CODEWITHSUNDEEP
pythonreturnconvergence
Yalom
Yalom

Reputation: 113

Calculating the rate of convergence of the code using newton method

My task is to write a program which calculates the rate of convergence of a method. I had to use the newton method to make an approximation of the root. This part of the code is ok and works well, but I will inculde it. 

x0 : start value

F: function

DF: jacobi matrix

tol : tolerance rate of the approximation. If it is reached the loop shall be stopped --> that`s why I calculate with count

maxit: maximum iterations

Important is that I was trying to do it for any n dimensions. 

def konv(x0, F, FD, tol, maxit):

#set counter of the iterations to zero and define an array for the values of x in the iteration 

    count = 0
    x = np.zeros([np.shape(x0)[0], maxit])

    x[:,0] = x0

#fill the array with the values given by the formula x_k+1 = x_k - ((DF(x_k))^(-1)*F(x_k))
#((DF(x_k))^(-1)*F(x_k)) = s

    for i in range(maxit):
        count = 1+i

        s =  np.linalg.solve(DF(x[..., i]), F(x[..., i]))
        x[..., i+1] = x[..., i] - s

        if np.all((np.linalg.norm(x[..., i+1]-x[..., i]) < tol*np.linalg.norm(x[..., i]))):
            break
#define an array which stores the errors
    e = np.zeros(count)

    for i in range(count):
        e[i] = np.linalg.norm(x[..., i] - x[..., count])

#return the rate of convergence

    return lambda e : np.log(e[2:]/e[1:-1]/np.log(e[1:-1])/e[:-2])

The main part:

if __name__ == "__main__":


    p = konv(x0, F, DF, tol, maxit)
    print(p)

The result I'm getting is:

[ 0.39384945  0.03214274] 6
<function konv.<locals>.<lambda> at 0x0000023312A82268>

What does this mean? Isn't it supposed to return a number? Why are there letters in my returned value?

Upvotes: 0

Views: 3159

Answers (1)

Ioannis Begleris
Ioannis Begleris

Reputation: 21

You are returning a function instead of a number by using the lambda function.

Simply return:

return np.log(e[2:]/e[1:-1]/np.log(e[1:-1])/e[:-2])

Upvotes: 2

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