Swift加速的平均值和标准差

Question

我正在研究加速计算Swift中数组的平均值和标准偏差。

我可以做的意思。我该如何做标准偏差？

let rr: [Double] = [ 18.0, 21.0, 41.0, 42.0, 48.0, 50.0, 55.0, 90.0 ] 

var mn: Double = 0.0 

vDSP_meanvD(rr, 1, &mn, vDSP_Length(rr.count)) 

print(mn) // prints correct mean as 45.6250 

// Standard Deviation should be 22.3155 

Answer 1

可以计算从平均值和 标准偏差均方值（比较https://en.wikipedia.org/wiki/Standard_deviation#Identities_and_mathematical_properties和https://en.wikipedia.org/wiki/Algebraic_formula_for_the_variance）：

import Accelerate 

let rr: [Double] = [ 18.0, 21.0, 41.0, 42.0, 48.0, 50.0, 55.0, 90.0 ] 

var mn: Double = 0.0 // mean value 
vDSP_meanvD(rr, 1, &mn, vDSP_Length(rr.count)) 

var ms: Double = 0.0 // mean square value 
vDSP_measqvD(rr, 1, &ms, vDSP_Length(rr.count)) 

let sddev = sqrt(ms - mn * mn) * sqrt(Double(rr.count)/Double(rr.count - 1)) 

print(mn, sddev) 
// 45.625 22.315513501982 

或者（适用于iOS 9.0及更高版本或MacOS的10.11及更高版本）使用vDSP_normalizeD：

var mn = 0.0 
var sddev = 0.0 
vDSP_normalizeD(rr, 1, nil, 1, &mn, &sddev, vDSP_Length(rr.count)) 
sddev *= sqrt(Double(rr.count)/Double(rr.count - 1)) 

print(mn, sddev) 
// 45.625 22.315513501982