class MonteCarloProbabilityGraph(object):
def __init__(self, window: Frame, arguments: dict, meridians=50):
"""
:param window: The frame which will draw the plot
:param arguments: a dictionary with {str: StringVar} entries
:param meridians: the number of meridians enclosing the radius r_b in the integral
"""
self.window = window
self.arguments = arguments
self.meridians = meridians
self.button = Button(master=window,
text='Simulate',
command=self.__plot_monte_carlo_probability)
self.button.pack()
self.probability = Label(master=window)
self.probability.pack()
self.error = Label(master=window)
self.error.pack()
self.fig = FigureCanvasTkAgg(figsize=(5, 5))
self.points = self.fig.add_subplot(111, projection='3d')
self.canvas = FigureCanvasTkAgg(self.fig, master=window)
self.__plot_monte_carlo_probability()
@staticmethod
def wire_frame_sphere(radius=1E-10,
n_meridians=20,
n_circles_latitude=None):
"""
:param radius: the radius for the sphere limiting with the meridians
:param n_meridians: the number of meridians
:param n_circles_latitude: the latitude of the meridians
:return: the coordinates for the meridians
"""
if n_circles_latitude is None:
n_circles_latitude = max(n_meridians / 2, 4)
u, v = np.mgrid[0:2 * np.pi:n_meridians * 1j,
0:np.pi:n_circles_latitude * 1j]
sphere_x = radius * np.cos(u) * np.sin(v)
sphere_y = radius * np.sin(u) * np.sin(v)
sphere_z = radius * np.cos(v)
return sphere_x, sphere_y, sphere_z
def __plot_monte_carlo_probability(self):
r_a, r_b, theta_a, theta_b, phi_a, phi_b, samples = [
float(e.get()) for e in self.arguments.values()
]
def psi_100_(r_i, theta_i, phi_i):
return np.abs(hy.hydrogen_1s(r_i, theta_i, phi_i))**2
p_1s, r, theta, phi, volume = methods.spherical_monte_carlo_integral(
psi_100_, r_a, r_b, theta_a, theta_b, phi_a, phi_b, int(samples))
self.points.clear()
self.points.set_title(
'\nMonte Carlo Integral of |\u03A8|^2\nin three dimensions',
fontsize=18)
x_ = r * np.sin(theta) * np.cos(phi)
y_ = r * np.sin(theta) * np.sin(phi)
z_ = r * np.cos(theta)
self.points.scatter3D(x_,
y_,
z_,
color='blue',
linewidths=0.1,
alpha=0.1)
self.points.plot_wireframe(*self.wire_frame_sphere(
r_b, self.meridians),
color='orange',
alpha=0.2)
# self.fig.savefig(fname='monte-carlo.png') # it saves locally the plotted image
self.probability['text'] = '\nProbability: ' + str(p_1s) + '\n'
self.error['text'] = 'Error: ' + str(
methods.spherical_monte_carlo_estimation_error(
psi_100_, r, theta, phi, volume, samples))
self.canvas.get_tk_widget().pack()
self.canvas.draw()
