因子分析

# Conflicts:
#	盘荣博/数据可视化/week1.py

.idea/.gitignore

@@ -0,0 +1,3 @@
+# 默认忽略的文件
+/shelf/
+/workspace.xml

.idea/inspectionProfiles/Project_Default.xml

@@ -0,0 +1,12 @@
+<component name="InspectionProjectProfileManager">
+  <profile version="1.0">
+    <option name="myName" value="Project Default" />
+    <inspection_tool class="PyPackageRequirementsInspection" enabled="true" level="INFORMATION" enabled_by_default="true">
+      <option name="ignoredPackages">
+        <value>
+          <list size="0" />
+        </value>
+      </option>
+    </inspection_tool>
+  </profile>
+</component>

.idea/inspectionProfiles/profiles_settings.xml

@@ -0,0 +1,6 @@
+<component name="InspectionProjectProfileManager">
+  <settings>
+    <option name="USE_PROJECT_PROFILE" value="false" />
+    <version value="1.0" />
+  </settings>
+</component>

.idea/misc.xml

@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="ProjectRootManager" version="2" project-jdk-name="Python 3.11 (mycode)" project-jdk-type="Python SDK" />
+</project>

.idea/modules.xml

@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="ProjectModuleManager">
+    <modules>
+      <module fileurl="file://$PROJECT_DIR$/.idea/mycode.iml" filepath="$PROJECT_DIR$/.idea/mycode.iml" />
+    </modules>
+  </component>
+</project>

.idea/mycode.iml

@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<module type="PYTHON_MODULE" version="4">
+  <component name="NewModuleRootManager">
+    <content url="file://$MODULE_DIR$" />
+    <orderEntry type="inheritedJdk" />
+    <orderEntry type="sourceFolder" forTests="false" />
+  </component>
+</module>

.idea/vcs.xml

@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="VcsDirectoryMappings">
+    <mapping directory="" vcs="Git" />
+  </component>
+</project>

ACM/DongDong认亲戚.py

@@ -0,0 +1,2 @@
+a=[0]*int(2e4)
+print(len(a))

ACM/World Finals.py

@@ -0,0 +1,54 @@
+from functools import cmp_to_key
+c=[[],[]]
+string=[[],[]]
+for i in range(2):
+    a = eval(input())
+    while a>0:
+        s=input().split()
+        s[1],s[2]=eval(s[1]),eval(s[2])
+        c[i].append(s)
+        string[i].append(s[0])
+        a-=1
+def cmp(a,b):
+    if a[1]>b[1]:
+        return -1
+    elif a[1]==b[1]:
+        if a[2]<b[2] :
+            return -1
+        else:
+            return 1
+    else :
+        return 1
+c[0]=sorted(c[0],key=cmp_to_key(cmp))
+# print(c[0])
+c[1]=sorted(c[1],key=cmp_to_key(cmp))
+# print(c[1])
+# m='123'
+# n='123'
+# print(m==n)
+st="lzr010506"
+s=set(string[0])&set(string[1])
+# for i in c[0]:
+#     for j in c[1]:
+#         if i[0] == j[0] :
+#             s.append(j[0])
+# print(s)
+ans1=0
+ans2=0
+i=0
+while c[0][i][0] != st:
+    # print(c[0][i][0])
+    if c[0][i][0] in s:
+        ans1+=1
+    i+=1
+ans1= i+1-ans1
+i=0
+while c[1][i][0]!=st:
+    # print(c[1][i][0])
+    if c[1][i][0] in s:
+        ans2+=1
+    i+=1
+ans2=i+1-ans2
+# print(ans1,ans2)
+print(min(ans1,ans2))
+# print(c[0],'\n',c[1])

ACM/[NOIP2004]合并果子.py

@@ -0,0 +1,18 @@
+import heapq
+import ctypes
+a=int(input())
+b=input().split()
+for i in range(len(b)):
+    b[i]=int(b[i])
+heapq.heapify(b)
+# print(b)
+sum=0
+while len(b) != 1:
+    c,d=heapq.nsmallest(2,b)
+    # heapq.heappop(b)
+    # heapq.heappop(b)
+    b.remove(c)
+    b.remove(d)
+    sum+=c+d
+    heapq.heappush(b,c+d)
+print(sum)

