Lab 3

package main

import (
    "fmt"
    "math"
    )

func main(){
    var (
        xVals = []float64{0.5, 0.6, 0.7, 0.8}
        yVals = []float64{-1, 0, 1, 5}
    )

    fmt.Printf("%-10s | %-10s | %-10s | %-10s\n", "xi", "Ln(xi)", "Rn(xi)", "dRn(xi)")

    for index, xVal := range xVals {
        fmt.Printf("%10.1f | %10.3f | %10e | %10e\n", xVal, ln(xVal, xVals, yVals), rn(x, xVals), deltaRn(x, xVals, yVals))
}

func lagrange(n int, x float64, values []float64) float64 {
    var product = 1.0

    for index, val := range values {
        if index != n {
            product *= (x - val) / (values[n] - val)
        }
    }

    return product
}

func ln(x float64, xVals []float64, yVals []float64) float64 {
    var sum = 0.0

    for i, yi := range yVals {
        sum += yi * lagrange(i, x, xVals)
    }

    return sum
}

func w(x float64, values []float64) float64 {
    var product = 1.0

    for _, val := range values {
        product *= x - val
    }

    return product
}

func rn(x float64, values []float64) float64 {
    return math.Abs(w(x, values)) / 24
}

func deltaRn(x float64, xVals []float64, yVals []float64) float64 {
    return math.Abs(rn(x, xVals)) / math.Abs(ln(x, xVals, yVals))
}