# 续写同一文件：analysis_project/src/readingarray/regression.py
# 每轮用当前参数计算误差和梯度，再同时更新参数；history 保留更新前的损失。
def train(x, y, steps=400, learning_rate=0.1):
    x, y = checked_xy(x, y)
    if steps < 1 or not np.isfinite(learning_rate) or learning_rate <= 0:
        raise ValueError("更新次数和学习率应为正数")
    bias, weight = 0.0, 0.0
    history = []
    for _ in range(steps):
        loss, grad_bias, grad_weight = loss_and_gradient(x, y, bias, weight)
        if not np.isfinite([loss, grad_bias, grad_weight]).all():
            raise ValueError("更新产生了非有限数，检查数据尺度与学习率")
        history.append(loss)
        bias -= learning_rate * grad_bias
        weight -= learning_rate * grad_weight
    history.append(loss_and_gradient(x, y, bias, weight)[0])
    return np.array([bias, weight]), np.array(history)


def solve_least_squares(x, y):
    x, y = checked_xy(x, y)
    design = np.column_stack((np.ones(x.size), x))
    parameters, _, _, _ = np.linalg.lstsq(design, y, rcond=None)
    return parameters