import numpy as np
import matplotlib.pyplot as plt
import PyQt5 as qt

ptot = 1000 # [MW]

def C1(x):
    return 30*x + 0.01*x**2

def C2(x):
    return 20*x + 0.02*x**2

def f(x):
    return C1(x[0]) + C2(x[1]) + x[-1] * (ptot - x[0] - x[1])

def grad(f, x, h=1e-4):
    res = []
    for i in range(len(x)):
        delta = f(x[:i] + [x[i] + h / 2] + x[i+1:]) - f(x[:i] + [x[i] - h / 2] + x[i+1:])
        res += [delta / h]
    return res

def norm(x):
    n = 0
    for d in x:
        n += d**2
    return np.sqrt(n)

def g(x):
    return norm(grad(f, x))

def minize(f, x0, h=1e-4, step=1e-1, tol=1e-8, N=1e4, echo=False):
    x = x0
    g = grad(f, x, h)
    print(g)
    n = 0
    prev = norm(g) + 2*tol
    print(prev, norm(g), abs(norm(g) - prev))
    while abs(norm(g) - prev) > tol:
        n += 1
        prev = norm(g)
        for i in range(len(x)):
            x[i] -= g[i] * step
        g = grad(f, x, h)
        if (n % 100 == 0) and echo:
            print("Itération ", n)
            print("norm(g) = ", norm(g))
            print("prev = ", prev)
            print("x = ", x)
            print("g = ", g)
        if n > N:
            return x
    
    return x

#print(f([500, 500, 40]))
#print(f([450, 450, 35]))
#print(C1(500))
#print(C2(500))
print(minize(g, [0, 0, 0]))