a python script for estimating derivatives from a table of inputs and outputs.

derivative_estimator.py

# derivative estimator.
cont = True
while cont:
    xs, ys = [], []
    while True:
        a = input('enter X: ')
        if len(a) < 1:
            break
        xs.append(float(a))
    
    xlen = len(xs)
    if xlen <= 1:
        print('too little Xs. Try again.')
        continue
    
    while True:
        a = input('enter Y(X): ')
        if len(a) < 1:
            break
        ys.append(float(a))
    
    ylen = len(ys)
    if ylen < xlen:
        print('ylen =/= xlen.')
    else:
        slopes = []
        for idx in range(1, xlen):
            slopes.append((ys[idx] - ys[idx-1]) / (xs[idx] - xs[idx-1]))
        
        avg_slopes = []
        for x in range(1, len(slopes)):
            avg_slopes.append((slopes[x] + slopes[x-1]) / 2)
        
        idx = 0
        for x in range(1, xlen):
            print(f'({ys[x]} - {ys[x-1]} = {ys[x] - ys[x-1]}) / ({xs[x]} - {xs[x-1]} = {xs[x] - xs[x-1]})) = {slopes[idx]}')
            idx += 1
        
        idx = 1
        for x in range(1, xlen-1):
            print(f'derivative for {xs[x]}: ({slopes[idx]} + {slopes[idx-1]}) / 2 = {(slopes[idx] + slopes[idx-1]) / 2}')
            idx += 1
    
    cont = len(input('continue? ')) > 0