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Posted to commits@commons.apache.org by er...@apache.org on 2018/02/02 13:28:59 UTC
[04/50] commons-numbers git commit: Small cleanup
Small cleanup
Project: http://git-wip-us.apache.org/repos/asf/commons-numbers/repo
Commit: http://git-wip-us.apache.org/repos/asf/commons-numbers/commit/8830e479
Tree: http://git-wip-us.apache.org/repos/asf/commons-numbers/tree/8830e479
Diff: http://git-wip-us.apache.org/repos/asf/commons-numbers/diff/8830e479
Branch: refs/heads/feature__NUMBERS-51__field
Commit: 8830e47976f109bda6cf9a763d7276c814a37b22
Parents: fc70d93
Author: Eric Barnhill <er...@apache.org>
Authored: Fri Jan 26 15:35:59 2018 +0100
Committer: Eric Barnhill <er...@apache.org>
Committed: Fri Jan 26 15:35:59 2018 +0100
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.../commons/numbers/complex/Complex.java.orig | 1320 ------------------
1 file changed, 1320 deletions(-)
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http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/8830e479/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/Complex.java.orig
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diff --git a/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/Complex.java.orig b/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/Complex.java.orig
deleted file mode 100644
index d3c7ce0..0000000
--- a/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/Complex.java.orig
+++ /dev/null
@@ -1,1320 +0,0 @@
-/*
- * 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 = 201701120L;
-
- /** The imaginary part. */
- private final double imaginary;
- /** The real part. */
- private final double real;
- /** Record whether this complex number is equal to NaN. */
- private final transient boolean isNaN;
- /** Record whether this complex number is infinite. */
- private final transient boolean isInfinite;
-
- /**
- * 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;
-
- isNaN = Double.isNaN(real) || Double.isNaN(imaginary);
- isInfinite = !isNaN &&
- (Double.isInfinite(real) || Double.isInfinite(imaginary));
- }
-
- /**
- * 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 (isNaN) {
- return Double.NaN;
- }
- if (isInfinite()) {
- return Double.POSITIVE_INFINITY;
- }
- if (Math.abs(real) < Math.abs(imaginary)) {
- if (imaginary == 0.0) {
- return Math.abs(real);
- }
- double q = real / imaginary;
- return Math.abs(imaginary) * Math.sqrt(1 + q * q);
- } else {
- if (real == 0.0) {
- return Math.abs(imaginary);
- }
- double q = imaginary / real;
- return Math.abs(real) * Math.sqrt(1 + q * q);
- }
- }
-
- /**
- * 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>
- * If either {@code this} or {@code addend} has a {@code NaN} value in
- * either part, {@link #NaN} is returned; otherwise {@code Infinite}
- * and {@code NaN} values are returned in the parts of the result
- * according to the rules for {@link java.lang.Double} arithmetic.
- *
- * @param addend Value to be added to this {@code Complex}.
- * @return {@code this + addend}.
- */
- public Complex add(Complex addend) {
- checkNotNull(addend);
- if (isNaN || addend.isNaN) {
- return NaN;
- }
-
- return createComplex(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) {
- if (isNaN || Double.isNaN(addend)) {
- return NaN;
- }
-
- return createComplex(real + addend, imaginary);
- }
-
- /**
- * Returns the conjugate of this complex number.
- * The conjugate of {@code a + bi} is {@code a - bi}.
- * <p>
- * {@link #NaN} is returned if either the real or imaginary
- * part of this Complex number equals {@code Double.NaN}.
- * </p><p>
- * If the imaginary part is infinite, and the real part is not
- * {@code NaN}, the returned value has infinite imaginary part
- * of the opposite sign, e.g. the conjugate of
- * {@code 1 + POSITIVE_INFINITY i} is {@code 1 - NEGATIVE_INFINITY i}.
- * </p>
- * @return the conjugate of this Complex object.
