function [Solution_matrix]=GaussElimination_Pivot(Augmented_matrix) % 2020-5-18 臻orz % inputs: % Augmented_matrix:增广矩阵，为n*(n+1)维矩阵 % outputs: % Solution_matrix:计算的解，为n1维矩阵 %initialize [row,col]=size(Augmented_matrix); Solution_matrix=zeros(row,1); %判定输入矩阵是否符合要求 if row~=col-1 disp('请输入n(n+1)维矩阵'); else for ii = 1:row-1 %找寻主元 max = ii; for jj = ii+1:row if abs(Augmented_matrix(jj,ii)) > abs(Augmented_matrix(max,ii)) max = jj; end end Augmented_matrix([ii,max],:) = Augmented_matrix([max,ii],:); if Augmented_matrix(ii,ii) == 0 disp(['第',num2str(ii),'个主元素为零']); return; end %开始消元 for jj = ii+1:row Augmented_matrix(jj,:) = Augmented_matrix(jj,:)-... Augmented_matrix(jj,ii)/Augmented_matrix(ii,ii)*Augmented_matrix(ii,:); end end %消元完毕，开始回代 if Augmented_matrix(row,row)==0 disp(['第',num2str(row),'个主元素为零']); return; end Solution_matrix(row)=Augmented_matrix(row,col)/Augmented_matrix(row,col-1); for ii=row-1:-1:1 Solution_matrix(ii)=(Augmented_matrix(ii,col)... -Augmented_matrix(ii,1:row)*Solution_matrix)/Augmented_matrix(ii,ii); end end end请问如何使用这个matlab函数，能否举一个例子

这个函数是用来解线性方程组的，输入的增广矩阵是由系数矩阵和常数列构成的。下面是一个例子：

假设有如下线性方程组：

2x + 3y - z = 1

4x - 2y + 3z = -2

-2x + 5y + 2z = 6

则可以将系数矩阵和常数列组成增广矩阵：

Augmented_matrix = [2 3 -1 1; 4 -2 3 -2; -2 5 2 6];

然后调用函数：

Solution_matrix = GaussElimination_Pivot(Augmented_matrix);

最终得到的 Solution_matrix 就是解向量，即 x、y、z 的值。

相关问题

逐行分析下面的代码：import random import numpy as np import pandas as pd import math from operator import itemgetter data_path = './ml-latest-small/' data = pd.read_csv(data_path+'ratings.csv') data.head() data.pivot(index='userId', columns='newId', values='rating') trainSet, testSet = {}, {} trainSet_len, testSet_len = 0, 0 pivot = 0.75 for ele in data.itertuples(): user, new, rating = getattr(ele, 'userId'), getattr(ele, 'newId'), getattr(ele, 'rating') if random.random() < pivot: trainSet.setdefault(user, {}) trainSet[user][new] = rating trainSet_len += 1 else: testSet.setdefault(user, {}) testSet[user][new] = rating testSet_len += 1 print('Split trainingSet and testSet success!') print('TrainSet = %s' % trainSet_len) print('TestSet = %s' % testSet_len) new_popular = {} for user, news in trainSet.items(): for new in news: if new not in new_popular: new_popular[new] = 0 new_popular[new] += 1 new_count = len(new_popular) print('Total movie number = %d' % new_count) print('Build user co-rated news matrix ...') new_sim_matrix = {} for user, news in trainSet.items(): for m1 in news: for m2 in news: if m1 == m2: continue new_sim_matrix.setdefault(m1, {}) new_sim_matrix[m1].setdefault(m2, 0) new_sim_matrix[m1][m2] += 1 print('Build user co-rated movies matrix success!') print('Calculating news similarity matrix ...') for m1, related_news in new_sim_matrix.items(): for m2, count in related_news.items(): if new_popular[m1] == 0 or new_popular[m2] == 0: new_sim_matrix[m1][m2] = 0 else: new_sim_matrix[m1][m2] = count / math.sqrt(new_popular[m1] * new_popular[m2]) print('Calculate news similarity matrix success!') k = 20 n = 10 aim_user = 20 rank ={} watched_news = trainSet[aim_user] for new, rating in watched_news.items(): for related_new, w in sorted(new_sim_matrix[new].items(), key=itemgetter(1), reverse=True)[:k]: if related_new in watched_news: continue rank.setdefault(related_new, 0) rank[related_new] += w * float(rating) rec_news = sorted(rank.items(), key=itemgetter(1), reverse=True)[:n] rec_news

这段代码是一个电影推荐系统的实现。下面是对代码的逐行分析：

1. `import random import numpy as np import pandas as pd import math from operator import itemgetter`：导入需要使用的库

2. `data_path = './ml-latest-small/' data = pd.read_csv(data_path+'ratings.csv') data.head()`：读取电影评分数据，将其存储在一个DataFrame中，并输出前5行数据

