Soal no 2 TakeHome UAS Metnum

import matplotlib.pyplot as plt # untuk memunculkan grafik

def clamped_cubic_spline(X, fx, f_aksen_awal_kurva, f_aksen_akhir_kurva, n):
    n = len(X) - 1
    h = [X[i+1] - X[i] for i in range(n)]
    alpha = [0] * (n+1)
    for i in range(0, n):
        alpha[i] = (3/h[i]) * (fx[i+1] - fx[i]) - (3/h[i-1]) * (fx[i] - fx[i-1])

    l = [1] + [0] * n
    u = [0] * (n+1)
    z = [0] * (n+1)

    l[1] = 2 * h[0]
    u[1] = 0.5
    z[1] = alpha[1] / l[1]

    for i in range(2, n):
        l[i] = 2 * (X[i] - X[i-1]) - h[i-1] * u[i-1]
        u[i] = h[i] / l[i]
        z[i] = (alpha[i] - h[i-1] * z[i-1]) / l[i]

    l[n] = h[n-1] * (2 - u[n-1])
    z[n] = (alpha[n] - h[n-1] * z[n-1]) / l[n]
    c = [0] * (n+1)
    b = [0] * (n+1)
    d = [0] * (n+1)

    c[n] = z[n]
    for j in range(n-1, -1, -1):
        c[j] = z[j] - u[j] * c[j+1]

    for i in range(n):
        b[i] = (fx[i+1] - fx[i]) / h[i] - h[i] * (c[i+1] + 2 * c[i]) / 3
        d[i] = (c[i+1] - c[i]) / (3 * h[i])

    a = fx

    ukuran_partisi = (X[-1] - X[0]) / n
    nilai_x = [X[0] + i * ukuran_partisi for i in range(n+1)]
    nilai_y = []
    for x in nilai_x:
        for i in range(n):
            if X[i] <= x <= X[i+1]:
                y = fx[i] + b[i] * (x - X[i]) + c[i] * (x - X[i])**2 + d[i] * (x - X[i])**3
                nilai_y.append(y)
                break

    return nilai_x, nilai_y, a, b, c, d

# KURVA 1
data_kurva_1 = [
    [1, 2, 5, 6, 7, 8, 10, 13, 17],                 # Data titik Xi
    [3.0, 3.7, 3.9, 4.2, 5.7, 6.6, 7.1, 6.7, 4.5]   # Data titik f(Xi)
]
x1 = data_kurva_1[0]
fx1 = data_kurva_1[1]
f_aksen_awal_kurva_1 = float(1.0)
f_aksen_akhir_kurva_1 = float(-0.67)
i_kurva_1 = 8

# KURVA 2
data_kurva_2 = [
    [17, 20, 23, 24, 25, 27, 27.7],         # Data titik Xi
    [4.5, 7.0, 6.1, 5.6, 5.8, 5.2, 4.1]     # Data titik f(Xi)
]
x2 = data_kurva_2[0]
fx2 = data_kurva_2[1]
f_aksen_awal_kurva_2 = float(1.0)
f_aksen_akhir_kurva_2 = float(-0.67)
i_kurva_2 = 6

# KURVA 3
data_kurva_3 = [
    [27.7, 28, 29, 30],     # Data titik Xi
    [4.1, 4.3, 4.1, 3.0]    # Data titik f(Xi)
]
x3 = data_kurva_3[0]
fx3 = data_kurva_3[1]
f_aksen_awal_kurva_3 = float(0.33)
f_aksen_akhir_kurva_3 = float(-1.5)
i_kurva_3 = 3

# Interpolasi dengan Clamped Cubic Spline
x_kurva_1, y_kurva_1, a1, b1, c1, d1 = clamped_cubic_spline(x1, fx1, f_aksen_awal_kurva_1, f_aksen_akhir_kurva_1, i_kurva_1)
x_kurva_2, y_kurva_2, a2, b2, c2, d2 = clamped_cubic_spline(x2, fx2, f_aksen_awal_kurva_2, f_aksen_akhir_kurva_2, i_kurva_2)
x_kurva_3, y_kurva_3, a3, b3, c3, d3 = clamped_cubic_spline(x3, fx3, f_aksen_awal_kurva_3, f_aksen_akhir_kurva_3, i_kurva_3)

plt.title('Kurva')

# Cetak hasil interpolasi

print("\n")
print("Hasil interpolasi Kurva 1:")
for i in range(len(x_kurva_1)):
    print(f"i = {i}, xi = {x1[i]}, a = {a1[i]:.4f}, b = {b1[i]:.4f}, c = {c1[i]:.4f}, d = {d1[i]:.4f}")
    # print(f"x = {x_kurva_1[i]:.4f}, y = {y_kurva_1[i]:.4f}")

print("\n")

print("Hasil Interpolasi Kurva 2:")
for i in range(len(x_kurva_2)):
    print(f"i = {i}, xi = {x2[i]}, a = {a2[i]:.4f}, b = {b2[i]:.4f}, c = {c2[i]:.4f}, d = {d2[i]:.4f}")
    # print(f"x = {x_kurva_2[i]:.10f}, y = {y_kurva_2[i]:.10f}")

print("\n")

print("Hasil interpolasi Kurva 3:")
for i in range(len(x_kurva_3)):
    print(f"i = {i}, xi = {x3[i]}, a = {a3[i]:.4f}, b = {b3[i]:.4f}, c = {c3[i]:.4f}, d = {d3[i]:.4f}")
    # print(f"x = {x_kurva_3[i]:.10f}, y = {y_kurva_3[i]:.10f}")

plt.plot(x_kurva_1, y_kurva_1, color='red', label='Kurva 1')
plt.plot(x_kurva_2, y_kurva_2, color='green', label='Kurva 2')
plt.plot(x_kurva_3, y_kurva_3, color='aqua', label='Kurva 3')

plt.xlabel('X')
plt.ylabel('f(X)')
plt.title('Interpolasi Clamped Cubic Spline')
plt.legend()
plt.grid(True)
plt.show()