CODEWITHSUNDEEP
scipyleast-squares
lhdgriver
lhdgriver

Reputation: 315

In Scipy LeastSq - How to add the penalty term

If the object function is enter image description here

How to code it in python? I've already coded the normal one: enter image description here

    import numpy as np  
    import scipy as sp  
    from scipy.optimize import leastsq 
    import pylab as pl

    m = 9  #the degree of the polynomial

    def real_func(x):
        return np.sin(2*np.pi*x) #sin(2 pi x)

    def fake_func(p, x):
        f = np.poly1d(p) #polynomial
        return f(x)


    def residuals(p, y, x):
        return y - fake_func(p, x)

    #randomly choose 9 points as x
    x = np.linspace(0, 1, 9)

    x_show = np.linspace(0, 1, 1000)

    y0 = real_func(x)
    #add normalize noise
    y1 = [np.random.normal(0, 0.1) + y for y in y0]


    p0 = np.random.randn(m)


    plsq = leastsq(residuals, p0, args=(y1, x))

    print 'Fitting Parameters ：', plsq[0] 

    pl.plot(x_show, real_func(x_show), label='real')
    pl.plot(x_show, fake_func(plsq[0], x_show), label='fitted curve')
    pl.plot(x, y1, 'bo', label='with noise')
    pl.legend()
    pl.show()

Upvotes: 0

Views: 1501

Answers (1)

Josef
Josef

Reputation: 22907

Since the penalization term is also just quadratic, you could just stack it together with thesquares of the error and use weights 1 for data and lambda for the penalization rows.

scipy.optimize.curvefit does weighted least squares, if you don't want to code it yourself.

Upvotes: 0

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