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.util;
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19 |
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20 | import java.lang.reflect.Array;
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21 | import java.util.ArrayList;
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22 | import java.util.Arrays;
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23 | import java.util.Collections;
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24 | import java.util.Comparator;
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25 | import java.util.Iterator;
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26 | import java.util.List;
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27 | import java.util.TreeSet;
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28 |
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29 | import agents.anac.y2019.harddealer.math3.Field;
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30 | import agents.anac.y2019.harddealer.math3.random.RandomGenerator;
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31 | import agents.anac.y2019.harddealer.math3.random.Well19937c;
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32 | import agents.anac.y2019.harddealer.math3.distribution.UniformIntegerDistribution;
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33 | import agents.anac.y2019.harddealer.math3.exception.DimensionMismatchException;
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34 | import agents.anac.y2019.harddealer.math3.exception.MathArithmeticException;
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35 | import agents.anac.y2019.harddealer.math3.exception.MathIllegalArgumentException;
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36 | import agents.anac.y2019.harddealer.math3.exception.MathInternalError;
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37 | import agents.anac.y2019.harddealer.math3.exception.NoDataException;
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38 | import agents.anac.y2019.harddealer.math3.exception.NonMonotonicSequenceException;
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39 | import agents.anac.y2019.harddealer.math3.exception.NotPositiveException;
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40 | import agents.anac.y2019.harddealer.math3.exception.NotStrictlyPositiveException;
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41 | import agents.anac.y2019.harddealer.math3.exception.NullArgumentException;
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42 | import agents.anac.y2019.harddealer.math3.exception.NumberIsTooLargeException;
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43 | import agents.anac.y2019.harddealer.math3.exception.NotANumberException;
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44 | import agents.anac.y2019.harddealer.math3.exception.util.LocalizedFormats;
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45 |
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46 | /**
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47 | * Arrays utilities.
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48 | *
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49 | * @since 3.0
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50 | */
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51 | public class MathArrays {
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52 |
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53 | /**
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54 | * Private constructor.
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55 | */
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56 | private MathArrays() {}
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57 |
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58 | /**
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59 | * Real-valued function that operate on an array or a part of it.
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60 | * @since 3.1
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61 | */
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62 | public interface Function {
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63 | /**
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64 | * Operates on an entire array.
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65 | *
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66 | * @param array Array to operate on.
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67 | * @return the result of the operation.
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68 | */
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69 | double evaluate(double[] array);
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70 | /**
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71 | * @param array Array to operate on.
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72 | * @param startIndex Index of the first element to take into account.
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73 | * @param numElements Number of elements to take into account.
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74 | * @return the result of the operation.
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75 | */
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76 | double evaluate(double[] array,
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77 | int startIndex,
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78 | int numElements);
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79 | }
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80 |
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81 | /**
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82 | * Create a copy of an array scaled by a value.
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83 | *
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84 | * @param arr Array to scale.
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85 | * @param val Scalar.
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86 | * @return scaled copy of array with each entry multiplied by val.
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87 | * @since 3.2
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88 | */
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89 | public static double[] scale(double val, final double[] arr) {
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90 | double[] newArr = new double[arr.length];
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91 | for (int i = 0; i < arr.length; i++) {
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92 | newArr[i] = arr[i] * val;
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93 | }
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94 | return newArr;
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95 | }
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96 |
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97 | /**
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98 | * <p>Multiply each element of an array by a value.</p>
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99 | *
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100 | * <p>The array is modified in place (no copy is created).</p>
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101 | *
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102 | * @param arr Array to scale
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103 | * @param val Scalar
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104 | * @since 3.2
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105 | */
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106 | public static void scaleInPlace(double val, final double[] arr) {
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107 | for (int i = 0; i < arr.length; i++) {
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108 | arr[i] *= val;
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109 | }
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110 | }
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111 |
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112 | /**
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113 | * Creates an array whose contents will be the element-by-element
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114 | * addition of the arguments.
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115 | *
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116 | * @param a First term of the addition.
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117 | * @param b Second term of the addition.
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118 | * @return a new array {@code r} where {@code r[i] = a[i] + b[i]}.
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119 | * @throws DimensionMismatchException if the array lengths differ.
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120 | * @since 3.1
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121 | */
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122 | public static double[] ebeAdd(double[] a, double[] b)
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123 | throws DimensionMismatchException {
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124 | checkEqualLength(a, b);
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125 |
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126 | final double[] result = a.clone();
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127 | for (int i = 0; i < a.length; i++) {
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128 | result[i] += b[i];
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129 | }
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130 | return result;
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131 | }
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132 | /**
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133 | * Creates an array whose contents will be the element-by-element
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134 | * subtraction of the second argument from the first.
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135 | *
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136 | * @param a First term.
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137 | * @param b Element to be subtracted.
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138 | * @return a new array {@code r} where {@code r[i] = a[i] - b[i]}.
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139 | * @throws DimensionMismatchException if the array lengths differ.
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140 | * @since 3.1
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141 | */
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142 | public static double[] ebeSubtract(double[] a, double[] b)
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143 | throws DimensionMismatchException {
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144 | checkEqualLength(a, b);
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145 |
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146 | final double[] result = a.clone();
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147 | for (int i = 0; i < a.length; i++) {
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148 | result[i] -= b[i];
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149 | }
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150 | return result;
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151 | }
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152 | /**
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153 | * Creates an array whose contents will be the element-by-element
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154 | * multiplication of the arguments.
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155 | *
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156 | * @param a First factor of the multiplication.
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157 | * @param b Second factor of the multiplication.
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158 | * @return a new array {@code r} where {@code r[i] = a[i] * b[i]}.
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159 | * @throws DimensionMismatchException if the array lengths differ.
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160 | * @since 3.1
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161 | */
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162 | public static double[] ebeMultiply(double[] a, double[] b)
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163 | throws DimensionMismatchException {
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164 | checkEqualLength(a, b);
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165 |
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166 | final double[] result = a.clone();
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167 | for (int i = 0; i < a.length; i++) {
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168 | result[i] *= b[i];
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169 | }
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170 | return result;
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171 | }
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172 | /**
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173 | * Creates an array whose contents will be the element-by-element
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174 | * division of the first argument by the second.
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175 | *
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176 | * @param a Numerator of the division.
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177 | * @param b Denominator of the division.
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178 | * @return a new array {@code r} where {@code r[i] = a[i] / b[i]}.
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179 | * @throws DimensionMismatchException if the array lengths differ.
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180 | * @since 3.1
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181 | */
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182 | public static double[] ebeDivide(double[] a, double[] b)
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183 | throws DimensionMismatchException {
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184 | checkEqualLength(a, b);
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185 |
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186 | final double[] result = a.clone();
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187 | for (int i = 0; i < a.length; i++) {
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188 | result[i] /= b[i];
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189 | }
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190 | return result;
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191 | }
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192 |
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193 | /**
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194 | * Calculates the L<sub>1</sub> (sum of abs) distance between two points.
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195 | *
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196 | * @param p1 the first point
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197 | * @param p2 the second point
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198 | * @return the L<sub>1</sub> distance between the two points
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199 | * @throws DimensionMismatchException if the array lengths differ.
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200 | */
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201 | public static double distance1(double[] p1, double[] p2)
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202 | throws DimensionMismatchException {
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203 | checkEqualLength(p1, p2);
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204 | double sum = 0;
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205 | for (int i = 0; i < p1.length; i++) {
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206 | sum += FastMath.abs(p1[i] - p2[i]);
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207 | }
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208 | return sum;
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209 | }
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210 |
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211 | /**
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212 | * Calculates the L<sub>1</sub> (sum of abs) distance between two points.
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213 | *
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214 | * @param p1 the first point
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215 | * @param p2 the second point
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216 | * @return the L<sub>1</sub> distance between the two points
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217 | * @throws DimensionMismatchException if the array lengths differ.
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218 | */
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219 | public static int distance1(int[] p1, int[] p2)
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220 | throws DimensionMismatchException {
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221 | checkEqualLength(p1, p2);
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222 | int sum = 0;
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223 | for (int i = 0; i < p1.length; i++) {
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224 | sum += FastMath.abs(p1[i] - p2[i]);
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225 | }
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226 | return sum;
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227 | }
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228 |
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229 | /**
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230 | * Calculates the L<sub>2</sub> (Euclidean) distance between two points.
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231 | *
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232 | * @param p1 the first point
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233 | * @param p2 the second point
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234 | * @return the L<sub>2</sub> distance between the two points
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235 | * @throws DimensionMismatchException if the array lengths differ.
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236 | */
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237 | public static double distance(double[] p1, double[] p2)
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238 | throws DimensionMismatchException {
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239 | checkEqualLength(p1, p2);
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240 | double sum = 0;
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241 | for (int i = 0; i < p1.length; i++) {
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242 | final double dp = p1[i] - p2[i];
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243 | sum += dp * dp;
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244 | }
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245 | return FastMath.sqrt(sum);
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246 | }
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247 |
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248 | /**
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249 | * Calculates the cosine of the angle between two vectors.
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250 | *
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251 | * @param v1 Cartesian coordinates of the first vector.
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252 | * @param v2 Cartesian coordinates of the second vector.
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253 | * @return the cosine of the angle between the vectors.
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254 | * @since 3.6
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255 | */
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256 | public static double cosAngle(double[] v1, double[] v2) {
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257 | return linearCombination(v1, v2) / (safeNorm(v1) * safeNorm(v2));
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258 | }
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259 |
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260 | /**
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261 | * Calculates the L<sub>2</sub> (Euclidean) distance between two points.
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262 | *
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263 | * @param p1 the first point
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264 | * @param p2 the second point
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265 | * @return the L<sub>2</sub> distance between the two points
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266 | * @throws DimensionMismatchException if the array lengths differ.
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267 | */
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268 | public static double distance(int[] p1, int[] p2)
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269 | throws DimensionMismatchException {
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270 | checkEqualLength(p1, p2);
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271 | double sum = 0;
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272 | for (int i = 0; i < p1.length; i++) {
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273 | final double dp = p1[i] - p2[i];
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274 | sum += dp * dp;
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275 | }
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276 | return FastMath.sqrt(sum);
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277 | }
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278 |
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279 | /**
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280 | * Calculates the L<sub>∞</sub> (max of abs) distance between two points.
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281 | *
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282 | * @param p1 the first point
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283 | * @param p2 the second point
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284 | * @return the L<sub>∞</sub> distance between the two points
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285 | * @throws DimensionMismatchException if the array lengths differ.
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286 | */
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287 | public static double distanceInf(double[] p1, double[] p2)
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288 | throws DimensionMismatchException {
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289 | checkEqualLength(p1, p2);
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290 | double max = 0;
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291 | for (int i = 0; i < p1.length; i++) {
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292 | max = FastMath.max(max, FastMath.abs(p1[i] - p2[i]));
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293 | }
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294 | return max;
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295 | }
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296 |
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297 | /**
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298 | * Calculates the L<sub>∞</sub> (max of abs) distance between two points.
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299 | *
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300 | * @param p1 the first point
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301 | * @param p2 the second point
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302 | * @return the L<sub>∞</sub> distance between the two points
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303 | * @throws DimensionMismatchException if the array lengths differ.
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304 | */
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305 | public static int distanceInf(int[] p1, int[] p2)
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306 | throws DimensionMismatchException {
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307 | checkEqualLength(p1, p2);
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308 | int max = 0;
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309 | for (int i = 0; i < p1.length; i++) {
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310 | max = FastMath.max(max, FastMath.abs(p1[i] - p2[i]));
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311 | }
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312 | return max;
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313 | }
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314 |
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315 | /**
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316 | * Specification of ordering direction.
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317 | */
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318 | public enum OrderDirection {
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319 | /** Constant for increasing direction. */
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320 | INCREASING,
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321 | /** Constant for decreasing direction. */
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322 | DECREASING
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323 | }
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324 |
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325 | /**
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326 | * Check that an array is monotonically increasing or decreasing.
