import math
import random
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits import mplot3d
from random import uniform

#a=[-5,5]
#a=[-5.12,5.12]
a=[-10,10]
def f1(x):
    return (x[0] - 3) ** 2 + (x[1] + 1) ** 2
def f2(x):
    return (1 - x[0]) ** 2 + 100 * (x[1] - x[0] ** 2) ** 2
def f3(x):
    return (20 + (x[0] ** 2 - 10 * np.cos(2 * 3.14 * x[0])) + (x[1] ** 2 - 10 * np.cos(2 * 3.14 * x[1])))
def f4(x):
    return (-abs(np.sin(x[0]) * np.cos(x[1]) * np.e**(abs(1 - (np.sqrt((x[0] ** 2) + (x[1] ** 2)) / 3.14)))))

def TS(f,x0,delta_x,N,eps,L):
    i=0
    t=[]
    x=x0
    v=f(x0)
    r=x
    while True:
        i=i+1
        x1 = x[0]
        x2 = x[1]
        dx1 = delta_x[0]
        dx2 = delta_x[1]
        omega=[]
        okolina=[[x1+dx1, x2+dx2],[x1+dx1, x2],[x1+dx1, x2-dx2],[x1, x2-dx2],[x1-dx1, x2-dx2],[x1-dx1, x2],[x1-dx1, x2+dx2],[x1, x2+dx2]]
        for j in okolina:
            if j[0]<a[0]:
                j[0]=a[0]
            elif j[0]>a[1]:
                j[0]=a[1]
            if j[1]<a[0]:
                j[1]=a[0]
            elif j[1]>a[1]:
                j[1]=a[1]
        for k in okolina:
            if k in t:
                continue
            else:
                if not omega:
                    omega.append(k)
                elif f(k)<f(omega[0]):
                    omega[0]=k
        if not omega:
            omega.append(okolina[0])
        else:
            x=omega[0]
        if(len(t)>L):
            t=t[1:]
        t.append(x)
        if i>N or np.abs(f(x)-f(r))<eps:
            break
        if f(x)<f(r):
            r=x
    return r,f(r)

def LS(f, x0, delta_x, N, eps):
    x=x0
    i=0

    for i in range(N):
        v=f(x)
        x1 = x[0]
        x2 = x[1]
        dx1 = delta_x[0]
        dx2 = delta_x[1]
        omega=[]
        okolina=[[x1+dx1, x2+dx2],[x1+dx1, x2],[x1+dx1, x2-dx2],[x1, x2-dx2],[x1-dx1, x2-dx2],[x1-dx1, x2],[x1-dx1, x2+dx2],[x1, x2+dx2]]
        for j in range(0,len(okolina)):

            xpom = okolina[j]
            if (xpom[0]<a[0]):
                xpom[0]=a[0]
            if (xpom[0]>a[1]):
                xpom[0]=a[1]
            if (xpom[1]<a[0]):
                xpom[1]=a[0]
            if (xpom[1]>a[1]):
                xpom[1]=a[1]
            vpom = f(xpom)
            if (vpom < v):
                omega.append(xpom)
        if (omega==[]):
            return (x, f(x))
        else:
            mini=f(omega[0])
            for k in range(0,len(omega)):
                if (f(omega[k])<=mini):
                    x=omega[k]
                    mini=f(x)
        if abs(f(x) - f(xpom)) < eps:
           break;
    return (x, f(x))
def ILS(f,x0,delta_x,N,eps):
    br=0
    memorija=[]
    x = LS(f, x0, delta_x,N, eps)
    memorija.append(x0)
    while br<N:
        x1=LS(f, Perturbacija(x,memorija),delta_x,N, eps)
        d = abs(x1[1] - x[1])
        if ((x1[1] < x[1]) and (x1[0] not in memorija)):
            x = x1
        memorija = AzuriranjeMemorije(x, x1, memorija)
        if (d >= eps):
            br=br+1
        else:
            return (x[0], x[1])

    return (x[0], x[1])

def Perturbacija(x,memorija):
    tacka = [uniform(a[0],a[1]),uniform(a[0],a[1])]
    if ((tacka in memorija) or (tacka == x[0])):
        tacka = Perturbacija(x, memorija)
    memorija.append(tacka)
    return tacka

def AzuriranjeMemorije(xpom,xrand,memorija):
    if (xpom[0] not in memorija):
        memorija.append(xpom[0])
    if (xrand[0] not in memorija):
        memorija.append(xrand[0])
    return memorija


primjer=TS(f4, [3, 3],[0.1, 0.1], 10000, 0, 1000)
print(primjer)
novi=[]
novi.append(primjer[0])
drugi = ILS(f4, [3, 3],[0.1, 0.1],10000, 0)
print("ILS: ",drugi)
novi.append(drugi[0])
a=novi[0] #tacka dobijena funkcijom TS
b=novi[1] #tacka dobijena funkcijom ILS
x1=np.linspace(-10,10,100)
x2=np.linspace(-10,10,100)
X1,X2=np.meshgrid(x1,x2)
X=[X1,X2]
Y=f4(X)
fig=plt.figure()
ax=plt.axes(projection='3d')
ax.contour(X1,X2,Y,50,cmap='binary')
ax.scatter(a[0],a[1],f4(a), color='blue',marker='x')
ax.scatter(b[0],b[1],f4(b), color='green',marker='x')
MIN=[3,-1]
MIN2=[1,1]
#ax.scatter(1,1,f2(MIN2),color='red',marker='o') #ekstremi za drugu funkciju
#ax.scatter(3,-1,f1(MIN),color='red',marker='o') #ekstremi za prvu funkciju
ax.set_xlabel('$x_1$')
ax.set_ylabel('$x_2$')
ax.set_zlabel('$f(x_1,x_2)$')
plt.show()