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Guruh talabasi Sobirov Ixlosbek Algoritmni loyihalash 3-amaliy topshiriq
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| Sana | 15.05.2024 | | Hajmi | 15,83 Kb. | | #234233 |
Bog'liq Sobirov Ixlosbek Algoritm loyihalash 3-amaliy topshiriq 1
310-22-guruh talabasi Sobirov Ixlosbek
Algoritmni loyihalash 3-amaliy topshiriq
topshiriq.Chiziqli dasturlash masalasi yechimi asosida xulosa va iqtisodiy tavsiyalar ishlab chiqish. Matematik model asosida iqtisodiy masala tuzishga namunalar.
Ushbu mavzular Python dasturlash tilida yozilgan.
import numpy as np
import matplotlib.pyplot as plt
x = np.array([1, 2, 3, 4, 5])
y = np.array([2, 3, 5, 4, 6])
coefficients = np.polyfit(x, y, 1) # 1- darajali (lineyka) model
model = np.poly1d(coefficients)
plt.scatter(x, y, color='blue', label='Ma`lumotlar') # Ma'lumotlarni tasvir qilish
plt.plot(x, model(x), color='red', label='Model') # Modelni tasvir qilish
plt.xlabel('X o`lchami')
plt.ylabel('Y o`lchami')
plt.title('Masala Yechish')
plt.legend()
plt.show()
mse = np.mean((model(x) - y) ** 2) # O`xshashlik yig`indisi (MSE) ni hisoblash
print("Mean Squared Error:", mse)
2-topshiriq. Jadval funksiya Fur`e qatoriga yoyish. Fur`e koeffisientlarini hisoblash. Qator hadlari sonini tanlash. Taqribiy integrallash formulasini tanlash, aniqligini baholash. Fur`e qatori asosida raqamli signallar yetakchi garmonikalarini aniqlash.
import numpy as np
import scipy.integrate as spi
def furier_series(func, interval, n_terms):
coefficients = []
for n in range(n_terms):
f_cos = lambda x: func(x) * np.cos(2 * np.pi * n * x / interval)
f_sin = lambda x: func(x) * np.sin(2 * np.pi * n * x / interval)
a_n = 2 * spi.quad(f_cos, 0, interval)[0] / interval
b_n = 2 * spi.quad(f_sin, 0, interval)[0] / interval
coefficients.append((a_n, b_n))
return coefficients
def find_series_length(coefficients, threshold=1e-10):
series_length = len(coefficients)
for i, (a_n, b_n) in enumerate(coefficients[::-1]):
if np.abs(a_n) < threshold and np.abs(b_n) < threshold:
series_length -= 1
else:
break
return series_length
def evaluate_integration_accuracy(func, interval, n_terms):
def find_harmonics(furier_coefficients, threshold=1e-10):
harmonics = []
for i, (a_n, b_n) in enumerate(furier_coefficients):
if np.abs(a_n) > threshold or np.abs(b_n) > threshold:
harmonics.append((i, a_n, b_n))
return harmonics
def test_function(x):
return np.sin(x) + np.sin(2 * x) + np.cos(3 * x)
n_terms = 10
coefficients = furier_series(test_function, 2 * np.pi, n_terms)
series_length = find_series_length(coefficients)
print("Qator Hadlari Soni:", series_length)
evaluate_integration_accuracy(test_function, 2 * np.pi, n_terms)
harmonics = find_harmonics(coefficients)
print("Yetakchi Garmonikalar:")
for i, a_n, b_n in harmonics:
print(f"Garmonika {i + 1}: a_n = {a_n}, b_n = {b_n}")
topshiriq. Axborotlar oqimini segmentlarga ajratish. dinamik dasturlash. chiziqli model. jarayon matematik modelini tuzishda eng kichik kvadratlar usulidan foydalanish.
import numpy as np
def segmentize(data, n_segments):
segment_length = len(data) // n_segments
segments = [data[i * segment_length : (i + 1) * segment_length] for i in range(n_segments)]
return segments
def linear_least_squares(x, y):
n = len(x)
sum_x = np.sum(x)
sum_y = np.sum(y)
sum_xy = np.sum(x * y)
sum_x_squared = np.sum(x**2)
slope = (n * sum_xy - sum_x * sum_y) / (n * sum_x_squared - sum_x**2)
intercept = (sum_y - slope * sum_x) / n
return slope, intercept
def least_squares_method(data):
n = len(data)
x = np.arange(n)
y = np.array(data)
slope, intercept = linear_least_squares(x, y)
model = slope * x + intercept
residuals = y - model
RSS = np.sum(residuals**2)
return slope, intercept, model, RSS
data = [10, 15, 20, 30, 40, 45, 50, 55, 60]
segments = segmentize(data, 3)
for i, segment in enumerate(segments):
slope, intercept, model, RSS = least_squares_method(segment)
print(f"Segment {i + 1}: Slope={slope}, Intercept={intercept}, RSS={RSS}")
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