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327 | *
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328 | * @param <T> the type of the elements in the specified array
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329 | * @param val Values.
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330 | * @param dir Ordering direction.
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331 | * @param strict Whether the order should be strict.
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332 | * @return {@code true} if sorted, {@code false} otherwise.
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333 | */
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334 | public static <T extends Comparable<? super T>> boolean isMonotonic(T[] val,
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335 | OrderDirection dir,
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336 | boolean strict) {
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337 | T previous = val[0];
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338 | final int max = val.length;
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339 | for (int i = 1; i < max; i++) {
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340 | final int comp;
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341 | switch (dir) {
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342 | case INCREASING:
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343 | comp = previous.compareTo(val[i]);
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344 | if (strict) {
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345 | if (comp >= 0) {
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346 | return false;
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347 | }
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348 | } else {
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349 | if (comp > 0) {
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350 | return false;
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351 | }
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352 | }
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353 | break;
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354 | case DECREASING:
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355 | comp = val[i].compareTo(previous);
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356 | if (strict) {
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357 | if (comp >= 0) {
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358 | return false;
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359 | }
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360 | } else {
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361 | if (comp > 0) {
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362 | return false;
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363 | }
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364 | }
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365 | break;
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366 | default:
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367 | // Should never happen.
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368 | throw new MathInternalError();
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369 | }
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370 |
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371 | previous = val[i];
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372 | }
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373 | return true;
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374 | }
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375 |
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376 | /**
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377 | * Check that an array is monotonically increasing or decreasing.
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378 | *
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379 | * @param val Values.
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380 | * @param dir Ordering direction.
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381 | * @param strict Whether the order should be strict.
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382 | * @return {@code true} if sorted, {@code false} otherwise.
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383 | */
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384 | public static boolean isMonotonic(double[] val, OrderDirection dir, boolean strict) {
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385 | return checkOrder(val, dir, strict, false);
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386 | }
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387 |
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388 | /**
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389 | * Check that both arrays have the same length.
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390 | *
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391 | * @param a Array.
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392 | * @param b Array.
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393 | * @param abort Whether to throw an exception if the check fails.
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394 | * @return {@code true} if the arrays have the same length.
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395 | * @throws DimensionMismatchException if the lengths differ and
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396 | * {@code abort} is {@code true}.
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397 | * @since 3.6
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398 | */
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399 | public static boolean checkEqualLength(double[] a,
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400 | double[] b,
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401 | boolean abort) {
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402 | if (a.length == b.length) {
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403 | return true;
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404 | } else {
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405 | if (abort) {
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406 | throw new DimensionMismatchException(a.length, b.length);
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407 | }
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408 | return false;
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409 | }
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410 | }
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411 |
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412 | /**
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413 | * Check that both arrays have the same length.
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414 | *
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415 | * @param a Array.
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416 | * @param b Array.
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417 | * @throws DimensionMismatchException if the lengths differ.
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418 | * @since 3.6
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419 | */
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420 | public static void checkEqualLength(double[] a,
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421 | double[] b) {
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422 | checkEqualLength(a, b, true);
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423 | }
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424 |
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425 |
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426 | /**
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427 | * Check that both arrays have the same length.
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428 | *
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429 | * @param a Array.
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430 | * @param b Array.
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431 | * @param abort Whether to throw an exception if the check fails.
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432 | * @return {@code true} if the arrays have the same length.
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433 | * @throws DimensionMismatchException if the lengths differ and
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434 | * {@code abort} is {@code true}.
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435 | * @since 3.6
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436 | */
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437 | public static boolean checkEqualLength(int[] a,
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438 | int[] b,
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439 | boolean abort) {
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440 | if (a.length == b.length) {
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441 | return true;
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442 | } else {
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443 | if (abort) {
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444 | throw new DimensionMismatchException(a.length, b.length);
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445 | }
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446 | return false;
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447 | }
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448 | }
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449 |
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450 | /**
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451 | * Check that both arrays have the same length.
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452 | *
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453 | * @param a Array.
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454 | * @param b Array.
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455 | * @throws DimensionMismatchException if the lengths differ.
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456 | * @since 3.6
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457 | */
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458 | public static void checkEqualLength(int[] a,
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459 | int[] b) {
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460 | checkEqualLength(a, b, true);
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461 | }
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462 |
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463 | /**
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464 | * Check that the given array is sorted.
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465 | *
|
---|
466 | * @param val Values.
|
---|
467 | * @param dir Ordering direction.
|
---|
468 | * @param strict Whether the order should be strict.
|
---|
469 | * @param abort Whether to throw an exception if the check fails.
|
---|
470 | * @return {@code true} if the array is sorted.
|
---|
471 | * @throws NonMonotonicSequenceException if the array is not sorted
|
---|
472 | * and {@code abort} is {@code true}.
|
---|
473 | */
|
---|
474 | public static boolean checkOrder(double[] val, OrderDirection dir,
|
---|
475 | boolean strict, boolean abort)
|
---|
476 | throws NonMonotonicSequenceException {
|
---|
477 | double previous = val[0];
|
---|
478 | final int max = val.length;
|
---|
479 |
|
---|
480 | int index;
|
---|
481 | ITEM:
|
---|
482 | for (index = 1; index < max; index++) {
|
---|
483 | switch (dir) {
|
---|
484 | case INCREASING:
|
---|
485 | if (strict) {
|
---|
486 | if (val[index] <= previous) {
|
---|
487 | break ITEM;
|
---|
488 | }
|
---|
489 | } else {
|
---|
490 | if (val[index] < previous) {
|
---|
491 | break ITEM;
|
---|
492 | }
|
---|
493 | }
|
---|
494 | break;
|
---|
495 | case DECREASING:
|
---|
496 | if (strict) {
|
---|
497 | if (val[index] >= previous) {
|
---|
498 | break ITEM;
|
---|
499 | }
|
---|
500 | } else {
|
---|
501 | if (val[index] > previous) {
|
---|
502 | break ITEM;
|
---|
503 | }
|
---|
504 | }
|
---|
505 | break;
|
---|
506 | default:
|
---|
507 | // Should never happen.
|
---|
508 | throw new MathInternalError();
|
---|
509 | }
|
---|
510 |
|
---|
511 | previous = val[index];
|
---|
512 | }
|
---|
513 |
|
---|
514 | if (index == max) {
|
---|
515 | // Loop completed.
|
---|
516 | return true;
|
---|
517 | }
|
---|
518 |
|
---|
519 | // Loop early exit means wrong ordering.
|
---|
520 | if (abort) {
|
---|
521 | throw new NonMonotonicSequenceException(val[index], previous, index, dir, strict);
|
---|
522 | } else {
|
---|
523 | return false;
|
---|
524 | }
|
---|
525 | }
|
---|
526 |
|
---|
527 | /**
|
---|
528 | * Check that the given array is sorted.
|
---|
529 | *
|
---|
530 | * @param val Values.
|
---|
531 | * @param dir Ordering direction.
|
---|
532 | * @param strict Whether the order should be strict.
|
---|
533 | * @throws NonMonotonicSequenceException if the array is not sorted.
|
---|
534 | * @since 2.2
|
---|
535 | */
|
---|
536 | public static void checkOrder(double[] val, OrderDirection dir,
|
---|
537 | boolean strict) throws NonMonotonicSequenceException {
|
---|
538 | checkOrder(val, dir, strict, true);
|
---|
539 | }
|
---|
540 |
|
---|
541 | /**
|
---|
542 | * Check that the given array is sorted in strictly increasing order.
|
---|
543 | *
|
---|
544 | * @param val Values.
|
---|
545 | * @throws NonMonotonicSequenceException if the array is not sorted.
|
---|
546 | * @since 2.2
|
---|
547 | */
|
---|
548 | public static void checkOrder(double[] val) throws NonMonotonicSequenceException {
|
---|
549 | checkOrder(val, OrderDirection.INCREASING, true);
|
---|
550 | }
|
---|
551 |
|
---|
552 | /**
|
---|
553 | * Throws DimensionMismatchException if the input array is not rectangular.
|
---|
554 | *
|
---|
555 | * @param in array to be tested
|
---|
556 | * @throws NullArgumentException if input array is null
|
---|
557 | * @throws DimensionMismatchException if input array is not rectangular
|
---|
558 | * @since 3.1
|
---|
559 | */
|
---|
560 | public static void checkRectangular(final long[][] in)
|
---|
561 | throws NullArgumentException, DimensionMismatchException {
|
---|
562 | MathUtils.checkNotNull(in);
|
---|
563 | for (int i = 1; i < in.length; i++) {
|
---|
564 | if (in[i].length != in[0].length) {
|
---|
565 | throw new DimensionMismatchException(
|
---|
566 | LocalizedFormats.DIFFERENT_ROWS_LENGTHS,
|
---|
567 | in[i].length, in[0].length);
|
---|
568 | }
|
---|
569 | }
|
---|
570 | }
|
---|
571 |
|
---|
572 | /**
|
---|
573 | * Check that all entries of the input array are strictly positive.
|
---|
574 | *
|
---|
575 | * @param in Array to be tested
|
---|
576 | * @throws NotStrictlyPositiveException if any entries of the array are not
|
---|
577 | * strictly positive.
|
---|
578 | * @since 3.1
|
---|
579 | */
|
---|
580 | public static void checkPositive(final double[] in)
|
---|
581 | throws NotStrictlyPositiveException {
|
---|
582 | for (int i = 0; i < in.length; i++) {
|
---|
583 | if (in[i] <= 0) {
|
---|
584 | throw new NotStrictlyPositiveException(in[i]);
|
---|
585 | }
|
---|
586 | }
|
---|
587 | }
|
---|
588 |
|
---|
589 | /**
|
---|
590 | * Check that no entry of the input array is {@code NaN}.
|
---|
591 | *
|
---|
592 | * @param in Array to be tested.
|
---|
593 | * @throws NotANumberException if an entry is {@code NaN}.
|
---|
594 | * @since 3.4
|
---|
595 | */
|
---|
596 | public static void checkNotNaN(final double[] in)
|
---|
597 | throws NotANumberException {
|
---|
598 | for(int i = 0; i < in.length; i++) {
|
---|
599 | if (Double.isNaN(in[i])) {
|
---|
600 | throw new NotANumberException();
|
---|
601 | }
|
---|
602 | }
|
---|
603 | }
|
---|
604 |
|
---|
605 | /**
|
---|
606 | * Check that all entries of the input array are >= 0.
|
---|
607 | *
|
---|
608 | * @param in Array to be tested
|
---|
609 | * @throws NotPositiveException if any array entries are less than 0.
|
---|
610 | * @since 3.1
|
---|
611 | */
|
---|
612 | public static void checkNonNegative(final long[] in)
|
---|
613 | throws NotPositiveException {
|
---|
614 | for (int i = 0; i < in.length; i++) {
|
---|
615 | if (in[i] < 0) {
|
---|
616 | throw new NotPositiveException(in[i]);
|
---|
617 | }
|
---|
618 | }
|
---|
619 | }
|
---|
620 |
|
---|
621 | /**
|
---|
622 | * Check all entries of the input array are >= 0.
|
---|
623 | *
|
---|
624 | * @param in Array to be tested
|
---|
625 | * @throws NotPositiveException if any array entries are less than 0.
|
---|
626 | * @since 3.1
|
---|
627 | */
|
---|
628 | public static void checkNonNegative(final long[][] in)
|
---|
629 | throws NotPositiveException {
|
---|
630 | for (int i = 0; i < in.length; i ++) {
|
---|
631 | for (int j = 0; j < in[i].length; j++) {
|
---|
632 | if (in[i][j] < 0) {
|
---|
633 | throw new NotPositiveException(in[i][j]);
|
---|
634 | }
|
---|
635 | }
|
---|
636 | }
|
---|
637 | }
|
---|
638 |
|
---|
639 | /**
|
---|
640 | * Returns the Cartesian norm (2-norm), handling both overflow and underflow.
