Features/harmonic mean

SigmaSwiftStatistics/Frequencies.swift

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+//
+//  Frequencies.swift
+//  SigmaSwiftStatistics
+//
+//  Created by Alan James Salmoni on 21/01/2017.
+//  Copyright © 2017 Evgenii Neumerzhitckii. All rights reserved.
+//
+
+import Foundation
+
+public extension Sigma {
+
+  public static func frequencies(values: [Double]) -> ([Double], [Int])? {
+    /*
+     This returns two lists from an array, the first containing the unique values and the second containing how often each value occurs.
+
+     Parameter values:
+     - Array of doubles to be analysed
+
+     Return values:
+     - Two arrays as a tuple:
+     - An array containing all the values that occur within the parameter's array (see uniqueValues)
+     - An array containing how often each value occurs in the parameter's array
+
+     Example:
+     Sigma.frequencies([1,2,3,4,5,4,3,5]) // ([1,2,3,4,5], [1, 1, 2, 2, 2])
+
+     Would this be better returned as a dictionary with each unique value a key and the frequency the value?
+
+     */
+    let count = values.count
+    if count == 0 { return nil }
+    let unique_vals = Sigma.uniqueValues(values: values)!.sorted(by: <)
+    let count_uniques = unique_vals.count
+    var frequencies = [Int](repeating: 0, count: count_uniques)
+    for (idx_uniques, unique_val) in unique_vals.enumerated() {
+      for datum in values {
+        if unique_val == datum {
+          frequencies[idx_uniques] += 1
+        }
+      }
+    }
+    return (unique_vals, frequencies)
+  }
+}

SigmaSwiftStatistics/GeometricMean.swift

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+//
+//  GeometricMean.swift
+//  SigmaSwiftStatistics
+//
+//  Created by Alan James Salmoni on 30/12/2016.
+//  Copyright © 2016 Evgenii Neumerzhitckii. All rights reserved.
+//
+import Foundation
+
+public extension Sigma {
+
+  public static func geometricMean(data: [Double]) -> Double? {
+    let count = data.count
+    if count == 0 {
+      return nil
+    }
+    var data_log: [Double] = []
+    var log_val: Double
+    for item in data {
+      log_val = log(item)
+      data_log.append(log_val)
+    }
+    let return_val = exp(average(data_log)!)
+    return return_val
+  }
+}

SigmaSwiftStatistics/HarmonicMean.swift

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+
+//
+//  HarmonicMean.swift
+//  SigmaSwiftStatistics
+//
+//  Created by Alan James Salmoni on 30/12/2016.
+//  Copyright © 2016 Evgenii Neumerzhitckii. All rights reserved.
+//
+import Foundation
+
+public extension Sigma {
+
+  public static func harmonicMean(data: [Double]) -> Double? {
+    let count = data.count
+    if count == 0 {
+      return nil
+    }
+    var data_inv: [Double] = []
+    var inv_val: Double
+    for item in data {
+      inv_val = 1.0 / item
+      data_inv.append(inv_val)
+    }
+    let m1 = average(data_inv)
+    let hm = 1.0 / m1!
+    return hm
+  }
+}

