Zad2 skończone

zad2/zad2.py

@@ -3,7 +3,11 @@ Komputerowa analiza danych
 Zadanie 2
 Michał Leśniak 195642
 """
+from math import sin
 from statistics import mean
+import matplotlib.pyplot as plt
+from chi2_normality import chi2normality_describe
+import numpy as np
 
 
 def var(lst):
@@ -30,41 +34,144 @@ def load_data(*args):
     return ret
 
 
-def model1(data):
-    lst_x = [x for x, _ in data]
-    lst_y = [y for _, y in data]
+def reglin(data, name, model):
+    model_func, use_reglinw, func_str = model
+    if use_reglinw:
+        Y, Z, param_str = reglinw(data, model_func)
+    else:
+        Y, Z, param_str = reglinp(data, model_func)
 
-    a = cov(lst_x, lst_y)/var(lst_x)
-    print(f'f(X) = {a} * X')
+    err = Y-Z
+    lst_err = np.transpose(err)[0].tolist()
+    lst_y = np.transpose(Y)[0].tolist()
+    lst_z = np.transpose(Z)[0].tolist()
+    mse = mean([x**2 for x in lst_err])
+    md = max([abs(x) for x in lst_err])
+    var_err = var(lst_err)
+    var_y = var(lst_y)
+    r2 = 1-(var_err/var_y)
+    if len(data[0]) > 2:
+        print(f'Regresja liniowa wielu zmiennych dla {name}:')
+    else:
+        print(f'Prosta regresja liniowa jednej zmiennej dla {name}:')
+    print(func_str)
+    print(param_str)
+    print(f'MSE={mse}')
+    print(f'maxD={md}')
+    print(f'VarErr<=VarY - {var_err<=var_y}')
+    print(f'r2={r2}')
+    chi2normality_describe(lst_err)
+
+    lst_z = np.transpose(Z)[0].tolist()
+
+    if len(data[0]) == 2:  # print 2D
+        lst_x, lst_y = zip(*data)
+        lst_x = list(lst_x)
+        lst_y = list(lst_y)
+        plt.figure(1)
+        ax = plt.axes()
+        ax.scatter(lst_x, lst_y)
+        ax.plot(lst_x, lst_z, 'r-')
+        ax.set_xlabel('X')
+        ax.set_ylabel('Y')
+        plt.grid(True)
+    elif len(data[0]) == 3:
+        lst_x1, lst_x2, lst_y = zip(*data)
+        lst_x1 = list(lst_x1)
+        lst_x2 = list(lst_x2)
+        lst_y = list(lst_y)
+        plt.figure(1)
+        ax = plt.axes(projection='3d')
+        ax.scatter(lst_x1, lst_x2, lst_y)
+        ax.scatter(lst_x1, lst_x2, lst_z, color='r')
+        ax.set_xlabel('X1')
+        ax.set_ylabel('X2')
+        ax.set_zlabel('Y')
+    else:
+        raise RuntimeError
+    plt.title(f'{name}\n{func_str}')
+    plt.figure(2)
+    plt.hist(err, 50)
+    plt.xlabel('Err')
+    plt.title(f'Histogram Err dla {name}\n{func_str}')
+    plt.grid(True)
+    plt.show()
 
 
-def model2(data):
-    lst_x = [x for x, _ in data]
-    lst_y = [y for _, y in data]
+def reglinp(data, model_func):
+    lst_x, lst_y = zip(*data)
+    lst_x = list(lst_x)
+    lst_y = list(lst_y)
+    return model_func(lst_x, lst_y)
 
+
+def reglinw(data, prepare_data):
+    X, Y = prepare_data(data)
+    XT = np.transpose(X)
+    XTX = np.matmul(XT, X)
+    try:
+        inv_XTX = np.linalg.inv(XTX)
+    except np.linang.LinAlgError:
+        print("XTX is not inversible")
+        raise
+    A = np.matmul(np.matmul(inv_XTX, XT), Y)
+    Z = np.matmul(X, A)
+
+    params = [a[0] for a in A]
+    params = params[1:] + params[:1]
+    param_str = []
+    for i in range(len(params)):
+        param_str.append(f'{chr(ord("a")+i)} = {params[i]}')
+    return Y, Z, '\n'.join(param_str)
+
+
+def model_func1(lst_x, lst_y):
+    a = mean([lst_y[i]*lst_x[i] for i in range(len(lst_x))]) / \
+        mean([x**2 for x in lst_x])
+    Y = np.array([list((y,)) for y in lst_y])
+    Z = np.array([list((a*x,))for x in lst_x])
+    return Y, Z, f'a = {a}'
+
+
+def model_func2(lst_x, lst_y):
     a = cov(lst_x, lst_y)/var(lst_x)
     b = mean(lst_y) - a*mean(lst_x)
-    print(f'f(X) = {a} * X + {b}')
+    Y = np.array([list((y,)) for y in lst_y])
+    Z = np.array([list((a*x+b,))for x in lst_x])
+    return Y, Z, f'a = {a}\nb = {b}'
+
+
+def model_func3(data):
+    return np.array([list((1.0, x**2, sin(x))) for x, _ in data]), np.array([list((y,)) for _, y in data])
+
+
+def model_func4(data):
+    return np.array([list((1.0, x1, x2)) for x1, x2, _ in data]), np.array([list((y,)) for _, _, y in data])
+
+
+def model_func5(data):
+    return np.array([list((1.0, x1**2, x1*x2, x2**2, x1, x2)) for x1, x2, _ in data]), np.array([list((y,)) for _, _, y in data])
+
+
+MODELS = [
+    (model_func1, False, '$f(X) = aX$'),
+    (model_func2, False, '$f(X) = aX + b$'),
+    (model_func3, True, '$f(X) = aX^2 + bsin(X) + c$'),
+    (model_func4, True, '$f(X_1, X_2) = aX_1 + bX_2 + c$'),
+    (model_func5, True,
+     r'$f(X_1, X_2) = a{X_1}^2 + bX_1 X_2 + c{X_2}^2 +dX_1 +eX_2 +f$')
+]
 
 
 def main():
     data1, data2, data3, data4 = load_data(
         'data1.csv', 'data2.csv', 'data3.csv', 'data4.csv')
-    print(var([x for x, _ in data1]))
-    print(cov([x for x, _ in data1], [y for _, y in data1]))
-    # print(data2)
-    # print(data3)
-    # print(data4)
-    model1(data1)
-    model1(data2)
-    model2(data1)
-    model2(data2)
-    x_mean = mean([x for x, _ in data1])
-    y_mean = mean([y for _, y in data1])
-    xy = sum([x*y for x, y in data1])
-    x_2 = sum([x**2 for x, _ in data1])
-    print(sum([2*x-2*x*y for x,y in data1])/len(data1))
-    print(xy/x_2)
+    for i in range(3):
+        reglin(data1, 'data1.csv', MODELS[i])
+        reglin(data2, 'data2.csv', MODELS[i])
+    for i in range(3, 5):
+        reglin(data3, 'data3.csv', MODELS[i])
+        reglin(data4, 'data4.csv', MODELS[i])
 
 
 if __name__ == '__main__':