|
---|
641 | * Translation of the minpack enorm subroutine.
|
---|
642 | *
|
---|
643 | * The redistribution policy for MINPACK is available
|
---|
644 | * <a href="http://www.netlib.org/minpack/disclaimer">here</a>, for
|
---|
645 | * convenience, it is reproduced below.</p>
|
---|
646 | *
|
---|
647 | * <table border="0" width="80%" cellpadding="10" align="center" bgcolor="#E0E0E0">
|
---|
648 | * <tr><td>
|
---|
649 | * Minpack Copyright Notice (1999) University of Chicago.
|
---|
650 | * All rights reserved
|
---|
651 | * </td></tr>
|
---|
652 | * <tr><td>
|
---|
653 | * Redistribution and use in source and binary forms, with or without
|
---|
654 | * modification, are permitted provided that the following conditions
|
---|
655 | * are met:
|
---|
656 | * <ol>
|
---|
657 | * <li>Redistributions of source code must retain the above copyright
|
---|
658 | * notice, this list of conditions and the following disclaimer.</li>
|
---|
659 | * <li>Redistributions in binary form must reproduce the above
|
---|
660 | * copyright notice, this list of conditions and the following
|
---|
661 | * disclaimer in the documentation and/or other materials provided
|
---|
662 | * with the distribution.</li>
|
---|
663 | * <li>The end-user documentation included with the redistribution, if any,
|
---|
664 | * must include the following acknowledgment:
|
---|
665 | * {@code This product includes software developed by the University of
|
---|
666 | * Chicago, as Operator of Argonne National Laboratory.}
|
---|
667 | * Alternately, this acknowledgment may appear in the software itself,
|
---|
668 | * if and wherever such third-party acknowledgments normally appear.</li>
|
---|
669 | * <li><strong>WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS"
|
---|
670 | * WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE
|
---|
671 | * UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND
|
---|
672 | * THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR
|
---|
673 | * IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES
|
---|
674 | * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE
|
---|
675 | * OR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY
|
---|
676 | * OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR
|
---|
677 | * USEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF
|
---|
678 | * THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4)
|
---|
679 | * DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION
|
---|
680 | * UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL
|
---|
681 | * BE CORRECTED.</strong></li>
|
---|
682 | * <li><strong>LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT
|
---|
683 | * HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF
|
---|
684 | * ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT,
|
---|
685 | * INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF
|
---|
686 | * ANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF
|
---|
687 | * PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER
|
---|
688 | * SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT
|
---|
689 | * (INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE,
|
---|
690 | * EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE
|
---|
691 | * POSSIBILITY OF SUCH LOSS OR DAMAGES.</strong></li>
|
---|
692 | * <ol></td></tr>
|
---|
693 | * </table>
|
---|
694 | *
|
---|
695 | * @param v Vector of doubles.
|
---|
696 | * @return the 2-norm of the vector.
|
---|
697 | * @since 2.2
|
---|
698 | */
|
---|
699 | public static double safeNorm(double[] v) {
|
---|
700 | double rdwarf = 3.834e-20;
|
---|
701 | double rgiant = 1.304e+19;
|
---|
702 | double s1 = 0;
|
---|
703 | double s2 = 0;
|
---|
704 | double s3 = 0;
|
---|
705 | double x1max = 0;
|
---|
706 | double x3max = 0;
|
---|
707 | double floatn = v.length;
|
---|
708 | double agiant = rgiant / floatn;
|
---|
709 | for (int i = 0; i < v.length; i++) {
|
---|
710 | double xabs = FastMath.abs(v[i]);
|
---|
711 | if (xabs < rdwarf || xabs > agiant) {
|
---|
712 | if (xabs > rdwarf) {
|
---|
713 | if (xabs > x1max) {
|
---|
714 | double r = x1max / xabs;
|
---|
715 | s1= 1 + s1 * r * r;
|
---|
716 | x1max = xabs;
|
---|
717 | } else {
|
---|
718 | double r = xabs / x1max;
|
---|
719 | s1 += r * r;
|
---|
720 | }
|
---|
721 | } else {
|
---|
722 | if (xabs > x3max) {
|
---|
723 | double r = x3max / xabs;
|
---|
724 | s3= 1 + s3 * r * r;
|
---|
725 | x3max = xabs;
|
---|
726 | } else {
|
---|
727 | if (xabs != 0) {
|
---|
728 | double r = xabs / x3max;
|
---|
729 | s3 += r * r;
|
---|
730 | }
|
---|
731 | }
|
---|
732 | }
|
---|
733 | } else {
|
---|
734 | s2 += xabs * xabs;
|
---|
735 | }
|
---|
736 | }
|
---|
737 | double norm;
|
---|
738 | if (s1 != 0) {
|
---|
739 | norm = x1max * Math.sqrt(s1 + (s2 / x1max) / x1max);
|
---|
740 | } else {
|
---|
741 | if (s2 == 0) {
|
---|
742 | norm = x3max * Math.sqrt(s3);
|
---|
743 | } else {
|
---|
744 | if (s2 >= x3max) {
|
---|
745 | norm = Math.sqrt(s2 * (1 + (x3max / s2) * (x3max * s3)));
|
---|
746 | } else {
|
---|
747 | norm = Math.sqrt(x3max * ((s2 / x3max) + (x3max * s3)));
|
---|
748 | }
|
---|
749 | }
|
---|
750 | }
|
---|
751 | return norm;
|
---|
752 | }
|
---|
753 |
|
---|
754 | /**
|
---|
755 | * A helper data structure holding a double and an integer value.
|
---|
756 | */
|
---|
757 | private static class PairDoubleInteger {
|
---|
758 | /** Key */
|
---|
759 | private final double key;
|
---|
760 | /** Value */
|
---|
761 | private final int value;
|
---|
762 |
|
---|
763 | /**
|
---|
764 | * @param key Key.
|
---|
765 | * @param value Value.
|
---|
766 | */
|
---|
767 | PairDoubleInteger(double key, int value) {
|
---|
768 | this.key = key;
|
---|
769 | this.value = value;
|
---|
770 | }
|
---|
771 |
|
---|
772 | /** @return the key. */
|
---|
773 | public double getKey() {
|
---|
774 | return key;
|
---|
775 | }
|
---|
776 |
|
---|
777 | /** @return the value. */
|
---|
778 | public int getValue() {
|
---|
779 | return value;
|
---|
780 | }
|
---|
781 | }
|
---|
782 |
|
---|
783 | /**
|
---|
784 | * Sort an array in ascending order in place and perform the same reordering
|
---|
785 | * of entries on other arrays. For example, if
|
---|
786 | * {@code x = [3, 1, 2], y = [1, 2, 3]} and {@code z = [0, 5, 7]}, then
|
---|
787 | * {@code sortInPlace(x, y, z)} will update {@code x} to {@code [1, 2, 3]},
|
---|
788 | * {@code y} to {@code [2, 3, 1]} and {@code z} to {@code [5, 7, 0]}.
|
---|
789 | *
|
---|
790 | * @param x Array to be sorted and used as a pattern for permutation
|
---|
791 | * of the other arrays.
|
---|
792 | * @param yList Set of arrays whose permutations of entries will follow
|
---|
793 | * those performed on {@code x}.
|
---|
794 | * @throws DimensionMismatchException if any {@code y} is not the same
|
---|
795 | * size as {@code x}.
|
---|
796 | * @throws NullArgumentException if {@code x} or any {@code y} is null.
|
---|
797 | * @since 3.0
|
---|
798 | */
|
---|
799 | public static void sortInPlace(double[] x, double[] ... yList)
|
---|
800 | throws DimensionMismatchException, NullArgumentException {
|
---|
801 | sortInPlace(x, OrderDirection.INCREASING, yList);
|
---|
802 | }
|
---|
803 |
|
---|
804 | /**
|
---|
805 | * Sort an array in place and perform the same reordering of entries on
|
---|
806 | * other arrays. This method works the same as the other
|
---|
807 | * {@link #sortInPlace(double[], double[][]) sortInPlace} method, but
|
---|
808 | * allows the order of the sort to be provided in the {@code dir}
|
---|
809 | * parameter.
|
---|
810 | *
|
---|
811 | * @param x Array to be sorted and used as a pattern for permutation
|
---|
812 | * of the other arrays.
|
---|
813 | * @param dir Order direction.
|
---|
814 | * @param yList Set of arrays whose permutations of entries will follow
|
---|
815 | * those performed on {@code x}.
|
---|
816 | * @throws DimensionMismatchException if any {@code y} is not the same
|
---|
817 | * size as {@code x}.
|
---|
818 | * @throws NullArgumentException if {@code x} or any {@code y} is null
|
---|
819 | * @since 3.0
|
---|
820 | */
|
---|
821 | public static void sortInPlace(double[] x,
|
---|
822 | final OrderDirection dir,
|
---|
823 | double[] ... yList)
|
---|
824 | throws NullArgumentException,
|
---|
825 | DimensionMismatchException {
|
---|
826 |
|
---|
827 | // Consistency checks.
|
---|
828 | if (x == null) {
|
---|
829 | throw new NullArgumentException();
|
---|
830 | }
|
---|
831 |
|
---|
832 | final int yListLen = yList.length;
|
---|
833 | final int len = x.length;
|
---|
834 |
|
---|
835 | for (int j = 0; j < yListLen; j++) {
|
---|
836 | final double[] y = yList[j];
|
---|
837 | if (y == null) {
|
---|
838 | throw new NullArgumentException();
|
---|
839 | }
|
---|
840 | if (y.length != len) {
|
---|
841 | throw new DimensionMismatchException(y.length, len);
|
---|
842 | }
|
---|
843 | }
|
---|
844 |
|
---|
845 | // Associate each abscissa "x[i]" with its index "i".
|
---|
846 | final List<PairDoubleInteger> list
|
---|
847 | = new ArrayList<PairDoubleInteger>(len);
|
---|
848 | for (int i = 0; i < len; i++) {
|
---|
849 | list.add(new PairDoubleInteger(x[i], i));
|
---|
850 | }
|
---|
851 |
|
---|
852 | // Create comparators for increasing and decreasing orders.
|
---|
853 | final Comparator<PairDoubleInteger> comp
|
---|
854 | = dir == MathArrays.OrderDirection.INCREASING ?
|
---|
855 | new Comparator<PairDoubleInteger>() {
|
---|
856 | /** {@inheritDoc} */
|
---|
857 | public int compare(PairDoubleInteger o1,
|
---|
858 | PairDoubleInteger o2) {
|
---|
859 | return Double.compare(o1.getKey(), o2.getKey());
|
---|
860 | }
|
---|
861 | } : new Comparator<PairDoubleInteger>() {
|
---|
862 | /** {@inheritDoc} */
|
---|
863 | public int compare(PairDoubleInteger o1,
|
---|
864 | PairDoubleInteger o2) {
|
---|
865 | return Double.compare(o2.getKey(), o1.getKey());
|
---|
866 | }
|
---|
867 | };
|
---|
868 |
|
---|
869 | // Sort.
|
---|
870 | Collections.sort(list, comp);
|
---|
871 |
|
---|
872 | // Modify the original array so that its elements are in
|
---|
873 | // the prescribed order.
|
---|
874 | // Retrieve indices of original locations.
|
---|
875 | final int[] indices = new int[len];
|
---|
876 | for (int i = 0; i < len; i++) {
|
---|
877 | final PairDoubleInteger e = list.get(i);
|
---|
878 | x[i] = e.getKey();
|
---|
879 | indices[i] = e.getValue();
|
---|
880 | }
|
---|
881 |
|
---|
882 | // In each of the associated arrays, move the
|
---|
883 | // elements to their new location.
|
---|
884 | for (int j = 0; j < yListLen; j++) {
|
---|
885 | // Input array will be modified in place.
