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package stats
import "math"
// Series is a container for a series of data
type Series []Coordinate
// Coordinate holds the data in a series
type Coordinate struct {
X, Y float64
}
// LinearRegression finds the least squares linear regression on data series
func LinearRegression(s Series) (regressions Series, err error) {
if len(s) == 0 {
return nil, EmptyInputErr
}
// Placeholder for the math to be done
var sum [5]float64
// Loop over data keeping index in place
i := 0
for ; i < len(s); i++ {
sum[0] += s[i].X
sum[1] += s[i].Y
sum[2] += s[i].X * s[i].X
sum[3] += s[i].X * s[i].Y
sum[4] += s[i].Y * s[i].Y
}
// Find gradient and intercept
f := float64(i)
gradient := (f*sum[3] - sum[0]*sum[1]) / (f*sum[2] - sum[0]*sum[0])
intercept := (sum[1] / f) - (gradient * sum[0] / f)
// Create the new regression series
for j := 0; j < len(s); j++ {
regressions = append(regressions, Coordinate{
X: s[j].X,
Y: s[j].X*gradient + intercept,
})
}
return regressions, nil
}
// ExponentialRegression returns an exponential regression on data series
func ExponentialRegression(s Series) (regressions Series, err error) {
if len(s) == 0 {
return nil, EmptyInputErr
}
var sum [6]float64
for i := 0; i < len(s); i++ {
if s[i].Y < 0 {
return nil, YCoordErr
}
sum[0] += s[i].X
sum[1] += s[i].Y
sum[2] += s[i].X * s[i].X * s[i].Y
sum[3] += s[i].Y * math.Log(s[i].Y)
sum[4] += s[i].X * s[i].Y * math.Log(s[i].Y)
sum[5] += s[i].X * s[i].Y
}
denominator := (sum[1]*sum[2] - sum[5]*sum[5])
a := math.Pow(math.E, (sum[2]*sum[3]-sum[5]*sum[4])/denominator)
b := (sum[1]*sum[4] - sum[5]*sum[3]) / denominator
for j := 0; j < len(s); j++ {
regressions = append(regressions, Coordinate{
X: s[j].X,
Y: a * math.Exp(b*s[j].X),
})
}
return regressions, nil
}
// LogarithmicRegression returns an logarithmic regression on data series
func LogarithmicRegression(s Series) (regressions Series, err error) {
if len(s) == 0 {
return nil, EmptyInputErr
}
var sum [4]float64
i := 0
for ; i < len(s); i++ {
sum[0] += math.Log(s[i].X)
sum[1] += s[i].Y * math.Log(s[i].X)
sum[2] += s[i].Y
sum[3] += math.Pow(math.Log(s[i].X), 2)
}
f := float64(i)
a := (f*sum[1] - sum[2]*sum[0]) / (f*sum[3] - sum[0]*sum[0])
b := (sum[2] - a*sum[0]) / f
for j := 0; j < len(s); j++ {
regressions = append(regressions, Coordinate{
X: s[j].X,
Y: b + a*math.Log(s[j].X),
})
}
return regressions, nil
}
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