1 | /*
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2 | * Licensed to the Apache Software Foundation (ASF) under one or more
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3 | * contributor license agreements. See the NOTICE file distributed with
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4 | * this work for additional information regarding copyright ownership.
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5 | * The ASF licenses this file to You under the Apache License, Version 2.0
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6 | * (the "License"); you may not use this file except in compliance with
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7 | * the License. You may obtain a copy of the License at
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8 | *
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9 | * http://www.apache.org/licenses/LICENSE-2.0
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10 | *
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11 | * Unless required by applicable law or agreed to in writing, software
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12 | * distributed under the License is distributed on an "AS IS" BASIS,
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13 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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14 | * See the License for the specific language governing permissions and
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15 | * limitations under the License.
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16 | */
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17 |
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18 | package agents.anac.y2019.harddealer.math3.complex;
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19 |
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20 | import java.io.Serializable;
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21 | import java.util.ArrayList;
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22 | import java.util.List;
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23 |
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24 | import agents.anac.y2019.harddealer.math3.FieldElement;
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25 | import agents.anac.y2019.harddealer.math3.exception.NotPositiveException;
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26 | import agents.anac.y2019.harddealer.math3.exception.NullArgumentException;
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27 | import agents.anac.y2019.harddealer.math3.exception.util.LocalizedFormats;
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28 | import agents.anac.y2019.harddealer.math3.util.FastMath;
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29 | import agents.anac.y2019.harddealer.math3.util.MathUtils;
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30 | import agents.anac.y2019.harddealer.math3.util.Precision;
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31 |
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32 | /**
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33 | * Representation of a Complex number, i.e. a number which has both a
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34 | * real and imaginary part.
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35 | * <p>
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36 | * Implementations of arithmetic operations handle {@code NaN} and
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37 | * infinite values according to the rules for {@link java.lang.Double}, i.e.
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38 | * {@link #equals} is an equivalence relation for all instances that have
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39 | * a {@code NaN} in either real or imaginary part, e.g. the following are
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40 | * considered equal:
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41 | * <ul>
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42 | * <li>{@code 1 + NaNi}</li>
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43 | * <li>{@code NaN + i}</li>
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44 | * <li>{@code NaN + NaNi}</li>
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45 | * </ul><p>
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46 | * Note that this contradicts the IEEE-754 standard for floating
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47 | * point numbers (according to which the test {@code x == x} must fail if
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48 | * {@code x} is {@code NaN}). The method
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49 | * {@link agents.anac.y2019.harddealer.math3.util.Precision#equals(double,double,int)
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50 | * equals for primitive double} in {@link agents.anac.y2019.harddealer.math3.util.Precision}
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51 | * conforms with IEEE-754 while this class conforms with the standard behavior
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52 | * for Java object types.</p>
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53 | *
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54 | */
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55 | public class Complex implements FieldElement<Complex>, Serializable {
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56 | /** The square root of -1. A number representing "0.0 + 1.0i" */
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57 | public static final Complex I = new Complex(0.0, 1.0);
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58 | // CHECKSTYLE: stop ConstantName
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59 | /** A complex number representing "NaN + NaNi" */
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60 | public static final Complex NaN = new Complex(Double.NaN, Double.NaN);
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61 | // CHECKSTYLE: resume ConstantName
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62 | /** A complex number representing "+INF + INFi" */
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63 | public static final Complex INF = new Complex(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY);
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64 | /** A complex number representing "1.0 + 0.0i" */
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65 | public static final Complex ONE = new Complex(1.0, 0.0);
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66 | /** A complex number representing "0.0 + 0.0i" */
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67 | public static final Complex ZERO = new Complex(0.0, 0.0);
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68 |
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69 | /** Serializable version identifier */
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70 | private static final long serialVersionUID = -6195664516687396620L;
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71 |
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72 | /** The imaginary part. */
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73 | private final double imaginary;
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74 | /** The real part. */
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75 | private final double real;
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76 | /** Record whether this complex number is equal to NaN. */
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77 | private final transient boolean isNaN;
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78 | /** Record whether this complex number is infinite. */
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79 | private final transient boolean isInfinite;
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80 |
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81 | /**
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82 | * Create a complex number given only the real part.
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83 | *
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84 | * @param real Real part.
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85 | */
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86 | public Complex(double real) {
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87 | this(real, 0.0);
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88 | }
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89 |
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90 | /**
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91 | * Create a complex number given the real and imaginary parts.
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92 | *
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93 | * @param real Real part.
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94 | * @param imaginary Imaginary part.
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95 | */
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96 | public Complex(double real, double imaginary) {
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97 | this.real = real;
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98 | this.imaginary = imaginary;
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99 |
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100 | isNaN = Double.isNaN(real) || Double.isNaN(imaginary);
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101 | isInfinite = !isNaN &&
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102 | (Double.isInfinite(real) || Double.isInfinite(imaginary));
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103 | }
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104 |
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105 | /**
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106 | * Return the absolute value of this complex number.
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107 | * Returns {@code NaN} if either real or imaginary part is {@code NaN}
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108 | * and {@code Double.POSITIVE_INFINITY} if neither part is {@code NaN},
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109 | * but at least one part is infinite.
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110 | *
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111 | * @return the absolute value.
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112 | */
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113 | public double abs() {
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114 | if (isNaN) {
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115 | return Double.NaN;
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116 | }
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117 | if (isInfinite()) {
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118 | return Double.POSITIVE_INFINITY;
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119 | }
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120 | if (FastMath.abs(real) < FastMath.abs(imaginary)) {
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121 | if (imaginary == 0.0) {
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122 | return FastMath.abs(real);
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123 | }
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124 | double q = real / imaginary;
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125 | return FastMath.abs(imaginary) * FastMath.sqrt(1 + q * q);
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126 | } else {
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127 | if (real == 0.0) {
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128 | return FastMath.abs(imaginary);
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129 | }
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130 | double q = imaginary / real;
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131 | return FastMath.abs(real) * FastMath.sqrt(1 + q * q);
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132 | }
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133 | }
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134 |
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135 | /**
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136 | * Returns a {@code Complex} whose value is
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137 | * {@code (this + addend)}.
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138 | * Uses the definitional formula
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139 | * <p>
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140 | * {@code (a + bi) + (c + di) = (a+c) + (b+d)i}
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141 | * </p>
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142 | * If either {@code this} or {@code addend} has a {@code NaN} value in
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143 | * either part, {@link #NaN} is returned; otherwise {@code Infinite}
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144 | * and {@code NaN} values are returned in the parts of the result
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145 | * according to the rules for {@link java.lang.Double} arithmetic.
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146 | *
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147 | * @param addend Value to be added to this {@code Complex}.
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148 | * @return {@code this + addend}.
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149 | * @throws NullArgumentException if {@code addend} is {@code null}.
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150 | */
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151 | public Complex add(Complex addend) throws NullArgumentException {
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152 | MathUtils.checkNotNull(addend);
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153 | if (isNaN || addend.isNaN) {
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154 | return NaN;
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155 | }
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156 |
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157 | return createComplex(real + addend.getReal(),
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158 | imaginary + addend.getImaginary());
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159 | }
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160 |
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161 | /**
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162 | * Returns a {@code Complex} whose value is {@code (this + addend)},
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163 | * with {@code addend} interpreted as a real number.
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164 | *
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165 | * @param addend Value to be added to this {@code Complex}.
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166 | * @return {@code this + addend}.
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167 | * @see #add(Complex)
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168 | */
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169 | public Complex add(double addend) {
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170 | if (isNaN || Double.isNaN(addend)) {
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171 | return NaN;
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172 | }
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173 |
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174 | return createComplex(real + addend, imaginary);
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175 | }
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176 |
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177 | /**
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178 | * Returns the conjugate of this complex number.
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179 | * The conjugate of {@code a + bi} is {@code a - bi}.
