laba_5_vm

# z = (x1 + 1)^2 + x1x2 + (x1–3*x2)^2
import random

precision = 0.0000000001


def func(x1, x2):
    return (x1 + 1) ** 2 + x1 * x2 + (x1 - 3 * x2) ** 2


def derivative1(x1, x2):
    # производная по 1 переменной
    return 4 * x1 + 2 - 5 * x2
    # 4 -5


def derivative2(x1, x2):
    # производная по 2 переменной
    return 18 * x2 - 5 * x1
    # -5 18


def test(x1, x2):
    # уравнение из примера
    return (2*x1-5*x2)**2+(3*x1-15)**2


def task1():
    h = 0.01
    x1 = -0.8
    x2 = -0.3
    n = 1000
    f = func(x1, x2)
    for i in range(1, n + 1):
        while True:
            f0 = f
            x1 += h
            f = func(x1, x2)
            if f - f0 > 0:
                break

        while True:
            f0 = f
            x2 += h
            f = func(x1, x2)
            if f - f0 > 0:
                break

        if abs(h) < precision / 2:
            break
        else:
            h -= h / 2
    print("\nx1 = %s\nx2 = %s\nF = %s\niter: %d" % (x1, x2, f, i))


# task1()


def task2():
    f = 1000
    x1, x2, n, h = -1, -1, 1000, 0.01
    for i in range(1, n):
        x10, x20 = x1, x2
        f0, f1, f2 = func(x1, x2), derivative1(x1, x2), derivative2(x1, x2)
        while True:
            f = func(x1, x2)
            x1 -= h * f1
            x2 -= h * f2
            if func(x1, x2) > f:
                break
        if ((x1 - x10) ** 2 + (x2 - x20) ** 2) ** 0.5 < precision * 10:
            print(x1, x2, f, i)
            break
        if abs(func(x1, x2) - f0) < precision * 0.0000001:
            print(x1, x2, f, i)
            break


# task2()


def task3():
    x1, x2, n = 1, 1, 1000
    for i in range(1, n + 1):
        x10, x20 = x1, x2
        f0, f1, f2 = func(x1, x2), derivative1(x1, x2), derivative2(x1, x2)
        while True:
            h = 0.00005
            x11, x21, a = x1, x2, 0
            while True:
                a += h
                fa = func(x11, x21)
                x11 -= a * f1
                x21 -= a * f2
                fb = func(x11, x21)
                if fb >= fa:
                    break
            f = func(x1, x2)
            x1 -= a * f1
            x2 -= a * f2
            if func(x1, x2) > f:
                break
        if ((x1 - x10) ** 2 + (x2 - x20) ** 2) ** 0.5 < precision * 10:
            print(x1, x2, f)
            break
        if abs(func(x1, x2) - f0) < precision * 0.000001:
            print(x1, x2, f)
            break


# task3()


def task4():
    x1, x2, n, alpha, beta = 1, 1, 1000, 0.1, 0.5
    for i in range(1, n + 1):
        x10, x20 = x1, x2
        f0, f1, f2 = func(x1, x2), derivative1(x1, x2), derivative2(x1, x2)
        lmd = alpha
        while True:
            lmd *= beta
            if func(x10 - lmd * f1, x20 - lmd * f2) < f0:
                break
        while True:
            f = func(x1, x2)
            x1 -= lmd * f1
            x2 -= lmd * f2
            if func(x1, x2) < f:
                break
        if ((x1 - x10) ** 2 + (x2 - x20) ** 2) ** 0.5 < precision * 10:
            print(x1, x2, f)
            break
        if abs(func(x1, x2) - f0) < precision * 0.000001:
            print(x1, x2, f)
            break


# task4()


def task5():
    x10, x20, alp, x1, x2 = 1, 1, 1, 1, 1
    while True:
        x1k = x1
        x2k = x2
        f, f1, f2 = func(x1, x2), derivative1(x1, x2), derivative2(x1, x2)
        f11, f12, f21, f22 = 4, -5, -5, 18
        delta = f11 * f22 - f12 * f21
        delta1 = f1 * f22 - f2 * f12
        delta2 = f11 * f2 - f21 * f1
        dx1 = -delta1 / delta
        dx2 = -delta2 / delta
        x1 += alp * dx1
        x2 += alp * dx2
        dev = ((x1 - x1k)**2 + (x2 - x2k)**2)**0.5
        if dev < precision:
            break
    print(x1, x2, f, f1, f2)


# task5()


def task6():
    x1, x2, h, n = 10, 10, 0.01, 100
    for i in range(1, n):
        while True:
            fa = func(x1, x2)
            y = x1
            y1 = y - h
            y2 = y + h
            f0, f1, f2 = func(y, x2), func(y1, x2), func(y2, x2)
            x1 -= (h / 2) * (f2 - f1) / (f2 - 2 * f0 + f1)
            if abs(x1 - y) < precision * 10000:
                break
        while True:
            y = x2
            y1 = y - h
            y2 = y + h
            f0, f1, f2 = func(x1, y), func(x1, y1), func(x1, y2)
            x2 -= (h / 2) * (f2 - f1) / (f2 - 2 * f0 + f1)
            if abs(x2 - y) < precision * 10000:
                break
        fb = func(x1, x2)
        if abs(fa - fb) < precision*0.0000001:
            break
    print(x1, x2, func(x1, x2), i)


# task6()


def task7():
    x1, y1 = 0, 0
    x, y = 0, 0
    f = func(x, y)
    f0 = f
    # здесь я спецом беру такой цикл, желательно подобрать range под свой варик
    # на 1000 делю чтобы закидывать дробные значения в функцию
    for x in range(-1000, 0):
        f = func(x/1000, y/1000)
        if f < f0:
            x1, y1, f0 = x, y, f
        for y in range(-1000, 0):
            f = func(x/1000, y/1000)
            if f < f0:
                x1, y1, f0 = x, y, f
    print(x1/1000, y1/1000, func(x1/1000, y1/1000))
    # -0.766 -0.213 0.234043


# task7()


def task8():
    n, xk, yk = 1000, 100, 100
    x, y = 0, 0
    x1, y1 = 0, 0
    f = func(x, y)
    f0 = f
    for i in range(1, n):
        rnd = random.randint(-8000, -2000) / 10000
        print(rnd)
        x = rnd
        f = func(x, y)
        if f < f0:
            x1, y1, f0 = x, y, f
        for j in range(1, n):
            rnd = random.randint(-8000, -2000) / 10000
            y = rnd
            f = func(x, y)
            if f < f0:
                x1, y1, f0 = x, y, f
        if f0 < 0.0001:
            break
    print(x1, y1, f0)


# task8()