3. `data.pivot(index='userId', columns='newId', values='rating')`：将数据按照用户ID和电影ID进行重塑，创建一个用户-电影评分的矩阵

4. `trainSet, testSet = {}, {} trainSet_len, testSet_len = 0, 0 pivot = 0.75`：初始化训练集和测试集，并设置训练集占比为0.75

5. `for ele in data.itertuples():`：遍历数据中的每一行

6. `user, new, rating = getattr(ele, 'userId'), getattr(ele, 'newId'), getattr(ele, 'rating')`：获取每一行数据中的用户ID、电影ID和评分

7. `if random.random() < pivot: trainSet.setdefault(user, {}) trainSet[user][new] = rating trainSet_len += 1 else: testSet.setdefault(user, {}) testSet[user][new] = rating testSet_len += 1`：根据训练集占比将数据划分为训练集和测试集，并统计训练集和测试集中的电影数量

8. `print('Split trainingSet and testSet success!') print('TrainSet = %s' % trainSet_len) print('TestSet = %s' % testSet_len)`：输出训练集和测试集的电影数量

9. `new_popular = {} for user, news in trainSet.items(): for new in news: if new not in new_popular: new_popular[new] = 0 new_popular[new] += 1`：统计每部电影的流行度（出现次数）

10. `new_count = len(new_popular) print('Total movie number = %d' % new_count)`：输出电影总数

11. `new_sim_matrix = {} for user, news in trainSet.items(): for m1 in news: for m2 in news: if m1 == m2: continue new_sim_matrix.setdefault(m1, {}) new_sim_matrix[m1].setdefault(m2, 0) new_sim_matrix[m1][m2] += 1`：构建用户-电影协同过滤矩阵，统计每对电影被多少个用户共同观看过

12. `print('Build user co-rated movies matrix success!')`：输出构建协同过滤矩阵成功信息

13. `for m1, related_news in new_sim_matrix.items(): for m2, count in related_news.items(): if new_popular[m1] == 0 or new_popular[m2] == 0: new_sim_matrix[m1][m2] = 0 else: new_sim_matrix[m1][m2] = count / math.sqrt(new_popular[m1] * new_popular[m2])`：计算电影之间的相似度，使用余弦相似度度量

14. `print('Calculate news similarity matrix success!')`：输出计算电影相似度成功信息

15. `k = 20 n = 10 aim_user = 20`：定义参数，包括推荐电影的数量和目标用户ID

16. `rank ={} watched_news = trainSet[aim_user] for new, rating in watched_news.items(): for related_new, w in sorted(new_sim_matrix[new].items(), key=itemgetter(1), reverse=True)[:k]: if related_new in watched_news: continue rank.setdefault(related_new, 0) rank[related_new] += w * float(rating) rec_news = sorted(rank.items(), key=itemgetter(1), reverse=True)[:n]`：为目标用户推荐电影，根据用户观看历史和电影相似度计算推荐度，并将推荐度排序输出前n个推荐电影。

# 读取评分数据文件 ratings = pd.read_csv("E:\\Recommender-System\\！Final\\ml-100k\\u.data", sep="\t", names=["user_id", "movie_id", "rating", "timestamp"]) # print(ratings) # 创建用户-电影评分矩阵 user_movie_matrix = pd.pivot_table(ratings, index="user_id", columns="movie_id", values="rating") print(user_movie_matrix.user_id) AttributeError: 'DataFrame' object has no attribute 'user_id'

根据您提供的代码，`user_movie_matrix`是一个以电影ID为列索引，以用户ID为行索引的DataFrame对象，因此无法访问`user_id`属性。如果您想访问行索引，可以使用`index`属性，例如：

import pandas as pd

# 读取评分数据文件
ratings = pd.read_csv("E:\\Recommender-System\\！Final\\ml-100k\\u.data", sep="\t", names=["user_id", "movie_id", "rating", "timestamp"])

# 创建用户-电影评分矩阵
user_movie_matrix = pd.pivot_table(ratings, index="user_id", columns="movie_id", values="rating")

# 访问行索引
print(user_movie_matrix.index)

上述代码中，`user_movie_matrix.index`将返回用户ID的行索引。如果您要访问列索引，可以使用`columns`属性，例如：

import pandas as pd

# 读取评分数据文件
ratings = pd.read_csv("E:\\Recommender-System\\！Final\\ml-100k\\u.data", sep="\t", names=["user_id", "movie_id", "rating", "timestamp"])

# 创建用户-电影评分矩阵
user_movie_matrix = pd.pivot_table(ratings, index="user_id", columns="movie_id", values="rating")

# 访问列索引
print(user_movie_matrix.columns)

上述代码中，`user_movie_matrix.columns`将返回电影ID的列索引。