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180 | * <p>
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181 | * {@link #NaN} is returned if either the real or imaginary
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182 | * part of this Complex number equals {@code Double.NaN}.
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183 | * </p><p>
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184 | * If the imaginary part is infinite, and the real part is not
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185 | * {@code NaN}, the returned value has infinite imaginary part
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186 | * of the opposite sign, e.g. the conjugate of
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187 | * {@code 1 + POSITIVE_INFINITY i} is {@code 1 - NEGATIVE_INFINITY i}.
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188 | * </p>
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189 | * @return the conjugate of this Complex object.
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190 | */
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191 | public Complex conjugate() {
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192 | if (isNaN) {
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193 | return NaN;
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194 | }
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195 |
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196 | return createComplex(real, -imaginary);
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197 | }
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198 |
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199 | /**
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200 | * Returns a {@code Complex} whose value is
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201 | * {@code (this / divisor)}.
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202 | * Implements the definitional formula
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203 | * <pre>
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204 | * <code>
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205 | * a + bi ac + bd + (bc - ad)i
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206 | * ----------- = -------------------------
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207 | * c + di c<sup>2</sup> + d<sup>2</sup>
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208 | * </code>
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209 | * </pre>
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210 | * but uses
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211 | * <a href="http://doi.acm.org/10.1145/1039813.1039814">
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212 | * prescaling of operands</a> to limit the effects of overflows and
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213 | * underflows in the computation.
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214 | * <p>
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215 | * {@code Infinite} and {@code NaN} values are handled according to the
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216 | * following rules, applied in the order presented:
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217 | * <ul>
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218 | * <li>If either {@code this} or {@code divisor} has a {@code NaN} value
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219 | * in either part, {@link #NaN} is returned.
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220 | * </li>
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221 | * <li>If {@code divisor} equals {@link #ZERO}, {@link #NaN} is returned.
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222 | * </li>
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223 | * <li>If {@code this} and {@code divisor} are both infinite,
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224 | * {@link #NaN} is returned.
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225 | * </li>
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226 | * <li>If {@code this} is finite (i.e., has no {@code Infinite} or
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227 | * {@code NaN} parts) and {@code divisor} is infinite (one or both parts
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228 | * infinite), {@link #ZERO} is returned.
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229 | * </li>
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230 | * <li>If {@code this} is infinite and {@code divisor} is finite,
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231 | * {@code NaN} values are returned in the parts of the result if the
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232 | * {@link java.lang.Double} rules applied to the definitional formula
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233 | * force {@code NaN} results.
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234 | * </li>
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235 | * </ul>
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236 | *
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237 | * @param divisor Value by which this {@code Complex} is to be divided.
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238 | * @return {@code this / divisor}.
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239 | * @throws NullArgumentException if {@code divisor} is {@code null}.
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240 | */
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241 | public Complex divide(Complex divisor)
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242 | throws NullArgumentException {
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243 | MathUtils.checkNotNull(divisor);
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244 | if (isNaN || divisor.isNaN) {
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245 | return NaN;
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246 | }
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247 |
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248 | final double c = divisor.getReal();
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249 | final double d = divisor.getImaginary();
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250 | if (c == 0.0 && d == 0.0) {
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251 | return NaN;
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252 | }
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253 |
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254 | if (divisor.isInfinite() && !isInfinite()) {
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255 | return ZERO;
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256 | }
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257 |
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258 | if (FastMath.abs(c) < FastMath.abs(d)) {
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259 | double q = c / d;
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260 | double denominator = c * q + d;
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261 | return createComplex((real * q + imaginary) / denominator,
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262 | (imaginary * q - real) / denominator);
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263 | } else {
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264 | double q = d / c;
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265 | double denominator = d * q + c;
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266 | return createComplex((imaginary * q + real) / denominator,
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267 | (imaginary - real * q) / denominator);
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268 | }
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269 | }
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270 |
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271 | /**
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272 | * Returns a {@code Complex} whose value is {@code (this / divisor)},
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273 | * with {@code divisor} interpreted as a real number.
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274 | *
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275 | * @param divisor Value by which this {@code Complex} is to be divided.
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276 | * @return {@code this / divisor}.
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277 | * @see #divide(Complex)
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278 | */
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279 | public Complex divide(double divisor) {
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280 | if (isNaN || Double.isNaN(divisor)) {
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281 | return NaN;
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282 | }
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283 | if (divisor == 0d) {
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284 | return NaN;
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285 | }
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286 | if (Double.isInfinite(divisor)) {
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287 | return !isInfinite() ? ZERO : NaN;
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288 | }
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289 | return createComplex(real / divisor,
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290 | imaginary / divisor);
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291 | }
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292 |
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293 | /** {@inheritDoc} */
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294 | public Complex reciprocal() {
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295 | if (isNaN) {
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296 | return NaN;
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297 | }
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298 |
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299 | if (real == 0.0 && imaginary == 0.0) {
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300 | return INF;
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301 | }
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302 |
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303 | if (isInfinite) {
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304 | return ZERO;
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305 | }
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306 |
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307 | if (FastMath.abs(real) < FastMath.abs(imaginary)) {
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308 | double q = real / imaginary;
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309 | double scale = 1. / (real * q + imaginary);
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310 | return createComplex(scale * q, -scale);
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311 | } else {
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312 | double q = imaginary / real;
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313 | double scale = 1. / (imaginary * q + real);
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314 | return createComplex(scale, -scale * q);
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315 | }
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316 | }
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317 |
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318 | /**
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319 | * Test for equality with another object.
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320 | * If both the real and imaginary parts of two complex numbers
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321 | * are exactly the same, and neither is {@code Double.NaN}, the two
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322 | * Complex objects are considered to be equal.
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323 | * The behavior is the same as for JDK's {@link Double#equals(Object)
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324 | * Double}:
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325 | * <ul>
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326 | * <li>All {@code NaN} values are considered to be equal,
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327 | * i.e, if either (or both) real and imaginary parts of the complex
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328 | * number are equal to {@code Double.NaN}, the complex number is equal
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329 | * to {@code NaN}.
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330 | * </li>
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331 | * <li>
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332 | * Instances constructed with different representations of zero (i.e.
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333 | * either "0" or "-0") are <em>not</em> considered to be equal.
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334 | * </li>
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335 | * </ul>
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336 | *
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337 | * @param other Object to test for equality with this instance.
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338 | * @return {@code true} if the objects are equal, {@code false} if object
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339 | * is {@code null}, not an instance of {@code Complex}, or not equal to
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340 | * this instance.
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341 | */
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342 | @Override
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343 | public boolean equals(Object other) {
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344 | if (this == other) {
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345 | return true;
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346 | }
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347 | if (other instanceof Complex){
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348 | Complex c = (Complex) other;
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349 | if (c.isNaN) {
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350 | return isNaN;
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351 | } else {
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352 | return MathUtils.equals(real, c.real) &&
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353 | MathUtils.equals(imaginary, c.imaginary);
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354 | }
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355 | }
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356 | return false;
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357 | }
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358 |
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359 | /**
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360 | * Test for the floating-point equality between Complex objects.
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361 | * It returns {@code true} if both arguments are equal or within the
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362 | * range of allowed error (inclusive).
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363 | *
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364 | * @param x First value (cannot be {@code null}).
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365 | * @param y Second value (cannot be {@code null}).
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366 | * @param maxUlps {@code (maxUlps - 1)} is the number of floating point
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367 | * values between the real (resp. imaginary) parts of {@code x} and
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368 | * {@code y}.
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369 | * @return {@code true} if there are fewer than {@code maxUlps} floating
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370 | * point values between the real (resp. imaginary) parts of {@code x}
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371 | * and {@code y}.
