a = 1
b = 2
printf ("%12.10f\n" , bisection(a, b))

def bisection(a, b) {
    while (true) {
        // 区間 (a, b) の中点 c = (a + b) / 2
        c = (a + b) / 2
        printf("%12.10f\t%13.10f\n", c, c - Math.sqrt(2))

        fc = f(c)
        if (Math.abs(fc) < 0.0000000001) break

        if (fc < 0) {
            // f(c) < 0 であれば, 解は区間 (c, b) の中に存在
            a = c
        } else {
            // f(c) > 0 であれば, 解は区間 (a, c) の中に存在
            b = c
        }
    }
    c
}

def f(x) {
    x * x - 2
}
a = 1
b = 2
printf ("%12.10f\n" , falseposition(a, b))

def falseposition(a, b) {
    while (true) {
        // 点 (a,f(a)) と 点 (b,f(b)) を結ぶ直線と x軸の交点
        c  = (a * f(b) - b * f(a)) / (f(b) - f(a))
        printf("%12.10f\t%13.10f\n", c, c - Math.sqrt(2))

        fc = f(c)
        if (Math.abs(fc) < 0.0000000001) break

        if (fc < 0) {
            // f(c) < 0 であれば, 解は区間 (c, b) の中に存在
            a = c
        } else {
            // f(c) > 0 であれば, 解は区間 (a, c) の中に存在
            b = c
        }
    }
    c
}

def f(x) {
    x * x - 2
}
x = 1
printf ("%12.10f\n" , iterative(x))

def iterative(x0) {
    while (true) {
        x1 = g(x0)
        printf("%12.10f\t%13.10f\n", x1, x1 - Math.sqrt(2))

        if (Math.abs(x1 - x0) < 0.0000000001) break
        x0 = x1
    }
    x1
}

def g(x) {
    (x / 2) + (1 / x)
}
x = 2
printf ("%12.10f\n" , newton(x))

def newton(x0) {
    while (true) {
        x1 = x0 - (f0(x0) / f1(x0))
        printf("%12.10f\t%13.10f\n", x1, x1 - Math.sqrt(2))

        if (Math.abs(x1 - x0) < 0.0000000001) break
        x0 = x1
    }
    x1
}

def f0(x) {
    x * x - 2
}

def f1(x) {
    2 * x
}
x = 2
printf ("%12.10f\n" , bailey(x))

def bailey(x0) {
    while (true) {
        x1 = x0 - (f0(x0) / (f1(x0) - (f0(x0) * f2(x0) / (2 * f1(x0)))))
        printf("%12.10f\t%13.10f\n", x1, x1 - Math.sqrt(2))

        if (Math.abs(x1 - x0) < 0.0000000001) break
        x0 = x1
    }
    x1
}

def f0(x) {
    x * x - 2
}

def f1(x) {
    2 * x
}

def f2(x) {
    2
}
x0 = 1
x1 = 2
printf ("%12.10f\n" , secant(x0, x1))

def secant(x0, x1) {
    while (true) {
        x2 = x1 - f(x1) * (x1 - x0) / (f(x1) - f(x0))
        printf("%12.10f\t%13.10f\n", x2, x2 - Math.sqrt(2))

        if (Math.abs(x2 - x1) < 0.0000000001) break
        x0 = x1
        x1 = x2
    }
    x2
}

def f(x) {
    x * x - 2
}
N = 3

def a = [[ 9.0,  2.0, 1.0,  1.0], [2.0, 8.0, -2.0, 1.0], [-1.0, -2.0, 7.0, -2.0], [1.0, -1.0, -2.0, 6.0]]  as double[][]
def b =  [20.0, 16.0, 8.0, 17.0] as double[]
def c =  [ 0.0,  0.0, 0.0,  0.0] as double[]

// ヤコビの反復法
jacobi(a,b,c)

println("解")
for (i in 0..N ) {
    printf ("%14.10f\t" , c[i])
}
println()

// ヤコビの反復法
def jacobi(a, b, x0) {
    def x1 =  [ 0.0,  0.0, 0.0,  0.0] as double[]

    while (true) {
        def finish = true
        for (i in 0..N ) {
            x1[i] = 0
            for (j in 0..N ) {
                if (j != i)
                    x1[i] += a[i][j] * x0[j]
            }
            x1[i] = (b[i] - x1[i]) / a[i][i]
            if (Math.abs(x1[i] - x0[i]) > 0.0000000001)
                finish = false
        }

        for (i in 0..N ) {
            x0[i] = x1[i]
            printf ("%14.10f\t" , x0[i])
        }
        println()

        if (finish) return
    }
}