极客教程R语言 矩阵
矩阵 是数字在行和列中的一种矩形排列。在一个矩阵中，我们知道行是水平方向的，列是垂直方向的。在R编程中，矩阵是二维的、同质的数据结构。这些是一些矩阵的例子：
创建一个矩阵
要在R语言中创建一个矩阵，你需要使用名为 matrix() 的函数 。 这个 matrix() 的参数是向量中元素的集合。你必须传递你希望在你的矩阵中拥有多少行和多少列。
注意： 默认情况下，矩阵是按列顺序排列的。
# R program to create a matrix
A = matrix(
# Taking sequence of elements
c(1, 2, 3, 4, 5, 6, 7, 8, 9),
# No of rows
nrow = 3,
# No of columns
ncol = 3,
# By default matrices are in column-wise order
# So this parameter decides how to arrange the matrix
byrow = TRUE
)
# Naming rows
rownames(A) = c("a", "b", "c")
# Naming columns
colnames(A) = c("c", "d", "e")
cat("The 3x3 matrix:\n")
print(A)
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输出：
The 3x3 matrix:
c d e
a 1 2 3
b 4 5 6
c 7 8 9
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创建特殊的矩阵
R允许通过使用传递给matrix()函数的参数来创建各种不同类型的矩阵。
- 所有行和列都由一个常数’k ‘ 填充的矩阵 ：
要创建这样一个矩阵，语法如下：
语法： matrix(k, m, n)
参数：
k： 常数
m： 行的数量
n： 列的数量
- 示例：
# R program to illustrate
# special matrices
# Matrix having 3 rows and 3 columns
# filled by a single constant 5
print(matrix(5, 3, 3))
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- 输出：
[,1] [,2] [,3]
[1,] 5 5 5
[2,] 5 5 5
[3,] 5 5 5
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- 对角线矩阵:
对角线矩阵是一个矩阵，其中主对角线以外的条目都是零。要创建这样一个矩阵，语法如下：
语法： diag(k, m, n)
参数：
k： 常数/数组
m： 行的数量
n： 列的数量
- 示例：
# R program to illustrate
# special matrices
# Diagonal matrix having 3 rows and 3 columns
# filled by array of elements (5, 3, 3)
print(diag(c(5, 3, 3), 3, 3))
R
- 输出：
[,1] [,2] [,3]
[1,] 5 0 0
[2,] 0 3 0
[3,] 0 0 3
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- 单位矩阵:
一个正方形矩阵，其中主对角线上的所有元素都是1，其他元素都是0。要创建这样的矩阵，语法如下：
语法： diag(k, m, n)
参数：
k： 1
m： 行的数量
n： 列的数量
- 示例：
# R program to illustrate
# special matrices
# Identity matrix having
# 3 rows and 3 columns
print(diag(1, 3, 3))
R
- 输出：
[,1] [,2] [,3]
[1,] 1 0 0
[2,] 0 1 0
[3,] 0 0 1
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矩阵度量
矩阵度量是指一旦创建了一个矩阵，那么
- 你如何知道矩阵的维度？
- 你怎么能知道矩阵中有多少行？
- 矩阵中有多少列？
- 矩阵中有多少个元素？ 是我们通常想要回答的问题。
例如：
# R program to illustrate
# matrix metrics
# Create a 3x3 matrix
A = matrix(
c(1, 2, 3, 4, 5, 6, 7, 8, 9),
nrow = 3,
ncol = 3,
byrow = TRUE
)
cat("The 3x3 matrix:\n")
print(A)
cat("Dimension of the matrix:\n")
print(dim(A))
cat("Number of rows:\n")
print(nrow(A))
cat("Number of columns:\n")
print(ncol(A))
cat("Number of elements:\n")
print(length(A))
# OR
print(prod(dim(A)))
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输出：
The 3x3 matrix:
[,1] [,2] [,3]
[1,] 1 2 3
[2,] 4 5 6
[3,] 7 8 9
Dimension of the matrix:
[1] 3 3
Number of rows:
[1] 3
Number of columns:
[1] 3
Number of elements:
[1] 9
[1] 9
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访问矩阵中的元素
我们可以使用与数据框架相同的约定来访问矩阵中的元素。所以，你会有一个矩阵，后面是一个方括号，在数组之间有一个逗号。逗号之前的值用于访问行，逗号之后的值用于访问列。让我们通过一个简单的R代码来说明这个问题。