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372 | *
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373 | * @see Precision#equals(double,double,int)
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374 | * @since 3.3
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375 | */
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376 | public static boolean equals(Complex x, Complex y, int maxUlps) {
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377 | return Precision.equals(x.real, y.real, maxUlps) &&
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378 | Precision.equals(x.imaginary, y.imaginary, maxUlps);
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379 | }
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380 |
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381 | /**
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382 | * Returns {@code true} iff the values are equal as defined by
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383 | * {@link #equals(Complex,Complex,int) equals(x, y, 1)}.
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384 | *
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385 | * @param x First value (cannot be {@code null}).
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386 | * @param y Second value (cannot be {@code null}).
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387 | * @return {@code true} if the values are equal.
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388 | *
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389 | * @since 3.3
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390 | */
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391 | public static boolean equals(Complex x, Complex y) {
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392 | return equals(x, y, 1);
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393 | }
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394 |
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395 | /**
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396 | * Returns {@code true} if, both for the real part and for the imaginary
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397 | * part, there is no double value strictly between the arguments or the
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398 | * difference between them is within the range of allowed error
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399 | * (inclusive). Returns {@code false} if either of the arguments is NaN.
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400 | *
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401 | * @param x First value (cannot be {@code null}).
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402 | * @param y Second value (cannot be {@code null}).
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403 | * @param eps Amount of allowed absolute error.
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404 | * @return {@code true} if the values are two adjacent floating point
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405 | * numbers or they are within range of each other.
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406 | *
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407 | * @see Precision#equals(double,double,double)
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408 | * @since 3.3
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409 | */
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410 | public static boolean equals(Complex x, Complex y, double eps) {
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411 | return Precision.equals(x.real, y.real, eps) &&
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412 | Precision.equals(x.imaginary, y.imaginary, eps);
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413 | }
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414 |
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415 | /**
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416 | * Returns {@code true} if, both for the real part and for the imaginary
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417 | * part, there is no double value strictly between the arguments or the
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418 | * relative difference between them is smaller or equal to the given
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419 | * tolerance. Returns {@code false} if either of the arguments is NaN.
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420 | *
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421 | * @param x First value (cannot be {@code null}).
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422 | * @param y Second value (cannot be {@code null}).
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423 | * @param eps Amount of allowed relative error.
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424 | * @return {@code true} if the values are two adjacent floating point
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425 | * numbers or they are within range of each other.
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426 | *
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427 | * @see Precision#equalsWithRelativeTolerance(double,double,double)
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428 | * @since 3.3
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429 | */
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430 | public static boolean equalsWithRelativeTolerance(Complex x, Complex y,
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431 | double eps) {
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432 | return Precision.equalsWithRelativeTolerance(x.real, y.real, eps) &&
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433 | Precision.equalsWithRelativeTolerance(x.imaginary, y.imaginary, eps);
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434 | }
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435 |
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436 | /**
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437 | * Get a hashCode for the complex number.
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438 | * Any {@code Double.NaN} value in real or imaginary part produces
|
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439 | * the same hash code {@code 7}.
|
---|
440 | *
|
---|
441 | * @return a hash code value for this object.
|
---|
442 | */
|
---|
443 | @Override
|
---|
444 | public int hashCode() {
|
---|
445 | if (isNaN) {
|
---|
446 | return 7;
|
---|
447 | }
|
---|
448 | return 37 * (17 * MathUtils.hash(imaginary) +
|
---|
449 | MathUtils.hash(real));
|
---|
450 | }
|
---|
451 |
|
---|
452 | /**
|
---|
453 | * Access the imaginary part.
|
---|
454 | *
|
---|
455 | * @return the imaginary part.
|
---|
456 | */
|
---|
457 | public double getImaginary() {
|
---|
458 | return imaginary;
|
---|
459 | }
|
---|
460 |
|
---|
461 | /**
|
---|
462 | * Access the real part.
|
---|
463 | *
|
---|
464 | * @return the real part.
|
---|
465 | */
|
---|
466 | public double getReal() {
|
---|
467 | return real;
|
---|
468 | }
|
---|
469 |
|
---|
470 | /**
|
---|
471 | * Checks whether either or both parts of this complex number is
|
---|
472 | * {@code NaN}.
|
---|
473 | *
|
---|
474 | * @return true if either or both parts of this complex number is
|
---|
475 | * {@code NaN}; false otherwise.
|
---|
476 | */
|
---|
477 | public boolean isNaN() {
|
---|
478 | return isNaN;
|
---|
479 | }
|
---|
480 |
|
---|
481 | /**
|
---|
482 | * Checks whether either the real or imaginary part of this complex number
|
---|
483 | * takes an infinite value (either {@code Double.POSITIVE_INFINITY} or
|
---|
484 | * {@code Double.NEGATIVE_INFINITY}) and neither part
|
---|
485 | * is {@code NaN}.
|
---|
486 | *
|
---|
487 | * @return true if one or both parts of this complex number are infinite
|
---|
488 | * and neither part is {@code NaN}.
|
---|
489 | */
|
---|
490 | public boolean isInfinite() {
|
---|
491 | return isInfinite;
|
---|
492 | }
|
---|
493 |
|
---|
494 | /**
|
---|
495 | * Returns a {@code Complex} whose value is {@code this * factor}.
|
---|
496 | * Implements preliminary checks for {@code NaN} and infinity followed by
|
---|
497 | * the definitional formula:
|
---|
498 | * <p>
|
---|
499 | * {@code (a + bi)(c + di) = (ac - bd) + (ad + bc)i}
|
---|
500 | * </p>
|
---|
501 | * Returns {@link #NaN} if either {@code this} or {@code factor} has one or
|
---|
502 | * more {@code NaN} parts.
|
---|
503 | * <p>
|
---|
504 | * Returns {@link #INF} if neither {@code this} nor {@code factor} has one
|
---|
505 | * or more {@code NaN} parts and if either {@code this} or {@code factor}
|
---|
506 | * has one or more infinite parts (same result is returned regardless of
|
---|
507 | * the sign of the components).
|
---|
508 | * </p><p>
|
---|
509 | * Returns finite values in components of the result per the definitional
|
---|
510 | * formula in all remaining cases.</p>
|
---|
511 | *
|
---|
512 | * @param factor value to be multiplied by this {@code Complex}.
|
---|
513 | * @return {@code this * factor}.
|
---|
514 | * @throws NullArgumentException if {@code factor} is {@code null}.
|
---|
515 | */
|
---|
516 | public Complex multiply(Complex factor)
|
---|
517 | throws NullArgumentException {
|
---|
518 | MathUtils.checkNotNull(factor);
|
---|
519 | if (isNaN || factor.isNaN) {
|
---|
520 | return NaN;
|
---|
521 | }
|
---|
522 | if (Double.isInfinite(real) ||
|
---|
523 | Double.isInfinite(imaginary) ||
|
---|
524 | Double.isInfinite(factor.real) ||
|
---|
525 | Double.isInfinite(factor.imaginary)) {
|
---|
526 | // we don't use isInfinite() to avoid testing for NaN again
|
---|
527 | return INF;
|
---|
528 | }
|
---|
529 | return createComplex(real * factor.real - imaginary * factor.imaginary,
|
---|
530 | real * factor.imaginary + imaginary * factor.real);
|
---|
531 | }
|
---|
532 |
|
---|
533 | /**
|
---|
534 | * Returns a {@code Complex} whose value is {@code this * factor}, with {@code factor}
|
---|
535 | * interpreted as a integer number.
|
---|
536 | *
|
---|
537 | * @param factor value to be multiplied by this {@code Complex}.
|
---|
538 | * @return {@code this * factor}.
|
---|
539 | * @see #multiply(Complex)
|
---|
540 | */
|
---|
541 | public Complex multiply(final int factor) {
|
---|
542 | if (isNaN) {
|
---|
543 | return NaN;
|
---|
544 | }
|
---|
545 | if (Double.isInfinite(real) ||
|
---|
546 | Double.isInfinite(imaginary)) {
|
---|
547 | return INF;
|
---|
548 | }
|
---|
549 | return createComplex(real * factor, imaginary * factor);
|
---|
550 | }
|
---|
551 |
|
---|
552 | /**
|
---|
553 | * Returns a {@code Complex} whose value is {@code this * factor}, with {@code factor}
|
---|
554 | * interpreted as a real number.
