Swift Accelerate for Mean & Standard Deviation

Question

I am looking at Accelerate to compute mean and standard deviation of arrays in Swift.

I can do the mean. How do I do the standard deviation?

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

You can compute the standard deviation from the mean value and the mean square value (compare https://en.wikipedia.org/wiki/Standard_deviation#Identities_and_mathematical_properties and 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

Alternatively (for iOS 9.0 and later or macOS 10.11 and later), use 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