LAB 3

import numpy as np
import math as mt
######TASK 1

#nodes = int(input("Enter the number of nodes: "))

### FUNCTION TO BE INTERPOLATED

def myFunction(x):
    return x**10 + x**4 + 3*x**2 - 2*x + 1


### TASK 1 & 2
### set chebyshev to true to use chebyshev nodes

def interpolation(nodes, a, b, point, chebyshev=False):
    step = (b-a)/(nodes-1)
    Matrix = np.zeros([3,nodes])

    if chebyshev == False:
        for i in range(0, nodes):
            Matrix[0][i] = a + i*step
            Matrix[1][i] = myFunction(Matrix[0][i])
    else:
        for i in range(0,nodes):
            xi = mt.cos(mt.pi * (2*i + 1) / (2*nodes + 2))
            zi = 0.5*((b-a)*xi + a + b)
            Matrix[0][i] = zi
            Matrix[1][i] = myFunction(Matrix[0][i])

    for i in range(0,nodes):
        nominator = 1
        denominator = 1
        for n, k in enumerate(Matrix[0]):
            if n != i:
                val = (point-k)
                nominator *= val
                val = (Matrix[0][i]-k)
                denominator *= val

        Matrix[2][i] = nominator/denominator * Matrix[1][i]
    return sum(Matrix[2])

### TASK 3

def maxError(a, b, step=0.01):
    maxim = abs(interpolation(31, a, b, a, True) - myFunction(a))
    maxIndex = a
    for i in np.arange(a+step, b, step):
        val = abs(interpolation(31, a, b, i, True) - myFunction(i))
        if val > maxim:
            maxim = val
            maxIndex = i

    return maxIndex, maxim


### TESTS

#print(interpolation(5,0,6.28,mt.pi/6))
#print(interpolation(31, -5, 5, 7, True))
#print(interpolation(31, -5, 5, 7, False))
#print(myFunction(7))

print(myFunction(7))
print(interpolation(31, 0, 8, 7, True))
ind, valueMax = maxError(-30.0, 30.0)
print(ind, valueMax)