"""
en este ejemplo veremos cómo usarlo para ajustar un conjunto de datos con una curva minimizando una función de error
"""

from pylab import *
from numpy import *
from numpy.random import normal
from scipy.optimize import fmin

# parametric function, x is the independent variable
# and c are the parameters.
# it's a polynomial of degree 2
fp = lambda c, x: c[0] + c[1] * x + c[2] * x * x
real_p = rand(3)

# error function to minimize
e = lambda p, x, y: (abs((fp(p, x) - y))).sum()

# generating data with noise
n = 30
x = linspace(0, 1, n)
y = fp(real_p, x) + normal(0, 0.05, n)

# fitting the data with fmin
p0 = rand(3)  # initial parameter value
p = fmin(e, p0, args=(x, y))

print("estimater parameters: ", p)
print("real parameters: ", real_p)

xx = linspace(0, 1, n * 3)
plot(x, y, "bo", xx, fp(real_p, xx), "g", xx, fp(p, xx), "r")

show()