|
---|
886 | final double[] yInPlace = yList[j];
|
---|
887 | final double[] yOrig = yInPlace.clone();
|
---|
888 |
|
---|
889 | for (int i = 0; i < len; i++) {
|
---|
890 | yInPlace[i] = yOrig[indices[i]];
|
---|
891 | }
|
---|
892 | }
|
---|
893 | }
|
---|
894 |
|
---|
895 | /**
|
---|
896 | * Creates a copy of the {@code source} array.
|
---|
897 | *
|
---|
898 | * @param source Array to be copied.
|
---|
899 | * @return the copied array.
|
---|
900 | */
|
---|
901 | public static int[] copyOf(int[] source) {
|
---|
902 | return copyOf(source, source.length);
|
---|
903 | }
|
---|
904 |
|
---|
905 | /**
|
---|
906 | * Creates a copy of the {@code source} array.
|
---|
907 | *
|
---|
908 | * @param source Array to be copied.
|
---|
909 | * @return the copied array.
|
---|
910 | */
|
---|
911 | public static double[] copyOf(double[] source) {
|
---|
912 | return copyOf(source, source.length);
|
---|
913 | }
|
---|
914 |
|
---|
915 | /**
|
---|
916 | * Creates a copy of the {@code source} array.
|
---|
917 | *
|
---|
918 | * @param source Array to be copied.
|
---|
919 | * @param len Number of entries to copy. If smaller then the source
|
---|
920 | * length, the copy will be truncated, if larger it will padded with
|
---|
921 | * zeroes.
|
---|
922 | * @return the copied array.
|
---|
923 | */
|
---|
924 | public static int[] copyOf(int[] source, int len) {
|
---|
925 | final int[] output = new int[len];
|
---|
926 | System.arraycopy(source, 0, output, 0, FastMath.min(len, source.length));
|
---|
927 | return output;
|
---|
928 | }
|
---|
929 |
|
---|
930 | /**
|
---|
931 | * Creates a copy of the {@code source} array.
|
---|
932 | *
|
---|
933 | * @param source Array to be copied.
|
---|
934 | * @param len Number of entries to copy. If smaller then the source
|
---|
935 | * length, the copy will be truncated, if larger it will padded with
|
---|
936 | * zeroes.
|
---|
937 | * @return the copied array.
|
---|
938 | */
|
---|
939 | public static double[] copyOf(double[] source, int len) {
|
---|
940 | final double[] output = new double[len];
|
---|
941 | System.arraycopy(source, 0, output, 0, FastMath.min(len, source.length));
|
---|
942 | return output;
|
---|
943 | }
|
---|
944 |
|
---|
945 | /**
|
---|
946 | * Creates a copy of the {@code source} array.
|
---|
947 | *
|
---|
948 | * @param source Array to be copied.
|
---|
949 | * @param from Initial index of the range to be copied, inclusive.
|
---|
950 | * @param to Final index of the range to be copied, exclusive. (This index may lie outside the array.)
|
---|
951 | * @return the copied array.
|
---|
952 | */
|
---|
953 | public static double[] copyOfRange(double[] source, int from, int to) {
|
---|
954 | final int len = to - from;
|
---|
955 | final double[] output = new double[len];
|
---|
956 | System.arraycopy(source, from, output, 0, FastMath.min(len, source.length - from));
|
---|
957 | return output;
|
---|
958 | }
|
---|
959 |
|
---|
960 | /**
|
---|
961 | * Compute a linear combination accurately.
|
---|
962 | * This method computes the sum of the products
|
---|
963 | * <code>a<sub>i</sub> b<sub>i</sub></code> to high accuracy.
|
---|
964 | * It does so by using specific multiplication and addition algorithms to
|
---|
965 | * preserve accuracy and reduce cancellation effects.
|
---|
966 | * <br/>
|
---|
967 | * It is based on the 2005 paper
|
---|
968 | * <a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.1547">
|
---|
969 | * Accurate Sum and Dot Product</a> by Takeshi Ogita, Siegfried M. Rump,
|
---|
970 | * and Shin'ichi Oishi published in SIAM J. Sci. Comput.
|
---|
971 | *
|
---|
972 | * @param a Factors.
|
---|
973 | * @param b Factors.
|
---|
974 | * @return <code>Σ<sub>i</sub> a<sub>i</sub> b<sub>i</sub></code>.
|
---|
975 | * @throws DimensionMismatchException if arrays dimensions don't match
|
---|
976 | */
|
---|
977 | public static double linearCombination(final double[] a, final double[] b)
|
---|
978 | throws DimensionMismatchException {
|
---|
979 | checkEqualLength(a, b);
|
---|
980 | final int len = a.length;
|
---|
981 |
|
---|
982 | if (len == 1) {
|
---|
983 | // Revert to scalar multiplication.
|
---|
984 | return a[0] * b[0];
|
---|
985 | }
|
---|
986 |
|
---|
987 | final double[] prodHigh = new double[len];
|
---|
988 | double prodLowSum = 0;
|
---|
989 |
|
---|
990 | for (int i = 0; i < len; i++) {
|
---|
991 | final double ai = a[i];
|
---|
992 | final double aHigh = Double.longBitsToDouble(Double.doubleToRawLongBits(ai) & ((-1L) << 27));
|
---|
993 | final double aLow = ai - aHigh;
|
---|
994 |
|
---|
995 | final double bi = b[i];
|
---|
996 | final double bHigh = Double.longBitsToDouble(Double.doubleToRawLongBits(bi) & ((-1L) << 27));
|
---|
997 | final double bLow = bi - bHigh;
|
---|
998 | prodHigh[i] = ai * bi;
|
---|
999 | final double prodLow = aLow * bLow - (((prodHigh[i] -
|
---|
1000 | aHigh * bHigh) -
|
---|
1001 | aLow * bHigh) -
|
---|
1002 | aHigh * bLow);
|
---|
1003 | prodLowSum += prodLow;
|
---|
1004 | }
|
---|
1005 |
|
---|
1006 |
|
---|
1007 | final double prodHighCur = prodHigh[0];
|
---|
1008 | double prodHighNext = prodHigh[1];
|
---|
1009 | double sHighPrev = prodHighCur + prodHighNext;
|
---|
1010 | double sPrime = sHighPrev - prodHighNext;
|
---|
1011 | double sLowSum = (prodHighNext - (sHighPrev - sPrime)) + (prodHighCur - sPrime);
|
---|
1012 |
|
---|
1013 | final int lenMinusOne = len - 1;
|
---|
1014 | for (int i = 1; i < lenMinusOne; i++) {
|
---|
1015 | prodHighNext = prodHigh[i + 1];
|
---|
1016 | final double sHighCur = sHighPrev + prodHighNext;
|
---|
1017 | sPrime = sHighCur - prodHighNext;
|
---|
1018 | sLowSum += (prodHighNext - (sHighCur - sPrime)) + (sHighPrev - sPrime);
|
---|
1019 | sHighPrev = sHighCur;
|
---|
1020 | }
|
---|
1021 |
|
---|
1022 | double result = sHighPrev + (prodLowSum + sLowSum);
|
---|
1023 |
|
---|
1024 | if (Double.isNaN(result)) {
|
---|
1025 | // either we have split infinite numbers or some coefficients were NaNs,
|
---|
1026 | // just rely on the naive implementation and let IEEE754 handle this
|
---|
1027 | result = 0;
|
---|
1028 | for (int i = 0; i < len; ++i) {
|
---|
1029 | result += a[i] * b[i];
|
---|
1030 | }
|
---|
1031 | }
|
---|
1032 |
|
---|
1033 | return result;
|
---|
1034 | }
|
---|
1035 |
|
---|
1036 | /**
|
---|
1037 | * Compute a linear combination accurately.
|
---|
1038 | * <p>
|
---|
1039 | * This method computes a<sub>1</sub>×b<sub>1</sub> +
|
---|
1040 | * a<sub>2</sub>×b<sub>2</sub> to high accuracy. It does
|
---|
1041 | * so by using specific multiplication and addition algorithms to
|
---|
1042 | * preserve accuracy and reduce cancellation effects. It is based
|
---|
1043 | * on the 2005 paper <a
|
---|
1044 | * href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.1547">
|
---|
1045 | * Accurate Sum and Dot Product</a> by Takeshi Ogita,
|
---|
1046 | * Siegfried M. Rump, and Shin'ichi Oishi published in SIAM J. Sci. Comput.
|
---|
1047 | * </p>
|
---|
1048 | * @param a1 first factor of the first term
|
---|
1049 | * @param b1 second factor of the first term
|
---|
1050 | * @param a2 first factor of the second term
|
---|
1051 | * @param b2 second factor of the second term
|
---|
1052 | * @return a<sub>1</sub>×b<sub>1</sub> +
|
---|
1053 | * a<sub>2</sub>×b<sub>2</sub>
|
---|
1054 | * @see #linearCombination(double, double, double, double, double, double)
|
---|
1055 | * @see #linearCombination(double, double, double, double, double, double, double, double)
|
---|
1056 | */
|
---|
1057 | public static double linearCombination(final double a1, final double b1,
|
---|
1058 | final double a2, final double b2) {
|
---|
1059 |
|
---|
1060 | // the code below is split in many additions/subtractions that may
|
---|
1061 | // appear redundant. However, they should NOT be simplified, as they
|
---|
1062 | // use IEEE754 floating point arithmetic rounding properties.
|
---|
1063 | // The variable naming conventions are that xyzHigh contains the most significant
|
---|
1064 | // bits of xyz and xyzLow contains its least significant bits. So theoretically
|
---|
1065 | // xyz is the sum xyzHigh + xyzLow, but in many cases below, this sum cannot
|
---|
1066 | // be represented in only one double precision number so we preserve two numbers
|
---|
1067 | // to hold it as long as we can, combining the high and low order bits together
|
---|
1068 | // only at the end, after cancellation may have occurred on high order bits
|
---|
1069 |
|
---|
1070 | // split a1 and b1 as one 26 bits number and one 27 bits number
|
---|
1071 | final double a1High = Double.longBitsToDouble(Double.doubleToRawLongBits(a1) & ((-1L) << 27));
|
---|
1072 | final double a1Low = a1 - a1High;
|
---|
1073 | final double b1High = Double.longBitsToDouble(Double.doubleToRawLongBits(b1) & ((-1L) << 27));
|
---|
1074 | final double b1Low = b1 - b1High;
|
---|
1075 |
|
---|
1076 | // accurate multiplication a1 * b1
|
---|
1077 | final double prod1High = a1 * b1;
|
---|
1078 | final double prod1Low = a1Low * b1Low - (((prod1High - a1High * b1High) - a1Low * b1High) - a1High * b1Low);
|
---|
1079 |
|
---|
1080 | // split a2 and b2 as one 26 bits number and one 27 bits number
|
---|
1081 | final double a2High = Double.longBitsToDouble(Double.doubleToRawLongBits(a2) & ((-1L) << 27));
|
---|
1082 | final double a2Low = a2 - a2High;
|
---|
1083 | final double b2High = Double.longBitsToDouble(Double.doubleToRawLongBits(b2) & ((-1L) << 27));
|
---|
1084 | final double b2Low = b2 - b2High;
|
---|
1085 |
|
---|
1086 | // accurate multiplication a2 * b2
|
---|
1087 | final double prod2High = a2 * b2;
|
---|
1088 | final double prod2Low = a2Low * b2Low - (((prod2High - a2High * b2High) - a2Low * b2High) - a2High * b2Low);
|
---|
1089 |
|
---|
1090 | // accurate addition a1 * b1 + a2 * b2
|
---|
1091 | final double s12High = prod1High + prod2High;
|
---|
1092 | final double s12Prime = s12High - prod2High;
|
---|
1093 | final double s12Low = (prod2High - (s12High - s12Prime)) + (prod1High - s12Prime);
|
---|
1094 |
|
---|
1095 | // final rounding, s12 may have suffered many cancellations, we try
|
---|
1096 | // to recover some bits from the extra words we have saved up to now
|
---|
1097 | double result = s12High + (prod1Low + prod2Low + s12Low);
|
---|
1098 |
|
---|
1099 | if (Double.isNaN(result)) {
|
---|
1100 | // either we have split infinite numbers or some coefficients were NaNs,
|
---|
1101 | // just rely on the naive implementation and let IEEE754 handle this
|
---|
1102 | result = a1 * b1 + a2 * b2;
|
---|
1103 | }
|
---|
1104 |
|
---|
1105 | return result;
|
---|
1106 | }
|
---|
1107 |
|
---|
1108 | /**
|
---|
1109 | * Compute a linear combination accurately.
