main.go

package main

import (
	"fmt"
	"math"

	"gonum.org/v1/gonum/stat/distuv"
)

const (
	alpha = 0.05 // Significance level of the statistical test. Must be greater than 0.
)

func normPPF(x float64) float64 {
	// Create a normal distribution
	dist := distuv.Normal{
		Mu:    0,
		Sigma: 1,
	}

	// Calculate PPF (percent point function) which is the inverse of the cumulative distribution function (CDF) of the normal distribution
	return dist.Quantile(x)
}

func sign(x float64) float64 {
	// Get sign of a float (-1 if negative, 0 if 0 and 1 if positive)
	if x < 0 {
		return -1
	} else if x == 0 {
		return 0
	} else {
		return 1
	}
}

func getValuesFromMap(mapping map[float64]int) []int {
	// Get values from map
	v := make([]int, 0, len(mapping))
	for _, value := range mapping {
		v = append(v, value)
	}

	return v
}

func countUniqueValues(arr []float64) map[float64]int {
	//Create a counter for values in an array
	dict := make(map[float64]int)
	for _, num := range arr {
		dict[num] = dict[num] + 1
	}
	return dict
}

// Mann-Kendall test ...
func MKtest(series []float64, alpha float64) (string, error) {
	// Pseudocode see https://up-rs-esp.github.io/mkt/

	// Get length of time series
	n := len(series)
	if n <= 1 {
		return "none", fmt.Errorf("Only one data point provided. No trend present.")
	}

	// Calculate S which is the number of positive differences minus the number of negative differences
	// If S is a positive number, observations obtained later in time tend to be larger than observations made earlier.
	// If S is a negative number, then observations made later in time tend to be smaller than observations made earlier.
	s := 0.0
	for k := 0; k < n-1; k++ {
		for j := k + 1; j < n; j++ {
			s += sign(series[j] - series[k])
		}
	}

	// Calculate unique observations
	uniq := countUniqueValues(series)
	g := len(uniq)
	varS, z := 0.0, 0.0

	// Calculate var(s)
	if g == n {
		// No tie case
		varS = float64((n * (n - 1) * (2*n + 5))) / 18
	} else {
		//  Ties in data case
		tp := getValuesFromMap(uniq)
		sumExpression := 0
		for i, _ := range tp {
			sumExpression += tp[i] * (tp[i] - 1) * (2*tp[i] + 5)
		}
		varS = float64((n*(n-1)*(2*n+5) + sumExpression)) / 18
	}

	// Compute the Mann-Kendall test statistic Z
	if s > 0 {
		z = float64(s-1) / math.Sqrt(float64(varS))
	} else if s == 0 {
		z = 0
	} else if s < 0 {
		z = float64(s+1) / math.Sqrt(float64(varS))
	}

	// Calculate the h value
	h := math.Abs(z) > normPPF(1-alpha/2)

	// Decide if we see trend in data (default: "none" which means no trend)
	trend := "none"
	if z < 0 && h == true {
		trend = "decreasing"
	} else if z > 0 && h == true {
		trend = "increasing"
	}

	return trend, nil
}

func main() {
	trend := []float64{444.86422078,
		442.03048113, 440.55915912, 430.17507337, 422.61711963,
		407.65081784, 404.60838605, 427.39930304, 433.34926929,
		437.40598052, 443.03321287, 442.89414329, 459.83770303,
		474.06537847, 454.72264949, 457.77727018, 455.55108019,
		459.04705359, 463.45009691, 461.49681143, 460.22330154,
		473.81861709, 479.75938288, 484.73895342, 481.59747338,
		480.1184492, 484.00466265, 479.56595413, 471.3967811,
		459.25010965, 460.79176371, 468.67765623, 491.64362735,
		492.22523428, 525.15392318, 533.23089641, 543.54148873,
		559.76465954, 573.59507116, 556.52540265, 551.68180752,
		526.80761937, 559.05410939, 572.5692387, 574.80430187,
		577.85605905, 596.31760844, 601.41447938, 609.78789718,
		602.2355323, 592.05365229, 608.66472746, 576.52373187,
		601.68847731, 660.22029991}

	trendIndication, err := MKtest(trend, alpha)
	if err != nil {
		fmt.Println(err)
	} else {
		fmt.Println(trendIndication)
	}
}