Program to find the transpose of a matrix using constant space
This approach works only for square matrices (i.e., – where no. of rows are equal to the number of columns). This algorithm is also known as an “in-place” algorithm as it uses no extra space to solve the problem.
Follow the given steps to solve the problem:
- Run a nested loop using two integer pointers i and j for 0 <= i < N and i+1 <= j < N
- Swap A[i][j] with A[j][i]
Below is the implementation of the above approach:
R
# Define the size of the matrixN <- 4# Create the matrixA <- matrix(c(1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4), nrow = N, ncol = N, byrow = TRUE)# Function to transpose the matrixtranspose <- function(A) { for (i in 1:(N - 1)) { for (j in (i + 1):N) { temp <- A[i, j] A[i, j] <- A[j, i] A[j, i] <- temp } } return(A)}# Transpose the matrixA <- transpose(A)# Print the modified matrixcat("Modified matrix is\n")for (i in 1:N) { for (j in 1:N) { cat(A[i, j], " ") } cat("\n")} |
Output:
Modified matrix is
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
The provided R program efficiently computes the transpose of a square matrix using constant space, following an in-place algorithm. By iterating through the matrix and swapping elements across the diagonal, it achieves this without any additional memory usage. This approach is particularly valuable for square matrices, offering an elegant and space-efficient solution for transposition tasks in data manipulation and linear algebra.
Reverse matrix in R
A transpose of a matrix is a new matrix that is obtained by swapping the rows and columns of the original matrix. In R, you can calculate the transpose of a matrix using nested for loops to iterate through the elements and rearrange them accordingly. Transposing a matrix is a fundamental operation in linear algebra and is useful in various mathematical and data analysis applications.
Contact Us