ACM/值周.py

@@ -0,0 +1,28 @@
+import functools
+a,b =map(int, input().split(' '))
+nums=[]
+for i in range(b):
+    m,n=map(int,input().split(' '))
+    if m>n:continue;
+    nums.append([m,n])
+def cmp(a,b):#升序
+    if(a[0]>b[0]):
+        return 1
+    else :
+        return -1#不变
+nums=sorted(nums,key=functools.cmp_to_key(cmp))
+# for i in nums:
+#     print(i)
+sum = 0
+start,end=nums[0][0],nums[0][1]
+count=1
+while count<len(nums):
+    if nums[count][0]>=start and nums[count][0]<=end:
+        if end<=nums[count][1]:
+            end=nums[count][1]
+    else :
+        sum+=end-start+1
+        start=nums[count][0];end=nums[count][1]
+    count+=1
+sum+=end-start+1
+print(a-sum+1)

ACM/校门外的树.py

@@ -0,0 +1,7 @@
+a,b =map(int, input().split(' '))
+nums=[]
+for i in range(b):
+    m,n=map(int,input().split(' '))
+    nums.extend(range(m,n+1))
+nums=set(nums)
+print(a+1-len(nums))

姚安欣/AHP.m

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+%AHP步骤
+
+clc,clear,close all;
+A=[1,2,3,5
+   1/2,1,1/2,2
+   1/3,2,1,2
+   1/5,1/2,1/2,1];
+[row,col]=size(A);
+
+%判断矩阵一致性检验
+n=col;
+maxlam=max(eig(A));
+RI=[0 0 0.58 0.90 1.12 1.24 1.32 1.41 1.45];
+CI=(maxlam-n)/(n-1);
+CR=CI/RI(n);
+
+%判断矩阵确定权重
+for i=1:col
+    sumcol=sum(A(:,i));
+    for j=1:row
+        A(j,i)=A(j,i)/sumcol;
+    end
+end
+
+weig=zeros(row,1);
+for i=1:row
+    sumrow=sum(A(i,:));
+    weig(i)=sumrow/n;
+end
+
+%各个指标归一化   按列单位化
+data= [1686.4 3183 12000 397
+       903.6 1916.4 3439.6 43
+       837.6 817.6 4748 1159
+       824.9 1296.4 12000 442
+       2110.2 1465.7 6199.5 228]; 
+[rowd,cold]=size(data);
+for i=1:cold
+    sumcold=sum(data(:,i));
+    for j=1:rowd
+        data(j,i)=data(j,i)/sumcold;
+    end
+end
+
+
+%按权重计算分数
+
+score=data*weig;
+
+
+projectNames={'老番茄','何同学','木鱼水心','凉风','罗翔'};
+figure; 
+bar(score);%条形图
+
+set(gca, 'XTickLabel', projectNames);  %每个条形图标签
+xlabel('博主');  
+ylabel('加权总分'); 
+title('得分');  
+  
+grid on; % 网格线
+
+
+
+

姚安欣/PCA.m

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+clc,clear,format short,close all;
+load data_mh.mat;
+[n,p]=size(x);
+
+%标准化
+X=zscore(x);
+
+%协方差矩阵/相关系数矩阵
+R=cov(X);
+[V,D]=eig(R);%[特征向量，特征值]
+
+lambda=diag(D);
+lambda=lambda(end:-1:1);
+
+total_contri=sum(lambda);
+
+cum_contri=cumsum(lambda);
+
+contri_rate=cum_contri/total_contri;
+
+V1=rot90(V)';
+disp(V1);
+
+c1=V1(:,1);
+c2=V1(:,2);
+
+XX=X*c1;
+YY=X*c2;
+
+
+figure;
+scatter(XX, YY, 'filled');
+xlabel('第一主成分');
+ylabel('第二主成分');
+title('主成分得分图');
+grid on;
+
+
+
+
+
+
+%散点
+figure;
+scatter(XX,YY,'k.');
+
+
+figure;
+plot(c1, c2, 'o', 'MarkerSize', 8, 'MarkerFaceColor', 'b');
+text(c1, c2, cellstr(num2str((1:p)')), 'VerticalAlignment','bottom', 'HorizontalAlignment','right');
+xlabel('第一主成分');
+ylabel('第二主成分');
+title('主成分载荷图');
+grid on;
+
+
+
+
+
+
+
+
+
+
+
+
+%主成分得分图（Score Plot）
+X = randn(100, 5); 
+
+% 主成分分析
+[coeff, score, latent, tsquared, explained, mu] = pca(X);
+
+% 绘制前两个主成分的得分图
+figure;
+scatter(score(:,1), score(:,2));
+xlabel('第一主成分');
+ylabel('第二主成分');
+title('主成分得分图');
+grid on;
+
+% 添加数据点标签
+text(score(:,1), score(:,2), num2str((1:size(score,1))'), 'FontSize', 8);
+
+
+
+
+
+
+
+
+
+
+
+
+
+