- */
- public Complex conjugate() {
- if (isNaN) {
- return NaN;
- }
-
- return createComplex(real, -imaginary);
- }
-
- /**
- * 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 either {@code this} or {@code divisor} has a {@code NaN} value
- * in either part, {@link #NaN} is returned.
- * </li>
- * <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}.
- */
- public Complex divide(Complex divisor) {
- checkNotNull(divisor);
- if (isNaN || divisor.isNaN) {
- return NaN;
- }
-
- final double c = divisor.getReal();
- final double d = divisor.getImaginary();
- if (c == 0.0 && d == 0.0) {
- return NaN;
- }
-
- if (divisor.isInfinite() && !isInfinite()) {
- return ZERO;
- }
-
- if (Math.abs(c) < Math.abs(d)) {
- double q = c / d;
- double denominator = c * q + d;
- return createComplex((real * q + imaginary) / denominator,
- (imaginary * q - real) / denominator);
- } else {
- double q = d / c;
- double denominator = d * q + c;
- return createComplex((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 (isNaN || Double.isNaN(divisor)) {
- return NaN;
- }
- if (divisor == 0d) {
- return NaN;
- }
- if (Double.isInfinite(divisor)) {
- return !isInfinite() ? ZERO : NaN;
- }
- return createComplex(real / divisor,
- imaginary / divisor);
- }
-
- /**
- * Returns the multiplicative inverse this instance.
- *
- * @return {@code 1 / this}.
- * @see #divide(Complex)
- */
- public Complex reciprocal() {
- if (isNaN) {
- return NaN;
- }
-
- if (real == 0.0 && imaginary == 0.0) {
- return INF;
- }
-
- if (isInfinite) {
- return ZERO;
- }
-
- if (Math.abs(real) < Math.abs(imaginary)) {
- double q = real / imaginary;
- double scale = 1. / (real * q + imaginary);
- return createComplex(scale * q, -scale);
- } else {
- double q = imaginary / real;
- double scale = 1. / (imaginary * q + real);
- return createComplex(scale, -scale * q);
- }
- }
-
- /**
- * 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;
- if (c.isNaN) {
- return isNaN;
- } else {
- 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 (isNaN) {
- return 7;
- }
-<<<<<<< HEAD
- 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();
-=======
- return 37 * (17 * hash(imaginary) +
- hash(real));
->>>>>>> eb-test
- }
-
- /**
- * Access the imaginary part.
- *
- * @return the imaginary part.
- */
- public double getImaginary() {
- return imaginary;
- }
-
- /**
- * Access the real part.
- *
- * @return the real part.
- */
- public double getReal() {
- return real;
- }
-
- /**
- * Checks whether either or both parts of this complex number is
- * {@code NaN}.
- *
- * @return true if either or both parts of this complex number is
- * {@code NaN}; false otherwise.
- */
- public boolean isNaN() {
- return isNaN;
- }
-
- /**
- * Checks whether either the real or imaginary part of this complex number
- * takes an infinite value (either {@code Double.POSITIVE_INFINITY} or
- * {@code Double.NEGATIVE_INFINITY}) and neither part
- * is {@code NaN}.
- *
- * @return true if one or both parts of this complex number are infinite
- * and neither part is {@code NaN}.
- */
- public boolean isInfinite() {
- return isInfinite;
- }
-
- /**
- * 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}.
