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calculus.go
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calculus.go
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package calculus // import "github.com/TheDemx27/calculus"
import (
"math"
"fmt"
)
////////////////////////////////////Symbolic////////////////////////////////////
func (fnc Function) SymDiff() string {
fmt.Println(fnc.ParseToks())
return "compiles..."
// exp := GroupTerms(fnc.GetToksAbstract, fnc.GetToksLit())
//
// switch (exp) {
// case "C*V":
// case "C*V^C":
// case "C*V^V":
// case "ln(V)":
// case "sin(V)":
// case "cos(V)":
// case "-sin(V)":
// case "-cos(V)":
// case "1/V":
// case "V*V":
// case "V/V":
// case "":
// }
// return exp
}
///////////////////////////////////Numerical////////////////////////////////////
/*
* Determines how many samples to use
*/
func SetPrec(defaultPrec int, usrPrec []int) int {
var prec int
if len(usrPrec) > 0 {
prec = usrPrec[0]
} else {
prec = defaultPrec
}
return prec
}
/*
* Implements functions defined in code of the form: func someFunc(float64) float64
*/
type cFunc func(float64) float64
/*
* Implementation of AntiDiff()
*/
func AntiDiff(f cFunc, a, b float64, i ...int) float64 {
n := SetPrec(10, i)
x, w := GlqNodes(n, f)
var sum float64
bma2 := (b - a) * .5
bpa2 := (b + a) * .5
for i, xi := range x {
sum += w[i] * f(bma2*xi+bpa2)
}
return bma2 * sum
}
func GlqNodes(n int, f cFunc) (node []float64, weight []float64) {
p := LegendrePoly(n)
pn := p[n]
n64 := float64(n)
dn := func(x float64) float64 {
return (x*pn(x) - p[n-1](x)) * n64 / (x*x - 1)
}
node = make([]float64, n)
for i := range node {
x0 := math.Cos(math.Pi * (float64(i+1) - .25) / (n64 + .5))
node[i] = NewtonRaphson(pn, dn, x0)
}
weight = make([]float64, n)
for i, x := range node {
dnx := dn(x)
weight[i] = 2 / ((1 - x*x) * dnx * dnx)
}
return
}
func LegendrePoly(n int) []cFunc {
r := make([]cFunc, n+1)
r[0] = func(float64) float64 { return 1 }
r[1] = func(x float64) float64 { return x }
for i := 2; i <= n; i++ {
i2m1 := float64(i*2 - 1)
im1 := float64(i - 1)
rm1 := r[i-1]
rm2 := r[i-2]
invi := 1 / float64(i)
r[i] = func(x float64) float64 {
return (i2m1*x*rm1(x) - im1*rm2(x)) * invi
}
}
return r
}
func NewtonRaphson(f, df cFunc, x0 float64) float64 {
for i := 0; i < 30; i++ {
x1 := x0 - f(x0)/df(x0)
if math.Abs(x1-x0) <= math.Abs(x0*1e-15) {
return x1
}
x0 = x1
}
panic("no convergence")
}
/*
* Implementation of Diff()
*/
func Diff(fn cFunc, point float64, usrPrec ...int) float64 {
prec := SetPrec(10000000, usrPrec)
h := 1 / float64(prec)
return (fn(point+h) - fn(point)) / h
}
/*
* Wrappers for Diff and AntiDiff for evaluating the function inputted as a string with the Function struct
*/
func (fnc Function) AntiDiff(lower float64, upper float64, usrPrec ...int) float64 {
if len(usrPrec) > 0 {
return AntiDiff(fnc.Eval, lower, upper, usrPrec[0])
} else {
return AntiDiff(fnc.Eval, lower, upper)
}
}
func (fnc Function) Diff(point float64, usrPrec ...int) float64 {
if len(usrPrec) > 0 {
return Diff(fnc.Eval, point, usrPrec[0])
} else {
return Diff(fnc.Eval, point)
}
}