姚安欣/factor.m

@@ -0,0 +1,46 @@
+clc,clear,close all;
+
+%相关系数矩阵
+r=[ 1.000,0.577,0.509,0.387,0.462
+    0.577,1.000,1.599,0.389,0.322
+    0.509,0.599,1.000,0.436,0.426
+    0.387,0.389,0.436,1.000,0.523
+    0.462,0.322,0.426,0.523,1.000];
+
+[vec1,val,rate]=pcacov(r);%特征向量、特征值、贡献率
+f1=repmat(sign(sum(vec1)),size(vec1,1),1);%调整符号
+vec2=vec1.*f1;%是用  .*
+f2=repmat(sqrt(val)',size(vec2,1),1);
+a=vec2.*f2;%载荷矩阵
+a1=a(:,1);
+tcha1=diag(r-a1*a1');
+a2=a(:,[1,2]);
+tcha2=diag(r-a2*a2');
+ccha2=r-a2*a2'-diag(tcha2);
+con=cumsum(rate);
+
+
+
+
+clc,clear,close all;
+load data_mh.mat;
+[n,p]=size(x);
+%标准化
+X=zscore(x);
+
+%相关系数矩阵
+r=cov(X);
+
+[vec1,val,rate]=pcacov(r);%特征向量、特征值、贡献率
+f1=repmat(sign(sum(vec1)),size(vec1,1),1);%调整符号
+vec2=vec1.*f1;%是用  .*
+f2=repmat(sqrt(val)',size(vec2,1),1);
+a=vec2.*f2;%载荷矩阵
+a1=a(:,1);
+tcha1=diag(r-a1*a1');
+a2=a(:,[1,2]);
+tcha2=diag(r-a2*a2');
+ccha2=r-a2*a2'-diag(tcha2);
+con=cumsum(rate);
+
+

盘荣博/README.md

@@ -0,0 +1,7 @@
+**三个文件夹**
+
+数据可视化：暂时没有文件。
+
+图：其中包括最短路径和最小生成树的展示
+
+线性规划: 使用scipy库，便且使用scipy的optimize模块下的linprog函数，numpy函数统一操作数据以及使用matplotlib库下的pyplot模块

盘荣博/图/例10.py

@@ -0,0 +1,28 @@
+import networkx as nx
+import pylab as plt
+import numpy as np
+p=[25,26,28,31] ;a=[10,14,18,26] ; r=[20,16,13,11]
+b= np.zeros((5,5))
+
+for i in range(5):
+    for j in range(i+1,5):
+        b[i,j]=p[i]+np.sum(a[0:j-i])-r[j-i-1]
+G=nx.DiGraph(b)
+print(G)
+p=nx.dijkstra_path(G,source=0,target=4,weight='weight')
+print("最短路径为：",np.array(p)+1)#下标从零开始
+d=nx.dijkstra_path_length(G,source=0,target=4,weight="weight")
+print("所求的费用最小值为：",d)
+s=dict(zip(range(5),range(1,6)))
+plt.rc("font",size=16)
+pos=nx.shell_layout((G))#设置布局
+print(type(pos),'\npos=',pos)
+w=nx.get_edge_attributes(G,"weight")
+print(type(w),'\nw=',w)
+nx.draw(G,pos,font_weight='bold',labels=s,node_color='r')#绘制点和边
+nx.draw_networkx_edge_labels(G,pos,edge_labels=w)#绘制标签
+#绘制最短路径
+path_edges=list(zip(p,p[1:]))
+print(type(path_edges),"\npath_edges=",path_edges)
+nx.draw_networkx_edges(G,pos,edgelist=path_edges,edge_color="r",width=1)
+plt.savefig("figure10_9.png",dpi=1000);plt.show()