|
---|
1110 | * <p>
|
---|
1111 | * This method computes a<sub>1</sub>×b<sub>1</sub> +
|
---|
1112 | * a<sub>2</sub>×b<sub>2</sub> + a<sub>3</sub>×b<sub>3</sub>
|
---|
1113 | * to high accuracy. It does so by using specific multiplication and
|
---|
1114 | * addition algorithms to preserve accuracy and reduce cancellation effects.
|
---|
1115 | * It is based on the 2005 paper <a
|
---|
1116 | * href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.1547">
|
---|
1117 | * Accurate Sum and Dot Product</a> by Takeshi Ogita,
|
---|
1118 | * Siegfried M. Rump, and Shin'ichi Oishi published in SIAM J. Sci. Comput.
|
---|
1119 | * </p>
|
---|
1120 | * @param a1 first factor of the first term
|
---|
1121 | * @param b1 second factor of the first term
|
---|
1122 | * @param a2 first factor of the second term
|
---|
1123 | * @param b2 second factor of the second term
|
---|
1124 | * @param a3 first factor of the third term
|
---|
1125 | * @param b3 second factor of the third term
|
---|
1126 | * @return a<sub>1</sub>×b<sub>1</sub> +
|
---|
1127 | * a<sub>2</sub>×b<sub>2</sub> + a<sub>3</sub>×b<sub>3</sub>
|
---|
1128 | * @see #linearCombination(double, double, double, double)
|
---|
1129 | * @see #linearCombination(double, double, double, double, double, double, double, double)
|
---|
1130 | */
|
---|
1131 | public static double linearCombination(final double a1, final double b1,
|
---|
1132 | final double a2, final double b2,
|
---|
1133 | final double a3, final double b3) {
|
---|
1134 |
|
---|
1135 | // the code below is split in many additions/subtractions that may
|
---|
1136 | // appear redundant. However, they should NOT be simplified, as they
|
---|
1137 | // do use IEEE754 floating point arithmetic rounding properties.
|
---|
1138 | // The variables naming conventions are that xyzHigh contains the most significant
|
---|
1139 | // bits of xyz and xyzLow contains its least significant bits. So theoretically
|
---|
1140 | // xyz is the sum xyzHigh + xyzLow, but in many cases below, this sum cannot
|
---|
1141 | // be represented in only one double precision number so we preserve two numbers
|
---|
1142 | // to hold it as long as we can, combining the high and low order bits together
|
---|
1143 | // only at the end, after cancellation may have occurred on high order bits
|
---|
1144 |
|
---|
1145 | // split a1 and b1 as one 26 bits number and one 27 bits number
|
---|
1146 | final double a1High = Double.longBitsToDouble(Double.doubleToRawLongBits(a1) & ((-1L) << 27));
|
---|
1147 | final double a1Low = a1 - a1High;
|
---|
1148 | final double b1High = Double.longBitsToDouble(Double.doubleToRawLongBits(b1) & ((-1L) << 27));
|
---|
1149 | final double b1Low = b1 - b1High;
|
---|
1150 |
|
---|
1151 | // accurate multiplication a1 * b1
|
---|
1152 | final double prod1High = a1 * b1;
|
---|
1153 | final double prod1Low = a1Low * b1Low - (((prod1High - a1High * b1High) - a1Low * b1High) - a1High * b1Low);
|
---|
1154 |
|
---|
1155 | // split a2 and b2 as one 26 bits number and one 27 bits number
|
---|
1156 | final double a2High = Double.longBitsToDouble(Double.doubleToRawLongBits(a2) & ((-1L) << 27));
|
---|
1157 | final double a2Low = a2 - a2High;
|
---|
1158 | final double b2High = Double.longBitsToDouble(Double.doubleToRawLongBits(b2) & ((-1L) << 27));
|
---|
1159 | final double b2Low = b2 - b2High;
|
---|
1160 |
|
---|
1161 | // accurate multiplication a2 * b2
|
---|
1162 | final double prod2High = a2 * b2;
|
---|
1163 | final double prod2Low = a2Low * b2Low - (((prod2High - a2High * b2High) - a2Low * b2High) - a2High * b2Low);
|
---|
1164 |
|
---|
1165 | // split a3 and b3 as one 26 bits number and one 27 bits number
|
---|
1166 | final double a3High = Double.longBitsToDouble(Double.doubleToRawLongBits(a3) & ((-1L) << 27));
|
---|
1167 | final double a3Low = a3 - a3High;
|
---|
1168 | final double b3High = Double.longBitsToDouble(Double.doubleToRawLongBits(b3) & ((-1L) << 27));
|
---|
1169 | final double b3Low = b3 - b3High;
|
---|
1170 |
|
---|
1171 | // accurate multiplication a3 * b3
|
---|
1172 | final double prod3High = a3 * b3;
|
---|
1173 | final double prod3Low = a3Low * b3Low - (((prod3High - a3High * b3High) - a3Low * b3High) - a3High * b3Low);
|
---|
1174 |
|
---|
1175 | // accurate addition a1 * b1 + a2 * b2
|
---|
1176 | final double s12High = prod1High + prod2High;
|
---|
1177 | final double s12Prime = s12High - prod2High;
|
---|
1178 | final double s12Low = (prod2High - (s12High - s12Prime)) + (prod1High - s12Prime);
|
---|
1179 |
|
---|
1180 | // accurate addition a1 * b1 + a2 * b2 + a3 * b3
|
---|
1181 | final double s123High = s12High + prod3High;
|
---|
1182 | final double s123Prime = s123High - prod3High;
|
---|
1183 | final double s123Low = (prod3High - (s123High - s123Prime)) + (s12High - s123Prime);
|
---|
1184 |
|
---|
1185 | // final rounding, s123 may have suffered many cancellations, we try
|
---|
1186 | // to recover some bits from the extra words we have saved up to now
|
---|
1187 | double result = s123High + (prod1Low + prod2Low + prod3Low + s12Low + s123Low);
|
---|
1188 |
|
---|
1189 | if (Double.isNaN(result)) {
|
---|
1190 | // either we have split infinite numbers or some coefficients were NaNs,
|
---|
1191 | // just rely on the naive implementation and let IEEE754 handle this
|
---|
1192 | result = a1 * b1 + a2 * b2 + a3 * b3;
|
---|
1193 | }
|
---|
1194 |
|
---|
1195 | return result;
|
---|
1196 | }
|
---|
1197 |
|
---|
1198 | /**
|
---|
1199 | * Compute a linear combination accurately.
|
---|
1200 | * <p>
|
---|
1201 | * This method computes a<sub>1</sub>×b<sub>1</sub> +
|
---|
1202 | * a<sub>2</sub>×b<sub>2</sub> + a<sub>3</sub>×b<sub>3</sub> +
|
---|
1203 | * a<sub>4</sub>×b<sub>4</sub>
|
---|
1204 | * to high accuracy. It does so by using specific multiplication and
|
---|
1205 | * addition algorithms to preserve accuracy and reduce cancellation effects.
|
---|
1206 | * It is based on the 2005 paper <a
|
---|
1207 | * href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.1547">
|
---|
1208 | * Accurate Sum and Dot Product</a> by Takeshi Ogita,
|
---|
1209 | * Siegfried M. Rump, and Shin'ichi Oishi published in SIAM J. Sci. Comput.
|
---|
1210 | * </p>
|
---|
1211 | * @param a1 first factor of the first term
|
---|
1212 | * @param b1 second factor of the first term
|
---|
1213 | * @param a2 first factor of the second term
|
---|
1214 | * @param b2 second factor of the second term
|
---|
1215 | * @param a3 first factor of the third term
|
---|
1216 | * @param b3 second factor of the third term
|
---|
1217 | * @param a4 first factor of the third term
|
---|
1218 | * @param b4 second factor of the third term
|
---|
1219 | * @return a<sub>1</sub>×b<sub>1</sub> +
|
---|
1220 | * a<sub>2</sub>×b<sub>2</sub> + a<sub>3</sub>×b<sub>3</sub> +
|
---|
1221 | * a<sub>4</sub>×b<sub>4</sub>
|
---|
1222 | * @see #linearCombination(double, double, double, double)
|
---|
1223 | * @see #linearCombination(double, double, double, double, double, double)
|
---|
1224 | */
|
---|
1225 | public static double linearCombination(final double a1, final double b1,
|
---|
1226 | final double a2, final double b2,
|
---|
1227 | final double a3, final double b3,
|
---|
1228 | final double a4, final double b4) {
|
---|
1229 |
|
---|
1230 | // the code below is split in many additions/subtractions that may
|
---|
1231 | // appear redundant. However, they should NOT be simplified, as they
|
---|
1232 | // do use IEEE754 floating point arithmetic rounding properties.
