ProgramGuruTo perform QR decomposition in R, you can use the qr() function. This function computes the QR decomposition of a matrix, representing it as the product of an orthogonal matrix Q and an upper triangular matrix R.
In this example,
mat using the matrix() function. This matrix represents the data we want to decompose.qr() function to perform QR decomposition on the matrix mat. We assign the result to a variable named qr_res.qr_res using the $qr attribute and assign it to a variable named Q.qr_res using the $qr attribute and assign it to a variable named R.Q and R to the console to see the results. This allows us to verify the decomposition.mat <- matrix(c(1, 2, 3, 4, 5, 6, 7, 8, 9), nrow = 3, byrow = TRUE)
qr_res <- qr(mat)
Q <- qr.Q(qr_res)
R <- qr.R(qr_res)
print('Orthogonal Matrix Q:')
print(Q)
print('Upper Triangular Matrix R:')
print(R)[1] "Orthogonal Matrix Q:"
[,1] [,2] [,3]
[1,] -0.1230915 0.9045340 0.4082483
[2,] -0.4923660 0.3015113 -0.8164966
[3,] -0.8616404 -0.3015113 0.4082483
[1] "Upper Triangular Matrix R:"
[,1] [,2] [,3]
[1,] -8.124038 -9.601136 -1.107823e+01
[2,] 0.000000 0.904534 1.809068e+00
[3,] 0.000000 0.000000 -2.220446e-16In this example,
mat using the matrix() function. This matrix represents another set of data we want to decompose.qr() function to perform QR decomposition on the matrix mat. We assign the result to a variable named qr_res.qr_res using the $qr attribute and assign it to a variable named Q.qr_res using the $qr attribute and assign it to a variable named R.Q and R to the console to see the results. This allows us to verify the decomposition.mat <- matrix(c(1, 2, 3, 4, 5, 6, 7, 8), nrow = 4, byrow = TRUE)
qr_res <- qr(mat)
Q <- qr.Q(qr_res)
R <- qr.R(qr_res)
print('Orthogonal Matrix Q:')
print(Q)
print('Upper Triangular Matrix R:')
print(R)[1] "Orthogonal Matrix Q:"
[,1] [,2]
[1,] -0.1091089 -0.8295151
[2,] -0.3273268 -0.4391550
[3,] -0.5455447 -0.0487950
[4,] -0.7637626 0.3415650
[1] "Upper Triangular Matrix R:"
[,1] [,2]
[1,] -9.165151 -10.9108945
[2,] 0.000000 -0.9759001In this tutorial, we learned How to Perform QR Decomposition in R language with well detailed examples.