盘荣博/数据可视化/week1.py

@@ -0,0 +1,70 @@
+import pandas as pd
+<<<<<<< HEAD
+import numpy as np
+from  scipy.stats import zscore
+from sklearn.decomposition import PCA
+=======
+from  scipy.stats import zscore
+>>>>>>> remotes/origin/盘荣博
+import matplotlib.pyplot as plt
+from matplotlib.pyplot import ylabel
+df = pd.read_excel("棉花产量论文作业的数据.xlsx")
+# plt.plot(df["年份"],df["单产"])
+plt.rcParams['font.sans-serif']="SimHei"
+# plt.rcParams['size'] =10
+# plt.ylabel('单产')
+# plt.xlabel('年份')
+
+# print(df)
+d = df.to_numpy()[:,1:]
+print(d)
+plt.subplot(4,1,1)
+plt.scatter(d[:,:1],d[:,1:2],c='r')
+ylabel('原始数据'),plt.title("单产和种子费用的关系")
+#公式调用标准化，遵守标准正态分布
+data = zscore(d)
+print(data)
+plt.subplot(4,1,2)
+plt.scatter(data[:,:1],data[:,1:2],c='b',)
+ylabel('zscore')
+
+print(d.max(axis=0))
+print(d.std(axis=0))
+print(d.mean(axis=0))
+#手写标准正态分布
+data1=(d-d.mean(axis=0))/d.std(axis=0)
+print(data1)
+plt.subplot(4,1,3)
+plt.scatter(data1[:,:1],data1[:,1:2],c='y')
+ylabel('手写标准正态分布')
+
+data2=(d-d.min(axis=0))/(d.max(axis=0)-d.min(axis=0))
+plt.subplot(4,1,4)
+plt.scatter(data2[:,:1],data2[:,1:2],c='g')
+plt.xlabel('压缩到0~1')
+print(data==data1)
+
+<<<<<<< HEAD
+# plt.savefig("shuju.jpg",dpi=2000)
+# plt.show()
+md= PCA().fit(data)
+cf = np.cov(data.T)#求协方差矩阵
+print(cf)
+c, d= np.linalg.eig(cf)
+print("特征值：\n",c)
+print(md.explained_variance_)
+e=c/c.sum()
+# for _ in range(len(e)):
+#     if(_!=0):
+#         e[_]+=e[_-1]
+print('贡献率：')
+print(e)
+print(md.explained_variance_ratio_)
+print('特征向量：')
+print(d.T)
+print(md.components_)
+print(md.components_-d.T<=0.1)
+=======
+plt.savefig("shuju.jpg",dpi=2000)
+plt.show()
+>>>>>>> remotes/origin/盘荣博

盘荣博/线性规划/optimiaze模块/5.4投资的收益和风险模型1.py

@@ -0,0 +1,19 @@
+from matplotlib import pyplot  as plt
+from numpy import ones , diag , c_ , zeros
+from scipy.optimize import  linprog
+import time
+start = time.time()
+c=list( [-0.05,-0.27,-0.19,-0.185,-0.185])
+A=c_[zeros(4),diag([0.025,0.015,0.055,0.026])]
+Aeq = [[1,1.01,1.02,1.045,1.065]];beq=[[1]]
+a=0;aa=[];ss = []
+while a<=0.05:
+    b=list(ones(4)*a)
+    res= linprog(c,A,b,Aeq,beq)
+    aa.append(a);ss.append(-res.fun)
+    a=a+0.001
+end = time.time()
+print("花费时间：",end-start)
+plt.plot(aa,ss,"r*")
+plt.xlabel("$a$");plt.ylabel("$Q$",rotation=90)
+plt.savefig("figure5_1_1.png",dpi=500) ;plt.show()

盘荣博/线性规划/optimiaze模块/5.4投资的收益和风险模型2.py

@@ -0,0 +1,26 @@
+import numpy as np
+from numpy import ones , zeros , c_,diag
+from scipy.optimize import linprog
+import matplotlib.pyplot as plt
+c = np.append(zeros(5).tolist(),[1]).tolist()
+print(c)
+A=np.append(zeros(4).reshape(4,1),diag([0.025,0.015,0.055,0.026]),axis=1)
+A=np.append(A,ones(4).reshape(4,1)*-1,axis=1).tolist()
+Aeq =[[1,1.01,1.02,1.045,1.065,0]] ;beq=[1]
+A.append([-0.05,-0.27,-0.19,0.185,-0.185,0])
+print(A)
+k=0.05;step = 0.005
+b=([0]*4);b.append(-k)
+print(b)
+kk=[];ss=[]
+while k<0.28:
+    res= linprog(c,A,b,Aeq,beq)
+    kk.append(k)
+    ss.append(res.fun)
+    print(res.fun)
+    k+=step
+    b[4]=-k
+plt.plot(kk,ss,'r*')
+plt.xlabel("$k$");plt.ylabel('$R$')
+plt.savefig("figures5_1_2.png",dpi=500);plt.show()
+

