Apply functions on matrices in R Programming - Step-by-Step Execution

Concept Flow - Apply functions on matrices

Start with Matrix

↓

Choose function to apply

↓

Select margin: rows or columns

↓

Apply function to each row/column

↓

Return result vector or matrix

We start with a matrix, pick a function, decide to apply it by rows or columns, then get the result.

Execution Sample

R Programming

mat <- matrix(1:6, nrow=2)
apply(mat, 1, sum)
apply(mat, 2, mean)

This code creates a 2x3 matrix, sums each row, then finds the mean of each column.

Execution Table

Step	Action	Matrix State	Function Applied	Result
1	Create matrix mat	[[1,3,5],[2,4,6]]	None	Matrix created
2	Apply sum by rows (margin=1)	[[1,3,5],[2,4,6]]	sum	[9, 12] (row sums)
3	Apply mean by columns (margin=2)	[[1,3,5],[2,4,6]]	mean	[1.5, 3.5, 5.5] (column means)
4	End	Same matrix	None	Finished applying functions

💡 All rows and columns processed, function applied as requested

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	Final
mat	NULL	[[1,3,5],[2,4,6]]	[[1,3,5],[2,4,6]]	[[1,3,5],[2,4,6]]	[[1,3,5],[2,4,6]]
result_row_sum	NULL	NULL	[9, 12]	[9, 12]	[9, 12]
result_col_mean	NULL	NULL	NULL	[1.5, 3.5, 5.5]	[1.5, 3.5, 5.5]

Key Moments - 3 Insights

Why does apply(mat, 1, sum) return a vector of length 2?

Because margin=1 means apply the function to each row. The matrix has 2 rows, so sum is calculated twice, once per row (see execution_table step 2).

What does margin=2 mean in apply(mat, 2, mean)?

Margin=2 means apply the function to each column. The matrix has 3 columns, so mean is calculated for each column separately (see execution_table step 3).

Does the original matrix change after apply?

No, apply does not modify the original matrix. It returns a new vector or matrix with results. The original matrix stays the same (see variable_tracker for 'mat').

Visual Quiz - 3 Questions

Look at the execution_table at step 2, what is the sum of the first row?

A 12

B 6

C 9

D 3

💡 Hint

Check the 'Result' column at step 2 in execution_table for row sums.

At which step does the mean function get applied to columns?

A Step 3

B Step 2

C Step 1

D Step 4

💡 Hint

Look at the 'Function Applied' column in execution_table to find when 'mean' is applied.

If we change margin=1 to margin=2 in apply(mat, 1, sum), what changes in the result?

A Sum is calculated for each row instead of columns

B Sum is calculated for each column instead of rows

C Result becomes a matrix instead of a vector

D No change in result

💡 Hint

Refer to key_moments about margin meaning and execution_table steps 2 and 3.

Concept Snapshot

apply(matrix, margin, function)
margin=1 applies function to rows
margin=2 applies function to columns
Returns vector or matrix of results
Original matrix stays unchanged

Full Transcript

This visual trace shows how to use the apply function on matrices in R. We start by creating a matrix named mat with 2 rows and 3 columns. Then, we apply the sum function to each row by setting margin=1, which returns a vector of row sums. Next, we apply the mean function to each column by setting margin=2, which returns a vector of column means. The original matrix remains unchanged throughout. The key points are that margin=1 means rows, margin=2 means columns, and apply returns new results without modifying the original matrix.

Practice

1. In R, what does the apply() function do when used on a matrix?

easy

A. It creates a new matrix with doubled values.

B. It converts the matrix into a vector.

C. It sorts the matrix elements in ascending order.

D. It applies a function to each row or column of the matrix.

Solution

1. Step 1: Understand the purpose of apply()

   The apply() function is designed to run a function on margins of an array or matrix.

2. Step 2: Identify what margins mean in a matrix

   Margin 1 means rows, margin 2 means columns. So apply() runs the function on each row or column.

