import sys
import subprocess
import math as mth
import cmath as cmt
import numpy as npy
import scipy.linalg as sla

alpha = 1
beta  = 1
dt = 0.1
iterations = 61

H = npy.array([[1,0],[0,2]])

if len(sys.argv) == 3:
    alpha = complex(sys.argv[1])
    beta = complex(sys.argv[2])

norm  = npy.linalg.norm([alpha, beta])
state = npy.array([alpha / norm, beta / norm])

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])
    theta = 2 * npy.arctan(abs(temp))
    phi = cmt.phase(temp)

    return (phi, theta)

def sphere2cart(phi, theta):
        return [
             mth.sin(theta) * mth.cos(phi),
             mth.sin(theta) * mth.sin(phi),
             -1 * mth.cos(theta)
        ]

historie = npy.array([bloch_map(state)])
f = open("data", "w")

for i in range(iterations):
    state = time_evolution(state)
    h = npy.dot(state, state)
    historie = npy.vstack([historie,bloch_map(state)])
    (phi, theta) = bloch_map(state)
    coords = sphere2cart(phi, theta)
    f.write(f"{coords[0]}; {coords[1]}; {coords[2]}; {(i + 1) / iterations}\n")

f.close()

subprocess.run(["gnuplot", "gnuplot.plt"])