fminIn this part of the example, we define a function f() and estimate the arguments that minimise it. For this we use fmin(), which has a similar interface to SciPy's fmin().
In [1]:
import pints
# Define a quadratic function f(x)
def f(x):
return 1 + (x[0] - 3) ** 2 + (x[1] + 5) ** 2
# Choose a starting point for the search
x0 = [1, 1]
# Find the arguments for which it is minimised
xopt, fopt = pints.fmin(f, x0, method=pints.XNES)
print(xopt)
print(fopt)
We can make a contour plot near the true solution to see how we're doing
In [3]:
import numpy as np
import matplotlib.pyplot as plt
x = np.linspace(0, 6, 100)
y = np.linspace(-10, 0, 100)
X, Y = np.meshgrid(x, y)
Z = f(np.stack((X, Y)))
plt.figure()
plt.contour(X, Y, Z)
plt.plot(xopt[0], xopt[1], 'x')
plt.show()
curve_fitIn this part of the example we fit a curve to some data, using curve_fit(), which has a similar interface to SciPy's curve_fit().
In [4]:
# Define a quadratic function `y = f(x|a, b, c)`
def f(x, a, b, c):
return a + b * x + c * x ** 2
# Generate some test noisy test data
x = np.linspace(-5, 5, 100)
e = np.random.normal(loc=0, scale=2, size=x.shape)
y = f(x, 9, 3, 1) + e
# Find the parameters that give the best fit
p0 = [0, 0, 0]
popt = pints.curve_fit(f, x, y, p0, method=pints.XNES)
print(popt)
Again, we can use matplotlib to have a look at the results
In [5]:
plt.figure()
plt.xlabel('x')
plt.ylabel('y')
plt.plot(x, y, 'x', label='Noisy data')
plt.plot(x, f(x, 9, 3, 1), label='Original function')
plt.plot(x, f(x, *popt), label='Esimated function')
plt.legend()
plt.show()