|
---|
1233 | // The variables naming conventions are that xyzHigh contains the most significant
|
---|
1234 | // bits of xyz and xyzLow contains its least significant bits. So theoretically
|
---|
1235 | // xyz is the sum xyzHigh + xyzLow, but in many cases below, this sum cannot
|
---|
1236 | // be represented in only one double precision number so we preserve two numbers
|
---|
1237 | // to hold it as long as we can, combining the high and low order bits together
|
---|
1238 | // only at the end, after cancellation may have occurred on high order bits
|
---|
1239 |
|
---|
1240 | // split a1 and b1 as one 26 bits number and one 27 bits number
|
---|
1241 | final double a1High = Double.longBitsToDouble(Double.doubleToRawLongBits(a1) & ((-1L) << 27));
|
---|
1242 | final double a1Low = a1 - a1High;
|
---|
1243 | final double b1High = Double.longBitsToDouble(Double.doubleToRawLongBits(b1) & ((-1L) << 27));
|
---|
1244 | final double b1Low = b1 - b1High;
|
---|
1245 |
|
---|
1246 | // accurate multiplication a1 * b1
|
---|
1247 | final double prod1High = a1 * b1;
|
---|
1248 | final double prod1Low = a1Low * b1Low - (((prod1High - a1High * b1High) - a1Low * b1High) - a1High * b1Low);
|
---|
1249 |
|
---|
1250 | // split a2 and b2 as one 26 bits number and one 27 bits number
|
---|
1251 | final double a2High = Double.longBitsToDouble(Double.doubleToRawLongBits(a2) & ((-1L) << 27));
|
---|
1252 | final double a2Low = a2 - a2High;
|
---|
1253 | final double b2High = Double.longBitsToDouble(Double.doubleToRawLongBits(b2) & ((-1L) << 27));
|
---|
1254 | final double b2Low = b2 - b2High;
|
---|
1255 |
|
---|
1256 | // accurate multiplication a2 * b2
|
---|
1257 | final double prod2High = a2 * b2;
|
---|
1258 | final double prod2Low = a2Low * b2Low - (((prod2High - a2High * b2High) - a2Low * b2High) - a2High * b2Low);
|
---|
1259 |
|
---|
1260 | // split a3 and b3 as one 26 bits number and one 27 bits number
|
---|
1261 | final double a3High = Double.longBitsToDouble(Double.doubleToRawLongBits(a3) & ((-1L) << 27));
|
---|
1262 | final double a3Low = a3 - a3High;
|
---|
1263 | final double b3High = Double.longBitsToDouble(Double.doubleToRawLongBits(b3) & ((-1L) << 27));
|
---|
1264 | final double b3Low = b3 - b3High;
|
---|
1265 |
|
---|
1266 | // accurate multiplication a3 * b3
|
---|
1267 | final double prod3High = a3 * b3;
|
---|
1268 | final double prod3Low = a3Low * b3Low - (((prod3High - a3High * b3High) - a3Low * b3High) - a3High * b3Low);
|
---|
1269 |
|
---|
1270 | // split a4 and b4 as one 26 bits number and one 27 bits number
|
---|
1271 | final double a4High = Double.longBitsToDouble(Double.doubleToRawLongBits(a4) & ((-1L) << 27));
|
---|
1272 | final double a4Low = a4 - a4High;
|
---|
1273 | final double b4High = Double.longBitsToDouble(Double.doubleToRawLongBits(b4) & ((-1L) << 27));
|
---|
1274 | final double b4Low = b4 - b4High;
|
---|
1275 |
|
---|
1276 | // accurate multiplication a4 * b4
|
---|
1277 | final double prod4High = a4 * b4;
|
---|
1278 | final double prod4Low = a4Low * b4Low - (((prod4High - a4High * b4High) - a4Low * b4High) - a4High * b4Low);
|
---|
1279 |
|
---|
1280 | // accurate addition a1 * b1 + a2 * b2
|
---|
1281 | final double s12High = prod1High + prod2High;
|
---|
1282 | final double s12Prime = s12High - prod2High;
|
---|
1283 | final double s12Low = (prod2High - (s12High - s12Prime)) + (prod1High - s12Prime);
|
---|
1284 |
|
---|
1285 | // accurate addition a1 * b1 + a2 * b2 + a3 * b3
|
---|
1286 | final double s123High = s12High + prod3High;
|
---|
1287 | final double s123Prime = s123High - prod3High;
|
---|
1288 | final double s123Low = (prod3High - (s123High - s123Prime)) + (s12High - s123Prime);
|
---|
1289 |
|
---|
1290 | // accurate addition a1 * b1 + a2 * b2 + a3 * b3 + a4 * b4
|
---|
1291 | final double s1234High = s123High + prod4High;
|
---|
1292 | final double s1234Prime = s1234High - prod4High;
|
---|
1293 | final double s1234Low = (prod4High - (s1234High - s1234Prime)) + (s123High - s1234Prime);
|
---|
1294 |
|
---|
1295 | // final rounding, s1234 may have suffered many cancellations, we try
|
---|
1296 | // to recover some bits from the extra words we have saved up to now
|
---|
1297 | double result = s1234High + (prod1Low + prod2Low + prod3Low + prod4Low + s12Low + s123Low + s1234Low);
|
---|
1298 |
|
---|
1299 | if (Double.isNaN(result)) {
|
---|
1300 | // either we have split infinite numbers or some coefficients were NaNs,
|
---|
1301 | // just rely on the naive implementation and let IEEE754 handle this
|
---|
1302 | result = a1 * b1 + a2 * b2 + a3 * b3 + a4 * b4;
|
---|
1303 | }
|
---|
1304 |
|
---|
1305 | return result;
|
---|
1306 | }
|
---|
1307 |
|
---|
1308 | /**
|
---|
1309 | * Returns true iff both arguments are null or have same dimensions and all
|
---|
1310 | * their elements are equal as defined by
|
---|
1311 | * {@link Precision#equals(float,float)}.
|
---|
1312 | *
|
---|
1313 | * @param x first array
|
---|
1314 | * @param y second array
|
---|
1315 | * @return true if the values are both null or have same dimension
|
---|
1316 | * and equal elements.
|
---|
1317 | */
|
---|
1318 | public static boolean equals(float[] x, float[] y) {
|
---|
1319 | if ((x == null) || (y == null)) {
|
---|
1320 | return !((x == null) ^ (y == null));
|
---|
1321 | }
|
---|
1322 | if (x.length != y.length) {
|
---|
1323 | return false;
|
---|
1324 | }
|
---|
1325 | for (int i = 0; i < x.length; ++i) {
|
---|
1326 | if (!Precision.equals(x[i], y[i])) {
|
---|
1327 | return false;
|
---|
1328 | }
|
---|
1329 | }
|
---|
1330 | return true;
|
---|
1331 | }
|
---|
1332 |
|
---|
1333 | /**
|
---|
1334 | * Returns true iff both arguments are null or have same dimensions and all
|
---|
1335 | * their elements are equal as defined by
|
---|
1336 | * {@link Precision#equalsIncludingNaN(double,double) this method}.
|
---|
1337 | *
|
---|
1338 | * @param x first array
|
---|
1339 | * @param y second array
|
---|
1340 | * @return true if the values are both null or have same dimension and
|
---|
1341 | * equal elements
|
---|
1342 | * @since 2.2
|
---|
1343 | */
|
---|
1344 | public static boolean equalsIncludingNaN(float[] x, float[] y) {
|
---|
1345 | if ((x == null) || (y == null)) {
|
---|
1346 | return !((x == null) ^ (y == null));
|
---|
1347 | }
|
---|
1348 | if (x.length != y.length) {
|
---|
1349 | return false;
|
---|
1350 | }
|
---|
1351 | for (int i = 0; i < x.length; ++i) {
|
---|
1352 | if (!Precision.equalsIncludingNaN(x[i], y[i])) {
|
---|
1353 | return false;
|
---|
1354 | }
|
---|
1355 | }
|
---|
1356 | return true;
|
---|
1357 | }
|
---|
1358 |
|
---|
1359 | /**
|
---|
1360 | * Returns {@code true} iff both arguments are {@code null} or have same
|
---|
1361 | * dimensions and all their elements are equal as defined by
|
---|
1362 | * {@link Precision#equals(double,double)}.
|
---|
1363 | *
|
---|
1364 | * @param x First array.
|
---|
1365 | * @param y Second array.
|
---|
1366 | * @return {@code true} if the values are both {@code null} or have same
|
---|
1367 | * dimension and equal elements.
|
---|
1368 | */
|
---|
1369 | public static boolean equals(double[] x, double[] y) {
|
---|
1370 | if ((x == null) || (y == null)) {
|
---|
1371 | return !((x == null) ^ (y == null));
|
---|
1372 | }
|
---|
1373 | if (x.length != y.length) {
|
---|
1374 | return false;
|
---|
1375 | }
|
---|
1376 | for (int i = 0; i < x.length; ++i) {
|
---|
1377 | if (!Precision.equals(x[i], y[i])) {
|
---|
1378 | return false;
|
---|
1379 | }
|
---|
1380 | }
|
---|
1381 | return true;
|
---|
1382 | }
|
---|
1383 |
|
---|
1384 | /**
|
---|
1385 | * Returns {@code true} iff both arguments are {@code null} or have same
|
---|
1386 | * dimensions and all their elements are equal as defined by
|
---|
1387 | * {@link Precision#equalsIncludingNaN(double,double) this method}.
|
---|
1388 | *
|
---|
1389 | * @param x First array.
|
---|
1390 | * @param y Second array.
|
---|
1391 | * @return {@code true} if the values are both {@code null} or have same
|
---|
1392 | * dimension and equal elements.
|
---|
1393 | * @since 2.2
|
---|
1394 | */
|
---|
1395 | public static boolean equalsIncludingNaN(double[] x, double[] y) {
|
---|
1396 | if ((x == null) || (y == null)) {
|
---|
1397 | return !((x == null) ^ (y == null));
|
---|
1398 | }
|
---|
1399 | if (x.length != y.length) {
|
---|
1400 | return false;
|
---|
1401 | }
|
---|
1402 | for (int i = 0; i < x.length; ++i) {
|
---|
1403 | if (!Precision.equalsIncludingNaN(x[i], y[i])) {
|
---|
1404 | return false;
|
---|
1405 | }
|
---|
1406 | }
|
---|
1407 | return true;
|
---|
1408 | }
|
---|
1409 |
|
---|
1410 | /**
|
---|
1411 | * Normalizes an array to make it sum to a specified value.
|
---|
1412 | * Returns the result of the transformation
|
---|
1413 | * <pre>
|
---|
1414 | * x |-> x * normalizedSum / sum
|
---|
1415 | * </pre>
|
---|
1416 | * applied to each non-NaN element x of the input array, where sum is the
|
---|
1417 | * sum of the non-NaN entries in the input array.
|
---|
1418 | * <p>
|
---|
1419 | * Throws IllegalArgumentException if {@code normalizedSum} is infinite
|
---|
1420 | * or NaN and ArithmeticException if the input array contains any infinite elements
|
---|
1421 | * or sums to 0.
|
---|
1422 | * <p>
|
---|
1423 | * Ignores (i.e., copies unchanged to the output array) NaNs in the input array.
|
---|
1424 | *
|
---|
1425 | * @param values Input array to be normalized
|
---|
1426 | * @param normalizedSum Target sum for the normalized array
|
---|
1427 | * @return the normalized array.
|
---|
1428 | * @throws MathArithmeticException if the input array contains infinite
|
---|
1429 | * elements or sums to zero.
|
---|
1430 | * @throws MathIllegalArgumentException if the target sum is infinite or {@code NaN}.
|
---|
1431 | * @since 2.1
|
---|
1432 | */
|
---|
1433 | public static double[] normalizeArray(double[] values, double normalizedSum)
|
---|
1434 | throws MathIllegalArgumentException, MathArithmeticException {
|
---|
1435 | if (Double.isInfinite(normalizedSum)) {
|
---|
1436 | throw new MathIllegalArgumentException(LocalizedFormats.NORMALIZE_INFINITE);
|
---|
1437 | }
|
---|
1438 | if (Double.isNaN(normalizedSum)) {
|
---|
1439 | throw new MathIllegalArgumentException(LocalizedFormats.NORMALIZE_NAN);
|
---|
1440 | }
|
---|
1441 | double sum = 0d;
|
---|
1442 | final int len = values.length;
|
---|
1443 | double[] out = new double[len];
|
---|
1444 | for (int i = 0; i < len; i++) {
|
---|
1445 | if (Double.isInfinite(values[i])) {
|
---|
1446 | throw new MathIllegalArgumentException(LocalizedFormats.INFINITE_ARRAY_ELEMENT, values[i], i);
|
---|
1447 | }
|
---|
1448 | if (!Double.isNaN(values[i])) {
|
---|
1449 | sum += values[i];
|
---|
1450 | }
|
---|
1451 | }
|
---|
1452 | if (sum == 0) {
|
---|
1453 | throw new MathArithmeticException(LocalizedFormats.ARRAY_SUMS_TO_ZERO);
|
---|
1454 | }
|
---|
1455 | for (int i = 0; i < len; i++) {
|
---|
1456 | if (Double.isNaN(values[i])) {
|
---|
1457 | out[i] = Double.NaN;
|
---|
1458 | } else {
|
---|
1459 | out[i] = values[i] * normalizedSum / sum;
|
---|
1460 | }
|
---|
1461 | }
|
---|
1462 | return out;
|
---|
1463 | }
|
---|
1464 |
|
---|
1465 | /** Build an array of elements.
|
---|
1466 | * <p>
|
---|
1467 | * Arrays are filled with field.getZero()
|
---|
1468 | *
|
---|
1469 | * @param <T> the type of the field elements
|
---|
1470 | * @param field field to which array elements belong
|
---|
1471 | * @param length of the array
|
---|
1472 | * @return a new array
|
---|
1473 | * @since 3.2
|
---|
1474 | */
|
---|
1475 | public static <T> T[] buildArray(final Field<T> field, final int length) {
|
---|
1476 | @SuppressWarnings("unchecked") // OK because field must be correct class
|
---|
1477 | T[] array = (T[]) Array.newInstance(field.getRuntimeClass(), length);
|
---|
1478 | Arrays.fill(array, field.getZero());
|
---|
1479 | return array;
|
---|
1480 | }
|
---|
1481 |
|
---|
1482 | /** Build a double dimension array of elements.
