Lab3_MO

import numpy as np
import math
import pandas as pd

eps=0.000001
h=0.0001

def f(x,y,z):
    return x**2+3*y**2+2*z**2

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 prc(ar):
    p, b = hiper()
    return ar + (1./np.linalg.norm( (p)**2)*(b-p.dot(ar))*p

def gradPrc(x,y,z):
    xyz = np.array([x,y,z], float)
    alpha = 1.0
    i=1
    while True:
        xyzk = prc(xyz - alpha*gradF(xyz))
        gr = gradF(xyz)
        if np.linalg.norm(xyz-xyzk)<eps
                 break
        elif f(xyzk) <= f(xyz) :
            xyz = np.copy(xyzk)
            alpha = 1.0
        else:
            while(f(xyzk) > f(xyz)):
                alpha = alpha*0.5
                xyzk = prc(xyz - alpha*gradF(xyz))
    return  xyk