'''留一交叉驗證'''
import numpy as np

# K折交叉驗證
data = [[12, 1896], [11, 1900], [11, 1904], [10.8, 1908], [10.8, 1912], [10.8, 1920], [10.6, 1924], [10.8, 1928],
        [10.3, 1932], [10.3, 1936], [10.3, 1948], [10.4, 1952], [10.5, 1956], [10.2, 1960], [10.0, 1964], [9.95, 1968],
        [10.14, 1972], [10.06, 1976], [10.25, 1980], [9.99, 1984], [9.92, 1988], [9.96, 1992], [9.84, 1996],
        [9.87, 2000], [9.85, 2004], [9.69, 2008]]

length = len(data)

# 得到訓練集和測試集
def Get_test_train(length, data, i):
    test_data = data[i]  # 測試集
    train_data = data[:]
    train_data.pop(i)  # 訓練集
    return train_data, test_data

# 得到線性回歸直線
def Get_line(train_data):
    time = []
    year = []
    average_year_time = 0
    average_year_year = 0

    for i in train_data:
        time.append(i[0])
        year.append(i[1])

    time = np.array(time)
    year = np.array(year)

    average_year = sum(year) / length  # year拔
    average_time = sum(time) / length  # time拔

    for i in train_data:
        average_year_time = average_year_time + i[0] * i[1]
        average_year_year = average_year_year + i[1] ** 2
    average_year_time = average_year_time / length  # (year, time)拔
    average_year_year = average_year_year / length  # (year, year)拔
    # 線性回歸：t = w0 + w1 * x
    w1 = (average_year_time - average_year * average_time) / (average_year_year - average_year * average_year)
    w0 = average_time - w1 * average_year
    return w0, w1

# 得到損失函數
def Get_loss_func(w0, w1, test_data):
    time_real = test_data[0]
    time_predict = eval('{} + {} * {}'.format(w0, w1, test_data[1]))
    loss = (time_predict - time_real) ** 2
    dic['t = {} + {}x'.format(w0, w1)] = loss
    return dic

if __name__ == '__main__':
    dic = {}  # 存放建為回歸直線，值為損失函數的字典

    for i in range(length):
        train_data, test_data = Get_test_train(length, data, i)
        w0, w1 = Get_line(train_data)
        Get_loss_func(w0, w1, test_data)
        dic = Get_loss_func(w0, w1, test_data)

    min_loss = min(dic.values())
    best_line = [k for k, v in dic.items() if v == min_loss][0]
    print('最佳回歸直線：', best_line)
    print('最小損失函數：', min_loss)

from sklearn.model_selection import LeaveOneOut

# 一維示例數據
data_dim1 = [1, 2, 3, 4, 5]

# 二維示例數據
data_dim2 = [[1, 1, 1, 1],
             [2, 2, 2, 2],
             [3, 3, 3, 3],
             [4, 4, 4, 4],
             [5, 5, 5, 5]]

loo = LeaveOneOut() # 實例化LOO對象

# 取LOO訓練、測試集數據索引
for train_idx, test_idx in loo.split(data_dim1):
    # train_idx 是指訓練數據在總數據集上的索引位置
    # test_idx 是指測試數據在總數據集上的索引位置
    print("train_index: %s, test_index %s" % (train_idx, test_idx))

# 取LOO訓練、測試集數據值
for train_idx, test_idx in loo.split(data_dim1):
    # train_idx 是指訓練數據在總數據集上的索引位置
    # test_idx 是指測試數據在總數據集上的索引位置
    train_data = [data_dim1[i] for i in train_idx]
    test_data = [data_dim1[i] for i in test_idx]
    print("train_data: %s, test_data %s" % (train_data, test_data))