访问行：
# R program to illustrate
# access rows in metrics
# Create a 3x3 matrix
A = matrix(
c(1, 2, 3, 4, 5, 6, 7, 8, 9),
nrow = 3,
ncol = 3,
byrow = TRUE
)
cat("The 3x3 matrix:\n")
print(A)
# Accessing first and second row
cat("Accessing first and second row\n")
print(A[1:2, ])
R
输出：
The 3x3 matrix:
[, 1] [, 2] [, 3]
[1, ] 1 2 3
[2, ] 4 5 6
[3, ] 7 8 9
Accessing first and second row
[, 1] [, 2] [, 3]
[1, ] 1 2 3
[2, ] 4 5 6
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访问列：
# R program to illustrate
# access columns in metrics
# Create a 3x3 matrix
A = matrix(
c(1, 2, 3, 4, 5, 6, 7, 8, 9),
nrow = 3,
ncol = 3,
byrow = TRUE
)
cat("The 3x3 matrix:\n")
print(A)
# Accessing first and second column
cat("Accessing first and second column\n")
print(A[, 1:2])
R
输出：
The 3x3 matrix:
[, 1] [, 2] [, 3]
[1, ] 1 2 3
[2, ] 4 5 6
[3, ] 7 8 9
Accessing first and second column
[, 1] [, 2]
[1, ] 1 2
[2, ] 4 5
[3, ] 7 8
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访问矩阵的元素：
# R program to illustrate
# access an entry in metrics
# Create a 3x3 matrix
A = matrix(
c(1, 2, 3, 4, 5, 6, 7, 8, 9),
nrow = 3,
ncol = 3,
byrow = TRUE
)
cat("The 3x3 matrix:\n")
print(A)
# Accessing 2
print(A[1, 2])
# Accessing 6
print(A[2, 3])
R
输出：
The 3x3 matrix:
[, 1] [, 2] [, 3]
[1, ] 1 2 3
[2, ] 4 5 6
[3, ] 7 8 9
[1] 2
[1] 6
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访问子矩阵：
我们可以使用 冒号(:) 操作符访问矩阵中的子矩阵。
# R program to illustrate
# access submatrices in a matrix
# Create a 3x3 matrix
A = matrix(
c(1, 2, 3, 4, 5, 6, 7, 8, 9),
nrow = 3,
ncol = 3,
byrow = TRUE
)
cat("The 3x3 matrix:\n")
print(A)
cat("Accessing the first three rows and the first two columns\n")
print(A[1:3, 1:2])
R
输出：
The 3x3 matrix:
[, 1] [, 2] [, 3]
[1, ] 1 2 3
[2, ] 4 5 6
[3, ] 7 8 9
Accessing the first three rows and the first two columns
[, 1] [, 2]
[1, ] 1 2
[2, ] 4 5
[3, ] 7 8
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修改矩阵的元素
在R中，你可以通过直接赋值来修改矩阵的元素。
例子：
# R program to illustrate
# editing elements in metrics
# Create a 3x3 matrix
A = matrix(
c(1, 2, 3, 4, 5, 6, 7, 8, 9),
nrow = 3,
ncol = 3,
byrow = TRUE
)
cat("The 3x3 matrix:\n")
print(A)
# Editing the 3rd rows and 3rd column element
# from 9 to 30
# by direct assignments
A[3, 3] = 30
cat("After edited the matrix\n")
print(A)
R
输出：
The 3x3 matrix:
[, 1] [, 2] [, 3]
[1, ] 1 2 3
[2, ] 4 5 6
[3, ] 7 8 9
After edited the matrix
[, 1] [, 2] [, 3]
[1, ] 1 2 3
[2, ] 4 5 6
[3, ] 7 8 30
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矩阵连接
矩阵连接是指合并现有矩阵的行或列。
行的连接：
行与矩阵的连接是用 rbind() 完成的 。
# R program to illustrate
# concatenation of a row in metrics
# Create a 3x3 matrix
A = matrix(
c(1, 2, 3, 4, 5, 6, 7, 8, 9),
nrow = 3,
ncol = 3,
byrow = TRUE
)
cat("The 3x3 matrix:\n")
print(A)
# Creating another 1x3 matrix
B = matrix(
