programming an interpolation polynom relating newton

[Hallo810]

Hello,
i try to programm an interpolation polynom relating newton. I get an interpolation polynom with the values, which is outcommented in the main-method. My problem is to get an interpolationpolynom with the values of an excel list. At the moment I receive the graph of the values without the interolationpolynom and I obtain this error message:

Error:
e:/Python Skripte/test2.py:34: RuntimeWarning: overflow encountered in double_scalars
  counter = counter * (X[i] - X[k-1])
e:/Python Skripte/test2.py:75: RuntimeWarning: invalid value encountered in double_scalars
  C[i] = (Y[i] - sum) / A[i][i]
e:/Python Skripte/test2.py:74: RuntimeWarning: invalid value encountered in double_scalars
  sum = sum + A[i][j] * C[j]

My python code is following:

import pandas as pd
import numpy as np
import numpy.linalg
import matplotlib.pyplot as plt

#Datensatz importieren
dataset = pd.read_excel('Path\...\data.xlsx')
values = dataset.values

valuesX = np.zeros(len(values))
for i in range(len(values)):
    valuesX[i] = values[i][0]

valuesY = np.zeros(len(values))
for j in range(len(values)):
    valuesY[j] = values[j][1]

#print(valuesY[:])

def newton_matrix(X):
    # """Setup the matrix of the LSE which is used to determine the coefficients
    # of the Newton-basis.  X are the x-coordinates of the nodes which are
    # used for interpolation."""
    # Matrix zweidimensional mit Nullen fuellen und 1. Spalte mit 1
    result = np.zeros((len(X), len(X)))
    for a in range(0, len(result)):
        result[a][0] = 1
    # zeilenmaessiges Befuellen der Matrix mit den entsprechenden Polynomen
    for i in range(1, len(result)):
        for j in range(1, i+1):
            counter = 1
            for k in range(1, j+1):
                counter = counter * (X[i] - X[k-1])
            result[i][j] = counter

    return result



def newton_polynomial(C, X):
    # """Take coefficients and interpolation point x-coordinates of the
    # Newton-polynomial and determine the corresponding interpolation polynomial."""
    # Bedingung muss erfuellt sein, ansonsten Abbruch der Methode
    assert len(C) == len(X)

    # Anlegen des Newton-Polynom; Methode poly1d erstellt ein Polynom mithilfe von True gibt er die faktorisierte
    # Form an
    result = np.poly1d([])

    # Erstellen des Interpolationspolynoms nach Newton; np.poly1d gibt fuer eine leere Liste 1 heraus
    for i in range(0, len(C)):
        X_new = []
        for j in range(0, i):
            X_new.append(X[j])
        X_poly = np.poly1d(X_new, True)
        result = result + C[i] * X_poly

    return result


def interpolating_polynomial(X,Y):
    #"""Determine the interpolating polynomial for the given NumPy arrays of x and y coordinates."""
    # Pruefen, ob Bedingung erfuellt wird, ansonsten Abbruch der Methode
    assert len(X) == len(Y)
    # Erstellen der Matrix A
    A = newton_matrix(X)
    # Erstellen des Vektors C
    C = np.zeros(len(A))
    # Koeffizienten des Newton-Polynoms bestimmen und als Polynom darstellen
    for i in range(len(A)):
        sum = 0
        for j in range(len(A)):
            sum = sum + A[i][j] * C[j]
        C[i] = (Y[i] - sum) / A[i][i]
    result = newton_polynomial(C, X)
    return result


def interpolation_plot(X,Y):
    p = interpolating_polynomial(X, Y)
    px = np.arange(min(X)-0.1, max(X)+0.11, 0.01)
    plt.grid(True)
    plt.plot(X, Y, "o")
    plt.plot(px, p(px))
    plt.show()


def main():
   # newton_matrix(np.array([-2., 0., 2.]))
   
   # X = np.array([0, 1, 2,3])
   # Y = np.array([-2.,3.,1.,2.])
    
    X = valuesX
    Y = valuesY
    interpolation_plot(X, Y)

if __name__ == "__main__": main()

In my ecxel list I have 215 x-values and 215 y-values.

Has anybody an idea?

Thank you very much.

Best regards

Gribouillis write Nov-14-2020, 02:57 PM:
Please post all code, output and errors (it it's entirety) between their respective tags. Refer to BBCode help topic on how to post. Use the "Preview Post" button to make sure the code is presented as you expect before hitting the "Post Reply/Thread" button.

[buran]

don't know about the error, but don't use sum as name, it's a built-in function and you override it