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auc.py
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201 lines (166 loc) · 5.39 KB
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import sys
import numpy as np
import scipy
import bisect
import matplotlib.pyplot as plt
from sklearn.metrics import roc_curve, auc
def f_lagrange(x, X, Y):
# print(X, Y)
def L(k, x, X):
n = len(X) - 1
return np.prod([(x - X[j]) / (X[k] - X[j]) for j in range(n + 1) if k != j])
n = len(X) - 1
return sum((Y[k] * L(k, x, X)) for k in range(n + 1))
def auc_trapezoidal_uniform(X, Y, precision, f):
# print('trapezoidal:')
a = X[0]
b = X[-1]
h = (b - a) / precision
somatorio = 0
X_trap = []
Y_trap = []
for i in range(precision + 1):
x_i = a + (i * h)
ind = bisect.bisect_left(X, x_i)
f_x_i = f(x_i, X[max(0, ind - 2): min(ind + 2, len(X))], Y[max(0, ind - 2): min(ind + 2, len(X))])
# print('x:', x_i, 'f(x):', f_x_i)
X_trap.append(x_i)
Y_trap.append(f_x_i)
if i > 0 and i < precision:
somatorio += 2 * f_x_i
else:
somatorio += f_x_i
return X_trap, Y_trap, (h / 2) * somatorio
def auc_trapezoidal_non_uniform(X, Y, f):
# print('trapezoidal:')
somatorio = 0
for i in range(1, len(X)):
h = X[i] - X[i - 1]
somatorio += (Y[i - 1] + Y[i]) * h / 2
return somatorio
def auc_boole(X, Y, a, b, f):
# print('boole:')
h = (b - a) / 4
coeficients = [7, 32, 12, 32, 7]
somatorio = 0
X_boole = []
Y_boole = []
for i, coef in enumerate(coeficients):
x_i = a + (i * h)
ind = bisect.bisect_left(X, x_i)
f_x_i = f(x_i, X[max(0, ind - 2): min(ind + 2, len(X))], Y[max(0, ind - 2): min(ind + 2, len(X))])
# print('x:', x_i, 'f(x):', f_x_i)
X_boole.append(x_i)
Y_boole.append(f_x_i)
somatorio += coef * f_x_i
return X_boole, Y_boole, 2 * h * somatorio / 45
def auc_simpson(X, Y, precision, f):
# print('simpson:')
a = X[0]
b = X[-1]
h = (b - a) / precision
somatorio = 0
X_simpson = []
Y_simpson = []
for i in range(precision + 1):
x_i = a + (i * h)
ind = bisect.bisect_left(X, x_i)
f_x_i = f(x_i, X[max(0, ind - 2): min(ind + 2, len(X))], Y[max(0, ind - 2): min(ind + 2, len(X))])
# print('x:', x_i, 'f(x):', f_x_i)
if i == 0:
X_simpson.append(X[0])
Y_simpson.append(Y[0])
somatorio += Y[0]
elif i == precision:
X_simpson.append(X[-1])
Y_simpson.append(Y[-1])
somatorio += Y[-1]
elif i % 2:
X_simpson.append(x_i)
Y_simpson.append(f_x_i)
somatorio += 4 * f_x_i
else:
X_simpson.append(x_i)
Y_simpson.append(f_x_i)
somatorio += 2 * f_x_i
return X_simpson, Y_simpson, h * somatorio / 3
def main():
np.random.seed(3)
# np.random.seed(9)
# X = [93.3, 98.9, 104.4]
# Y = [1548, 1544, 1538]
# print(f(100, X, Y))
size = 98
X = sorted(np.unique(np.random.uniform(size=size)))
Y = sorted(np.random.uniform(size=len(X)*2))
Y = Y[98:199]
X = np.append(X, (0, 1))
Y = np.append(Y, (np.random.uniform(size=1), np.random.uniform(size=1)))
X = sorted(X)
Y = sorted(Y)
# for i in range(len(Y)):
# if Y[i] < X[i]:
# Y[i] = X[i] + (X[i] - Y[i])
# print(X, Y)
precision = 20
X_trap, Y_trap, auc_trap_uni = auc_trapezoidal_uniform(X, Y, precision, f_lagrange)
auc_trap_non_uni = auc_trapezoidal_non_uniform(X, Y, f_lagrange)
# print(auc_trap_uni, auc_trap_non_uni)
X_simpson, Y_simpson, auc_simp = auc_simpson(X, Y, precision, f_lagrange)
X_boole, Y_boole, auc_boo = auc_boole(X, Y, 0.0, 0.25, f_lagrange)
X_boole2, Y_boole2, auc_boo2 = auc_boole(X, Y, 0.25, 0.5, f_lagrange)
X_boole.extend(X_boole2)
Y_boole.extend(Y_boole2)
auc_boo += auc_boo2
X_boole2, Y_boole2, auc_boo2 = auc_boole(X, Y, 0.5, 0.75, f_lagrange)
X_boole.extend(X_boole2)
Y_boole.extend(Y_boole2)
auc_boo += auc_boo2
X_boole2, Y_boole2, auc_boo2 = auc_boole(X, Y, 0.75, 1.0, f_lagrange)
X_boole.extend(X_boole2)
Y_boole.extend(Y_boole2)
auc_boo += auc_boo2
plt.figure()
lw = 2
plt.plot(X, Y, color='darkorange',
lw=lw, label='original ROC curve (area = %0.4f)' % auc(X, Y))
plt.plot([0, 1], [0, 1], color='navy', lw=lw, linestyle='--')
plt.plot(X_trap, Y_trap, color='darkblue',
lw=lw, label='trapezoidal ROC curve (area = %0.4f)' % auc_trap_uni)
plt.xlim([0.0, 1.0])
plt.ylim([0.0, 1.0005])
plt.xlabel('False Positive Rate')
plt.ylabel('True Positive Rate')
plt.title('Receiver operating characteristic example')
plt.legend(loc="lower right")
plt.show()
plt.figure()
lw = 2
plt.plot(X, Y, color='darkorange',
lw=lw, label='original ROC curve (area = %0.4f)' % auc(X, Y))
plt.plot([0, 1], [0, 1], color='navy', lw=lw, linestyle='--')
plt.plot(X_boole, Y_boole, color='darkred',
lw=lw, label='boole ROC curve (area = %0.4f)' % auc_boo)
plt.xlim([0.0, 1.0])
plt.ylim([0.0, 1.0005])
plt.xlabel('False Positive Rate')
plt.ylabel('True Positive Rate')
plt.title('Receiver operating characteristic example')
plt.legend(loc="lower right")
plt.show()
plt.figure()
lw = 2
plt.plot(X, Y, color='darkorange',
lw=lw, label='original ROC curve (area = %0.4f)' % auc(X, Y))
plt.plot([0, 1], [0, 1], color='navy', lw=lw, linestyle='--')
plt.plot(X_simpson, Y_simpson, color='yellow',
lw=lw, label='simpson ROC curve (area = %0.4f)' % auc_simp)
plt.xlim([0.0, 1.0])
plt.ylim([0.0, 1.0005])
plt.xlabel('False Positive Rate')
plt.ylabel('True Positive Rate')
plt.title('Receiver operating characteristic example')
plt.legend(loc="lower right")
plt.show()
if __name__ == "__main__":
main()