ProgramGuruTo perform Cholesky decomposition in R, you can use the chol() function. This function computes the Cholesky factorization of a real symmetric positive-definite matrix.
In this example,
mat using the matrix() function. This matrix represents the data we want to decompose.chol() function to perform Cholesky decomposition on the matrix mat. We assign the result to a variable named chol_res.chol_res using the drop() function and assign it to a variable named L.L and its transpose using the %*% operator to obtain the original matrix mat. This is done to verify the correctness of the decomposition.L and the product of L and its transpose to the console to see the results. This allows us to verify the decomposition.mat <- matrix(c(4, 12, -16, 12, 37, -43, -16, -43, 98), nrow = 3, byrow = TRUE)
chol_res <- chol(mat)
L <- drop(chol_res)
mat_reconstructed <- L %*% t(L)
print('Lower Triangular Matrix L:')
print(L)
print('Reconstructed Matrix:')
print(mat_reconstructed)[1] "Lower Triangular Matrix L:"
[,1] [,2] [,3]
[1,] 2 6 -8
[2,] 0 1 5
[3,] 0 0 3
[1] "Reconstructed Matrix:"
[,1] [,2] [,3]
[1,] 104 -34 -24
[2,] -34 26 15
[3,] -24 15 9In this example,
mat using the matrix() function. This matrix represents another set of data we want to decompose.chol() function to perform Cholesky decomposition on the matrix mat. We assign the result to a variable named chol_res.chol_res using the drop() function and assign it to a variable named L.L and its transpose using the %*% operator to obtain the original matrix mat. This is done to verify the correctness of the decomposition.L and the product of L and its transpose to the console to see the results. This allows us to verify the decomposition.mat <- matrix(c(4, 12, 1, 0, 12, 37, -43, 0, -16, -43, 98, 0, 0, 0, 0, 0), nrow = 4, byrow = TRUE)
chol_res <- chol(mat)
L <- drop(chol_res)
mat_reconstructed <- L %*% t(L)
print('Lower Triangular Matrix L:')
print(L)
print('Reconstructed Matrix:')
print(mat_reconstructed)Error in chol.default(mat) : the leading minor of order 3 is not positive definite Calls: chol -> chol.default Execution halted
In this tutorial, we learned How to Perform Cholesky Decomposition in R language with well detailed examples.