|
---|
555 | *
|
---|
556 | * @param factor value to be multiplied by this {@code Complex}.
|
---|
557 | * @return {@code this * factor}.
|
---|
558 | * @see #multiply(Complex)
|
---|
559 | */
|
---|
560 | public Complex multiply(double factor) {
|
---|
561 | if (isNaN || Double.isNaN(factor)) {
|
---|
562 | return NaN;
|
---|
563 | }
|
---|
564 | if (Double.isInfinite(real) ||
|
---|
565 | Double.isInfinite(imaginary) ||
|
---|
566 | Double.isInfinite(factor)) {
|
---|
567 | // we don't use isInfinite() to avoid testing for NaN again
|
---|
568 | return INF;
|
---|
569 | }
|
---|
570 | return createComplex(real * factor, imaginary * factor);
|
---|
571 | }
|
---|
572 |
|
---|
573 | /**
|
---|
574 | * Returns a {@code Complex} whose value is {@code (-this)}.
|
---|
575 | * Returns {@code NaN} if either real or imaginary
|
---|
576 | * part of this Complex number is {@code Double.NaN}.
|
---|
577 | *
|
---|
578 | * @return {@code -this}.
|
---|
579 | */
|
---|
580 | public Complex negate() {
|
---|
581 | if (isNaN) {
|
---|
582 | return NaN;
|
---|
583 | }
|
---|
584 |
|
---|
585 | return createComplex(-real, -imaginary);
|
---|
586 | }
|
---|
587 |
|
---|
588 | /**
|
---|
589 | * Returns a {@code Complex} whose value is
|
---|
590 | * {@code (this - subtrahend)}.
|
---|
591 | * Uses the definitional formula
|
---|
592 | * <p>
|
---|
593 | * {@code (a + bi) - (c + di) = (a-c) + (b-d)i}
|
---|
594 | * </p>
|
---|
595 | * If either {@code this} or {@code subtrahend} has a {@code NaN]} value in either part,
|
---|
596 | * {@link #NaN} is returned; otherwise infinite and {@code NaN} values are
|
---|
597 | * returned in the parts of the result according to the rules for
|
---|
598 | * {@link java.lang.Double} arithmetic.
|
---|
599 | *
|
---|
600 | * @param subtrahend value to be subtracted from this {@code Complex}.
|
---|
601 | * @return {@code this - subtrahend}.
|
---|
602 | * @throws NullArgumentException if {@code subtrahend} is {@code null}.
|
---|
603 | */
|
---|
604 | public Complex subtract(Complex subtrahend)
|
---|
605 | throws NullArgumentException {
|
---|
606 | MathUtils.checkNotNull(subtrahend);
|
---|
607 | if (isNaN || subtrahend.isNaN) {
|
---|
608 | return NaN;
|
---|
609 | }
|
---|
610 |
|
---|
611 | return createComplex(real - subtrahend.getReal(),
|
---|
612 | imaginary - subtrahend.getImaginary());
|
---|
613 | }
|
---|
614 |
|
---|
615 | /**
|
---|
616 | * Returns a {@code Complex} whose value is
|
---|
617 | * {@code (this - subtrahend)}.
|
---|
618 | *
|
---|
619 | * @param subtrahend value to be subtracted from this {@code Complex}.
|
---|
620 | * @return {@code this - subtrahend}.
|
---|
621 | * @see #subtract(Complex)
|
---|
622 | */
|
---|
623 | public Complex subtract(double subtrahend) {
|
---|
624 | if (isNaN || Double.isNaN(subtrahend)) {
|
---|
625 | return NaN;
|
---|
626 | }
|
---|
627 | return createComplex(real - subtrahend, imaginary);
|
---|
628 | }
|
---|
629 |
|
---|
630 | /**
|
---|
631 | * Compute the
|
---|
632 | * <a href="http://mathworld.wolfram.com/InverseCosine.html" TARGET="_top">
|
---|
633 | * inverse cosine</a> of this complex number.
|
---|
634 | * Implements the formula:
|
---|
635 | * <p>
|
---|
636 | * {@code acos(z) = -i (log(z + i (sqrt(1 - z<sup>2</sup>))))}
|
---|
637 | * </p>
|
---|
638 | * Returns {@link Complex#NaN} if either real or imaginary part of the
|
---|
639 | * input argument is {@code NaN} or infinite.
|
---|
640 | *
|
---|
641 | * @return the inverse cosine of this complex number.
|
---|
642 | * @since 1.2
|
---|
643 | */
|
---|
644 | public Complex acos() {
|
---|
645 | if (isNaN) {
|
---|
646 | return NaN;
|
---|
647 | }
|
---|
648 |
|
---|
649 | return this.add(this.sqrt1z().multiply(I)).log().multiply(I.negate());
|
---|
650 | }
|
---|
651 |
|
---|
652 | /**
|
---|
653 | * Compute the
|
---|
654 | * <a href="http://mathworld.wolfram.com/InverseSine.html" TARGET="_top">
|
---|
655 | * inverse sine</a> of this complex number.
|
---|
656 | * Implements the formula:
|
---|
657 | * <p>
|
---|
658 | * {@code asin(z) = -i (log(sqrt(1 - z<sup>2</sup>) + iz))}
|
---|
659 | * </p><p>
|
---|
660 | * Returns {@link Complex#NaN} if either real or imaginary part of the
|
---|
661 | * input argument is {@code NaN} or infinite.</p>
|
---|
662 | *
|
---|
663 | * @return the inverse sine of this complex number.
|
---|
664 | * @since 1.2
|
---|
665 | */
|
---|
666 | public Complex asin() {
|
---|
667 | if (isNaN) {
|
---|
668 | return NaN;
|
---|
669 | }
|
---|
670 |
|
---|
671 | return sqrt1z().add(this.multiply(I)).log().multiply(I.negate());
|
---|
672 | }
|
---|
673 |
|
---|
674 | /**
|
---|
675 | * Compute the
|
---|
676 | * <a href="http://mathworld.wolfram.com/InverseTangent.html" TARGET="_top">
|
---|
677 | * inverse tangent</a> of this complex number.
|
---|
678 | * Implements the formula:
|
---|
679 | * <p>
|
---|
680 | * {@code atan(z) = (i/2) log((i + z)/(i - z))}
|
---|
681 | * </p><p>
|
---|
682 | * Returns {@link Complex#NaN} if either real or imaginary part of the
|
---|
683 | * input argument is {@code NaN} or infinite.</p>
|
---|
684 | *
|
---|
685 | * @return the inverse tangent of this complex number
|
---|
686 | * @since 1.2
|
---|
687 | */
|
---|
688 | public Complex atan() {
|
---|
689 | if (isNaN) {
|
---|
690 | return NaN;
|
---|
691 | }
|
---|
692 |
|
---|
693 | return this.add(I).divide(I.subtract(this)).log()
|
---|
694 | .multiply(I.divide(createComplex(2.0, 0.0)));
|
---|
695 | }
|
---|
696 |
|
---|
697 | /**
|
---|
698 | * Compute the
|
---|
699 | * <a href="http://mathworld.wolfram.com/Cosine.html" TARGET="_top">
|
---|
700 | * cosine</a> of this complex number.
|
---|
701 | * Implements the formula:
|
---|
702 | * <p>
|
---|
703 | * {@code cos(a + bi) = cos(a)cosh(b) - sin(a)sinh(b)i}
|
---|
704 | * </p><p>
|
---|
705 | * where the (real) functions on the right-hand side are
|
---|
706 | * {@link FastMath#sin}, {@link FastMath#cos},
|
---|
707 | * {@link FastMath#cosh} and {@link FastMath#sinh}.