- */
- public Complex multiply(Complex factor) {
- checkNotNull(factor);
- if (isNaN || factor.isNaN) {
- return NaN;
- }
- if (Double.isInfinite(real) ||
- Double.isInfinite(imaginary) ||
- Double.isInfinite(factor.real) ||
- Double.isInfinite(factor.imaginary)) {
- // we don't use isInfinite() to avoid testing for NaN again
- return INF;
- }
- return createComplex(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) {
- if (isNaN) {
- return NaN;
- }
- if (Double.isInfinite(real) ||
- Double.isInfinite(imaginary)) {
- return INF;
- }
- return createComplex(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) {
- if (isNaN || Double.isNaN(factor)) {
- return NaN;
- }
- if (Double.isInfinite(real) ||
- Double.isInfinite(imaginary) ||
- Double.isInfinite(factor)) {
- // we don't use isInfinite() to avoid testing for NaN again
- return INF;
- }
- return createComplex(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() {
- if (isNaN) {
- return NaN;
- }
-
- return createComplex(-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>
- * If either {@code this} or {@code subtrahend} has a {@code NaN]} value in either part,
- * {@link #NaN} is returned; otherwise infinite and {@code NaN} values are
- * returned in the parts of the result according to the rules for
- * {@link java.lang.Double} arithmetic.
- *
- * @param subtrahend value to be subtracted from this {@code Complex}.
- * @return {@code this - subtrahend}.
- */
- public Complex subtract(Complex subtrahend) {
- checkNotNull(subtrahend);
- if (isNaN || subtrahend.isNaN) {
- return NaN;
- }
-
- return createComplex(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) {
- if (isNaN || Double.isNaN(subtrahend)) {
- return NaN;
- }
- return createComplex(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>
- * Returns {@link Complex#NaN} if either real or imaginary part of the
- * input argument is {@code NaN} or infinite.
- *
- * @return the inverse cosine of this complex number.
- */
- public Complex acos() {
- if (isNaN) {
- return NaN;
- }
-
- 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.
- * Implements the formula:
- * <p>
- * {@code asin(z) = -i (log(sqrt(1 - z<sup>2</sup>) + iz))}
- * </p><p>
- * Returns {@link Complex#NaN} if either real or imaginary part of the
- * input argument is {@code NaN} or infinite.</p>
- *
- * @return the inverse sine of this complex number.
- */
- public Complex asin() {
- if (isNaN) {
- return NaN;
- }
-
- 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>
- * Returns {@link Complex#NaN} if either real or imaginary part of the
- * input argument is {@code NaN} or infinite.</p>
- *
- * @return the inverse tangent of this complex number
- */
- public Complex atan() {
- if (isNaN) {
- return NaN;
- }
-
- 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/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>
- * Returns {@link Complex#NaN} if either real or imaginary part of the
- * input argument is {@code NaN}.
- * </p><p>
- * Infinite values in real or imaginary parts of the input may result in
- * infinite or NaN values returned in parts of the result.</p>
- * <pre>
- * Examples:
- * <code>
- * cos(1 ± INFINITY i) = 1 \u2213 INFINITY i
- * cos(±INFINITY + i) = NaN + NaN i
- * cos(±INFINITY ± INFINITY i) = NaN + NaN i
- * </code>
- * </pre>
- *
- * @return the cosine of this complex number.
- */
- public Complex cos() {
- if (isNaN) {
- return NaN;
- }
-
- return createComplex(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>
- * Returns {@link Complex#NaN} if either real or imaginary part of the
- * input argument is {@code NaN}.
- * </p>
- * Infinite values in real or imaginary parts of the input may result in
- * infinite or NaN values returned in parts of the result.
- * <pre>
- * Examples:
- * <code>
- * cosh(1 ± INFINITY i) = NaN + NaN i
- * cosh(±INFINITY + i) = INFINITY ± INFINITY i
- * cosh(±INFINITY ± INFINITY i) = NaN + NaN i
- * </code>
- * </pre>
- *
- * @return the hyperbolic cosine of this complex number.
- */
- public Complex cosh() {
- if (isNaN) {
- return NaN;
- }
-
- return createComplex(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}.
- * <p>
- * Returns {@link Complex#NaN} if either real or imaginary part of the
- * input argument is {@code NaN}.
- * </p>
- * Infinite values in real or imaginary parts of the input may result in
- * infinite or NaN values returned in parts of the result.
