <p> |
| * If either real or imaginary part (or both) is NaN, NaN is returned. |
| * Infinite parts are handled as {@code Math.atan2} handles them, |
| * essentially treating finite parts as zero in the presence of an |
| * infinite coordinate and returning a multiple of pi/4 depending on |
| * the signs of the infinite parts. |
| * See the javadoc for {@code Math.atan2} for full details. |
| * |
| * @return the argument of {@code this}. |
| */ |
| public double getArgument() { |
| return Math.atan2(getImaginary(), getReal()); |
| } |
| |
| /** |
| * Compute the argument of this complex number. |
| * C++11 syntax |
| * |
| * @return the argument of {@code this}. |
| */ |
| public double arg() { |
| return getArgument(); |
| } |
| |
| /** |
| * Computes the n-th roots of this complex number. |
| * The nth roots are defined by the formula: |
| * <pre> |
| * <code> |
| * z<sub>k</sub> = abs<sup>1/n</sup> (cos(phi + 2πk/n) + i (sin(phi + 2πk/n)) |
| * </code> |
| * </pre> |
| * for <i>{@code k=0, 1, ..., n-1}</i>, where {@code abs} and {@code phi} |
| * are respectively the {@link #abs() modulus} and |
| * {@link #getArgument() argument} of this complex number. |
| * <p> |
| * If one or both parts of this complex number is NaN, a list with just |
| * one element, {@link #NaN} is returned. |
| * if neither part is NaN, but at least one part is infinite, the result |
| * is a one-element list containing {@link #INF}. |
| * |
| * @param n Degree of root. |
| * @return a List of all {@code n}-th roots of {@code this}. |
| */ |
| public List<Complex> nthRoot(int n) { |
| |
| if (n <= 0) { |
| throw new RuntimeException("cannot compute nth root for null or negative n: {0}"); |
| } |
| |
| final List<Complex> result = new ArrayList<Complex>(); |
| |
| // nth root of abs -- faster / more accurate to use a solver here? |
| final double nthRootOfAbs = Math.pow(abs(), 1.0 / n); |
| |
| // Compute nth roots of complex number with k = 0, 1, ... n-1 |
| final double nthPhi = getArgument() / n; |
| final double slice = 2 * Math.PI / n; |
| double innerPart = nthPhi; |
| for (int k = 0; k < n ; k++) { |
| // inner part |
| final double realPart = nthRootOfAbs * Math.cos(innerPart); |
| final double imaginaryPart = nthRootOfAbs * Math.sin(innerPart); |
| result.add(createComplex(realPart, imaginaryPart)); |
| innerPart += slice; |
| } |
| |
| return result; |
| } |
| |
| /** |
| * Create a complex number given the real and imaginary parts. |
| * |
| * @param realPart Real part. |
| * @param imaginaryPart Imaginary part. |
| * @return a new complex number instance. |
| * @see #valueOf(double, double) |
| */ |
| protected Complex createComplex(double realPart, |
| double imaginaryPart) { |
| return new Complex(realPart, imaginaryPart); |
| } |
| |
| /** |
| * Create a complex number given the real and imaginary parts. |
| * |
| * @param realPart Real part. |
| * @param imaginaryPart Imaginary part. |
| * @return a Complex instance. |
| */ |
| public static Complex valueOf(double realPart, |
| double imaginaryPart) { |
| return new Complex(realPart, imaginaryPart); |
| } |
| |
| /** |
| * Create a complex number given only the real part. |
| * |
| * @param realPart Real part. |
| * @return a Complex instance. |
| */ |
| public static Complex valueOf(double realPart) { |
| return new Complex(realPart); |
| } |
| |
| /** |
| * Resolve the transient fields in a deserialized Complex Object. |
| * Subclasses will need to override {@link #createComplex} to |
| * deserialize properly. |
| * |
| * @return A Complex instance with all fields resolved. |
| */ |
| protected final Object readResolve() { |
| return new Complex(real, imaginary); |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| public String toString() { |
| return "(" + real + ", " + imaginary + ")"; |
| } |
| |
| /** |
| * Checks that an object is not null. |
| * |
| * @param o Object to be checked. |
| */ |
| private static void checkNotNull(Object o) { |
| if (o == null) { |
| throw new RuntimeException("Null Argument to Complex Method"); |
| } |
| } |
| |
| /** |
| * Check that the argument is positive and throw a RuntimeException |
| * if it is not. |
| * @param arg {@code int} to check |
| */ |
| private static void checkNotNegative(int arg) { |
| if (arg <= 0) { |
| throw new RuntimeException("Complex: Non-positive argument"); |
| } |
| } |
| |
| /** |
| * Check that the argument is positive and throw a RuntimeException |
| * if it is not. |
| * @param arg {@code double} to check |
| */ |
| private static void checkNotNegative(double arg) { |
| if (arg <= 0) { |
| throw new RuntimeException("Complex: Non-positive argument"); |
| } |
| } |
| |
| /** |
| * Returns {@code true} if the values are equal according to semantics of |
| * {@link Double#equals(Object)}. |
| * |
| * @param x Value |
| * @param y Value |
| * @return {@code new Double(x).equals(new Double(y))} |
| */ |
| private static boolean equals(double x, double y) { |
| return new Double(x).equals(new Double(y)); |
| } |
| |
| private static boolean neitherInfiniteNorZeroNorNaN(double d) { |
| if (!Double.isNaN(d) && !Double.isInfinite(d) && d != 0) { |
| return true; |
| } else return false; |
| } |
| } |
