// Autocorrelation tests whether or not a generator produces independent results.
// The parameters are the dataset ds,
// start, the first index looked at by the test
// and jump, the ith index looked starting at (start)
func Autocorrelation(ds *RandGenerator.Dataset, start, jump int) (float64, float64) {
// Index1 and Index2 keep tracks of when to break from the loop, as the array will be out of bounds when index2 is exceeds M
var (
index1 = start
index2 = start + jump
total = 0.0
k int
)
// Summation of each of the potentially correlated indices
for k = 0; index2 < ds.Len(); k++ {
total += ds.Get(index1) * ds.Get(index2)
index1 = start + jump*k
index2 = start + jump*(k+1)
}
// Now, take the total and divide it by the number of iterations + 1
mu := total / float64((k + 1))
mu -= 0.25 // Magic number provided by Professor Lipschultz in the slides
// calculate the variance
squaredVal := float64(13*k + 7)
demoninator := float64(12 * (k + 1))
variance := math.Sqrt(squaredVal) / demoninator
return mu, variance
}
// The first option maps the difference between the value and the mean to a binary enum
func generateMeanRuns(ds *RandGenerator.Dataset) []bool {
runs := make([]bool, ds.Len())
mean := ds.Mean()
for i := 0; int(i) < int(ds.Len()); i++ {
point := ds.Get(i)
runs[i] = math.Signbit(point - mean)
}
return runs
}
// The second method takes the difference between increasing indices and maps the sign of the difference to a binary result
func generateDifferenceRuns(ds *RandGenerator.Dataset) []bool {
runs := make([]bool, ds.Len()-1)
for i := 0; i < ds.Len()-1; i++ {
point1 := ds.Get(i)
point2 := ds.Get(i + 1)
runs[i] = math.Signbit(point1 - point2)
}
return runs
}
func KolmogorovSmirnov(ds *RandGenerator.Dataset) float64 {
ds = ds.Subset(0, 100).Sort() // only select the first 100 numbers, and sort them
max := 0.0
// Find the maximum difference from the expected value to the observed value
for i := 0; i < ds.Len(); i++ {
observed := ds.Get(i)
expected := float64(i) / float64(ds.Len())
distence := math.Abs(observed - expected)
if distence > max {
max = distence
}
}
return max
}
func ChiSquared(ds *RandGenerator.Dataset) float64 {
var buckets []int = make([]int, 10)
for i := 0; i < 10; i++ {
buckets[i] = 0
}
for i := 0; i < ds.Len(); i++ {
num := ds.Get(i)
switch {
case num < 0.1:
buckets[0] += 1
case 0.1 <= num && num < 0.2:
buckets[1] += 1
case 0.2 <= num && num < 0.3:
buckets[2] += 1
case 0.3 <= num && num < 0.4:
buckets[3] += 1
case 0.4 <= num && num < 0.5:
buckets[4] += 1
case 0.5 <= num && num < 0.6:
buckets[5] += 1
case 0.6 <= num && num < 0.7:
buckets[6] += 1
case 0.7 <= num && num < 0.8:
buckets[7] += 1
case 0.8 <= num && num < 0.9:
buckets[8] += 1
case 0.9 <= num && num < 1.0:
buckets[9] += 1
default:
log.Fatal("Generate produced a value greater than 1.0")
}
}
testStatistic := 0.0
for _, bucket := range buckets {
var expected = ds.Len() / 10.0
bucketVal := float64(bucket)
testStatistic += ((bucketVal - float64(expected)) * (bucketVal - float64(expected))) / float64(expected)
}
return testStatistic
}
func main() {
app := cli.NewApp()
var (
size int
outputFile string
gen RandGenerator.Generator
ds *RandGenerator.Dataset
)
const (
SEED = 122949823
)
app.Flags = []cli.Flag{
cli.IntFlag{
Name: "n",
Value: 10000,
Usage: "number of elements to generate. Defaults to 10000. NOTE: Kolgorov only uses the first 100",
Destination: &size,
}, cli.StringFlag{
Name: "f",
Value: "output.txt",
Usage: "File to which the output is written, defaults to output.txt",
Destination: &outputFile,
},
}
// Specifies how to interact with the command line tool.
// See https://github.com/codegangsta/cli for explanation
app.Commands = []cli.Command{
{
Name: "kolmogorov",
Aliases: []string{"k"},
Usage: "run the Kolmogov-Smirnov Test for uniformity",
Action: func(c *cli.Context) {
println("Please specify a subcommand. See -h for a list of commands.")
