用python+numpy编程实现逻辑回归模型，在给定数据集上，绘制损失函数曲线图。使用混淆矩阵、错误率、精度、查全率、查准率、F1指标评估逻辑回归模型性能表现，初始权值w为0，写出代码

好的，我可以回答你的问题。以下是实现逻辑回归模型的 Python 代码示例，包括绘制损失函数曲线图和评估模型性能表现的指标：

import numpy as np
import matplotlib.pyplot as plt

# 定义sigmoid函数
def sigmoid(z):
    return 1 / (1 + np.exp(-z))

# 定义损失函数
def loss(y_hat, y):
    return (-y * np.log(y_hat) - (1 - y) * np.log(1 - y_hat)).mean()

# 定义逻辑回归模型和梯度下降算法
def logistic_regression(X, y, lr=0.01, num_iters=1000):
    m, n = X.shape
    w = np.zeros((n, 1))
    b = 0
    cost_list = []
    
    for i in range(num_iters):
        # 计算预测值和损失函数
        y_hat = sigmoid(np.dot(X, w) + b)
        J = loss(y_hat, y)
        cost_list.append(J)

        # 计算梯度并更新参数
        dw = np.dot(X.T, (y_hat - y)) / m
        db = np.mean(y_hat - y)
        w -= lr * dw
        b -= lr * db

    return w, b, cost_list

# 生成一个样本数据集
np.random.seed(0)
m = 100
X = np.random.randn(m, 2)
w_true = np.array([[1], [2]])
b_true = 3
y_true = sigmoid(np.dot(X, w_true) + b_true) > 0.5
y_true = y_true.astype(int)

# 初始化模型参数并进行训练
w_init = np.zeros((2, 1))
b_init = 0
w_trained, b_trained, cost_list = logistic_regression(X, y_true, lr=0.1, num_iters=1000)

# 绘制损失函数曲线图
plt.plot(cost_list)
plt.xlabel('Iteration')
plt.ylabel('Cost')
plt.show()

# 评估模型性能表现
y_pred = sigmoid(np.dot(X, w_trained) + b_trained) > 0.5
y_pred = y_pred.astype(int)

TP = np.sum((y_pred == 1) & (y_true == 1))
FP = np.sum((y_pred == 1) & (y_true == 0))
TN = np.sum((y_pred == 0) & (y_true == 0))
FN = np.sum((y_pred == 0) & (y_true == 1))

accuracy = (TP + TN) / (TP + FP + TN + FN)
error_rate = (FP + FN) / (TP + FP + TN + FN)
precision = TP / (TP + FP)
recall = TP / (TP + FN)
F1 = 2 * precision * recall / (precision + recall)

print('Accuracy: {:.2f}'.format(accuracy))
print('Error rate: {:.2f}'.format(error_rate))
print('Precision: {:.2f}'.format(precision))
print('Recall: {:.2f}'.format(recall))
print('F1 score: {:.2f}'.format(F1))