Matrix factorization is a very important problem. There are supercomputers built just to do matrix factorizations. Every second you are on an airplane, matrices are being factorized. Radars that track flights use a technique called Kalman filtering. At the heart of Kalman Filtering is a Matrix Factorization operation. Kalman Filters are solving linear systems of equations when they track your flight using radars. Write an R function to factorize a square matrix A into LU or LDU, whichever you prefer.
my_func = function(M){
if(dim(M)[1]!=dim(M)[2]){
return('Stop!! Not a square matrix')
}
rows = columns = dim(M)[1]
U = M
L = D = diag(rows)
for (j in 1:(columns-1)){
for (i in (j+1):rows){
L[i,j] = (U[i,j]/U[j,j])
U[i,] = U[i,]-(U[j,]*L[i,j])
}
}
diag(D) = diag(U)
for (l in 1:rows){
U[l,] = U[l,]/U[l,l]
}
LDU = list(L,D,U)
return(LDU)
}
M = matrix(c(1,3,6,2,3,5,-1,7,-3),nrow=3,ncol = 3)
my_func(M)## [[1]]
## [,1] [,2] [,3]
## [1,] 1 0.000000 0
## [2,] 3 1.000000 0
## [3,] 6 2.333333 1
##
## [[2]]
## [,1] [,2] [,3]
## [1,] 1 0 0.00000
## [2,] 0 -3 0.00000
## [3,] 0 0 -20.33333
##
## [[3]]
## [,1] [,2] [,3]
## [1,] 1 2 -1.000000
## [2,] 0 1 -3.333333
## [3,] 0 0 1.000000