Divide Each Row of Matrix by Vector Elements in R

In this article, we will discuss how to divide each row of the matrix by vector elements in R Programming Language.

Method 1: Using standard division

Initially, the transpose of the matrix is computed, to interchange the rows and columns. Initially, if the dimensions of the matrix were n * m , transpose converts the dimensions to m * n. The transpose of the matrix needs to be computed because the boolean division operator "/" is applied column-wise, and we need to compute row-wise division. The division operation is then applied using transpose matrix as one operand and vector as the other. The transpose of this result is then taken, to preserve the order of rows and columns again. 

Syntax:

t(transpose_matrix/vector)

Example:

# creating matrix 
matrix <- matrix(1:12,ncol=3)

print ("Original Matrix")
print (matrix)

# creating vector
vec <- c(1:3)

# transpose matrix
trans_mat <- t(matrix)

# computing division 
div <- t(trans_mat/vec)

print ("Division matrix")
print (div)

Output

[1] "Original Matrix"
    [,1] [,2] [,3]
[1,]    1    5    9
[2,]    2    6   10
[3,]    3    7   11
[4,]    4    8   12
[1] "Division matrix"
    [,1] [,2]     [,3]
[1,]    1  2.5 3.000000
[2,]    2  3.0 3.333333
[3,]    3  3.5 3.666667
[4,]    4  4.0 4.000000

Method 2: Using sweep() method

This method in R language returns an array obtained from an input array by sweeping out a summary statistic. The method is used to compute arithmetic operations on the data frame over the chosen axis. For, row-wise operation the chosen axis is 2 and the operand becomes the row of the data frame. The result has to be stored in another variable. The time incurred in this operation is equivalent to the number of rows in the data frame. The data type of the resultant column is the largest compatible data type.

Syntax: sweep (df , axis, vec, op)

Parameter :

• df - DataFrame
• axis - To compute it row-wise, use axis = 1 and for column-wise, use axis = 2
• vec - The vector to apply on the data frame
• op - The operator to apply

Example:

# creating matrix 
matrix <- matrix(1:12,ncol=3)

print ("Original Matrix")
print (matrix)

# creating vector
vec <- c(1:3)

# computing division 
div <- sweep(matrix, 2, vec, "/")

print ("Division matrix")
print (div)

Output

[1] "Original Matrix"
    [,1] [,2] [,3]
[1,]    1    5    9
[2,]    2    6   10
[3,]    3    7   11
[4,]    4    8   12
[1] "Division matrix"
    [,1] [,2]     [,3]
[1,]    1  2.5 3.000000
[2,]    2  3.0 3.333333
[3,]    3  3.5 3.666667
[4,]    4  4.0 4.000000

Method 3 : Using rep() method

rep(x) method in R is used to replicate the values in vector x. It takes as an argument the "each" argument, where each element is repeated each number of times. The rep() function replicates numeric values, or text, or the values of a vector for a specific number of times.

Syntax: rep ( vec, each = )

Parameter : 

• vec : The vector whose value is replicated. 
• each : non-negative integer. Other inputs will be coerced to an integer or double vector and the first element taken. 

The idea of the application of rep() method here is to create a replication of the vector and stack it together, to create a number of copies equivalent to the number of rows. This is followed by the division of the involved matrices. 

Example:

# creating matrix 
matrix <- matrix(1:16,ncol=2)

print ("Original Matrix")
print (matrix)

# creating vector
vec <- c(1:2)

# calculating rows
rows <- nrow(matrix)

# computing division 
div <- matrix / rep(vec, each = rows)

print ("Division matrix")
print (div)

Output

[1] "Original Matrix"
    [,1] [,2]
[1,]    1    9
[2,]    2   10
[3,]    3   11
[4,]    4   12
[5,]    5   13
[6,]    6   14
[7,]    7   15
[8,]    8   16
[1] "Division matrix"
    [,1] [,2]
[1,]    1  4.5
[2,]    2  5.0
[3,]    3  5.5
[4,]    4  6.0
[5,]    5  6.5
[6,]    6  7.0
[7,]    7  7.5
[8,]    8  8.0

Method 4: Using apply() method

The apply() method is a form of collection method, which is used to apply transformations over the entire specified object. apply() method takes as input the data frame or matrix and gives output in vector, list, or array.

Syntax: apply(matrix , axis , FUN)

Parameter : 

• matrix : an array or matrix
• axis :  indicator of the axis over which transformation is applied
  • axis =1 : row-wise manipulation
  • axis =2 : column-wise manipulation
  • axis=c(1,2) : the manipulation is performed on rows and columns
• FUN: tells which function to apply.

The transpose of the result has to be computed to preserve the order after the application of the apply() method because the apply() method returns the transposed matrix. 

Example:

# creating matrix 
matrix <- matrix(1:16,ncol=2)

print ("Original Matrix")
print (matrix)

# creating vector
vec <- c(1:2)

# calculating rows
rows <- nrow(matrix)

# computing division 
div <- t(apply(matrix, 1, "/", vec))

print ("Division matrix")
print (div)

Output

[1] "Original Matrix"
    [,1] [,2]
[1,]    1    9
[2,]    2   10
[3,]    3   11
[4,]    4   12
[5,]    5   13
[6,]    6   14
[7,]    7   15
[8,]    8   16
[1] "Division matrix"
    [,1] [,2]
[1,]    1  4.5
[2,]    2  5.0
[3,]    3  5.5
[4,]    4  6.0
[5,]    5  6.5
[6,]    6  7.0
[7,]    7  7.5
[8,]    8  8.0

Method 5 : Using %*% operator

The %*% operator is a special kind of multiplication operator, defined for the purpose of matrix multiplication.  This operator is used to multiply a matrix with its transpose.  Initially, the diagonal matrix is computed for the specified vector, using the diag() function in R. It takes as argument the inverse of the vector, and then this matrix is multiplied with the original matrix to produce the division. This eliminates the need of explicit division, because the inverse is already taken into account. 

Syntax: diag( x )

Parameter :

x: vector to be present as the diagonal elements.

Example:

# creating matrix 
matrix <- matrix(1:16,ncol=2)

print ("Original Matrix")
print (matrix)

# creating vector
vec <- c(1:2)

# calculating rows
rows <- nrow(matrix)

# computing division 
div <- matrix %*% diag(1 / vec)

print ("Division matrix")
print (div)

Output

[1] "Original Matrix"
    [,1] [,2]
[1,]    1    9
[2,]    2   10
[3,]    3   11
[4,]    4   12
[5,]    5   13
[6,]    6   14
[7,]    7   15
[8,]    8   16
[1] "Division matrix"
    [,1] [,2]
[1,]    1  4.5
[2,]    2  5.0
[3,]    3  5.5
[4,]    4  6.0
[5,]    5  6.5
[6,]    6  7.0
[7,]    7  7.5
[8,]    8  8.0