import numpy as npimport matplotlib.pyplot as pltfrom scipy.interpolate import CubicSplineX=[0,6,10,13,17,20,28]Y_1=[15.67,20.33,30.67,25.33,35.10,30.31,28.5]Y_2=[15.67,17.11,20.89,15.00,10.56,10.44,8.5]n=len(X)-1def spline(X: list, Y: list)-> list: Coefflist=[] #write cubic spline interpolation n=len(X)-1 a=Y h=[X[i+1]-X[i] for i in range(n)] alpha=[0]+[3*(a[i+1]-a[i])/h[i]-3*(a[i]-a[i-1])/h[i-1] for i in range(1,n)] l=[1] mu=[0] z=[0] for i in range(1,n): l+=[2*(X[i+1]-X[i-1])-h[i-1]*mu[i-1]] mu+=[h[i]/l[i]] z+=[(alpha[i]-h[i-1]*z[i-1])/l[i]] l+=[1] z+=[0] c=[0]*(n+1) b=[0]*n d=[0]*n for j in range(n-1,-1,-1): c[j]=z[j]-mu[j]*c[j+1] b[j]=(a[j+1]-a[j])/h[j]-h[j]*(c[j+1]+2*c[j])/3 d[j]=(c[j+1]-c[j])/(3*h[j]) Coefflist=[a[:n],b,c,d] return Coefflistfullspline_1=spline(X,Y_1)fullspline_2=spline(X,Y_2)def splinecoef_to_poly(coeff): n=len(coeff[0]) polylist=[] for i in range(n): polylist+=[[coeff[0][i],coeff[1][i],coeff[2][i],coeff[3][i]]] return polylistimport pandas as pddef poly_to_dataframe(polynomial_coeff): df=pd.DataFrame(polynomial_coeff,columns=['a','b','c','d'],index=X[:-1]) return dfprint("First Weight Sample: \n",poly_to_dataframe(splinecoef_to_poly(fullspline_1)))print("\n")print("Second Weight Sample: \n",poly_to_dataframe(splinecoef_to_poly(fullspline_2)))data_1=splinecoef_to_poly(fullspline_1)data_2=splinecoef_to_poly(fullspline_2)def spline_eval(data: list, x: float)-> float: n=len(data) for i in range(n): if x>=X[i] and x<=X[i+1]: return data[i][0]+data[i][1]*(x-X[i])+data[i][2]*(x-X[i])**2+data[i][3]*(x-X[i])**3def spline_plot(data: list, X: list, Y: list)-> None: n=len(data) x=np.linspace(X[0],X[n],100) y=[spline_eval(data,i) for i in x] plt.plot(x,y) plt.plot(X,Y,'o') spline_plot(data_1,X,Y_1)plt.show()spline_plot(data_2,X,Y_2)plt.show()def differ_forward(point,step,data): point_1=point point_2=point+step flag=None for i in range(len(X)): if point>=X[i] and point<=X[i+1]: flag=i break if flag==None: return "Error" else: x_1=data[flag][0]+data[flag][1]*(point_1-X[flag])+data[flag][2]*(point_1-X[flag])**2+data[flag][3]*(point_1-X[flag])**3 x_2=data[flag][0]+data[flag][1]*(point_2-X[flag])+data[flag][2]*(point_2-X[flag])**2+data[flag][3]*(point_2-X[flag])**3 return (x_2-x_1)/stepdef maxval(X:list,Y:list,stepsize:float,roundoff:int): X_diff=np.arange(X[0],X[-1],stepsize) data=splinecoef_to_poly(spline(X,Y)) Y_diff=[differ_forward(i,stepsize,data) for i in X_diff] Y_interp=[spline_eval(data,i) for i in X_diff] abs_list=[round(abs(i),roundoff) for i in Y_diff] null_list=[] for i in range(len(abs_list)): if abs_list[i]==0: null_list+=[i] max_candidate=[] for i in null_list: if Y_diff[i+1]<Y_diff[i]: max_candidate+=[i] max_elements=[Y_interp[i] for i in max_candidate] max_element=max(max_elements) val=X_diff[Y_interp.index(max_element)] return val,max_elementprint(maxval(X,Y_1,0.0001,2))print(maxval(X,Y_2,0.0001,2))def lagrange(A,B): n=len(A) def L(i,x): l=1 for j in range(n): if j!=i: l*=(x-A[j])/(A[i]-A[j]) return l def P(x): p=0 for i in range(n): p+=B[i]*L(i,x) return p return Pdef lagrange_plot(A,B): P=lagrange(A,B) x=np.linspace(A[0],A[-1],100) y=[P(i) for i in x] plt.plot(x,y) plt.plot(A,B,'o') lagrange_plot(X,Y_1)spline_plot(data_1,X,Y_1)plt.legend(['Lagrange','Spline'])plt.show()lagrange_plot(X,Y_2)spline_plot(data_2,X,Y_2)plt.legend(['Lagrange','Spline'])plt.show()Modify this code so that it should look different but should give same output , dont change the data points , change things such as varable name , functions name , data arrays name , plot colours , plot legends etc

import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import CubicSpline
import pandas as pd

# Data points
x_points=[0,6,10,13,17,20,28]
y_points1=[15.67,20.33,30.67,25.33,35.10,30.31,28.5]
y_points2=[15.67,17.11,20.89,15.00,10.56,10.44,8.5]

# Function to calculate cubic spline interpolation
def cubic_spline_interpolation(x_values: list, y_values: list)-> list:
    # Your code here
    pass

# Function to convert spline coefficients to polynomial
def convert_spline_to_poly(coefficients):
    # Your code here
    pass

# Function to convert polynomial to dataframe
def convert_poly_to_dataframe(polynomial_coefficients):
    # Your code here
    pass

# Function to evaluate spline
def evaluate_spline(data: list, x: float)-> float:
    # Your code here
    pass

# Function to plot spline
def plot_spline(data: list, x_values: list, y_values: list)-> None:
    # Your code here
    pass

# Function to calculate forward difference
def forward_difference(point, step, data):
    # Your code here
    pass

# Function to find maximum value
def find_max_value(x_values:list, y_values:list, step_size:float, round_off:int):
    # Your code here
    pass

# Function for Lagrange interpolation
def lagrange_interpolation(A,B):
    # Your code here
    pass

# Function to plot Lagrange interpolation
def plot_lagrange_interpolation(A,B):
    # Your code here
    pass

# Plotting
plot_lagrange_interpolation(x_points, y_points1)
plot_spline(data_1, x_points, y_points1)
plt.legend(['Lagrange Interpolation','Cubic Spline Interpolation'])
plt.show()

plot_lagrange_interpolation(x_points, y_points2)
plot_spline(data_2, x_points, y_points2)
plt.legend(['Lagrange Interpolation','Cubic Spline Interpolation'])
plt.show()