|
---|
708 | * </p><p>
|
---|
709 | * Returns {@link Complex#NaN} if either real or imaginary part of the
|
---|
710 | * input argument is {@code NaN}.
|
---|
711 | * </p><p>
|
---|
712 | * Infinite values in real or imaginary parts of the input may result in
|
---|
713 | * infinite or NaN values returned in parts of the result.</p>
|
---|
714 | * <pre>
|
---|
715 | * Examples:
|
---|
716 | * <code>
|
---|
717 | * cos(1 ± INFINITY i) = 1 \u2213 INFINITY i
|
---|
718 | * cos(±INFINITY + i) = NaN + NaN i
|
---|
719 | * cos(±INFINITY ± INFINITY i) = NaN + NaN i
|
---|
720 | * </code>
|
---|
721 | * </pre>
|
---|
722 | *
|
---|
723 | * @return the cosine of this complex number.
|
---|
724 | * @since 1.2
|
---|
725 | */
|
---|
726 | public Complex cos() {
|
---|
727 | if (isNaN) {
|
---|
728 | return NaN;
|
---|
729 | }
|
---|
730 |
|
---|
731 | return createComplex(FastMath.cos(real) * FastMath.cosh(imaginary),
|
---|
732 | -FastMath.sin(real) * FastMath.sinh(imaginary));
|
---|
733 | }
|
---|
734 |
|
---|
735 | /**
|
---|
736 | * Compute the
|
---|
737 | * <a href="http://mathworld.wolfram.com/HyperbolicCosine.html" TARGET="_top">
|
---|
738 | * hyperbolic cosine</a> of this complex number.
|
---|
739 | * Implements the formula:
|
---|
740 | * <pre>
|
---|
741 | * <code>
|
---|
742 | * cosh(a + bi) = cosh(a)cos(b) + sinh(a)sin(b)i
|
---|
743 | * </code>
|
---|
744 | * </pre>
|
---|
745 | * where the (real) functions on the right-hand side are
|
---|
746 | * {@link FastMath#sin}, {@link FastMath#cos},
|
---|
747 | * {@link FastMath#cosh} and {@link FastMath#sinh}.
|
---|
748 | * <p>
|
---|
749 | * Returns {@link Complex#NaN} if either real or imaginary part of the
|
---|
750 | * input argument is {@code NaN}.
|
---|
751 | * </p>
|
---|
752 | * Infinite values in real or imaginary parts of the input may result in
|
---|
753 | * infinite or NaN values returned in parts of the result.
|
---|
754 | * <pre>
|
---|
755 | * Examples:
|
---|
756 | * <code>
|
---|
757 | * cosh(1 ± INFINITY i) = NaN + NaN i
|
---|
758 | * cosh(±INFINITY + i) = INFINITY ± INFINITY i
|
---|
759 | * cosh(±INFINITY ± INFINITY i) = NaN + NaN i
|
---|
760 | * </code>
|
---|
761 | * </pre>
|
---|
762 | *
|
---|
763 | * @return the hyperbolic cosine of this complex number.
|
---|
764 | * @since 1.2
|
---|
765 | */
|
---|
766 | public Complex cosh() {
|
---|
767 | if (isNaN) {
|
---|
768 | return NaN;
|
---|
769 | }
|
---|
770 |
|
---|
771 | return createComplex(FastMath.cosh(real) * FastMath.cos(imaginary),
|
---|
772 | FastMath.sinh(real) * FastMath.sin(imaginary));
|
---|
773 | }
|
---|
774 |
|
---|
775 | /**
|
---|
776 | * Compute the
|
---|
777 | * <a href="http://mathworld.wolfram.com/ExponentialFunction.html" TARGET="_top">
|
---|
778 | * exponential function</a> of this complex number.
|
---|
779 | * Implements the formula:
|
---|
780 | * <pre>
|
---|
781 | * <code>
|
---|
782 | * exp(a + bi) = exp(a)cos(b) + exp(a)sin(b)i
|
---|
783 | * </code>
|
---|
784 | * </pre>
|
---|
785 | * where the (real) functions on the right-hand side are
|
---|
786 | * {@link FastMath#exp}, {@link FastMath#cos}, and
|
---|
787 | * {@link FastMath#sin}.
|
---|
788 | * <p>
|
---|
789 | * Returns {@link Complex#NaN} if either real or imaginary part of the
|
---|
790 | * input argument is {@code NaN}.
|
---|
791 | * </p>
|
---|
792 | * Infinite values in real or imaginary parts of the input may result in
|
---|
793 | * infinite or NaN values returned in parts of the result.
|
---|
794 | * <pre>
|
---|
795 | * Examples:
|
---|
796 | * <code>
|
---|
797 | * exp(1 ± INFINITY i) = NaN + NaN i
|
---|
798 | * exp(INFINITY + i) = INFINITY + INFINITY i
|
---|
799 | * exp(-INFINITY + i) = 0 + 0i
|
---|
800 | * exp(±INFINITY ± INFINITY i) = NaN + NaN i
|
---|
801 | * </code>
|
---|
802 | * </pre>
|
---|
803 | *
|
---|
804 | * @return <code><i>e</i><sup>this</sup></code>.
|
---|
805 | * @since 1.2
|
---|
806 | */
|
---|
807 | public Complex exp() {
|
---|
808 | if (isNaN) {
|
---|
809 | return NaN;
|
---|
810 | }
|
---|
811 |
|
---|
812 | double expReal = FastMath.exp(real);
|
---|
813 | return createComplex(expReal * FastMath.cos(imaginary),
|
---|
814 | expReal * FastMath.sin(imaginary));
|
---|
815 | }
|
---|
816 |
|
---|
817 | /**
|
---|
818 | * Compute the
|
---|
819 | * <a href="http://mathworld.wolfram.com/NaturalLogarithm.html" TARGET="_top">
|
---|
820 | * natural logarithm</a> of this complex number.
|
---|
821 | * Implements the formula:
|
---|
822 | * <pre>
|
---|
823 | * <code>
|
---|
824 | * log(a + bi) = ln(|a + bi|) + arg(a + bi)i
|
---|
825 | * </code>
|
---|
826 | * </pre>
|
---|
827 | * where ln on the right hand side is {@link FastMath#log},
|
---|
828 | * {@code |a + bi|} is the modulus, {@link Complex#abs}, and
|
---|
829 | * {@code arg(a + bi) = }{@link FastMath#atan2}(b, a).
|
---|
830 | * <p>
|
---|
831 | * Returns {@link Complex#NaN} if either real or imaginary part of the
|
---|
832 | * input argument is {@code NaN}.
|
---|
833 | * </p>
|
---|
834 | * Infinite (or critical) values in real or imaginary parts of the input may
|
---|
835 | * result in infinite or NaN values returned in parts of the result.
|
---|
836 | * <pre>
|
---|
837 | * Examples:
|
---|
838 | * <code>
|
---|
839 | * log(1 ± INFINITY i) = INFINITY ± (π/2)i
|
---|
840 | * log(INFINITY + i) = INFINITY + 0i
|
---|
841 | * log(-INFINITY + i) = INFINITY + πi
|
---|
842 | * log(INFINITY ± INFINITY i) = INFINITY ± (π/4)i
|
---|
843 | * log(-INFINITY ± INFINITY i) = INFINITY ± (3π/4)i
|
---|
844 | * log(0 + 0i) = -INFINITY + 0i
|
---|
845 | * </code>
|
---|
846 | * </pre>
|
---|
847 | *
|
---|
848 | * @return the value <code>ln this</code>, the natural logarithm
|
---|
849 | * of {@code this}.
|
---|
850 | * @since 1.2
|
---|
851 | */
|
---|
852 | public Complex log() {
|
---|
853 | if (isNaN) {
|
---|
854 | return NaN;
|
---|
855 | }
|
---|
856 |
|
---|
857 | return createComplex(FastMath.log(abs()),
|
---|
858 | FastMath.atan2(imaginary, real));
|
---|
859 | }
|
---|
860 |
|
---|
861 | /**
|
---|
862 | * Returns of value of this complex number raised to the power of {@code x}.
