199 lines
7.7 KiB
Python
Executable File
199 lines
7.7 KiB
Python
Executable File
#!/usr/bin/env python3
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import sys, os
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import matplotlib.pyplot as plt
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from random import random, choice
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import numpy as np
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from time import sleep
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import argparse
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"""
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MNI TP3 - 27 janvier 2020
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Dylan Voisin - M1 Informatique Luminy
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Franck Palacios - M1 Informatique Luminy
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Notes:
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- u1 et u2 ne semblent pas orthogonaux, ceci est dû à la non utilisation
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d'une échelle 1:1 pour l'affichage des points
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- u1 et u2 ne sont pas proportionnels par rapport à lambda mais à la
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distance entre le barycentre et le point le plus éloigné selon la
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composante x ou y
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- u1 est orienté «vers la droite» et u2 «vers le haut» dans ce programme
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"""
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def acquérir_depuis_fichier(filename):
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# l_pts = []
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# with open(filename) as f:
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# for line in f:
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# split = line.split()
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# if len(split) == 2:
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# l_pts.append(list(map(float, split)))
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# return np.array(l_pts)
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return np.loadtxt(filename)
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def calc_barycentre(l_pts):
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x = sum(l_pts[:,0]) / len(l_pts)
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y = sum(l_pts[:,1]) / len(l_pts)
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return x, y
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def centrer_points(l_pts, barycentre):
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return l_pts - barycentre
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def calc_matrice_corrélation(l_pts):
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c_pts = centrer_points(l_pts, calc_barycentre(l_pts))
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A = np.array([
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[sum(pt[0] ** 2 for pt in c_pts), sum(pt[0] * pt[1] for pt in c_pts)],
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[sum(pt[0] * pt[1] for pt in c_pts), sum(pt[1] ** 2 for pt in c_pts)]
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])
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return A
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def diagonaliser_matrice22(m):
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a, b, c, d = m[0][0], m[0][1], m[1][0], m[1][1]
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discr = (-d - a) ** 2 - 4 * (a * d - b**2)
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lambda1 = ((d + a) + discr ** .5) / 2
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lambda2 = ((d + a) - discr ** .5) / 2
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if lambda1 != 0:
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if a - lambda1 != 0 and b != 0:
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u1 = np.array([-b, (a-lambda1)])
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u1 *= -1 if b > 0 else 1
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else:
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u1 = np.array([lambda1, 0])
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u2 = np.array([-u1[1], u1[0]])
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else:
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if a - lambda2 != 0 and b != 0:
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u2 = np.array([-b, (a-lambda2)])
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u2 *= -1 if b < 0 else 1
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else:
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u2 = np.array([lambda2, 0])
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u1 = np.array([u2[1], -u2[0]])
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return u1, u2, lambda1, lambda2
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def get_info_affichage(l_pts):
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"""renvoie les vecteurs u1 et u2 pour l'affichage ainsi que xmin, xmax, ymin, ymax"""
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bary = calc_barycentre(l_pts)
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u1, u2 = diagonaliser_matrice22(calc_matrice_corrélation(l_pts))[:2]
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dist = min(max(l_pts[:,0]) - bary[0], max(l_pts[:,1]) - bary[1])
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dist_x = max(l_pts[:,0]) - min(l_pts[:,0])
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dist_y = max(l_pts[:,1]) - min(l_pts[:,1])
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x_range = min(l_pts[:,0]) - 0.1 * dist_x, max(l_pts[:,0]) + 0.1 * dist_x
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y_range = min(l_pts[:,1]) - 0.1 * dist_y, max(l_pts[:,1]) + 0.1 * dist_y
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u1 = u1 / np.linalg.norm(u1) * dist
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u2 = u2 / np.linalg.norm(u2) * 1/2 * dist
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return u1, u2, x_range, y_range, dist
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def visualiser_nuage(l_pts):
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bary = calc_barycentre(l_pts)
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u1, u2 = diagonaliser_matrice22(calc_matrice_corrélation(l_pts))[:2]
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dist = min(max(l_pts[:,0]) - bary[0], max(l_pts[:,1]) - bary[1])
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u1 = u1 / np.linalg.norm(u1) * dist
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u2 = u2 / np.linalg.norm(u2) * 1/2 * dist
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ax = plt.axes()
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# plot du nuage
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plt.scatter(l_pts[:,0], l_pts[:,1])
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ax.arrow(*bary, *u1, head_length=0.1*dist, head_width=0.1*dist, ec="black", fc="white")
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ax.arrow(*bary, *u2, head_length=0.1*dist, head_width=0.1*dist, ec="black", fc="white")
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# ax.set_aspect('equal')
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plt.show()
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def animation_nuage(l_pts, loops=10, time_sleep=2, delta_bruit=3):
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plt.ion()
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fig = plt.figure()
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ax = fig.add_subplot(111)
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fig.canvas.draw()
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# nuage courant (pas de do while en Python)
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bary = calc_barycentre(l_pts)