c(10, 11, 12),
nrow = 1,
ncol = 3
)
cat("The 1x3 matrix:\n")
print(B)
# Add a new row using rbind()
C = rbind(A, B)
cat("After concatenation of a row:\n")
print(C)
R
输出：
The 3x3 matrix:
[, 1] [, 2] [, 3]
[1, ] 1 2 3
[2, ] 4 5 6
[3, ] 7 8 9
The 1x3 matrix:
[, 1] [, 2] [, 3]
[1, ] 10 11 12
After concatenation of a row:
[, 1] [, 2] [, 3]
[1, ] 1 2 3
[2, ] 4 5 6
[3, ] 7 8 9
[4, ] 10 11 12
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列的连接：
列与矩阵的连接是通过 cbind() 完成的 。
# R program to illustrate
# concatenation of a column in metrics
# Create a 3x3 matrix
A = matrix(
c(1, 2, 3, 4, 5, 6, 7, 8, 9),
nrow = 3,
ncol = 3,
byrow = TRUE
)
cat("The 3x3 matrix:\n")
print(A)
# Creating another 3x1 matrix
B = matrix(
c(10, 11, 12),
nrow = 3,
ncol = 1,
byrow = TRUE
)
cat("The 3x1 matrix:\n")
print(B)
# Add a new column using cbind()
C = cbind(A, B)
cat("After concatenation of a column:\n")
print(C)
R
输出：
The 3x3 matrix:
[, 1] [, 2] [, 3]
[1, ] 1 2 3
[2, ] 4 5 6
[3, ] 7 8 9
The 3x1 matrix:
[, 1]
[1, ] 10
[2, ] 11
[3, ] 12
After concatenation of a column:
[, 1] [, 2] [, 3] [, 4]
[1, ] 1 2 3 10
[2, ] 4 5 6 11
[3, ] 7 8 9 12
R
尺寸不一致： 注意，在做这个矩阵连接之前，你必须确保矩阵之间尺寸的一致性。
# R program to illustrate
# Dimension inconsistency in metrics concatenation
# Create a 3x3 matrix
A = matrix(
c(1, 2, 3, 4, 5, 6, 7, 8, 9),
nrow = 3,
ncol = 3,
byrow = TRUE
)
cat("The 3x3 matrix:\n")
print(A)
# Creating another 1x3 matrix
B = matrix(
c(10, 11, 12),
nrow = 1,
ncol = 3,
)
cat("The 1x3 matrix:\n")
print(B)
# This will give an error
# because of dimension inconsistency
C = cbind(A, B)
cat("After concatenation of a column:\n")
print(C)
R
输出：
The 3x3 matrix:
[, 1] [, 2] [, 3]
[1, ] 1 2 3
[2, ] 4 5 6
[3, ] 7 8 9
The 1x3 matrix:
[, 1] [, 2] [, 3]
[1, ] 10 11 12
Error in cbind(A, B) : number of rows of matrices must match (see arg 2)
R
删除矩阵的行和列
要删除一行或一列，首先需要访问该行或列，然后在该行或列前插入一个负号。它表示你必须删除该行或列。
行的删除：
# R program to illustrate
# row deletion in metrics
# Create a 3x3 matrix
A = matrix(
c(1, 2, 3, 4, 5, 6, 7, 8, 9),
nrow = 3,
ncol = 3,
byrow = TRUE
)
cat("Before deleting the 2nd row\n")
print(A)
# 2nd-row deletion
A = A[-2, ]
cat("After deleted the 2nd row\n")
print(A)
R
输出：
Before deleting the 2nd row
[, 1] [, 2] [, 3]
[1, ] 1 2 3
[2, ] 4 5 6
[3, ] 7 8 9
After deleted the 2nd row
[, 1] [, 2] [, 3]
[1, ] 1 2 3
[2, ] 7 8 9
R
列的删除：
# R program to illustrate
# column deletion in metrics
# Create a 3x3 matrix
A = matrix(
c(1, 2, 3, 4, 5, 6, 7, 8, 9),
nrow = 3,
ncol = 3,
byrow = TRUE
)
cat("Before deleting the 2nd column\n")
print(A)
# 2nd-row deletion
A = A[, -2]
cat("After deleted the 2nd column\n")
print(A)
R
输出：
Before deleting the 2nd column
[, 1] [, 2] [, 3]
[1, ] 1 2 3
[2, ] 4 5 6
[3, ] 7 8 9
After deleted the 2nd column
[, 1] [, 2]
[1, ] 1 3
[2, ] 4 6
[3, ] 7 9
R