|
---|
863 | * Implements the formula:
|
---|
864 | * <pre>
|
---|
865 | * <code>
|
---|
866 | * y<sup>x</sup> = exp(x·log(y))
|
---|
867 | * </code>
|
---|
868 | * </pre>
|
---|
869 | * where {@code exp} and {@code log} are {@link #exp} and
|
---|
870 | * {@link #log}, respectively.
|
---|
871 | * <p>
|
---|
872 | * Returns {@link Complex#NaN} if either real or imaginary part of the
|
---|
873 | * input argument is {@code NaN} or infinite, or if {@code y}
|
---|
874 | * equals {@link Complex#ZERO}.</p>
|
---|
875 | *
|
---|
876 | * @param x exponent to which this {@code Complex} is to be raised.
|
---|
877 | * @return <code> this<sup>x</sup></code>.
|
---|
878 | * @throws NullArgumentException if x is {@code null}.
|
---|
879 | * @since 1.2
|
---|
880 | */
|
---|
881 | public Complex pow(Complex x)
|
---|
882 | throws NullArgumentException {
|
---|
883 | MathUtils.checkNotNull(x);
|
---|
884 | return this.log().multiply(x).exp();
|
---|
885 | }
|
---|
886 |
|
---|
887 | /**
|
---|
888 | * Returns of value of this complex number raised to the power of {@code x}.
|
---|
889 | *
|
---|
890 | * @param x exponent to which this {@code Complex} is to be raised.
|
---|
891 | * @return <code>this<sup>x</sup></code>.
|
---|
892 | * @see #pow(Complex)
|
---|
893 | */
|
---|
894 | public Complex pow(double x) {
|
---|
895 | return this.log().multiply(x).exp();
|
---|
896 | }
|
---|
897 |
|
---|
898 | /**
|
---|
899 | * Compute the
|
---|
900 | * <a href="http://mathworld.wolfram.com/Sine.html" TARGET="_top">
|
---|
901 | * sine</a>
|
---|
902 | * of this complex number.
|
---|
903 | * Implements the formula:
|
---|
904 | * <pre>
|
---|
905 | * <code>
|
---|
906 | * sin(a + bi) = sin(a)cosh(b) - cos(a)sinh(b)i
|
---|
907 | * </code>
|
---|
908 | * </pre>
|
---|
909 | * where the (real) functions on the right-hand side are
|
---|
910 | * {@link FastMath#sin}, {@link FastMath#cos},
|
---|
911 | * {@link FastMath#cosh} and {@link FastMath#sinh}.
|
---|
912 | * <p>
|
---|
913 | * Returns {@link Complex#NaN} if either real or imaginary part of the
|
---|
914 | * input argument is {@code NaN}.
|
---|
915 | * </p><p>
|
---|
916 | * Infinite values in real or imaginary parts of the input may result in
|
---|
917 | * infinite or {@code NaN} values returned in parts of the result.
|
---|
918 | * <pre>
|
---|
919 | * Examples:
|
---|
920 | * <code>
|
---|
921 | * sin(1 ± INFINITY i) = 1 ± INFINITY i
|
---|
922 | * sin(±INFINITY + i) = NaN + NaN i
|
---|
923 | * sin(±INFINITY ± INFINITY i) = NaN + NaN i
|
---|
924 | * </code>
|
---|
925 | * </pre>
|
---|
926 | *
|
---|
927 | * @return the sine of this complex number.
|
---|
928 | * @since 1.2
|
---|
929 | */
|
---|
930 | public Complex sin() {
|
---|
931 | if (isNaN) {
|
---|
932 | return NaN;
|
---|
933 | }
|
---|
934 |
|
---|
935 | return createComplex(FastMath.sin(real) * FastMath.cosh(imaginary),
|
---|
936 | FastMath.cos(real) * FastMath.sinh(imaginary));
|
---|
937 | }
|
---|
938 |
|
---|
939 | /**
|
---|
940 | * Compute the
|
---|
941 | * <a href="http://mathworld.wolfram.com/HyperbolicSine.html" TARGET="_top">
|
---|
942 | * hyperbolic sine</a> of this complex number.
|
---|
943 | * Implements the formula:
|
---|
944 | * <pre>
|
---|
945 | * <code>
|
---|
946 | * sinh(a + bi) = sinh(a)cos(b)) + cosh(a)sin(b)i
|
---|
947 | * </code>
|
---|
948 | * </pre>
|
---|
949 | * where the (real) functions on the right-hand side are
|
---|
950 | * {@link FastMath#sin}, {@link FastMath#cos},
|
---|
951 | * {@link FastMath#cosh} and {@link FastMath#sinh}.
|
---|
952 | * <p>
|
---|
953 | * Returns {@link Complex#NaN} if either real or imaginary part of the
|
---|
954 | * input argument is {@code NaN}.
|
---|
955 | * </p><p>
|
---|
956 | * Infinite values in real or imaginary parts of the input may result in
|
---|
957 | * infinite or NaN values returned in parts of the result.
|
---|
958 | * <pre>
|
---|
959 | * Examples:
|
---|
960 | * <code>
|
---|
961 | * sinh(1 ± INFINITY i) = NaN + NaN i
|
---|
962 | * sinh(±INFINITY + i) = ± INFINITY + INFINITY i
|
---|
963 | * sinh(±INFINITY ± INFINITY i) = NaN + NaN i
|
---|
964 | * </code>
|
---|
965 | * </pre>
|
---|
966 | *
|
---|
967 | * @return the hyperbolic sine of {@code this}.
|
---|
968 | * @since 1.2
|
---|
969 | */
|
---|
970 | public Complex sinh() {
|
---|
971 | if (isNaN) {
|
---|
972 | return NaN;
|
---|
973 | }
|
---|
974 |
|
---|
975 | return createComplex(FastMath.sinh(real) * FastMath.cos(imaginary),
|
---|
976 | FastMath.cosh(real) * FastMath.sin(imaginary));
|
---|
977 | }
|
---|
978 |
|
---|
979 | /**
|
---|
980 | * Compute the
|
---|
981 | * <a href="http://mathworld.wolfram.com/SquareRoot.html" TARGET="_top">
|
---|
982 | * square root</a> of this complex number.
|
---|
983 | * Implements the following algorithm to compute {@code sqrt(a + bi)}:
|
---|
984 | * <ol><li>Let {@code t = sqrt((|a| + |a + bi|) / 2)}</li>
|
---|
985 | * <li><pre>if {@code a ≥ 0} return {@code t + (b/2t)i}
|
---|
986 | * else return {@code |b|/2t + sign(b)t i }</pre></li>
|
---|
987 | * </ol>
|
---|
988 | * where <ul>
|
---|
989 | * <li>{@code |a| = }{@link FastMath#abs}(a)</li>
|
---|
990 | * <li>{@code |a + bi| = }{@link Complex#abs}(a + bi)</li>
|
---|
991 | * <li>{@code sign(b) = }{@link FastMath#copySign(double,double) copySign(1d, b)}
|
---|
992 | * </ul>
|
---|
993 | * <p>
|
---|
994 | * Returns {@link Complex#NaN} if either real or imaginary part of the
|
---|
995 | * input argument is {@code NaN}.
|
---|
996 | * </p>
|
---|
997 | * Infinite values in real or imaginary parts of the input may result in
|
---|
998 | * infinite or NaN values returned in parts of the result.