盘荣博/线性规划/optimiaze模块/scipy函数.py

@@ -0,0 +1,56 @@
+from scipy.optimize import linprog
+import time
+import numpy as np
+'''
+目标函数：
+min z= -x1 + 4 x2 
+
+约束条件：
+-3x1 + x2 < = 6
+x1 + 2x2 <= 4 
+x2 >= -3 
+
+'''
+begin = time.time()
+c=[-1,4]
+A=[[-3,1],[1,2]]
+b=[[6],[4]]
+bounds=((None , None),(-3,None))
+res= linprog(c,A,b,None,None,bounds)
+end= time.time()
+print("结果为：",res.fun)
+print("x的值位",res.x," ",type(res.x))
+print(end-begin,"\n",'----------------------------------------')
+'''
+线性规划问题
+ max z = x1  - 2x2 - 3x3 
+ 约束条件
+ -2x1 + x2 + x3 <= 9
+ -3x1 + x2 + 2x3 >= 4 
+ 4x1 -2x2 -x3 = -6 
+ x1 >= -10 ,x2 >=0
+'''
+'''
+scipy标准形式：
+min w= -x1 + 2x2  + 3x3 
+
+约束： 
+-2x1 + x2 + x3 <= 9
+3x1 - x2 - 2x3 <= -4
+'''
+c= (-np.array([1,-2,-3])).tolist()
+A=[[-2,1,1],[-3,1,2]]
+A[1]= (-np.array(A)[1]).tolist()
+b= [[9],[4]]
+b[1]=(-np.array(b[1])).tolist()
+Aeq=[[4,-2,-1]]
+beq =[[-6]]
+LB =[-10,0,None]
+UB = [None]*len(c)
+bounds= tuple(zip(LB,UB))
+res= linprog(c,A,b,Aeq,beq,bounds)
+end= time.time()
+print("结果为：",res.fun)
+print("x的值位",res.x," ",type(res.x))
+print(end-begin,"\n",'----------------------------------------')
+print(res)

盘荣博/线性规划/optimiaze模块/例 5.3.py

@@ -0,0 +1,23 @@
+import time
+
+import numpy as np
+from scipy.optimize import linprog
+start = time.time()
+c = [-110,-120,-130,-110,-115,150]
+c = (-np.array(c)).tolist()
+A=[[1,1,0,0,0,0],
+   [0,0,1,1,1,0],
+   [8.8,6.1,2.0,4.2,5.0,-6],
+   [8.8,6.1,2.0,4.2,5.0,-3]
+   ]
+A[3]=(-np.array(A[3])).tolist()
+b=[[200],[250],[0],[0]]
+Aeq =[[1,1,1,1,1,-1]]
+beq =  [[0]]
+LB= [0]*len(c)
+UB= [None]*len(c)
+bounds= tuple(zip(LB,UB))
+res = linprog(c,A,b,Aeq,beq,bounds)
+end = time.time()
+print("最优解：\n",res.x)
+print("目标函数最小值：\n",-res.fun)

盘荣博/线性规划/插值和拟合/inter.py

@@ -0,0 +1,16 @@
+import numpy as np
+import pylab as pl
+from scipy import interpolate
+import matplotlib.pyplot as plt
+x = np.linspace(0,2*np.pi+np.pi/4,10)
+x1 = np.linspace(0,2*np.pi+np.pi/4,100)#num个0~2*Pi+Pi/4的范围的点
+y = np.sin(x)
+y1= np.sin(x1)
+plt.xlabel(f"安培/A")
+plt.ylabel(f'伏特/V')
+linear_ = interpolate.interp1d(x,y)
+print(linear_(x1))
+plt.rcParams['font.sans-serif'] = ['SimSun']#设置字体
+plt.plot(x,y,'o',label=f"原始数据")
+plt.plot(x1,linear_(x1),"*",label="线性插入")
+pl.show()

盘荣博/线性规划/插值和拟合/test1.py

@@ -0,0 +1,27 @@
+from scipy import  optimize
+import numpy as np
+
+c= np.array([-1,4])
+A=np.array([[-3,1],[1,2]])
+b=np.array([6,4])#小于关系
+Aeq=np.array([[1,1,1]])#相等
+beq = np.array([7])#
+bounds = ((None,None),(-3,None))
+res = optimize.linprog(c,A,b,None,None,bounds=bounds)
+print("目标函数最小值：",res.fun)#目标函数最优解
+print("最优解",res.x)#求得的最优解
+
+
+c = [-1,2,3]
+A=[[-2,1,1],[3,-1,-2]]
+b=[[9],[-4]]
+Aeq =[[4,-2,-1]]
+beq=[-6]
+LB=[-10,0,None]
+UB = [None]*len(c)
+print(UB)
+bound = tuple(zip(LB,UB))
+print(zip(LB,UB),'\n',bound)
+res = optimize.linprog(c,A,b,Aeq,beq,bounds=bound)
+print("函数的最小值为",res.fun)
+print("最优解为：",res.x)