Forward Interpolation.py

# Forward Interpolation
def u_cal(u, n):

    temp = u;
    for i in range(1, n):
        temp = temp * (u - i);
    return temp;

# calculating factorial of given number n

def fact(n):
    f = 1;
    for i in range(2, n + 1):
        f *= i;
    return f;

# Driver Code

# Number of values given
n = 4; # Manual Input
x = [ 45, 50, 55, 60 ]; # Equation y0, y1, y2, y3, y4......

# y[][] is used for difference table
# with y[][0] used for input

y = [[0 for i in range(n)]
        for j in range(n)];

y[0][0] = 0.7071;  # Manual input the Y values
y[1][0] = 0.7660;
y[2][0] = 0.8192;
y[3][0] = 0.8660;

# Calculating the forward difference

for i in range(1, n):
    for j in range(n - i):
        y[j][i] = y[j + 1][i - 1] - y[j][i - 1];
        
        print("");

        print("x\t", "y\t", "\tDeltaY", "\tDelta^2Y", "\tDelta^3Y",.....);

# Displaying the forward difference table
for i in range(n):
    print(x[i], end = "\t");
    for j in range(n - i):
        print(y[i][j], end = "\t");
    print("");

# Value to interpolate at

value = 50; # Manual input

# initializing u and sum

sum = y[0][0];
u = (value - x[0]) / (x[1] - x[0]);
for i in range(1,n):
    sum = sum + (u_cal(u, i) * y[0][i]) / fact(i);

print("\nValue of Y at", value, "is", round(sum, 5));