SigmaSwiftStatistics/Ranks.swift

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+//
+//  Ranks.swift
+//  SigmaSwiftStatistics
+//
+//  Created by Alan James Salmoni on 21/01/2017.
+//  Copyright © 2017 Evgenii Neumerzhitckii. All rights reserved.
+//
+
+import Foundation
+
+public extension Sigma {
+
+  /*
+   this ranks a vector (single dimensional array) of floats.
+
+   Parameter values:
+   - Array of doubles to be ranked
+   - Start value for ranking (defaults to 1)
+   - How to deal with ties. Defaults to "mean"
+   - "mean" uses the arithmetic mean,
+   - "max" uses the maximum possible rank for all ties
+   - "min" uses the minimum rank for all ties
+   - "first" awards a descending rank starting so first occurence gets the highest rank down to the last
+   - "last" awards an ascending rank starting so the last occurance gets the highest rank down to the first
+
+   Returns:
+   - Array of floats with the rank of each item
+
+   Examples:
+   Sigma.rank([2,3,6,5,3]) // [1.0, 2.5, 5.0, 4.0, 2.5]
+   Sigma.rank([100,100,100,100], start: 10) // [11.5, 11.5, 11.5, 11.5]
+   Sigma.rank([100,100,100,100], ties: "max") // [1.0, 1.0, 1.0, 1.0]
+   Sigma.rank([100,100,100,100], ties: "min") // [4.0, 4.0, 4.0, 4.0]
+   Sigma.rank([100,100,100,100], ties: "first") // [1.0, 2.0, 3.0, 4.0]
+   Sigma.rank([100,100,100,100], ties: "last") // [4.0, 3.0, 2.0, 1.0]
+
+   */
+
+  public static func rank(_ values: [Double], start: Double = 1.0, ties: String = "mean") -> [Double]? {
+    let count_all = values.count
+    if count_all == 0 {
+      return nil
+    }
+    var rank: Double
+    if ties == "mean" {
+      rank = start - 0.5
+    }
+    else if ties == "max" || ties == "min" || ties == "first" || ties == "last" {
+      rank = start - 1.0
+    }
+    else {
+      return nil
+    }
+    var increment: Double
+    var tiny_increment: Double
+    var unique_vals: [Double]
+    var unique_freqs: [Int]
+    (unique_vals, unique_freqs) = Sigma.frequencies(values: values)!
+    var ranks = [Double](repeating: 0, count: count_all)
+    for (idx, value) in unique_vals.enumerated() {
+      increment = Double(unique_freqs[idx])
+      tiny_increment = 1.0
+      for idx in 0...(count_all - 1) {
+        if value == values[idx] {
+          if ties == "mean" {
+            ranks[idx] = rank + (increment / 2.0)
+          }
+          else if ties == "min" {
+            ranks[idx] = rank + 1
+          }
+          else if ties == "max" {
+            ranks[idx] = rank + increment
+          }
+          else if ties == "first" {
+            ranks[idx] = rank + tiny_increment
+            tiny_increment += 1
+          }
+          else if ties == "last" {
+            ranks[idx] = rank + increment - tiny_increment + 1.0
+            tiny_increment += 1
+          }
+        }
+      }
+      rank += increment
+    }
+    return ranks
+  }
+}

SigmaSwiftStatistics/UniqueValues.swift

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+//
+//  UniqueValues.swift
+//  SigmaSwiftStatistics
+//
+//  Created by Alan James Salmoni on 21/01/2017.
+//  Copyright © 2017 Evgenii Neumerzhitckii. All rights reserved.
+//
+
+import Foundation
+
+public extension Sigma {
+
+  /*
+   This returns a list of the values within a vector without regard to frequency
+
+   Parameter values:
+   - Array of doubles to be analysed
+
+   Return values:
+   - An unsorted array containing all values that occur within the parameter array. All duplicates are returned as a single value
+
+   Example:
+   Sigma.uniqueValues([1,2,3,4,5,4,3,5]) // [1,2,3,4,5]
+
+   */
+
+  public static func uniqueValues(values: [Double]) -> [Double]? {
+    let count = Double(values.count)
+    if count == 0 { return nil }
+    let unique = Array(Set(values))
+    return unique
+  }
+}

SigmaSwiftStatisticsTests/FrequenciesTests.swift

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+import XCTest
+import SigmaSwiftStatistics
+
+class FrequenciesTests: XCTestCase {
+// MARK: - Frequencies
+
+  func testEmptyArray() {
+    if let _ = Sigma.frequencies(values: []) {
+      XCTFail()
+    }
+    else {
+      XCTAssertNil(nil)
+    }
+  }
+
+  func testSingleArray() {
+    if let result = Sigma.frequencies(values: [-99.999]) {
+      let (unique_values, value_frequencies) = result
+      // (-99.999, [1])
+      XCTAssertEqual([-99.999], unique_values)
+      XCTAssertEqual([1], value_frequencies)
+    }
+    else {
+      XCTAssertNil(nil)
+    }
+  }
+
+  func testHomogenousArray() {
+    if let result = Sigma.frequencies(values: [-99.999, -99.999, -99.999, -99.999, -99.999, -99.999]) {
+      let (unique_values, value_frequencies) = result
+      // (-99.999, [6])
+      XCTAssertEqual([-99.999], unique_values)
+      XCTAssertEqual([6], value_frequencies)
+    }
+    else {
+      XCTAssertNil(nil)
+    }
+  }
+
+  func testPositiveArray() {
+    if let result = Sigma.frequencies(values: [6,2,9999,9999,2,79,6,6]) {
+      let (unique_values, value_frequencies) = result
+      // (2,6,79,9999, [2,3,1,2])
+      XCTAssertEqual([2,6,79,9999], unique_values)
+      XCTAssertEqual([2,3,1,2], value_frequencies)
+    }
+    else {
+      XCTAssertNil(nil)
+    }
+  }
+
+  func testNegativeArray() {
+    if let result = Sigma.frequencies(values: [-99.999, -0.0001, -99.999, -99.999, -99.999, -99.999]) {
+      let (unique_values, value_frequencies) = result
+      // (-99.999, [1])
+      XCTAssertEqual([-99.999, -0.0001], unique_values)
+      XCTAssertEqual([5,1], value_frequencies)
+    }
+    else {
+      XCTAssertNil(nil)
+    }
+  }
+
+  func testMixedArray() {
+    if let result = Sigma.frequencies(values: [-99.999, -99.999, -99.999, 99.999, -99.999, 99.999]) {
+      let (unique_values, value_frequencies) = result
+      // (-99.999, [1])
+      XCTAssertEqual([-99.999, 99.999], unique_values)
+      XCTAssertEqual([4,2], value_frequencies)
+    }
+  }
+}

