nelder

import math
from sympy import *
import sympy as sym
from sympy.abc import *

x, y, r = sym.symbols('x y r')


def nelder_mead(func):
    alpha = 1
    beta = 0.5
    gamma = 2
    i = 3000
    v1 = (0, 1)
    v2 = (1, 0)
    v3 = (1, 1)

    for i in range(i):
        a = func.subs({x: v1[0], y: v1[1]})
        b = func.subs({x: v2[0], y: v2[1]})
        c = func.subs({x: v3[0], y: v3[1]})
        adict = {v1: a, v2: b, v3: c}
        points = sorted(adict.items(), key=lambda p: p[0])
        b = points[0][0]
        g = points[1][0]
        w = points[2][0]
        mid = ((g[0] + b[0]) / 2, (g[1] + b[1]) / 2)

        # отражение
        xr = (mid[0] + alpha * (mid[0] - w[0]), mid[1] + alpha * (mid[1] - w[1]))
        if func.subs({x: xr[0], y: xr[1]}) < func.subs({x: g[0], y: g[1]}):
            w = xr
        else:
            if func.subs({x: xr[0], y: xr[1]}) < func.subs({x: w[0], y: w[1]}):
                w = xr
            c = ((w[0] + mid[0]) / 2, (w[1] + mid[1]) / 2)
            if func.subs({x: b[0], y: b[1]}) < func.subs({x: w[0], y: w[1]}):
                w = c
        if func.subs({x: xr[0], y: xr[1]}) < func.subs({x: b[0], y: b[1]}):

            # растяжение
            xe = (mid[0] + gamma * (xr[0] - mid[0]), mid[1] + gamma * (xr[1] - mid[1]))
            if func.subs({x: xe[0], y: xe[1]}) < func.subs({x: xr[0], y: xr[1]}):
                w = xe
            else:
                w = xr
        if func.subs({x: xr[0], y: xr[1]}) > func.subs({x: g[0], y: g[1]}):

            # сжатие
            xc = (mid[0] + beta * (w[0] - mid[0]), mid[1] + beta * (w[1] - mid[1]))
            if func.subs({x: xc[0], y: xc[1]}) < func.subs({x: w[0], y: w[1]}):
                w = xc

        # переобозначим точки: b = best, g = good, w = worst — соответственно.
        v1 = w
        v2 = g
        v3 = b
        if math.sqrt((((func.subs({x: g[0], y: g[1]}) - func.subs({x: mid[0], y: mid[1]})) ** 2) / 3)) > 10 ** (-10):
            continue
        return b