|
---|
1483 | * <p>
|
---|
1484 | * Arrays are filled with field.getZero()
|
---|
1485 | *
|
---|
1486 | * @param <T> the type of the field elements
|
---|
1487 | * @param field field to which array elements belong
|
---|
1488 | * @param rows number of rows in the array
|
---|
1489 | * @param columns number of columns (may be negative to build partial
|
---|
1490 | * arrays in the same way <code>new Field[rows][]</code> works)
|
---|
1491 | * @return a new array
|
---|
1492 | * @since 3.2
|
---|
1493 | */
|
---|
1494 | @SuppressWarnings("unchecked")
|
---|
1495 | public static <T> T[][] buildArray(final Field<T> field, final int rows, final int columns) {
|
---|
1496 | final T[][] array;
|
---|
1497 | if (columns < 0) {
|
---|
1498 | T[] dummyRow = buildArray(field, 0);
|
---|
1499 | array = (T[][]) Array.newInstance(dummyRow.getClass(), rows);
|
---|
1500 | } else {
|
---|
1501 | array = (T[][]) Array.newInstance(field.getRuntimeClass(),
|
---|
1502 | new int[] {
|
---|
1503 | rows, columns
|
---|
1504 | });
|
---|
1505 | for (int i = 0; i < rows; ++i) {
|
---|
1506 | Arrays.fill(array[i], field.getZero());
|
---|
1507 | }
|
---|
1508 | }
|
---|
1509 | return array;
|
---|
1510 | }
|
---|
1511 |
|
---|
1512 | /**
|
---|
1513 | * Calculates the <a href="http://en.wikipedia.org/wiki/Convolution">
|
---|
1514 | * convolution</a> between two sequences.
|
---|
1515 | * <p>
|
---|
1516 | * The solution is obtained via straightforward computation of the
|
---|
1517 | * convolution sum (and not via FFT). Whenever the computation needs
|
---|
1518 | * an element that would be located at an index outside the input arrays,
|
---|
1519 | * the value is assumed to be zero.
|
---|
1520 | *
|
---|
1521 | * @param x First sequence.
|
---|
1522 | * Typically, this sequence will represent an input signal to a system.
|
---|
1523 | * @param h Second sequence.
|
---|
1524 | * Typically, this sequence will represent the impulse response of the system.
|
---|
1525 | * @return the convolution of {@code x} and {@code h}.
|
---|
1526 | * This array's length will be {@code x.length + h.length - 1}.
|
---|
1527 | * @throws NullArgumentException if either {@code x} or {@code h} is {@code null}.
|
---|
1528 | * @throws NoDataException if either {@code x} or {@code h} is empty.
|
---|
1529 | *
|
---|
1530 | * @since 3.3
|
---|
1531 | */
|
---|
1532 | public static double[] convolve(double[] x, double[] h)
|
---|
1533 | throws NullArgumentException,
|
---|
1534 | NoDataException {
|
---|
1535 | MathUtils.checkNotNull(x);
|
---|
1536 | MathUtils.checkNotNull(h);
|
---|
1537 |
|
---|
1538 | final int xLen = x.length;
|
---|
1539 | final int hLen = h.length;
|
---|
1540 |
|
---|
1541 | if (xLen == 0 || hLen == 0) {
|
---|
1542 | throw new NoDataException();
|
---|
1543 | }
|
---|
1544 |
|
---|
1545 | // initialize the output array
|
---|
1546 | final int totalLength = xLen + hLen - 1;
|
---|
1547 | final double[] y = new double[totalLength];
|
---|
1548 |
|
---|
1549 | // straightforward implementation of the convolution sum
|
---|
1550 | for (int n = 0; n < totalLength; n++) {
|
---|
1551 | double yn = 0;
|
---|
1552 | int k = FastMath.max(0, n + 1 - xLen);
|
---|
1553 | int j = n - k;
|
---|
1554 | while (k < hLen && j >= 0) {
|
---|
1555 | yn += x[j--] * h[k++];
|
---|
1556 | }
|
---|
1557 | y[n] = yn;
|
---|
1558 | }
|
---|
1559 |
|
---|
1560 | return y;
|
---|
1561 | }
|
---|
1562 |
|
---|
1563 | /**
|
---|
1564 | * Specification for indicating that some operation applies
|
---|
1565 | * before or after a given index.
|
---|
1566 | */
|
---|
1567 | public enum Position {
|
---|
1568 | /** Designates the beginning of the array (near index 0). */
|
---|
1569 | HEAD,
|
---|
1570 | /** Designates the end of the array. */
|
---|
1571 | TAIL
|
---|
1572 | }
|
---|
1573 |
|
---|
1574 | /**
|
---|
1575 | * Shuffle the entries of the given array.
|
---|
1576 | * The {@code start} and {@code pos} parameters select which portion
|
---|
1577 | * of the array is randomized and which is left untouched.
|
---|
1578 | *
|
---|
1579 | * @see #shuffle(int[],int,Position,RandomGenerator)
|
---|
1580 | *
|
---|
1581 | * @param list Array whose entries will be shuffled (in-place).
|
---|
1582 | * @param start Index at which shuffling begins.
|
---|
1583 | * @param pos Shuffling is performed for index positions between
|
---|
1584 | * {@code start} and either the end (if {@link Position#TAIL})
|
---|
1585 | * or the beginning (if {@link Position#HEAD}) of the array.
|
---|
1586 | */
|
---|
1587 | public static void shuffle(int[] list,
|
---|
1588 | int start,
|
---|
1589 | Position pos) {
|
---|
1590 | shuffle(list, start, pos, new Well19937c());
|
---|
1591 | }
|
---|
1592 |
|
---|
1593 | /**
|
---|
1594 | * Shuffle the entries of the given array, using the
|
---|
1595 | * <a href="http://en.wikipedia.org/wiki/Fisher–Yates_shuffle#The_modern_algorithm">
|
---|
1596 | * Fisher–Yates</a> algorithm.
|
---|
1597 | * The {@code start} and {@code pos} parameters select which portion
|
---|
1598 | * of the array is randomized and which is left untouched.
|
---|
1599 | *
|
---|
1600 | * @param list Array whose entries will be shuffled (in-place).
|
---|
1601 | * @param start Index at which shuffling begins.
|
---|
1602 | * @param pos Shuffling is performed for index positions between
|
---|
1603 | * {@code start} and either the end (if {@link Position#TAIL})
|
---|
1604 | * or the beginning (if {@link Position#HEAD}) of the array.
|
---|
1605 | * @param rng Random number generator.
|
---|
1606 | */
|
---|
1607 | public static void shuffle(int[] list,
|
---|
1608 | int start,
|
---|
1609 | Position pos,
|
---|
1610 | RandomGenerator rng) {
|
---|
1611 | switch (pos) {
|
---|
1612 | case TAIL: {
|
---|
1613 | for (int i = list.length - 1; i >= start; i--) {
|
---|
1614 | final int target;
|
---|
1615 | if (i == start) {
|
---|
1616 | target = start;
|
---|
1617 | } else {
|
---|
1618 | // NumberIsTooLargeException cannot occur.
|
---|
1619 | target = new UniformIntegerDistribution(rng, start, i).sample();
|
---|
1620 | }
|
---|
1621 | final int temp = list[target];
|
---|
1622 | list[target] = list[i];
|
---|
1623 | list[i] = temp;
|
---|
1624 | }
|
---|
1625 | }
|
---|
1626 | break;
|
---|
1627 | case HEAD: {
|
---|
1628 | for (int i = 0; i <= start; i++) {
|
---|
1629 | final int target;
|
---|
1630 | if (i == start) {
|
---|
1631 | target = start;
|
---|
1632 | } else {
|
---|
1633 | // NumberIsTooLargeException cannot occur.
|
---|
1634 | target = new UniformIntegerDistribution(rng, i, start).sample();
|
---|
1635 | }
|
---|
1636 | final int temp = list[target];
|
---|
1637 | list[target] = list[i];
|
---|
1638 | list[i] = temp;
|
---|
1639 | }
|
---|
1640 | }
|
---|
1641 | break;
|
---|
1642 | default:
|
---|
1643 | throw new MathInternalError(); // Should never happen.
|
---|
1644 | }
|
---|
1645 | }
|
---|
1646 |
|
---|
1647 | /**
|
---|
1648 | * Shuffle the entries of the given array.
|
---|
1649 | *
|
---|
1650 | * @see #shuffle(int[],int,Position,RandomGenerator)
|
---|
1651 | *
|
---|
1652 | * @param list Array whose entries will be shuffled (in-place).
|
---|
1653 | * @param rng Random number generator.
|
---|
1654 | */
|
---|
1655 | public static void shuffle(int[] list,
|
---|
1656 | RandomGenerator rng) {
|
---|
1657 | shuffle(list, 0, Position.TAIL, rng);
|
---|
1658 | }
|
---|
1659 |
|
---|
1660 | /**
|
---|
1661 | * Shuffle the entries of the given array.
|
---|
1662 | *
|
---|
1663 | * @see #shuffle(int[],int,Position,RandomGenerator)
|
---|
1664 | *
|
---|
1665 | * @param list Array whose entries will be shuffled (in-place).
|
---|
1666 | */
|
---|
1667 | public static void shuffle(int[] list) {
|
---|
1668 | shuffle(list, new Well19937c());
|
---|
1669 | }
|
---|
1670 |
|
---|
1671 | /**
|
---|
1672 | * Returns an array representing the natural number {@code n}.
|
---|
1673 | *
|
---|
1674 | * @param n Natural number.
|
---|
1675 | * @return an array whose entries are the numbers 0, 1, ..., {@code n}-1.
|
---|
1676 | * If {@code n == 0}, the returned array is empty.
|
---|
1677 | */
|
---|
1678 | public static int[] natural(int n) {
|
---|
1679 | return sequence(n, 0, 1);
|
---|
1680 | }
|
---|
1681 | /**
|
---|
1682 | * Returns an array of {@code size} integers starting at {@code start},
|
---|
1683 | * skipping {@code stride} numbers.
|
---|
1684 | *
|
---|
1685 | * @param size Natural number.
|
---|
1686 | * @param start Natural number.
|
---|
1687 | * @param stride Natural number.
|
---|
1688 | * @return an array whose entries are the numbers
|
---|
1689 | * {@code start, start + stride, ..., start + (size - 1) * stride}.
|
---|
1690 | * If {@code size == 0}, the returned array is empty.
|
---|
1691 | *
|
---|
1692 | * @since 3.4
|
---|
1693 | */
|
---|
1694 | public static int[] sequence(int size,
|
---|
1695 | int start,
|
---|
1696 | int stride) {
|
---|
1697 | final int[] a = new int[size];
|
---|
1698 | for (int i = 0; i < size; i++) {
|
---|
1699 | a[i] = start + i * stride;
|
---|
1700 | }
|
---|
1701 | return a;
|
---|
1702 | }
|
---|
1703 | /**
|
---|
1704 | * This method is used
|
---|
1705 | * to verify that the input parameters designate a subarray of positive length.
|
---|
1706 | * <p>
|
---|
1707 | * <ul>
|
---|
1708 | * <li>returns <code>true</code> iff the parameters designate a subarray of
|
---|
1709 | * positive length</li>
|
---|
1710 | * <li>throws <code>MathIllegalArgumentException</code> if the array is null or
|
---|
1711 | * or the indices are invalid</li>
|
---|
1712 | * <li>returns <code>false</li> if the array is non-null, but
|
---|
1713 | * <code>length</code> is 0.
|
---|
1714 | * </ul></p>
|
---|
1715 | *
|
---|
1716 | * @param values the input array
|
---|
1717 | * @param begin index of the first array element to include
|
---|
1718 | * @param length the number of elements to include
|
---|
1719 | * @return true if the parameters are valid and designate a subarray of positive length
|
---|
1720 | * @throws MathIllegalArgumentException if the indices are invalid or the array is null
|
---|
1721 | * @since 3.3
|
---|
1722 | */
|
---|
1723 | public static boolean verifyValues(final double[] values, final int begin, final int length)
|
---|
1724 | throws MathIllegalArgumentException {
|
---|
1725 | return verifyValues(values, begin, length, false);
|
---|
1726 | }
|
---|
1727 |
|
---|
1728 | /**
|
---|
1729 | * This method is used
|
---|
1730 | * to verify that the input parameters designate a subarray of positive length.
