special

package main

import (
	"fmt"

	"github.com/go-numerics/special"
)

func main() {
	fmt.Println(special.Gamma(4.5))              // 11.631728396567448
	fmt.Println(special.Erfc(10))                // 2.088487583762545e-45
	fmt.Println(special.Ndtr(-30))               // 4.906713927148187e-198
	fmt.Println(special.Ndtri(1e-300))           // -37.0470962993612
	fmt.Println(special.GammaP(2.5, 1.5))        // regularised lower incomplete gamma
	fmt.Println(special.BetaIncInv(2, 3, 0.975)) // a beta quantile
	fmt.Println(special.Jv(2.5, 10))             // Bessel function of real order
}

x, _ := ndarray.Linspace(-5, 5, 1_000_001)
p, _ := nd.Ndtr(x)

package main

import (
	"fmt"

	"github.com/go-numerics/special"
	"github.com/go-plot/plot"
)

func init() { register("bessel", bessel) }

// Bessel functions of the first kind, integer and real order, with Jv.
func bessel() *plot.Figure {
	x := linspace(0, 20, 400)
	fig, axs := plot.Subplots(1, 1, plot.FigSize(6.4, 4))
	ax := axs[0][0]
	for _, v := range []float64{0, 1, 2, 2.5} {
		y := make([]float64, len(x))
		for i, s := range x {
			y[i] = special.Jv(v, s)
		}
		ax.Plot(x, y, plot.Label(fmt.Sprintf(`$J_{%g}(x)$`, v)))
	}
	ax.Axhline(0, plot.Color("gray"), plot.LineWidth(0.8))
	ax.SetTitle("Jv: Bessel functions of the first kind")
	ax.SetXLabel(`$x$`)
	ax.Legend()
	return fig
}

package main

import (
	"github.com/go-numerics/special"
	"github.com/go-plot/plot"
)

func init() { register("gamma", gamma) }

// Gamma on the real line: one curve per interval between its poles at
// 0, -1, -2, -3, so that no line is drawn across a pole.
func gamma() *plot.Figure {
	fig, axs := plot.Subplots(1, 1, plot.FigSize(6.4, 4))
	ax := axs[0][0]
	pieces := [][2]float64{{-4, -3}, {-3, -2}, {-2, -1}, {-1, 0}, {0, 5}}
	for k, p := range pieces {
		x := linspace(p[0]+0.005, p[1]-0.005, 300)
		if k == len(pieces)-1 {
			x = linspace(p[0]+0.005, p[1], 300)
		}
		y := make([]float64, len(x))
		for i, s := range x {
			y[i] = special.Gamma(s)
		}
		if k == len(pieces)-1 {
			ax.Plot(x, y, plot.Color("C0"), plot.Label(`$\Gamma(x)$`))
		} else {
			ax.Plot(x, y, plot.Color("C0"))
		}
	}
	x := linspace(0.05, 5, 200)
	lg := make([]float64, len(x))
	for i, s := range x {
		lg[i] = special.LogGamma(s)
	}
	ax.Plot(x, lg, plot.Color("C1"), plot.LineStyle("--"), plot.Label(`$\log\Gamma(x)$`))
	ax.Axhline(0, plot.Color("gray"), plot.LineWidth(0.8))
	ax.SetYLim(-8, 8)
	ax.SetXLim(-4, 5)
	ax.SetTitle("Gamma and LogGamma")
	ax.SetXLabel(`$x$`)
	ax.Legend(plot.Loc("lower right"))
	return fig
}

package main

import (
	"github.com/go-numerics/special"
	"github.com/go-plot/plot"
)

func init() { register("ndtr", ndtr) }

// The lower tail of the normal distribution and the complementary error
// function, on a log scale, down to the subnormal range of float64.
func ndtr() *plot.Figure {
	x := linspace(-38, 0, 400)
	p := make([]float64, len(x))
	for i, s := range x {
		p[i] = special.Ndtr(s)
	}
	z := linspace(0, 26.5, 400)
	q := make([]float64, len(z))
	for i, s := range z {
		q[i] = special.Erfc(s)
	}
	fig, axs := plot.Subplots(1, 2, plot.FigSize(8, 3.6))
	axs[0][0].Plot(x, p)
	axs[0][0].SetYScale("log")
	axs[0][0].SetYLim(1e-320, 10)
	axs[0][0].SetTitle(`Ndtr($x$)`)
	axs[0][0].SetXLabel(`$x$`)
	axs[0][1].Plot(z, q, plot.Color("C1"))
	axs[0][1].SetYScale("log")
	axs[0][1].SetYLim(1e-320, 10)
	axs[0][1].SetTitle(`Erfc($x$)`)
	axs[0][1].SetXLabel(`$x$`)
	fig.TightLayout()
	return fig
}