3. Final Answer:

   It applies a function to each row or column of the matrix. -> Option D

4. Quick Check:

   apply() = function on rows/columns [OK]

Hint: Remember: MARGIN=1 rows, MARGIN=2 columns in apply() [OK]

Common Mistakes:

• Thinking apply() changes matrix shape automatically
• Confusing apply() with sorting or vector conversion
• Using apply() without specifying margin

2. Which of the following is the correct syntax to calculate the sum of each column in a matrix m using apply() in R?

easy

A. apply(m, 2, sum)

B. apply(m, sum, 2)

C. apply(m, 1, sum)

D. apply(sum, m, 2)

Solution

1. Step 1: Identify margin for columns

   In apply(), margin 2 means columns.

2. Step 2: Check function placement

   The function to apply (sum) is the third argument, so syntax is apply(m, 2, sum).

3. Final Answer:

   apply(m, 2, sum) -> Option A

4. Quick Check:

   sum columns = apply(m, 2, sum) [OK]

Hint: Use margin=2 for columns in apply() [OK]

Common Mistakes:

• Using margin=1 for columns instead of 2
• Swapping function and margin arguments
• Missing the function argument

3. What is the output of the following R code?

m <- matrix(1:6, nrow=2)
apply(m, 1, max)

medium

A. [1] 3 6

B. [1] 4 5

C. [1] 5 6

D. [1] 2 4

Solution

1. Step 1: Understand the matrix structure

   The matrix m is created with values 1 to 6, 2 rows: Row 1: 1, 3, 5 Row 2: 2, 4, 6

2. Step 2: Apply max function on rows (margin=1)

   Max of row 1 is 5, max of row 2 is 6.

3. Final Answer:

   [1] 5 6 -> Option C

4. Quick Check:

   max per row = 5, 6 [OK]

Hint: Check matrix layout before applying functions [OK]

Common Mistakes:

• Confusing rows and columns in margin
• Misreading matrix values
• Assuming apply returns matrix instead of vector

4. Identify the error in this R code snippet:

m <- matrix(1:9, nrow=3)
apply(m, 3, mean)

medium

A. apply() cannot be used with mean.

B. Margin 3 is invalid for a 2D matrix.

C. Matrix m is not created properly.

D. The function mean is not defined.

Solution

1. Step 1: Check matrix dimensions

   The matrix m has 2 dimensions (rows and columns).

2. Step 2: Validate margin argument

   Margin 3 refers to a third dimension, which does not exist in a 2D matrix.

3. Final Answer:

   Margin 3 is invalid for a 2D matrix. -> Option B

4. Quick Check:

   Margin must be 1 or 2 for matrices [OK]

Hint: Use only 1 or 2 as margin for 2D matrices [OK]

Common Mistakes:

• Using margin > 2 for 2D matrices
• Assuming apply works on non-existent dimensions
• Confusing apply() with array functions

5. You have a matrix m of numeric values. You want to create a new vector that contains the mean of each row but only for rows where the sum is greater than 10. Which R code correctly does this using apply()?

hard

A. apply(m, 1, function(x) if(sum(x) > 10) mean(x) else NA)[!is.na(.)]

B. apply(m, 1, function(x) if(sum(x) > 10) mean(x))

C. apply(m, 1, function(x) mean(x[sum(x) > 10]))

D. apply(m, 2, function(x) if(sum(x) > 10) mean(x))

Solution

1. Step 1: Understand the requirement

   We want mean of each row only if that row's sum is > 10, else exclude it.

2. Step 2: Analyze each option

   A returns NA for rows not >10 but does not remove them. C incorrectly filters inside mean. D uses margin=2 (columns) instead of rows.

3. Step 3: Correct approach

   apply(m, 1, function(x) if(sum(x) > 10) mean(x) else NA)[!is.na(.)] returns NA for rows with sum ≤ 10, then removes NAs with [!is.na(.)], giving only desired means.

4. Final Answer:

   apply(m, 1, function(x) if(sum(x) > 10) mean(x) else NA)[!is.na(.)] -> Option A

5. Quick Check:

   Filter rows by sum > 10, then mean [OK]

Hint: Use if-else inside apply and remove NA after [OK]

Common Mistakes:

• Using margin=2 instead of 1 for rows
• Not handling rows with sum ≤ 10 properly
• Trying to filter inside mean() incorrectly