- * <pre>
- * Examples:
- * <code>
- * exp(1 ± INFINITY i) = NaN + NaN i
- * exp(INFINITY + i) = INFINITY + INFINITY i
- * exp(-INFINITY + i) = 0 + 0i
- * exp(±INFINITY ± INFINITY i) = NaN + NaN i
- * </code>
- * </pre>
- *
- * @return <code><i>e</i><sup>this</sup></code>.
- */
- public Complex exp() {
- if (isNaN) {
- return NaN;
- }
-
- double expReal = Math.exp(real);
- return createComplex(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).
- * <p>
- * Returns {@link Complex#NaN} if either real or imaginary part of the
- * input argument is {@code NaN}.
- * </p>
- * Infinite (or critical) values in real or imaginary parts of the input may
- * result in infinite or NaN values returned in parts of the result.
- * <pre>
- * Examples:
- * <code>
- * log(1 ± INFINITY i) = INFINITY ± (π/2)i
- * log(INFINITY + i) = INFINITY + 0i
- * log(-INFINITY + i) = INFINITY + πi
- * log(INFINITY ± INFINITY i) = INFINITY ± (π/4)i
- * log(-INFINITY ± INFINITY i) = INFINITY ± (3π/4)i
- * log(0 + 0i) = -INFINITY + 0i
- * </code>
- * </pre>
- *
- * @return the value <code>ln this</code>, the natural logarithm
- * of {@code this}.
- */
- public Complex log() {
- if (isNaN) {
- return NaN;
- }
- return createComplex(Math.log(abs()),
- 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.
- * <p>
- * Returns {@link Complex#NaN} if either real or imaginary part of the
- * input argument is {@code NaN} or infinite, or if {@code y}
- * equals {@link Complex#ZERO}.</p>
- *
- * @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 && imaginary == 0) {
- if (x.real > 0 && x.imaginary == 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 && imaginary == 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}.
- * <p>
- * Returns {@link Complex#NaN} if either real or imaginary part of the
- * input argument is {@code NaN}.
- * </p><p>
- * Infinite values in real or imaginary parts of the input may result in
- * infinite or {@code NaN} values returned in parts of the result.
- * <pre>
- * Examples:
- * <code>
- * sin(1 ± INFINITY i) = 1 ± INFINITY i
- * sin(±INFINITY + i) = NaN + NaN i
- * sin(±INFINITY ± INFINITY i) = NaN + NaN i
- * </code>
- * </pre>
- *
- * @return the sine of this complex number.
- */
- public Complex sin() {
- if (isNaN) {
- return NaN;
- }
-
- return createComplex(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}.
- * <p>
- * Returns {@link Complex#NaN} if either real or imaginary part of the
- * input argument is {@code NaN}.
- * </p><p>
- * Infinite values in real or imaginary parts of the input may result in
- * infinite or NaN values returned in parts of the result.
- * <pre>
- * Examples:
- * <code>
- * sinh(1 ± INFINITY i) = NaN + NaN i
- * sinh(±INFINITY + i) = ± INFINITY + INFINITY i
- * sinh(±INFINITY ± INFINITY i) = NaN + NaN i
- * </code>
- * </pre>
- *
- * @return the hyperbolic sine of {@code this}.
- */
- public Complex sinh() {
- if (isNaN) {
- return NaN;
- }
-
- return createComplex(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>
- * <p>
- * Returns {@link Complex#NaN} if either real or imaginary part of the
- * input argument is {@code NaN}.
- * </p>
- * Infinite values in real or imaginary parts of the input may result in
- * infinite or NaN values returned in parts of the result.
- * <pre>
- * Examples:
- * <code>
- * sqrt(1 ± INFINITY i) = INFINITY + NaN i
- * sqrt(INFINITY + i) = INFINITY + 0i
- * sqrt(-INFINITY + i) = 0 + INFINITY i
- * sqrt(INFINITY ± INFINITY i) = INFINITY + NaN i
- * sqrt(-INFINITY ± INFINITY i) = NaN ± INFINITY i
- * </code>
- * </pre>
- *
- * @return the square root of {@code this}.
