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| import matplotlib.pyplot as plt
import numpy as np
import random as rd
import csv
# Grandeurs
xname = 't'
xunit = 'years'
yname = 'd'
yunit = 'km'
# Données
uax = 'y' # axe des incertitudes dominantes
data_live = [
]
data_prep = [
]
with open('data.csv', newline='') as data:
reader = csv.reader(data, delimiter=';', quotechar='|')
for datum in reader:
x = np.float64(datum[0])
y = np.float64(datum[1])
#u = np.float64(datum[2])
u = y*0.1
data_prep.append([x, y, u])
data_prep2 = [[x + 10*rd.random(), y + rd.random(), u] for x,y,u in data_prep]
class Data:
def __init__(self, lists, uax):
arr = np.array(lists)
self.x = arr[:, 0]
self.y = arr[:, 1]
self.u = arr[:, 2]
self.uax = uax
def __iter__(self):
self.current = 0
return self
def __next__(self):
if self.current >= len(self.x):
raise StopIteration
i = self.current
self.current += 1
return Data([[self.x[i], self.y[i], self.u[i]]], self.uax)
# Conversion vers classe Data plus exploitable
data = Data(data_prep + data_live, uax)
data2 = Data(data_prep2 + data_live, uax)
if len(data_live) != 0: data_live = Data(data_live, uax)
def plot_data(data, data_highlight=[], reg=True):
# Plot des points
if uax == 'x': xerr = data.u; yerr = None;
elif uax == 'y': xerr = None; yerr = data.u;
plt.errorbar(
x=data.x,
y=data.y,
xerr=xerr,
yerr=yerr,
marker='+', linestyle='None', elinewidth=1)
# Plot des points mis en Ă©vidence
color = plt.gca().get_lines()[-1].get_color()
for datum in data_highlight:
plt.scatter(datum.x, datum.y, color=color, marker='x')
if reg:
# Calcul de coefs de régression linéaire
u = data.u if np.count_nonzero(data.u) > 0 else np.ones(len(data.u))
S11 = np.sum(1 / (u*u))
Sxx = np.sum(data.x*data.x / (u*u))
Syy = np.sum(data.y*data.y / (u*u))
Sxy = np.sum(data.x*data.y / (u*u))
Sx1 = np.sum(data.x / (u*u))
Sy1 = np.sum(data.y / (u*u))
d = (S11 * Sxx - Sx1*Sx1)
a = (S11 * Sxy - Sx1 * Sy1) / d
b = (Sxx * Sy1 - Sx1 * Sxy) / d
ua = np.sqrt(S11 / d)
ub = np.sqrt(Sxx / d)
uainv = np.abs(1/a * (1/a**2)*ua)
ubinv = np.abs(b/a * np.sqrt((ua*b/a**2)**2 + (ub/a**2)**2))
chi2 = np.sum(((a*data.x + b - data.y)/data.u)**2)
chi2red = chi2 / (len(data.x) - 2)
print("____________________")
print('Ajustement: {} = a.{} + b'.format(yname, xname))
print("a = {}({})".format(a, ua))
print("b = {}({})".format(b, ub))
print("____________________")
print('Ajustement: {} = {}/a - b/a'.format(xname, yname))
print("1/a = {}({})".format(1/a, uainv))
print("-b/a = {}({})".format(-b/a, ubinv))
print("____________________")
print('Chi2 réduit')
print("chi2red = {}".format(chi2red))
print("")
# Calcul de y(predict_x) pour estimer un point sur la droite
print("____________________")
print('Prédiction de {}({})'.format(yname, xname))
predict_x = 4
predict_y = predict_x * a + b
upredict_y = np.sqrt((predict_x * ua)**2 + ub**2)
print("{}({} = {}) = {}({})".format(yname, xname, predict_x, predict_y, upredict_y))
# Calcul de x(predict_y) pour estimer un point sur la droite
print('Prédiction de {}({})'.format(xname, yname))
predict_y = 36.50
predict_x = predict_y/a - b/a
upredict_x = np.sqrt((predict_y * uainv)**2 + ubinv**2)
print("{}({} = {}) = {}({})".format(xname, yname, predict_y, predict_x, upredict_x))
# Arrondi aux chiffres significatifs des coefficients
decimal_a = -int(np.log10(ua) + (-1 if ua <= 1 else 0))
ua_round = np.round(ua, decimal_a)
a_round = np.round(a, decimal_a)
decimal_b = -int(np.log10(ub) + (-1 if ub <= 1 else 0))
ub_round = np.round(ub, decimal_b)
b_round = np.round(b, decimal_b)
# Affichage de la régression linéaire
s = 'a = {} $\pm$ {} ; b = {} $\pm$ {} ; $\chi_r^2$ = {:.3f}'.format(a_round, ua_round, b_round, ub_round, chi2red)
x_min, x_max = plt.xlim()
x_space = np.linspace(x_min, x_max, 2)
plt.plot(x_space, a*x_space + b, color=color, linewidth=1, label=s)
plt.xlim(x_min, x_max) # Un reset des limites est nécessaire
plot_data(data, data_live)
plot_data(data2)
plt.title('Ajustement: {} = a.{} + b ; {} = {}/a - b/a'.format(yname, xname, xname, yname))
plt.xlabel(xname + ' / ' + xunit)
plt.ylabel(yname + ' / ' + yunit)
plt.legend()
# Affichage
plt.show()
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