R - 矩陣

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矩陣是R物件，其元素以二維矩形佈局排列。它們包含相同原子型別的元素。雖然我們可以建立一個只包含字元或邏輯值的矩陣，但它們並沒有多大用處。我們使用包含數值元素的矩陣進行數學計算。

可以使用matrix()函式建立矩陣。

語法

在R中建立矩陣的基本語法為：

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

以下是所用引數的說明：

• data 是輸入向量，它成為矩陣的資料元素。

• nrow 是要建立的行數。

• ncol 是要建立的列數。

• byrow 是一個邏輯線索。如果為 TRUE，則按行排列輸入向量元素。

• dimname 是分配給行和列的名稱。

示例

建立一個以數字向量作為輸入的矩陣。

# 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)

執行上述程式碼後，將產生以下結果：

     [,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

訪問矩陣元素

可以使用元素的列和行索引訪問矩陣的元素。我們考慮上面的矩陣P來查詢下面的特定元素。

# 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])

執行上述程式碼後，將產生以下結果：

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

矩陣計算

使用R運算子對矩陣執行各種數學運算。運算的結果也是一個矩陣。

參與運算的矩陣的維數（行數和列數）應相同。

矩陣加法和減法

# 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)

執行上述程式碼後，將產生以下結果：

     [,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

矩陣乘法和除法

# 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)

執行上述程式碼後，將產生以下結果：

     [,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