|
---|
999 | * <pre>
|
---|
1000 | * Examples:
|
---|
1001 | * <code>
|
---|
1002 | * sqrt(1 ± INFINITY i) = INFINITY + NaN i
|
---|
1003 | * sqrt(INFINITY + i) = INFINITY + 0i
|
---|
1004 | * sqrt(-INFINITY + i) = 0 + INFINITY i
|
---|
1005 | * sqrt(INFINITY ± INFINITY i) = INFINITY + NaN i
|
---|
1006 | * sqrt(-INFINITY ± INFINITY i) = NaN ± INFINITY i
|
---|
1007 | * </code>
|
---|
1008 | * </pre>
|
---|
1009 | *
|
---|
1010 | * @return the square root of {@code this}.
|
---|
1011 | * @since 1.2
|
---|
1012 | */
|
---|
1013 | public Complex sqrt() {
|
---|
1014 | if (isNaN) {
|
---|
1015 | return NaN;
|
---|
1016 | }
|
---|
1017 |
|
---|
1018 | if (real == 0.0 && imaginary == 0.0) {
|
---|
1019 | return createComplex(0.0, 0.0);
|
---|
1020 | }
|
---|
1021 |
|
---|
1022 | double t = FastMath.sqrt((FastMath.abs(real) + abs()) / 2.0);
|
---|
1023 | if (real >= 0.0) {
|
---|
1024 | return createComplex(t, imaginary / (2.0 * t));
|
---|
1025 | } else {
|
---|
1026 | return createComplex(FastMath.abs(imaginary) / (2.0 * t),
|
---|
1027 | FastMath.copySign(1d, imaginary) * t);
|
---|
1028 | }
|
---|
1029 | }
|
---|
1030 |
|
---|
1031 | /**
|
---|
1032 | * Compute the
|
---|
1033 | * <a href="http://mathworld.wolfram.com/SquareRoot.html" TARGET="_top">
|
---|
1034 | * square root</a> of <code>1 - this<sup>2</sup></code> for this complex
|
---|
1035 | * number.
|
---|
1036 | * Computes the result directly as
|
---|
1037 | * {@code sqrt(ONE.subtract(z.multiply(z)))}.
|
---|
1038 | * <p>
|
---|
1039 | * Returns {@link Complex#NaN} if either real or imaginary part of the
|
---|
1040 | * input argument is {@code NaN}.
|
---|
1041 | * </p>
|
---|
1042 | * Infinite values in real or imaginary parts of the input may result in
|
---|
1043 | * infinite or NaN values returned in parts of the result.
|
---|
1044 | *
|
---|
1045 | * @return the square root of <code>1 - this<sup>2</sup></code>.
|
---|
1046 | * @since 1.2
|
---|
1047 | */
|
---|
1048 | public Complex sqrt1z() {
|
---|
1049 | return createComplex(1.0, 0.0).subtract(this.multiply(this)).sqrt();
|
---|
1050 | }
|
---|
1051 |
|
---|
1052 | /**
|
---|
1053 | * Compute the
|
---|
1054 | * <a href="http://mathworld.wolfram.com/Tangent.html" TARGET="_top">
|
---|
1055 | * tangent</a> of this complex number.
|
---|
1056 | * Implements the formula:
|
---|
1057 | * <pre>
|
---|
1058 | * <code>
|
---|
1059 | * tan(a + bi) = sin(2a)/(cos(2a)+cosh(2b)) + [sinh(2b)/(cos(2a)+cosh(2b))]i
|
---|
1060 | * </code>
|
---|
1061 | * </pre>
|
---|
1062 | * where the (real) functions on the right-hand side are
|
---|
1063 | * {@link FastMath#sin}, {@link FastMath#cos}, {@link FastMath#cosh} and
|
---|
1064 | * {@link FastMath#sinh}.
|
---|
1065 | * <p>
|
---|
1066 | * Returns {@link Complex#NaN} if either real or imaginary part of the
|
---|
1067 | * input argument is {@code NaN}.
|
---|
1068 | * </p>
|
---|
1069 | * Infinite (or critical) values in real or imaginary parts of the input may
|
---|
1070 | * result in infinite or NaN values returned in parts of the result.
|
---|
1071 | * <pre>
|
---|
1072 | * Examples:
|
---|
1073 | * <code>
|
---|
1074 | * tan(a ± INFINITY i) = 0 ± i
|
---|
1075 | * tan(±INFINITY + bi) = NaN + NaN i
|
---|
1076 | * tan(±INFINITY ± INFINITY i) = NaN + NaN i
|
---|
1077 | * tan(±π/2 + 0 i) = ±INFINITY + NaN i
|
---|
1078 | * </code>
|
---|
1079 | * </pre>
|
---|
1080 | *
|
---|
1081 | * @return the tangent of {@code this}.
|
---|
1082 | * @since 1.2
|
---|
1083 | */
|
---|
1084 | public Complex tan() {
|
---|
1085 | if (isNaN || Double.isInfinite(real)) {
|
---|
1086 | return NaN;
|
---|
1087 | }
|
---|
1088 | if (imaginary > 20.0) {
|
---|
1089 | return createComplex(0.0, 1.0);
|
---|
1090 | }
|
---|
1091 | if (imaginary < -20.0) {
|
---|
1092 | return createComplex(0.0, -1.0);
|
---|
1093 | }
|
---|
1094 |
|
---|
1095 | double real2 = 2.0 * real;
|
---|
1096 | double imaginary2 = 2.0 * imaginary;
|
---|
1097 | double d = FastMath.cos(real2) + FastMath.cosh(imaginary2);
|
---|
1098 |
|
---|
1099 | return createComplex(FastMath.sin(real2) / d,
|
---|
1100 | FastMath.sinh(imaginary2) / d);
|
---|
1101 | }
|
---|
1102 |
|
---|
1103 | /**
|
---|
1104 | * Compute the
|
---|
1105 | * <a href="http://mathworld.wolfram.com/HyperbolicTangent.html" TARGET="_top">
|
---|
1106 | * hyperbolic tangent</a> of this complex number.
|
---|
1107 | * Implements the formula:
|
---|
1108 | * <pre>
|
---|
1109 | * <code>
|
---|
1110 | * tan(a + bi) = sinh(2a)/(cosh(2a)+cos(2b)) + [sin(2b)/(cosh(2a)+cos(2b))]i
|
---|
1111 | * </code>
|
---|
1112 | * </pre>
|
---|
1113 | * where the (real) functions on the right-hand side are
|
---|
1114 | * {@link FastMath#sin}, {@link FastMath#cos}, {@link FastMath#cosh} and
|
---|
1115 | * {@link FastMath#sinh}.
|
---|
1116 | * <p>
|
---|
1117 | * Returns {@link Complex#NaN} if either real or imaginary part of the
|
---|
1118 | * input argument is {@code NaN}.
|
---|
1119 | * </p>
|
---|
1120 | * Infinite values in real or imaginary parts of the input may result in
|
---|
1121 | * infinite or NaN values returned in parts of the result.
|
---|
1122 | * <pre>
|
---|
1123 | * Examples:
|
---|
1124 | * <code>
|
---|
1125 | * tanh(a ± INFINITY i) = NaN + NaN i
|
---|
1126 | * tanh(±INFINITY + bi) = ±1 + 0 i
|
---|
1127 | * tanh(±INFINITY ± INFINITY i) = NaN + NaN i
|
---|
1128 | * tanh(0 + (π/2)i) = NaN + INFINITY i
|
---|
1129 | * </code>
|
---|
1130 | * </pre>
|
---|
1131 | *
|
---|
1132 | * @return the hyperbolic tangent of {@code this}.
|
---|
1133 | * @since 1.2
|
---|
1134 | */
|
---|
1135 | public Complex tanh() {
|
---|
1136 | if (isNaN || Double.isInfinite(imaginary)) {
|
---|
1137 | return NaN;
|
---|
1138 | }
|
---|
1139 | if (real > 20.0) {
|
---|
1140 | return createComplex(1.0, 0.0);
|
---|
1141 | }
|
---|
1142 | if (real < -20.0) {
|
---|
1143 | return createComplex(-1.0, 0.0);
|
---|
1144 | }
|
---|
1145 | double real2 = 2.0 * real;
|
---|
1146 | double imaginary2 = 2.0 * imaginary;
|
---|
1147 | double d = FastMath.cosh(real2) + FastMath.cos(imaginary2);
|
---|
1148 |
|
---|
1149 | return createComplex(FastMath.sinh(real2) / d,
|
---|
1150 | FastMath.sin(imaginary2) / d);
|
---|
1151 | }
|
---|
1152 |
|
---|
1153 |
|
---|
1154 |
|
---|
1155 | /**
|
---|
1156 | * Compute the argument of this complex number.
