[2] | 1 | #region License Information
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| 2 | /* HeuristicLab
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[12012] | 3 | * Copyright (C) 2002-2015 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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[2] | 4 | *
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| 5 | * This file is part of HeuristicLab.
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| 6 | *
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| 7 | * HeuristicLab is free software: you can redistribute it and/or modify
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| 8 | * it under the terms of the GNU General Public License as published by
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| 9 | * the Free Software Foundation, either version 3 of the License, or
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| 10 | * (at your option) any later version.
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| 11 | *
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| 12 | * HeuristicLab is distributed in the hope that it will be useful,
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| 13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 15 | * GNU General Public License for more details.
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| 16 | *
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| 17 | * You should have received a copy of the GNU General Public License
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| 18 | * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
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| 19 | */
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| 20 | #endregion
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| 21 |
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| 22 | using System;
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| 23 | using System.Collections.Generic;
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[14029] | 24 | using System.Diagnostics.Contracts;
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[3452] | 25 | using System.Linq;
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[2] | 26 |
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[3462] | 27 | namespace HeuristicLab.Common {
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| 28 | public static class EnumerableStatisticExtensions {
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[2] | 29 | /// <summary>
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[3452] | 30 | /// Calculates the median element of the enumeration.
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[2] | 31 | /// </summary>
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| 32 | /// <param name="values"></param>
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| 33 | /// <returns></returns>
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[3452] | 34 | public static double Median(this IEnumerable<double> values) {
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[14029] | 35 | // See unit tests for comparison with naive implementation
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| 36 | return Quantile(values, 0.5);
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| 37 | }
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| 38 |
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| 39 | /// <summary>
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| 40 | /// Calculates the alpha-quantile element of the enumeration.
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| 41 | /// </summary>
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| 42 | /// <param name="values"></param>
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| 43 | /// <returns></returns>
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| 44 | public static double Quantile(this IEnumerable<double> values, double alpha) {
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| 45 | // See unit tests for comparison with naive implementation
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[5809] | 46 | double[] valuesArr = values.ToArray();
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| 47 | int n = valuesArr.Length;
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[3452] | 48 | if (n == 0) throw new InvalidOperationException("Enumeration contains no elements.");
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[2] | 49 |
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[14029] | 50 | // "When N is even, statistics books define the median as the arithmetic mean of the elements k = N/2
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| 51 | // and k = N/2 + 1 (that is, N/2 from the bottom and N/2 from the top).
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| 52 | // If you accept such pedantry, you must perform two separate selections to find these elements."
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[2] | 53 |
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[14029] | 54 | // return the element at Math.Ceiling (if n*alpha is fractional) or the average of two elements if n*alpha is integer.
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| 55 | var pos = n * alpha;
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| 56 | Contract.Assert(pos >= 0);
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| 57 | Contract.Assert(pos < n);
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| 58 | bool isInteger = Math.Round(pos).IsAlmost(pos);
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| 59 | if (isInteger) {
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| 60 | return 0.5 * (Select((int)pos - 1, valuesArr) + Select((int)pos, valuesArr));
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[2] | 61 | } else {
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[14029] | 62 | return Select((int)Math.Ceiling(pos) - 1, valuesArr);
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[2] | 63 | }
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| 64 | }
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| 65 |
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[14029] | 66 | // Numerical Recipes in C++, §8.5 Selecting the Mth Largest, O(n)
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| 67 | // Given k in [0..n-1] returns an array value from array arr[0..n-1] such that k array values are
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| 68 | // less than or equal to the one returned. The input array will be rearranged to have this value in
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| 69 | // location arr[k], with all smaller elements moved to arr[0..k-1] (in arbitrary order) and all
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| 70 | // larger elements in arr[k+1..n-1] (also in arbitrary order).
