MO_Lab4

import numpy as np
import math
import pandas as pd
from scipy import optimize

eps=0.000001
h=0.0001

def f(ar):
    x = ar[0]
    y = ar[1]
    z = ar[2]
    return x**2+8*y**2+0.001*x*y-x-y

def hiper():
    return (np.array([2,1,3]),1)

def dFx(ar):
    x = ar[0]
    y = ar[1]
    z = ar[2]
    return (f(x+h,y,z)-f(x-h,y,z))/(2*h)

def dFy(ar):
    x = ar[0]
    y = ar[1]
    z = ar[2]
    return (f(x,y+h,z)-f(x,y-h,z))/(2*h)

def dFz(ar):
    x = ar[0]
    y = ar[1]
    z = ar[2]
    return (f(x,y,z+h)-f(x,y,z-h))/(2*h)

def gradF(ar):
    return np.array([dFx(ar), dFy(ar),dFz(ar)], float)


def gradSopr(x,y,z):
    #1 step
    xkj = np.array([x,y,z], float)
    k=0
    #2 step
    j=0
    skj = -gradF(xkj)
    #3 step
    while True:# Минимизацию нужно заменить на Golden Selection
        lmbd = optimize.minimize(lambda l: f(xkj+l*skj), [0,1,0], method='nelder-mead').x   #[0,1,0] - начальная точка
        xkj1 = xkj + lmbd*skj
        omega = (np.linalg.norm(gradF(xkj1))**2)/(np.linalg.norm(gradF(xkj))**2)
        skj1 = gradF(xkj1) + omega*skj
        if np.linalg.norm(skj1)<eps or np.linalg.norm(xkj1 - xkj)<eps:
            break
        elif j<n:
            j++
        else:
            xkj = xkj1
            j=0
            skj = -gradF(xkj)
            k++