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我有一系列座標，我想找到線性迴歸，因此我可以找到線的方位。我使用的是從斯威夫特算法俱樂部Linear Regression algorithm在這組座標：從一組座標中找出線性迴歸方位並未給出所需的結果
51.48163827836369, -0.019464668521006683
51.481654860705667, -0.019452641350085287
51.481674140657908, -0.01943882290242982
51.481690344713748, -0.019423713183982727
51.481705506128442, -0.019419045258473489
51.481722553489625, -0.01940979681751287
51.48173752576799, -0.019412687104136239
51.48174912673462, -0.019409150632213823
51.4817646359283, -0.019389300889997685
51.481779676567427, -0.019388957697628939
51.481792568262044, -0.019402453532393338
51.481804168699682, -0.019415663863242116
51.481822746271966, -0.019423725406568337
51.481838162880258, -0.019428618620622728
51.481855587496689, -0.01942372804705883
51.481867836051975, -0.019430554178484272
51.481883136496599, -0.019432972610502475
51.481899505688553, -0.019425501321734373
51.481914919015246, -0.019424832166464512
51.481932613348015, -0.019457392982985766
51.481949346615657, -0.019472056279255412
51.481968002664601, -0.019458232757642691
51.481986902059589, -0.019446792660346546
51.482003086257393, -0.019433403642779012
使用darrinward.com添加這一個地圖，我得到這個路徑，移動大致北：
所以從那裏，得到軸承我回歸的第一個座標的經度（獲得緯度），：
let regression = linearRegression(longitudes, latitudes)
let firstRegressionCoordinate = CLLocationCoordinate2D(latitude: regression(firstCoordinate.longitude), longitude:firstCoordinate.longitude)
let lastRegressionCoordinate = CLLocationCoordinate2D(latitude: regression(lastCoordinate.longitude), longitude: lastCoordinate.longitude)
return firstRegressionCoordinate.bearing(to: lastRegressionCoordinate)
我的軸承功能正常工作，並給了我一個156.20969º的方位。考慮到實際路徑，我期望的數字更接近0º，或接近360º。
我覺得問題不在於線性迴歸算法或軸承功能，而在於我要求的座標以確定方位。我是否要求錯誤的東西？還有別的我應該做的不同嗎？
完整的代碼，可以在操場上運行：
import CoreLocation
public extension FloatingPoint {
public var degreesToRadians: Self { return self * .pi/180 }
public var radiansToDegrees: Self { return self * 180/.pi }
}
extension CLLocationCoordinate2D {
///Returns the initial bearing of travel to another coordinate
func bearing(to: CLLocationCoordinate2D) -> CLLocationDegrees {
let fromLatRadians = latitude.degreesToRadians
let fromLongRadians = longitude.degreesToRadians
let toLatRadians = to.latitude.degreesToRadians
let toLongRadians = to.longitude.degreesToRadians
let y = sin(toLongRadians - fromLongRadians) * cos(toLatRadians)
let x = cos(fromLatRadians) * sin(toLatRadians) - sin(fromLatRadians) * cos(toLatRadians) * cos(toLongRadians - fromLongRadians)
var bearing = atan2(y, x).radiansToDegrees
bearing = (bearing + 360.0).truncatingRemainder(dividingBy: 360.0)
return bearing
}
}
extension Array where Element == CLLocationCoordinate2D {
func linearRegressionBearing() -> Double {
var longitudes = [CLLocationDegrees]()
var latitudes = [CLLocationDegrees]()
for coordinate in self {
longitudes.append(coordinate.longitude)
latitudes.append(coordinate.latitude)
}
let regression = linearRegression(longitudes, latitudes)
let firstCoordinate = CLLocationCoordinate2D(latitude: regression(self.first!.longitude), longitude: self.first!.longitude)
let lastCoordinate = CLLocationCoordinate2D(latitude: regression(self.last!.longitude), longitude: self.last!.longitude)
return firstCoordinate.bearing(to: lastCoordinate)
}
}
// A closed form solution
func average(_ input: [Double]) -> Double {
return input.reduce(0, +)/Double(input.count)
}
func multiply(_ a: [Double], _ b: [Double]) -> [Double] {
return zip(a, b).map(*)
}
func linearRegression(_ xs: [Double], _ ys: [Double]) -> (Double) -> Double {
let sum1 = average(multiply(xs, ys)) - average(xs) * average(ys)
let sum2 = average(multiply(xs, xs)) - pow(average(xs), 2)
let slope = sum1/sum2
let intercept = average(ys) - slope * average(xs)
return { x in intercept + slope * x }
}
let coordinates = [
CLLocationCoordinate2D(latitude: 51.48163827836369, longitude: -0.019464668521006683),
CLLocationCoordinate2D(latitude: 51.481654860705667, longitude: -0.019452641350085287),
CLLocationCoordinate2D(latitude: 51.481674140657908, longitude: -0.01943882290242982),
CLLocationCoordinate2D(latitude: 51.481690344713748, longitude: -0.019423713183982727),
CLLocationCoordinate2D(latitude: 51.481705506128442, longitude: -0.019419045258473489),
CLLocationCoordinate2D(latitude: 51.481722553489625, longitude: -0.01940979681751287),
CLLocationCoordinate2D(latitude: 51.48173752576799, longitude: -0.019412687104136239),
CLLocationCoordinate2D(latitude: 51.48174912673462, longitude: -0.019409150632213823),
CLLocationCoordinate2D(latitude: 51.4817646359283, longitude: -0.019389300889997685),
CLLocationCoordinate2D(latitude: 51.481779676567427, longitude: -0.019388957697628939),
CLLocationCoordinate2D(latitude: 51.481792568262044, longitude: -0.019402453532393338),
CLLocationCoordinate2D(latitude: 51.481804168699682, longitude: -0.019415663863242116),
CLLocationCoordinate2D(latitude: 51.481822746271966, longitude: -0.019423725406568337),
CLLocationCoordinate2D(latitude: 51.481838162880258, longitude: -0.019428618620622728),
CLLocationCoordinate2D(latitude: 51.481855587496689, longitude: -0.01942372804705883),
CLLocationCoordinate2D(latitude: 51.481867836051975, longitude: -0.019430554178484272),
CLLocationCoordinate2D(latitude: 51.481883136496599, longitude: -0.019432972610502475),
CLLocationCoordinate2D(latitude: 51.481899505688553, longitude: -0.019425501321734373),
CLLocationCoordinate2D(latitude: 51.481914919015246, longitude: -0.019424832166464512),
CLLocationCoordinate2D(latitude: 51.481932613348015, longitude: -0.019457392982985766),
CLLocationCoordinate2D(latitude: 51.481949346615657, longitude: -0.019472056279255412),
CLLocationCoordinate2D(latitude: 51.481968002664601, longitude: -0.019458232757642691),
CLLocationCoordinate2D(latitude: 51.481986902059589, longitude: -0.019446792660346546),
CLLocationCoordinate2D(latitude: 51.482003086257393, longitude: -0.019433403642779012)
]
coordinates.linearRegressionBearing()