- */
- public Complex sqrt() {
- if (isNaN) {
- return NaN;
- }
-
- if (real == 0.0 && imaginary == 0.0) {
- return createComplex(0.0, 0.0);
- }
-
- double t = Math.sqrt((Math.abs(real) + abs()) / 2.0);
- if (real >= 0.0) {
- return createComplex(t, imaginary / (2.0 * t));
- } else {
- return createComplex(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)))}.
- * <p>
- * Returns {@link Complex#NaN} if either real or imaginary part of the
- * input argument is {@code NaN}.
- * </p>
- * Infinite values in real or imaginary parts of the input may result in
- * infinite or NaN values returned in parts of the result.
- *
- * @return the square root of <code>1 - this<sup>2</sup></code>.
- */
- public Complex sqrt1z() {
- return createComplex(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}.
- * <p>
- * Returns {@link Complex#NaN} if either real or imaginary part of the
- * input argument is {@code NaN}.
- * </p>
- * Infinite (or critical) values in real or imaginary parts of the input may
- * result in infinite or NaN values returned in parts of the result.
- * <pre>
- * Examples:
- * <code>
- * tan(a ± INFINITY i) = 0 ± i
- * tan(±INFINITY + bi) = NaN + NaN i
- * tan(±INFINITY ± INFINITY i) = NaN + NaN i
- * tan(±π/2 + 0 i) = ±INFINITY + NaN i
- * </code>
- * </pre>
- *
- * @return the tangent of {@code this}.
- */
- public Complex tan() {
- if (isNaN || Double.isInfinite(real)) {
- return NaN;
- }
- if (imaginary > 20.0) {
- return createComplex(0.0, 1.0);
- }
- if (imaginary < -20.0) {
- return createComplex(0.0, -1.0);
- }
-
- double real2 = 2.0 * real;
- double imaginary2 = 2.0 * imaginary;
- double d = Math.cos(real2) + Math.cosh(imaginary2);
-
- return createComplex(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}.
- * <p>
- * Returns {@link Complex#NaN} if either real or imaginary part of the
- * input argument is {@code NaN}.
- * </p>
- * Infinite values in real or imaginary parts of the input may result in
- * infinite or NaN values returned in parts of the result.
- * <pre>
- * Examples:
- * <code>
- * tanh(a ± INFINITY i) = NaN + NaN i
- * tanh(±INFINITY + bi) = ±1 + 0 i
- * tanh(±INFINITY ± INFINITY i) = NaN + NaN i
- * tanh(0 + (π/2)i) = NaN + INFINITY i
- * </code>
- * </pre>
- *
- * @return the hyperbolic tangent of {@code this}.
- */
- public Complex tanh() {
- if (isNaN || Double.isInfinite(imaginary)) {
- return NaN;
- }
- if (real > 20.0) {
- return createComplex(1.0, 0.0);
- }
- if (real < -20.0) {
- return createComplex(-1.0, 0.0);
- }
- double real2 = 2.0 * real;
- double imaginary2 = 2.0 * imaginary;
- double d = Math.cosh(real2) + Math.cos(imaginary2);
-
- return createComplex(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());
- }
-
- /**
- * 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>();
-
- if (isNaN) {
- result.add(NaN);
- return result;
- }
- if (isInfinite()) {
- result.add(INF);
- return result;
- }
-
- // 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) {
- if (Double.isNaN(realPart) ||
- Double.isNaN(imaginaryPart)) {
- return NaN;
- }
- 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) {
- if (Double.isNaN(realPart)) {
- return NaN;
- }
- 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 createComplex(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");
- }
- }
-
- /**
- * 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));
- }
-
- /**
- * Returns an integer hash code representing the given double value.
- *
- * @param value the value to be hashed
- * @return the hash code
- */
- private static int hash(double value) {
- return new Double(value).hashCode();
- }
-}