统计建模与R软件习题二答案

# 习题2

# 2.1

x=c(1,2,3)

y=c(4,5,6)

e=c(rep(1,3))

z=2*x+y+e;z

x%*%y # 若x，y如答案那样定义为矩阵，则不能用%*%,因为，维数不对应，

x%o%y 

# 答案

x<-matrix(1:3,nrow=3)

y<-matrix(4:6,nrow=3)

e<-matrix(c(1,1,1),nrow=3)

z<-2*x+y+e;z

crossprod(x,y)#内积

outer(x,y)#外积

# 2.2

A=matrix(1:20,4,5);A

B=matrix(1:20,4,5,byrow=T);B

C=A+B;C

D=crossprod(A,B);D# D=A%*%B;D 错误 维数不对应，题目有错，本来就不可能AB

E=A*B;E

F=A[1:3,1:3];F

G=B[,c(1,2,4,5)];G # G<-B[1:4,-3];G 注意-3的用法

# 答案

A<-matrix(1:20,nrow=4)

B<-matrix(1:20,nrow=4,byrow=T)

C<-A+B;C

#D<-AB#不存在AB这种写法

E<-A*B;E

F<-A[1:3,1:3];F

G<-B[1:4,-3];G

# 2.3

x=c(rep(1,5),rep(2,3),rep(3,4),rep(4,2));x

#答案同上

# 2.4

Hilbert=function(n=5){

  H=matrix(0,nrow=n,ncol=n)

  for (i in 1:n){

    for (j in 1:n)

      H[i,j]=1/(i+j-1)

  }

  H # 返回值，

  list(Hmatrix=H,det=det(H),sol=solve(H),eig=eigen(H)) # 多元返回值

}

H=Hilbert(5);H

det(H)

solve(H)

eigen(H)

# 学会了function，对上述进行以下修改

funcH=function(n=5) {

	H=matrix(0,n,n)

	for (i in 1:n) {

		for (j in 1:n) {

			H[i,j]=1/(i+j-1)

		}

	}

	H # 返回值，输入H

	# list(Hmatrix=H,det=det(H),sol=solve(H),eig=eigen(H))

	# 也可以以列表形式输出多个返回值，同时能给每个元素定义元素名

	# 如 list(Hilbert=H)

  list(Hilbert=H)

}

funcH()

#2.4答案 5价Hilbert矩阵

n<-5

x<-array(0,dim=c(n,n))

for(i in 1:n){

  for(j in 1:n){

    x[i,j]<-1/(i+j-1)

  }

}

x

det(x)#矩阵行列式

solve(x)#逆矩阵

eigen(x)#特征值与特征向量

# 2.5 data.frame()

studentdata=data.frame('姓名'=c('张三','李四','王五','赵六','丁一'),

                       '性别'=c('女','男','女','男','女'),'年龄'=c(14,15,16,14,15),

                       '身高'=c(156,165,157,162,159),'体重'=c(42,49,41.5,52,45.5))

#studentdata=data.frame('序号'=1:5,'姓名'=c('张三','李四','王五','赵六','丁一'),

#                       '性别'=c('女','男','女','男','女'),'年龄'=c(14,15,16,14,15),

#                       '身高'=c(156,165,157,162,159),'体重'=c(42,49,41.5,52,45.5))

# 不需要输入序号。

write.table(studentdata,'Re2.5.txt')

# 答案

student<-data.frame(name=c("zhangsan","lisi","wangwu","zhaoliu","dingyi"),

                    sex=c("f","m","f","m","f"),

                    age=c("14","15","16","14","15"),

                    height=c("156","165","157","162","159"),

                    weight=c("42","49","41.5","52","45.5"))

# 2.6

st=read.table('Re2.5.txt',header=T)

write.csv(st,'Re2.5.csv')

#2.6 答案

student1<-write.table(student,file="student1.txt")

student2<-read.table("student1.txt",head=T)

student3<-write.csv(student2,file="student3.csv")

# 2.7

func=function(n) {

  if (n<=0) "要求输入一个正整数"

  else {

    while(n!=1) {

      if (n%%2==0) n=n/2

      else n=3*n+1}

    "运算成功"

  }

} # R中定义的函数，没有专门的返回值设置，只相当于代码复制粘贴，

func(8) #返回值为代码的输出值

# 答案

#2.7

func<-function(n){

  if(n<=0) list("要求输入一个正整数")

  else{

    repeat{

      if(n==1) break

      else if(n%%2==0){n<-n/2}

      else n<-3*n+1}

    list("运算成功")

  }

}