SigmaSwiftStatisticsTests/GeometricMeanTests.swift

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+import XCTest
+import SigmaSwiftStatistics
+
+class GeometricMeanTests: XCTestCase {
+
+  func testGeometricMean_Normal() {
+    let data_array = [0.52662978,  0.77362142,  0.57550701, 0.04158415,  0.03447811,
+                      0.08848505,  0.5236469 ,  0.25523548,  0.89229563,  0.71272614,
+                      0.17107995,  0.26764894,  0.27308645,  0.38404429,  0.12755542,
+                      0.9856573 ,  0.91394384,  0.50584635,  0.31623642,  0.13751698,
+                      0.68101821,  0.71853529,  0.66112074,  0.71656707,  0.35927775,
+                      0.76151524,  0.94317209,  0.01808385,  0.36550638,  0.9901121 ,
+                      0.60259119,  0.62285146,  0.61310069,  0.55510847,  0.15929895,
+                      0.80369179,  0.26319102,  0.49952759,  0.34527164,  0.08919652,
+                      0.61979169,  0.43286263,  0.42874006,  0.1784381 ,  0.51625026,
+                      0.74231264,  0.34506245,  0.70310094,  0.09531878,  0.02909812]
+    if let result = Sigma.geometricMean(data: data_array) {
+      XCTAssertEqualWithAccuracy(0.34079044910152717, result, accuracy: 0.000000000000001)
+    }
+    else {
+      XCTAssertNil(nil)
+    }
+  }
+
+  func testGeometricMean_EmptyArray() {
+    let data_array: [Double] = []
+    if let _ = Sigma.geometricMean(data: data_array) {
+      XCTFail()
+    }
+    else {
+      XCTAssertNil(nil)
+    }
+  }
+
+  func testGeometricMean_SingleElement() {
+    let data_array = [0.52662978]
+    if let result = Sigma.geometricMean(data: data_array) {
+      XCTAssertEqualWithAccuracy(0.52662978000000005, result, accuracy: 0.000000000000001)
+    }
+    else {
+      XCTAssertNil(nil)
+    }
+  }
+
+}

SigmaSwiftStatisticsTests/HarmonicMeanTests.swift

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+import XCTest
+import SigmaSwiftStatistics
+
+class HarmonicMeanTests: XCTestCase {
+
+  func testHarmonicMean_Normal() {
+    let data_array = [0.52662978,  0.77362142,  0.57550701, 0.04158415,  0.03447811,
+                      0.08848505,  0.5236469 ,  0.25523548,  0.89229563,  0.71272614,
+                      0.17107995,  0.26764894,  0.27308645,  0.38404429,  0.12755542,
+                      0.9856573 ,  0.91394384,  0.50584635,  0.31623642,  0.13751698,
+                      0.68101821,  0.71853529,  0.66112074,  0.71656707,  0.35927775,
+                      0.76151524,  0.94317209,  0.01808385,  0.36550638,  0.9901121 ,
+                      0.60259119,  0.62285146,  0.61310069,  0.55510847,  0.15929895,
+                      0.80369179,  0.26319102,  0.49952759,  0.34527164,  0.08919652,
+                      0.61979169,  0.43286263,  0.42874006,  0.1784381 ,  0.51625026,
+                      0.74231264,  0.34506245,  0.70310094,  0.09531878,  0.02909812]
+    if let result = Sigma.harmonicMean(data: data_array) {
+      XCTAssertEqualWithAccuracy(0.17589575818127001, result, accuracy: 0.000000000000001)
+    }
+    else {
+      XCTAssertNil(nil)
+    }
+  }
+
+  func testGeometricMean_EmptyArray() {
+    let data_array: [Double] = []
+    if let _ = Sigma.harmonicMean(data: data_array) {
+      XCTFail()
+    }
+    else {
+      XCTAssertNil(nil)
+    }
+  }
+
+  func testGeometricMean_SingleElement() {
+    let data_array = [0.52662978]
+    if let result = Sigma.harmonicMean(data: data_array) {
+      XCTAssertEqualWithAccuracy(0.52662978000000005, result, accuracy: 0.000000000000001)
+    }
+    else {
+      XCTAssertNil(nil)
+    }
+  }
+
+}