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| 71 | //
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| 72 | // Could be changed to Select<T> where T is IComparable but in this case is significantly slower for double values
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| 73 | private static double Select(int k, double[] arr) {
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| 74 | Contract.Assert(arr.GetLowerBound(0) == 0);
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| 75 | Contract.Assert(k >= 0 && k < arr.Length);
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| 76 | int i, ir, j, l, mid, n = arr.Length;
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| 77 | double a;
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| 78 | l = 0;
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| 79 | ir = n - 1;
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| 80 | for (; ; ) {
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| 81 | if (ir <= l + 1) {
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| 82 | // Active partition contains 1 or 2 elements.
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| 83 | if (ir == l + 1 && arr[ir] < arr[l]) {
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| 84 | // if (ir == l + 1 && arr[ir].CompareTo(arr[l]) < 0) {
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| 85 | // Case of 2 elements.
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| 86 | // SWAP(arr[l], arr[ir]);
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| 87 | double temp = arr[l];
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| 88 | arr[l] = arr[ir];
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| 89 | arr[ir] = temp;
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| 90 | }
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| 91 | return arr[k];
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| 92 | } else {
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| 93 | mid = (l + ir) >> 1; // Choose median of left, center, and right elements
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| 94 | {
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| 95 | // SWAP(arr[mid], arr[l + 1]); // as partitioning element a. Also
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| 96 | double temp = arr[mid];
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| 97 | arr[mid] = arr[l + 1];
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| 98 | arr[l + 1] = temp;
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| 99 | }
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| 100 |
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| 101 | if (arr[l] > arr[ir]) {
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| 102 | // if (arr[l].CompareTo(arr[ir]) > 0) { // rearrange so that arr[l] arr[ir] <= arr[l+1],
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| 103 | // SWAP(arr[l], arr[ir]); . arr[ir] >= arr[l+1]
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| 104 | double temp = arr[l];
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| 105 | arr[l] = arr[ir];
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| 106 | arr[ir] = temp;
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| 107 | }
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| 108 |
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| 109 | if (arr[l + 1] > arr[ir]) {
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| 110 | // if (arr[l + 1].CompareTo(arr[ir]) > 0) {
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| 111 | // SWAP(arr[l + 1], arr[ir]);
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| 112 | double temp = arr[l + 1];
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| 113 | arr[l + 1] = arr[ir];
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| 114 | arr[ir] = temp;
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| 115 | }
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| 116 | if (arr[l] > arr[l + 1]) {
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| 117 | //if (arr[l].CompareTo(arr[l + 1]) > 0) {
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| 118 | // SWAP(arr[l], arr[l + 1]);
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| 119 | double temp = arr[l];
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| 120 | arr[l] = arr[l + 1];
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| 121 | arr[l + 1] = temp;
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| 122 |
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| 123 | }
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| 124 | i = l + 1; // Initialize pointers for partitioning.
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| 125 | j = ir;
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| 126 | a = arr[l + 1]; // Partitioning element.
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| 127 | for (; ; ) { // Beginning of innermost loop.
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| 128 | do i++; while (arr[i] < a /* arr[i].CompareTo(a) < 0 */); // Scan up to find element > a.
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| 129 | do j--; while (arr[j] > a /* arr[j].CompareTo(a) > 0 */); // Scan down to find element < a.
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| 130 | if (j < i) break; // Pointers crossed. Partitioning complete.
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| 131 | {
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| 132 | // SWAP(arr[i], arr[j]);
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| 133 | double temp = arr[i];
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| 134 | arr[i] = arr[j];
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| 135 | arr[j] = temp;
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| 136 | }
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| 137 | } // End of innermost loop.
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| 138 | arr[l + 1] = arr[j]; // Insert partitioning element.
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| 139 | arr[j] = a;
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| 140 | if (j >= k) ir = j - 1; // Keep active the partition that contains the
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| 141 | if (j <= k) l = i; // kth element.
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| 142 | }
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| 143 | }
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| 144 | }
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| 145 |
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[8564] | 146 | /// <summary>
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| 147 | /// Calculates the range (max - min) of the enumeration.
