import math as mth
import cmath as cmt
import numpy as npy
import scipy.linalg as sla
#import matplotlib.pyplot as plt

alpha = 1 / npy.sqrt(2)
beta  = 1 / npy.sqrt(2)
state = npy.array([alpha, beta])

dt = 0.2
iterations = 20

H = npy.array([[2,-2j],[2j,3]])


def time_evolution(state, dt = dt):
    return npy.dot(state, sla.expm(-1j * dt * H))

def bloch_map(state):
    temp  = npy.conj(state[0] / state[1])
    phi   = 2 * npy.arctan(1 / abs(temp))
    theta = npy.arctan(temp.imag / temp.real)
    return npy.array([phi, theta])

def sphere2cart(phi, theta):
        return [
             mth.sin(theta) * mth.cos(phi),
             mth.sin(theta) * mth.sin(phi),
             mth.cos(theta)
        ]

historie = npy.array([bloch_map(state)])
for i in range(iterations):
    state = time_evolution(state)
    h = npy.dot(state, state)
    historie = npy.vstack([historie,bloch_map(state)]) 
    coords = bloch_map(state)
    coords = sphere2cart(coords[0], coords[1])
    print(f"{coords[0]}; {coords[1]}; {coords[2]}")

import plotting
plotting.phi(historie[:,0])