|
---|
1157 | * The argument is the angle phi between the positive real axis and
|
---|
1158 | * the point representing this number in the complex plane.
|
---|
1159 | * The value returned is between -PI (not inclusive)
|
---|
1160 | * and PI (inclusive), with negative values returned for numbers with
|
---|
1161 | * negative imaginary parts.
|
---|
1162 | * <p>
|
---|
1163 | * If either real or imaginary part (or both) is NaN, NaN is returned.
|
---|
1164 | * Infinite parts are handled as {@code Math.atan2} handles them,
|
---|
1165 | * essentially treating finite parts as zero in the presence of an
|
---|
1166 | * infinite coordinate and returning a multiple of pi/4 depending on
|
---|
1167 | * the signs of the infinite parts.
|
---|
1168 | * See the javadoc for {@code Math.atan2} for full details.
|
---|
1169 | *
|
---|
1170 | * @return the argument of {@code this}.
|
---|
1171 | */
|
---|
1172 | public double getArgument() {
|
---|
1173 | return FastMath.atan2(getImaginary(), getReal());
|
---|
1174 | }
|
---|
1175 |
|
---|
1176 | /**
|
---|
1177 | * Computes the n-th roots of this complex number.
|
---|
1178 | * The nth roots are defined by the formula:
|
---|
1179 | * <pre>
|
---|
1180 | * <code>
|
---|
1181 | * z<sub>k</sub> = abs<sup>1/n</sup> (cos(phi + 2πk/n) + i (sin(phi + 2πk/n))
|
---|
1182 | * </code>
|
---|
1183 | * </pre>
|
---|
1184 | * for <i>{@code k=0, 1, ..., n-1}</i>, where {@code abs} and {@code phi}
|
---|
1185 | * are respectively the {@link #abs() modulus} and
|
---|
1186 | * {@link #getArgument() argument} of this complex number.
|
---|
1187 | * <p>
|
---|
1188 | * If one or both parts of this complex number is NaN, a list with just
|
---|
1189 | * one element, {@link #NaN} is returned.
|
---|
1190 | * if neither part is NaN, but at least one part is infinite, the result
|
---|
1191 | * is a one-element list containing {@link #INF}.
|
---|
1192 | *
|
---|
1193 | * @param n Degree of root.
|
---|
1194 | * @return a List of all {@code n}-th roots of {@code this}.
|
---|
1195 | * @throws NotPositiveException if {@code n <= 0}.
|
---|
1196 | * @since 2.0
|
---|
1197 | */
|
---|
1198 | public List<Complex> nthRoot(int n) throws NotPositiveException {
|
---|
1199 |
|
---|
1200 | if (n <= 0) {
|
---|
1201 | throw new NotPositiveException(LocalizedFormats.CANNOT_COMPUTE_NTH_ROOT_FOR_NEGATIVE_N,
|
---|
1202 | n);
|
---|
1203 | }
|
---|
1204 |
|
---|
1205 | final List<Complex> result = new ArrayList<Complex>();
|
---|
1206 |
|
---|
1207 | if (isNaN) {
|
---|
1208 | result.add(NaN);
|
---|
1209 | return result;
|
---|
1210 | }
|
---|
1211 | if (isInfinite()) {
|
---|
1212 | result.add(INF);
|
---|
1213 | return result;
|
---|
1214 | }
|
---|
1215 |
|
---|
1216 | // nth root of abs -- faster / more accurate to use a solver here?
|
---|
1217 | final double nthRootOfAbs = FastMath.pow(abs(), 1.0 / n);
|
---|
1218 |
|
---|
1219 | // Compute nth roots of complex number with k = 0, 1, ... n-1
|
---|
1220 | final double nthPhi = getArgument() / n;
|
---|
1221 | final double slice = 2 * FastMath.PI / n;
|
---|
1222 | double innerPart = nthPhi;
|
---|
1223 | for (int k = 0; k < n ; k++) {
|
---|
1224 | // inner part
|
---|
1225 | final double realPart = nthRootOfAbs * FastMath.cos(innerPart);
|
---|
1226 | final double imaginaryPart = nthRootOfAbs * FastMath.sin(innerPart);
|
---|
1227 | result.add(createComplex(realPart, imaginaryPart));
|
---|
1228 | innerPart += slice;
|
---|
1229 | }
|
---|
1230 |
|
---|
1231 | return result;
|
---|
1232 | }
|
---|
1233 |
|
---|
1234 | /**
|
---|
1235 | * Create a complex number given the real and imaginary parts.
|
---|
1236 | *
|
---|
1237 | * @param realPart Real part.
|
---|
1238 | * @param imaginaryPart Imaginary part.
|
---|
1239 | * @return a new complex number instance.
|
---|
1240 | * @since 1.2
|
---|
1241 | * @see #valueOf(double, double)
|
---|
1242 | */
|
---|
1243 | protected Complex createComplex(double realPart,
|
---|
1244 | double imaginaryPart) {
|
---|
1245 | return new Complex(realPart, imaginaryPart);
|
---|
1246 | }
|
---|
1247 |
|
---|
1248 | /**
|
---|
1249 | * Create a complex number given the real and imaginary parts.
|
---|
1250 | *
|
---|
1251 | * @param realPart Real part.
|
---|
1252 | * @param imaginaryPart Imaginary part.
|
---|
1253 | * @return a Complex instance.
|
---|
1254 | */
|
---|
1255 | public static Complex valueOf(double realPart,
|
---|
1256 | double imaginaryPart) {
|
---|
1257 | if (Double.isNaN(realPart) ||
|
---|
1258 | Double.isNaN(imaginaryPart)) {
|
---|
1259 | return NaN;
|
---|
1260 | }
|
---|
1261 | return new Complex(realPart, imaginaryPart);
|
---|
1262 | }
|
---|
1263 |
|
---|
1264 | /**
|
---|
1265 | * Create a complex number given only the real part.
|
---|
1266 | *
|
---|
1267 | * @param realPart Real part.
|
---|
1268 | * @return a Complex instance.
|
---|
1269 | */
|
---|
1270 | public static Complex valueOf(double realPart) {
|
---|
1271 | if (Double.isNaN(realPart)) {
|
---|
1272 | return NaN;
|
---|
1273 | }
|
---|
1274 | return new Complex(realPart);
|
---|
1275 | }
|
---|
1276 |
|
---|
1277 | /**
|
---|
1278 | * Resolve the transient fields in a deserialized Complex Object.
|
---|
1279 | * Subclasses will need to override {@link #createComplex} to
|
---|
1280 | * deserialize properly.
|
---|
1281 | *
|
---|
1282 | * @return A Complex instance with all fields resolved.
|
---|
1283 | * @since 2.0
|
---|
1284 | */
|
---|
1285 | protected final Object readResolve() {
|
---|
1286 | return createComplex(real, imaginary);
|
---|
1287 | }
|
---|
1288 |
|
---|
1289 | /** {@inheritDoc} */
|
---|
1290 | public ComplexField getField() {
|
---|
1291 | return ComplexField.getInstance();
|
---|
1292 | }
|
---|
1293 |
|
---|
1294 | /** {@inheritDoc} */
|
---|
1295 | @Override
|
---|
1296 | public String toString() {
|
---|
1297 | return "(" + real + ", " + imaginary + ")";
|
---|
1298 | }
|
---|
1299 |
|
---|
1300 | }
|
---|