|
---|
1731 | * <p>
|
---|
1732 | * <ul>
|
---|
1733 | * <li>returns <code>true</code> iff the parameters designate a subarray of
|
---|
1734 | * non-negative length</li>
|
---|
1735 | * <li>throws <code>IllegalArgumentException</code> if the array is null or
|
---|
1736 | * or the indices are invalid</li>
|
---|
1737 | * <li>returns <code>false</li> if the array is non-null, but
|
---|
1738 | * <code>length</code> is 0 unless <code>allowEmpty</code> is <code>true</code>
|
---|
1739 | * </ul></p>
|
---|
1740 | *
|
---|
1741 | * @param values the input array
|
---|
1742 | * @param begin index of the first array element to include
|
---|
1743 | * @param length the number of elements to include
|
---|
1744 | * @param allowEmpty if <code>true</code> then zero length arrays are allowed
|
---|
1745 | * @return true if the parameters are valid
|
---|
1746 | * @throws MathIllegalArgumentException if the indices are invalid or the array is null
|
---|
1747 | * @since 3.3
|
---|
1748 | */
|
---|
1749 | public static boolean verifyValues(final double[] values, final int begin,
|
---|
1750 | final int length, final boolean allowEmpty) throws MathIllegalArgumentException {
|
---|
1751 |
|
---|
1752 | if (values == null) {
|
---|
1753 | throw new NullArgumentException(LocalizedFormats.INPUT_ARRAY);
|
---|
1754 | }
|
---|
1755 |
|
---|
1756 | if (begin < 0) {
|
---|
1757 | throw new NotPositiveException(LocalizedFormats.START_POSITION, Integer.valueOf(begin));
|
---|
1758 | }
|
---|
1759 |
|
---|
1760 | if (length < 0) {
|
---|
1761 | throw new NotPositiveException(LocalizedFormats.LENGTH, Integer.valueOf(length));
|
---|
1762 | }
|
---|
1763 |
|
---|
1764 | if (begin + length > values.length) {
|
---|
1765 | throw new NumberIsTooLargeException(LocalizedFormats.SUBARRAY_ENDS_AFTER_ARRAY_END,
|
---|
1766 | Integer.valueOf(begin + length), Integer.valueOf(values.length), true);
|
---|
1767 | }
|
---|
1768 |
|
---|
1769 | if (length == 0 && !allowEmpty) {
|
---|
1770 | return false;
|
---|
1771 | }
|
---|
1772 |
|
---|
1773 | return true;
|
---|
1774 |
|
---|
1775 | }
|
---|
1776 |
|
---|
1777 | /**
|
---|
1778 | * This method is used
|
---|
1779 | * to verify that the begin and length parameters designate a subarray of positive length
|
---|
1780 | * and the weights are all non-negative, non-NaN, finite, and not all zero.
|
---|
1781 | * <p>
|
---|
1782 | * <ul>
|
---|
1783 | * <li>returns <code>true</code> iff the parameters designate a subarray of
|
---|
1784 | * positive length and the weights array contains legitimate values.</li>
|
---|
1785 | * <li>throws <code>IllegalArgumentException</code> if any of the following are true:
|
---|
1786 | * <ul><li>the values array is null</li>
|
---|
1787 | * <li>the weights array is null</li>
|
---|
1788 | * <li>the weights array does not have the same length as the values array</li>
|
---|
1789 | * <li>the weights array contains one or more infinite values</li>
|
---|
1790 | * <li>the weights array contains one or more NaN values</li>
|
---|
1791 | * <li>the weights array contains negative values</li>
|
---|
1792 | * <li>the start and length arguments do not determine a valid array</li></ul>
|
---|
1793 | * </li>
|
---|
1794 | * <li>returns <code>false</li> if the array is non-null, but
|
---|
1795 | * <code>length</code> is 0.
|
---|
1796 | * </ul></p>
|
---|
1797 | *
|
---|
1798 | * @param values the input array
|
---|
1799 | * @param weights the weights array
|
---|
1800 | * @param begin index of the first array element to include
|
---|
1801 | * @param length the number of elements to include
|
---|
1802 | * @return true if the parameters are valid and designate a subarray of positive length
|
---|
1803 | * @throws MathIllegalArgumentException if the indices are invalid or the array is null
|
---|
1804 | * @since 3.3
|
---|
1805 | */
|
---|
1806 | public static boolean verifyValues(
|
---|
1807 | final double[] values,
|
---|
1808 | final double[] weights,
|
---|
1809 | final int begin,
|
---|
1810 | final int length) throws MathIllegalArgumentException {
|
---|
1811 | return verifyValues(values, weights, begin, length, false);
|
---|
1812 | }
|
---|
1813 |
|
---|
1814 | /**
|
---|
1815 | * This method is used
|
---|
1816 | * to verify that the begin and length parameters designate a subarray of positive length
|
---|
1817 | * and the weights are all non-negative, non-NaN, finite, and not all zero.
|
---|
1818 | * <p>
|
---|
1819 | * <ul>
|
---|
1820 | * <li>returns <code>true</code> iff the parameters designate a subarray of
|
---|
1821 | * non-negative length and the weights array contains legitimate values.</li>
|
---|
1822 | * <li>throws <code>MathIllegalArgumentException</code> if any of the following are true:
|
---|
1823 | * <ul><li>the values array is null</li>
|
---|
1824 | * <li>the weights array is null</li>
|
---|
1825 | * <li>the weights array does not have the same length as the values array</li>
|
---|
1826 | * <li>the weights array contains one or more infinite values</li>
|
---|
1827 | * <li>the weights array contains one or more NaN values</li>
|
---|
1828 | * <li>the weights array contains negative values</li>
|
---|
1829 | * <li>the start and length arguments do not determine a valid array</li></ul>
|
---|
1830 | * </li>
|
---|
1831 | * <li>returns <code>false</li> if the array is non-null, but
|
---|
1832 | * <code>length</code> is 0 unless <code>allowEmpty</code> is <code>true</code>.
|
---|
1833 | * </ul></p>
|
---|
1834 | *
|
---|
1835 | * @param values the input array.
|
---|
1836 | * @param weights the weights array.
|
---|
1837 | * @param begin index of the first array element to include.
|
---|
1838 | * @param length the number of elements to include.
|
---|
1839 | * @param allowEmpty if {@code true} than allow zero length arrays to pass.
|
---|
1840 | * @return {@code true} if the parameters are valid.
|
---|
1841 | * @throws NullArgumentException if either of the arrays are null
|
---|
1842 | * @throws MathIllegalArgumentException if the array indices are not valid,
|
---|
1843 | * the weights array contains NaN, infinite or negative elements, or there
|
---|
1844 | * are no positive weights.
|
---|
1845 | * @since 3.3
|
---|
1846 | */
|
---|
1847 | public static boolean verifyValues(final double[] values, final double[] weights,
|
---|
1848 | final int begin, final int length, final boolean allowEmpty) throws MathIllegalArgumentException {
|
---|
1849 |
|
---|
1850 | if (weights == null || values == null) {
|
---|
1851 | throw new NullArgumentException(LocalizedFormats.INPUT_ARRAY);
|
---|
1852 | }
|
---|
1853 |
|
---|
1854 | checkEqualLength(weights, values);
|
---|
1855 |
|
---|
1856 | boolean containsPositiveWeight = false;
|
---|
1857 | for (int i = begin; i < begin + length; i++) {
|
---|
1858 | final double weight = weights[i];
|
---|
1859 | if (Double.isNaN(weight)) {
|
---|
1860 | throw new MathIllegalArgumentException(LocalizedFormats.NAN_ELEMENT_AT_INDEX, Integer.valueOf(i));
|
---|
1861 | }
|
---|
1862 | if (Double.isInfinite(weight)) {
|
---|
1863 | throw new MathIllegalArgumentException(LocalizedFormats.INFINITE_ARRAY_ELEMENT, Double.valueOf(weight), Integer.valueOf(i));
|
---|
1864 | }
|
---|
1865 | if (weight < 0) {
|
---|
1866 | throw new MathIllegalArgumentException(LocalizedFormats.NEGATIVE_ELEMENT_AT_INDEX, Integer.valueOf(i), Double.valueOf(weight));
|
---|
1867 | }
|
---|
1868 | if (!containsPositiveWeight && weight > 0.0) {
|
---|
1869 | containsPositiveWeight = true;
|
---|
1870 | }
|
---|
1871 | }
|
---|
1872 |
|
---|
1873 | if (!containsPositiveWeight) {
|
---|
1874 | throw new MathIllegalArgumentException(LocalizedFormats.WEIGHT_AT_LEAST_ONE_NON_ZERO);
|
---|
1875 | }
|
---|
1876 |
|
---|
1877 | return verifyValues(values, begin, length, allowEmpty);
|
---|
1878 | }
|
---|
1879 |
|
---|
1880 | /**
|
---|
1881 | * Concatenates a sequence of arrays. The return array consists of the
|
---|
1882 | * entries of the input arrays concatenated in the order they appear in
|
---|
1883 | * the argument list. Null arrays cause NullPointerExceptions; zero
|
---|
1884 | * length arrays are allowed (contributing nothing to the output array).
|
---|
1885 | *
|
---|
1886 | * @param x list of double[] arrays to concatenate
|
---|
1887 | * @return a new array consisting of the entries of the argument arrays
|
---|
1888 | * @throws NullPointerException if any of the arrays are null
|
---|
1889 | * @since 3.6
|
---|
1890 | */
|
---|
1891 | public static double[] concatenate(double[] ...x) {
|
---|
1892 | int combinedLength = 0;
|
---|
1893 | for (double[] a : x) {
|
---|
1894 | combinedLength += a.length;
|
---|
1895 | }
|
---|
1896 | int offset = 0;
|
---|
1897 | int curLength = 0;
|
---|
1898 | final double[] combined = new double[combinedLength];
|
---|
1899 | for (int i = 0; i < x.length; i++) {
|
---|
1900 | curLength = x[i].length;
|
---|
1901 | System.arraycopy(x[i], 0, combined, offset, curLength);
|
---|
1902 | offset += curLength;
|
---|
1903 | }
|
---|
1904 | return combined;
|
---|
1905 | }
|
---|
1906 |
|
---|
1907 | /**
|
---|
1908 | * Returns an array consisting of the unique values in {@code data}.
|
---|
1909 | * The return array is sorted in descending order. Empty arrays
|
---|
1910 | * are allowed, but null arrays result in NullPointerException.
|
---|
1911 | * Infinities are allowed. NaN values are allowed with maximum
|
---|
1912 | * sort order - i.e., if there are NaN values in {@code data},
|
---|
1913 | * {@code Double.NaN} will be the first element of the output array,
|
---|
1914 | * even if the array also contains {@code Double.POSITIVE_INFINITY}.
|
---|
1915 | *
|
---|
1916 | * @param data array to scan
|
---|
1917 | * @return descending list of values included in the input array
|
---|
1918 | * @throws NullPointerException if data is null
|
---|
1919 | * @since 3.6
|
---|
1920 | */
|
---|
1921 | public static double[] unique(double[] data) {
|
---|
1922 | TreeSet<Double> values = new TreeSet<Double>();
|
---|
1923 | for (int i = 0; i < data.length; i++) {
|
---|
1924 | values.add(data[i]);
|
---|
1925 | }
|
---|
1926 | final int count = values.size();
|
---|
1927 | final double[] out = new double[count];
|
---|
1928 | Iterator<Double> iterator = values.iterator();
|
---|
1929 | int i = 0;
|
---|
1930 | while (iterator.hasNext()) {
|
---|
1931 | out[count - ++i] = iterator.next();
|
---|
1932 | }
|
---|
1933 | return out;
|
---|
1934 | }
|
---|
1935 | }
|
---|