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u1, u2, x_range, y_range, dist = get_info_affichage(l_pts)
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sc = ax.scatter(l_pts[:,0], l_pts[:,1])
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arr1 = ax.arrow(*bary, *u1, head_length=0.1*dist, head_width=0.1*dist, ec="black", fc="white")
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arr2 = ax.arrow(*bary, *u2, head_length=0.1*dist, head_width=0.1*dist, ec="black", fc="white")
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plt.title("itération 0")
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fig.canvas.flush_events()
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fig.canvas.draw()
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fig.canvas.flush_events()
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sleep(time_sleep) # attente avant animation suivante
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for i in range(loops):
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plt.title("itération " + str(i+1))
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# aléa
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ran = np.random.random(l_pts.shape) * 2 * delta_bruit - delta_bruit
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l_pts += ran
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# recalcul des données
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bary = calc_barycentre(l_pts)
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u1, u2, x_range, y_range, dist = get_info_affichage(l_pts)
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ax.set_xlim(*x_range)
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ax.set_ylim(*y_range)
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# plot
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sc.set_offsets(l_pts) # repositionnement des points
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arr1.remove() # on enlève les vecteurs
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arr2.remove()
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arr1 = ax.arrow(*bary, *u1, head_length=0.1*dist, head_width=0.1*dist, ec="black", fc="white")
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arr2 = ax.arrow(*bary, *u2, head_length=0.1*dist, head_width=0.1*dist, ec="black", fc="white")
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fig.canvas.flush_events()
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fig.canvas.draw() # on redessine
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fig.canvas.flush_events()
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sleep(time_sleep) # attente avant animation suivante
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def main(argv):
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parser = argparse.ArgumentParser()
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gps = parser.add_mutually_exclusive_group(required=True)
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gpi = parser.add_mutually_exclusive_group(required=True)
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gpi.add_argument("-i", "--input",
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help="input file for dots - if none, generate dots")
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gpi.add_argument("-f", "--function",
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help="function to use to generate dots, ex -f 3*x+4")
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parser.add_argument("-N", "--nb-dots", type=int, default=500,
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help="number of dots to generate (from 0 to NB_DOTS) from function")
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gps.add_argument("-s", "--show", action="store_true",
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help="show cloud of dots with u1 and u2")
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gps.add_argument("-l", "--loop", type=int, default=10,
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help="number of loop to show/perform on randomized dots from originals ones")
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parser.add_argument("-d", "--delay", type=float, default=2,
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help="amount of time between each loop")
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parser.add_argument("-n", "--noise", type = float, default=10,
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help="maximum value of the noise applied between each step")
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if not argv:
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parser.print_usage()
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sys.exit(0)
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args = parser.parse_args(argv)
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if args.input:
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if not os.path.isfile(args.input):
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print("File", args.input, "not found.", file=sys.stderr)
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sys.exit(1)
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else:
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l_pts = acquérir_depuis_fichier(args.input)
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else:
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l_pts = []
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n = args.nb_dots # nombre de points
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f = lambda x: eval(args.function) # fonction génératrice de la ditribution
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delta_bruit = 0 # bruit généré, 0 si on en veut aucun
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for i in range(n):
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y = f(i) + choice((-1, 1)) * random() * delta_bruit/2
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l_pts.append([i, y])
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l_pts = np.array(l_pts)
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if args.show:
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visualiser_nuage(l_pts)
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elif args.loop:
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animation_nuage(l_pts, args.loop, args.delay, args.noise)
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if __name__ == "__main__":
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# if len(sys.argv) == 2:
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# l_pts = acquérir_depuis_fichier(sys.argv[1])
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# else:
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# l_pts = []
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# n = 500 # nombre de points
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# f = lambda x: x/2 + 3 # fonction génératrice de la ditribution
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# delta_bruit = 10 # bruit généré, 0 si on en veut aucun
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# for i in range(n):
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# y = f(i) + choice((-1, 1)) * random() * delta_bruit/2
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# l_pts.append([i, y])
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# l_pts = np.array(l_pts)
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# # np.savetxt("pts.txt", l_pts, "%f")
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# u1, u2 = diagonaliser_matrice22(calc_matrice_corrélation(l_pts))[:2]
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# # print(f"{u1/np.linalg.norm(u1)=}\n{u2/np.linalg.norm(u2)=}")
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# visualiser_nuage(l_pts)
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# animation_nuage(l_pts, 20, delta_bruit=100)
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main(sys.argv[1:])
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