cli.ShowSubcommandHelp(c)
},
Subcommands: []cli.Command{
{
Name: "stdlib",
Usage: "uses the Golang standard library generator, found in 'golang.org/pkg/math/rand'",
Action: func(c *cli.Context) {
gen = rand.New(rand.NewSource(SEED))
ds = RandGenerator.NewDataset(gen, size)
fmt.Printf("Standard Library Kolmogorov Test Statistic:\t%f\n", StatTests.KolmogorovSmirnov(ds))
},
}, {
Name: "lipschultz",
Usage: "uses the generator seeded as a = 101427, c = 321, m = 1 << 16",
Action: func(c *cli.Context) {
gen = RandGenerator.LipschultzGen()
gen.Seed(SEED)
ds = RandGenerator.NewDataset(gen, size)
fmt.Printf("Lipschultz Kolmogorov Test Statistic:\t%f\n", StatTests.KolmogorovSmirnov(ds))
},
}, {
Name: "randu",
Usage: "uses the generator seeded as a = 65539, c = 0, m = 1 << 31",
Action: func(c *cli.Context) {
gen = RandGenerator.NewRANDUGen()
gen.Seed(SEED)
ds = RandGenerator.NewDataset(gen, size)
fmt.Printf("RANDU Kolmogorov Test Statistic:\t%f\n", StatTests.KolmogorovSmirnov(ds))
},
},
},
}, {
Name: "runs",
Aliases: []string{"r"},
Usage: "runs Test for independence",
Action: func(c *cli.Context) {
cli.ShowSubcommandHelp(c)
},
Subcommands: []cli.Command{
{
Name: "stdlib",
Usage: "uses the Golang standard library generator, found in 'golang.org/pkg/math/rand'",
Action: func(c *cli.Context) {
gen = rand.New(rand.NewSource(SEED))
ds = RandGenerator.NewDataset(gen, size)
fmt.Printf("Standard Library Run Test Statistic:\t%f\n", StatTests.Run(ds, StatTests.DIFFERENCE))
},
}, {
Name: "lipschultz",
Usage: "uses the generator seeded as a = 101427, c = 321, m = 1 << 16",
Action: func(c *cli.Context) {
gen = RandGenerator.LipschultzGen()
gen.Seed(SEED)
ds = RandGenerator.NewDataset(gen, size)
fmt.Printf("Lipschultz Run Test Statistic:\t%f\n", StatTests.Run(ds, StatTests.DIFFERENCE))
},
}, {
Name: "randu",
Usage: "uses the generator seeded as a = 65539, c = 0, m = 1 << 31",
Action: func(c *cli.Context) {
gen = RandGenerator.NewRANDUGen()
gen.Seed(SEED)
ds = RandGenerator.NewDataset(gen, size)
fmt.Printf("RANDU Run Test Statistic:\t%f\n", StatTests.Run(ds, StatTests.DIFFERENCE))
},
},
},
}, {
Name: "autocorrelation",
Aliases: []string{"a"},
Usage: "autocorrelation test for independence",
Action: func(c *cli.Context) {
cli.ShowSubcommandHelp(c)
os.Exit(0)
},
Subcommands: []cli.Command{
{
Name: "stdlib",
Usage: "uses the Golang standard library generator, found in 'golang.org/pkg/math/rand'",
Action: func(c *cli.Context) {
gen = rand.New(rand.NewSource(SEED))
ds = RandGenerator.NewDataset(gen, size)
mu, variance := StatTests.Autocorrelation(ds, 1, 3)
fmt.Printf("Standard Library Autocorrelation Test Statistic:\t%f\n", mu/variance)
},
}, {
Name: "lipschultz",
Usage: "uses the generator seeded as a = 101427, c = 321, m = 1 << 16",
Action: func(c *cli.Context) {
gen = RandGenerator.LipschultzGen()
gen.Seed(SEED)
ds = RandGenerator.NewDataset(gen, size)
mu, variance := StatTests.Autocorrelation(ds, 1, 3)
fmt.Printf("Lipschultz Autocorrelation Test Statistic:\t%f\n", mu/variance)
},
}, {
Name: "randu",
Usage: "uses the generator seeded as a = 65539, c = 0, m = 1 << 31",
Action: func(c *cli.Context) {
gen = RandGenerator.NewRANDUGen()
gen.Seed(SEED)
ds = RandGenerator.NewDataset(gen, size)
mu, variance := StatTests.Autocorrelation(ds, 1, 3)
fmt.Printf("RANDU Autocorrelation Test Statistic:\t%f\n", mu/variance)
},
},
},
}, {
Name: "chi",
Aliases: []string{"c"},
Usage: "Chi-Square Frequency Test for uniformity",
Action: func(c *cli.Context) {
cli.ShowSubcommandHelp(c)
},
Subcommands: []cli.Command{
{
Name: "stdlib",
Usage: "uses the Golang standard library generator, found in 'golang.org/pkg/math/rand'",
Action: func(c *cli.Context) {
gen = rand.New(rand.NewSource(SEED))
ds = RandGenerator.NewDataset(gen, size)
fmt.Printf("Standard Library Chi Square Test Statistic:\t%f\n", StatTests.ChiSquared(ds))
},
}, {
Name: "lipschultz",
Usage: "uses the generator seeded as a = 101427, c = 321, m = 1 << 16",
Action: func(c *cli.Context) {
gen = RandGenerator.LipschultzGen()
gen.Seed(SEED)
ds = RandGenerator.NewDataset(gen, size)
fmt.Printf("Lipschultz Chi Square Test Statistic:\t%f\n", StatTests.ChiSquared(ds))
},
}, {
Name: "randu",
Usage: "uses the generator seeded as a = 65539, c = 0, m = 1 << 31",
Action: func(c *cli.Context) {
gen = RandGenerator.NewRANDUGen()
gen.Seed(SEED)
ds = RandGenerator.NewDataset(gen, size)
fmt.Printf("RANDU Chi Square Test Statistic:\t%f\n", StatTests.ChiSquared(ds))
},
},
},
},
}
app.Run(os.Args)
file, err := os.Create(outputFile)
if err != nil {
panic(err)
}
// close file on exit and check for its returned error
defer func() {
if err := file.Close(); err != nil {
panic(err)
}
}()
w := bufio.NewWriter(file)
defer w.Flush()
for i := 0; i < ds.Len(); i++ {
val := ds.Get(i)
w.WriteString(fmt.Sprintf("%f\n", val))
}
}