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| 148 | /// </summary>
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| 149 | /// <param name="values"></param>
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| 150 | /// <returns></returns>
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| 151 | public static double Range(this IEnumerable<double> values) {
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| 152 | double min = double.PositiveInfinity;
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| 153 | double max = double.NegativeInfinity;
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| 154 | int i = 0;
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| 155 | foreach (var e in values) {
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| 156 | if (min > e) min = e;
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| 157 | if (max < e) max = e;
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| 158 | i++;
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| 159 | }
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[8605] | 160 | if (i < 1) throw new ArgumentException("The enumerable must contain at least two elements", "values");
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[8564] | 161 | return max - min;
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| 162 | }
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[2] | 163 |
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[8564] | 164 |
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[2] | 165 | /// <summary>
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[14029] | 166 | /// Calculates the sample standard deviation of values.
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[2] | 167 | /// </summary>
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| 168 | /// <param name="values"></param>
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| 169 | /// <returns></returns>
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[3452] | 170 | public static double StandardDeviation(this IEnumerable<double> values) {
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[2] | 171 | return Math.Sqrt(Variance(values));
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| 172 | }
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| 173 |
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| 174 | /// <summary>
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[14029] | 175 | /// Calculates the population standard deviation of values.
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[2] | 176 | /// </summary>
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| 177 | /// <param name="values"></param>
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| 178 | /// <returns></returns>
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[14029] | 179 | public static double StandardDeviationPop(this IEnumerable<double> values) {
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| 180 | return Math.Sqrt(VariancePop(values));
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| 181 | }
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| 182 |
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| 183 | /// <summary>
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| 184 | /// Calculates the sample variance of values. (sum (x - x_mean)² / (n-1))
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| 185 | /// </summary>
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| 186 | /// <param name="values"></param>
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| 187 | /// <returns></returns>
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[3452] | 188 | public static double Variance(this IEnumerable<double> values) {
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[14029] | 189 | return Variance(values, true);
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| 190 | }
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| 191 |
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| 192 | /// <summary>
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| 193 | /// Calculates the population variance of values. (sum (x - x_mean)² / n)
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| 194 | /// </summary>
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| 195 | /// <param name="values"></param>
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| 196 | /// <returns></returns>
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| 197 | public static double VariancePop(this IEnumerable<double> values) {
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| 198 | return Variance(values, false);
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| 199 | }
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| 200 |
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| 201 | private static double Variance(IEnumerable<double> values, bool sampleVariance) {
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[3984] | 202 | int m_n = 0;
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| 203 | double m_oldM = 0.0;
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| 204 | double m_newM = 0.0;
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| 205 | double m_oldS = 0.0;
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| 206 | double m_newS = 0.0;
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| 207 | foreach (double x in values) {
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| 208 | m_n++;
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| 209 | if (m_n == 1) {
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| 210 | m_oldM = m_newM = x;
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| 211 | m_oldS = 0.0;
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| 212 | } else {
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| 213 | m_newM = m_oldM + (x - m_oldM) / m_n;
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| 214 | m_newS = m_oldS + (x - m_oldM) * (x - m_newM);
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[2] | 215 |
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[3984] | 216 | // set up for next iteration
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| 217 | m_oldM = m_newM;
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| 218 | m_oldS = m_newS;
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[2] | 219 | }
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| 220 | }
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[4652] | 221 |
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[14029] | 222 | if (m_n == 0) return double.NaN;
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| 223 | if (m_n == 1) return 0.0;
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[4652] | 224 |
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[14029] | 225 | if (sampleVariance) return m_newS / (m_n - 1);
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| 226 | else return m_newS / m_n;
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[4652] | 227 | }
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[5809] | 228 |
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| 229 | public static IEnumerable<double> LimitToRange(this IEnumerable<double> values, double min, double max) {
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[8531] | 230 | if (min > max) throw new ArgumentException(string.Format("Minimum {0} is larger than maximum {1}.", min, max));
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[5809] | 231 | foreach (var x in values) {
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| 232 | if (double.IsNaN(x)) yield return (max + min) / 2.0;
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| 233 | else if (x < min) yield return min;
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| 234 | else if (x > max) yield return max;
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| 235 | else yield return x;
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| 236 | }
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| 237 | }
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[2] | 238 | }
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| 239 | }
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