Galianoxd

import numpy as np

# EXERCISE 1. GROUP LI 1-A EXAM. Below this line.

def de2bi_a(d):
    x = np.fix(d)
    b = []

    while x/2 > 0:
        b.append(x%2)
        x = x//2

    b = np.array(b, dtype = np.int8)
    return np.flipud(b);

def de2bi_b(d):
    x = abs(d) - abs(int(d))
    b = []
    counter = len(str(x)) - 2

    while counter > 0:
        x = x*2
        aux = round(int(x))
        b.append(aux)
        if x > 1:
            x = x - int(x)
        counter = counter - 1

    b = np.array(b, dtype=np.int8)
    return b

def de2bi_total(d):
    dec = de2bi_a(d)
    frac = de2bi_b(d)
    exp = de2bi_a((len(dec) - 1) + 127)
    result = []

    if (d < 0):
        result.append(1)
    else:
        result.append(0)

    for i in exp:
        result.append(i)

    counter = 0

    for i in dec:
        if counter > 0:
            result.append(i)
        counter = counter + 1

    for i in frac:
        result.append(i)
        counter = counter + 1

    while counter < 24:
        result.append(0)
        counter = counter + 1

    result = np.array(result, dtype=np.int8)
    return result

r = de2bi_total(2345.640625)
np.savez('exercise_1', r)

# EXERCISE 2. GROUP LI 1-A EXAM. Below this line.

def lagrange_fundamental(i, x, nodes):
    result = float(1)

    for j in range(len(nodes)):
        if (j != i):
            result = result * ((x-nodes[j])/(nodes[i]-nodes[j]))
        else:
            result = result

    return result

def lagrange_polynomial(x, nodes, values):
    result = float(0)

    for j in range(len(nodes)):
        result += lagrange_fundamental(j, x, nodes) * values[j]

    return result

nodes = np.array([2,4,5,7,8,10], dtype = float)
values = np.array([2,6,5,5,6,2], dtype = float)
mesh = np.linspace(2,10,100)

v = lagrange_polynomial(mesh, nodes, values)
np.savez('exercise_2', v)