Lab/Sem2/Matlab/Lab-4.py at main · ifsvivek/Lab · GitHub

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"""Converted from Lab-4.ipynb"""

# 1. Use Newtons forward interpolation to obtain the interpolating polynomial and hence
# calculate y(2) for the following: x: 1 3 5 7 9
# y: 6 10 62 210 502

from sympy import *
import numpy as np
n = int( input ('Enter number of data points : ') )
x = np . zeros (( n ) )
y = np . zeros (( n , n ) )

print ('Enter data for x and y: ')
for i in range ( n ):
    x[i] = float ( input ( 'x['+str( i )+']= ') )
    y[i][0] = float ( input ( 'y['+str( i )+']= ') )

for i in range (1 , n ):
    for j in range (0 , n-i ):
        y[j][i] = y[j+1][i-1] - y[j][i-1]
print ('\nFORWARD DIFFERENCE TABLE \n') ;
for i in range (0 , n ):
    print ('%0.2f ' %( x[i]) , end='')
    for j in range (0 , n-i ):
        print ('\t\t%0.2f ' %( y[i][j]) , end='')
    print ()

t= symbols ('t')
f=[]
p=( t-x[0])/( x[1]-x[0])
f . append ( p )
for i in range (1 , n-1 ):
    f . append ( f[i-1]*( p-i )/( i+1 ) )
    poly =y[0][0]
for i in range ( n-1 ):
    poly = poly +y[0][i+1]*f[i]
simp_poly = simplify ( poly )
print ('\nTHE INTERPOLATING POLYNOMIAL IS\n') ;
pprint ( simp_poly )

inter = input ('Do you want to interpolate at a point (y/n)? ') # y
if inter =='y':
    a= float ( input ('enter the point ') ) #2
    interpol = lambdify (t , simp_poly )
    result = interpol ( a )
    print ('\nThe value of the function at ' ,a ,'is\n', result ) ;

# 2. Use Newtons backward interpolation to obtain the interpolating polynomial and
# hence calculate y(8) for the following data: x: 1 3 5 7 9
# y: 6 10 62 210 502

from sympy import *
import numpy as np

print (" This will use Newton 's backword intepolation formula ")

n = int( input ('Enter number of data points : ') )

x = np . zeros (( n ) )
y = np . zeros (( n , n ) )

print ('Enter data for x and y: ')
for i in range ( n ):
    x[i] = float ( input ( 'x['+str( i )+']= ') )
    y[i][0] = float ( input ( 'y['+str( i )+']= ') )

for i in range (1 , n ):
    for j in range ( n-1 , i-2 ,-1 ):
        y[j][i] = y[j][i-1] - y[j-1][i-1]
print ('\nBACKWARD DIFFERENCE TABLE \n') ;
for i in range (0 , n ):
    print ('%0.2f ' %( x[i]) , end='')
    for j in range (0 , i+1 ):
        print ('\t%0.2f ' %( y[i][j]) , end='')
    print ()

t= symbols ('t')
f=[]
p=( t-x[n-1])/( x[1]-x[0])
f . append ( p )
for i in range (1 , n-1 ):
    f . append ( f[i-1]*( p+i )/( i+1 ) )
poly =y[n-1][0]
print ( poly )
for i in range ( n-1 ):
    poly = poly +y[n-1][i+1]*f[i]
    simp_poly = simplify ( poly )
print ('\nTHE INTERPOLATING POLYNOMIAL IS\n') ;
pprint ( simp_poly )

inter = input ('Do you want to interpolate at a point (y/n)? ')
if inter =='y':
    a= float ( input ('enter the point ') )
    interpol = lambdify (t , simp_poly )
    result = interpol ( a )
    print ('\nThe value of the function at ' ,a ,'is\n', result ) ;