R语言矩阵

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2023-03-14

矩阵是其中元素以二维矩形布局排列的R对象。它们包含相同原子类型的元素。虽然我们可以创建一个仅包含字符或仅包含逻辑值的矩阵，但它们没有太多用处。我们使用包含数学元素的矩阵来在数学计算中使用。

矩阵可通过使用matrix()函数来创建。

语法

在R中创建矩阵的基本语法是 -

matrix(data, nrow, ncol, byrow, dimnames)

以下是使用的参数的描述 -

data - 是将要转为矩阵元素的输入向量。
nrow - 是要创建的行数。
ncol - 是要创建的列数。
byrow - 是一个逻辑线索。如果为TRUE，则输入向量元素按行排列。
dimname - 是分配给行和列的名称。

例子

创建一个使用数字向量作为输入的矩阵，参考以下代码 -

# Elements are arranged sequentially by row.
M <- matrix(c(3:14), nrow = 4, byrow = TRUE)
print(M)

# Elements are arranged sequentially by column.
N <- matrix(c(3:14), nrow = 4, byrow = FALSE)
print(N)

# Define the column and row names.
rownames = c("row1", "row2", "row3", "row4")
colnames = c("col1", "col2", "col3")

P <- matrix(c(3:14), nrow = 4, byrow = TRUE, dimnames = list(rownames, colnames))
print(P)

当我们执行上述代码时，会产生以下结果 -

     [,1] [,2] [,3]
[1,]    3    4    5
[2,]    6    7    8
[3,]    9   10   11
[4,]   12   13   14
     [,1] [,2] [,3]
[1,]    3    7   11
[2,]    4    8   12
[3,]    5    9   13
[4,]    6   10   14
     col1 col2 col3
row1    3    4    5
row2    6    7    8
row3    9   10   11
row4   12   13   14

访问矩阵的元素

可以使用元素的列和行索引来访问矩阵的元素。我们考虑上面的矩阵P来找到下面的具体元素。

# Define the column and row names.
rownames = c("row1", "row2", "row3", "row4")
colnames = c("col1", "col2", "col3")

# Create the matrix.
P <- matrix(c(3:14), nrow = 4, byrow = TRUE, dimnames = list(rownames, colnames))

# Access the element at 3rd column and 1st row.
print(P[1,3])

# Access the element at 2nd column and 4th row.
print(P[4,2])

# Access only the  2nd row.
print(P[2,])

# Access only the 3rd column.
print(P[,3])

当我们执行上述代码时，会产生以下结果 -

[1] 5
[1] 13
col1 col2 col3 
   6    7    8 
row1 row2 row3 row4 
   5    8   11   14

矩阵计算

使用R运算符对矩阵执行各种数学运算，操作的结果也是一个矩阵。

操作中涉及的矩阵的尺寸(行数和列数)应相同。

矩阵加法与减法运算示例 -

# Create two 2x3 matrices.
matrix1 <- matrix(c(3, 9, -1, 4, 2, 6), nrow = 2)
print(matrix1)

matrix2 <- matrix(c(5, 2, 0, 9, 3, 4), nrow = 2)
print(matrix2)

# Add the matrices.
result <- matrix1 + matrix2
cat("Result of addition","\n")
print(result)

# Subtract the matrices
result <- matrix1 - matrix2
cat("Result of subtraction","\n")
print(result)

当我们执行上述代码时，会产生以下结果 -

     [,1] [,2] [,3]
[1,]    3   -1    2
[2,]    9    4    6
     [,1] [,2] [,3]
[1,]    5    0    3
[2,]    2    9    4
Result of addition 
     [,1] [,2] [,3]
[1,]    8   -1    5
[2,]   11   13   10
Result of subtraction 
     [,1] [,2] [,3]
[1,]   -2   -1   -1
[2,]    7   -5    2

矩阵乘法与除法运算示例

# Create two 2x3 matrices.
matrix1 <- matrix(c(3, 9, -1, 4, 2, 6), nrow = 2)
print(matrix1)

matrix2 <- matrix(c(5, 2, 0, 9, 3, 4), nrow = 2)
print(matrix2)

# Multiply the matrices.
result <- matrix1 * matrix2
cat("Result of multiplication","\n")
print(result)

# Divide the matrices
result <- matrix1 / matrix2
cat("Result of division","\n")
print(result)

当我们执行上述代码时，会产生以下结果 -

     [,1] [,2] [,3]
[1,]    3   -1    2
[2,]    9    4    6
     [,1] [,2] [,3]
[1,]    5    0    3
[2,]    2    9    4
Result of multiplication 
     [,1] [,2] [,3]
[1,]   15    0    6
[2,]   18   36   24
Result of division 
     [,1]      [,2]      [,3]
[1,]  0.6      -Inf 0.6666667
[2,]  4.5 0.4444444 1.5000000