func ExampleHistogram() {
x := make([]float64, 101)
for i := range x {
x[i] = 1.1 * float64(i) // x data ranges from 0 to 110
}
dividers := []float64{7, 20, 100, 1000}
fmt.Println(`Histogram counts the amount of data in the bins specified by
the dividers. In this data set, there are 7 data points less than 7 (dividers[0]),
12 data points between 7 and 20 (dividers[2] and dividers[1]), and 0 data points
above 1000. Since dividers has length 4, there will be 5 bins.`)
hist := Histogram(nil, dividers, x, nil)
fmt.Printf("Hist = %v\n", hist)
fmt.Println()
fmt.Println("For ease, the floats Span function can be used to set the dividers")
nBins := 10
// Create one fewer divider than bins, but add two to work with Span (see
// note below)
dividers = make([]float64, nBins+1)
min, _ := floats.Min(x)
max, _ := floats.Max(x)
floats.Span(dividers, min, max)
// Span includes the min and the max. Trim the dividers to create 10 buckets
dividers = dividers[1 : len(dividers)-1]
fmt.Println("len dividers = ", len(dividers))
hist = Histogram(nil, dividers, x, nil)
fmt.Printf("Hist = %v\n", hist)
fmt.Println()
fmt.Println(`Histogram also works with weighted data, and allows reusing of
the count field in order to avoid extra garbage`)
weights := make([]float64, len(x))
for i := range weights {
weights[i] = float64(i + 1)
}
Histogram(hist, dividers, x, weights)
fmt.Printf("Weighted Hist = %v\n", hist)
// Output:
// Histogram counts the amount of data in the bins specified by
// the dividers. In this data set, there are 7 data points less than 7 (dividers[0]),
// 12 data points between 7 and 20 (dividers[2] and dividers[1]), and 0 data points
// above 1000. Since dividers has length 4, there will be 5 bins.
// Hist = [7 12 72 10 0]
//
// For ease, the floats Span function can be used to set the dividers
// len dividers = 9
// Hist = [11 10 10 10 9 11 10 10 9 11]
//
// Histogram also works with weighted data, and allows reusing of
// the count field in order to avoid extra garbage
// Weighted Hist = [77 175 275 375 423 627 675 775 783 1067]
}
func ExampleHistogram() {
x := make([]float64, 101)
for i := range x {
x[i] = 1.1 * float64(i) // x data ranges from 0 to 110
}
dividers := []float64{0, 7, 20, 100, 1000}
fmt.Println(`Histogram counts the amount of data in the bins specified by
the dividers. In this data set, there are 7 data points less than 7 (between dividers[0]
and dividers[1]), 12 data points between 7 and 20 (dividers[1] and dividers[2]),
and 0 data points above 1000. Since dividers has length 5, there will be 4 bins.`)
hist := Histogram(nil, dividers, x, nil)
fmt.Printf("Hist = %v\n", hist)
fmt.Println()
fmt.Println("For ease, the floats Span function can be used to set the dividers")
nBins := 10
dividers = make([]float64, nBins+1)
min := floats.Min(x)
max := floats.Max(x)
// Increase the maximum divider so that the maximum value of x is contained
// within the last bucket.
max += 1
floats.Span(dividers, min, max)
// Span includes the min and the max. Trim the dividers to create 10 buckets
hist = Histogram(nil, dividers, x, nil)
fmt.Printf("Hist = %v\n", hist)
fmt.Println()
fmt.Println(`Histogram also works with weighted data, and allows reusing of
the count field in order to avoid extra garbage`)
weights := make([]float64, len(x))
for i := range weights {
weights[i] = float64(i + 1)
}
Histogram(hist, dividers, x, weights)
fmt.Printf("Weighted Hist = %v\n", hist)
// Output:
// Histogram counts the amount of data in the bins specified by
// the dividers. In this data set, there are 7 data points less than 7 (between dividers[0]
// and dividers[1]), 12 data points between 7 and 20 (dividers[1] and dividers[2]),
// and 0 data points above 1000. Since dividers has length 5, there will be 4 bins.
// Hist = [7 12 72 10]
//
// For ease, the floats Span function can be used to set the dividers
// Hist = [11 10 10 10 10 10 10 10 10 10]
//
// Histogram also works with weighted data, and allows reusing of
// the count field in order to avoid extra garbage
// Weighted Hist = [66 165 265 365 465 565 665 765 865 965]
}
// computeMove computes how far can be moved replacing each index. The results
// are stored into move.
func computeMove(move []float64, minIdx int, A mat64.Matrix, ab *mat64.Dense, xb []float64, nonBasicIdx []int) error {
// Find ae.
col := mat64.Col(nil, nonBasicIdx[minIdx], A)
aCol := mat64.NewVector(len(col), col)
// d = - Ab^-1 Ae
nb, _ := ab.Dims()
d := make([]float64, nb)
dVec := mat64.NewVector(nb, d)
err := dVec.SolveVec(ab, aCol)
if err != nil {
return ErrLinSolve
}
floats.Scale(-1, d)
for i, v := range d {
if math.Abs(v) < dRoundTol {
d[i] = 0
}
}
// If no di < 0, then problem is unbounded.
if floats.Min(d) >= 0 {
return ErrUnbounded
}
// move = bhat_i / - d_i, assuming d is negative.
bHat := xb // ab^-1 b
for i, v := range d {
if v >= 0 {
move[i] = math.Inf(1)
} else {
move[i] = bHat[i] / math.Abs(v)
}
}
return nil
}
// checkProbQuantContinuous checks that the Prob, Rand, and Quantile are all consistent.
// checkProbContinuous only checks that Prob is a valid distribution (integrates
// to 1 and greater than 0). However, this is also true if the PDF of a different
// distribution is used. This checks that PDF is also consistent with the
// CDF implementation and the random samples.
func checkProbQuantContinuous(t *testing.T, i int, xs []float64, c cumulantProber, tol float64) {
ps := make([]float64, 101)
floats.Span(ps, 0, 1)
var xp, x float64
for i, p := range ps {
x = c.Quantile(p)
if p == 0 {
xp = x
if floats.Min(xs) < x {
t.Errorf("Sample of x less than Quantile(0). Case %v.", i)
break
}
continue
}
if p == 1 {
if floats.Max(xs) > x {
t.Errorf("Sample of x greater than Quantile(1). Case %v.", i)
break
}
}
// The integral of the PDF between xp and x should be the difference in
// the quantiles.
q := quad.Fixed(c.Prob, xp, x, 1000, nil, 0)
if math.Abs(q-(p-ps[i-1])) > 1e-10 {
t.Errorf("Integral of PDF doesn't match quantile. Case %v. Want %v, got %v.", i, p-ps[i-1], q)
break
}
pEst := stat.CDF(x, stat.Empirical, xs, nil)
if math.Abs(pEst-p) > tol {
t.Errorf("Empirical CDF doesn't match quantile. Case %v.", i)
}
xp = x
}
}