The singular value decomposition decomposes matrix A into A = U D V^T, where U and V are orthogonal matrices and D is a diagonal matrix. U is the left singular vectors of A. V is the right singular vectors of A.
Usage
svd_byname(a, which = c("d", "u", "v"))Arguments
- a
A matrix to be decomposed.
- which
The matrix to be returned. Default is "d". See details.
Details
which determines the part of the singular value decomposition to be returned.
"d" (default) gives the D matrix.
"u" gives the U matrix.
"v" gives the V matrix (not its transpose).
Examples
A = matrix(c(4, 0,
3, -5), nrow = 2, ncol = 2, byrow = TRUE,
dimnames = list(c("r1", "r2"), c("c1", "c2"))) %>%
setrowtype("Product") %>% setcoltype("Industry")
A
#> c1 c2
#> r1 4 0
#> r2 3 -5
#> attr(,"rowtype")
#> [1] "Product"
#> attr(,"coltype")
#> [1] "Industry"
svd_byname(A) # Gives D matrix, by default
#> c1 c2
#> r1 6.324555 0.000000
#> r2 0.000000 3.162278
#> attr(,"rowtype")
#> [1] "Product"
#> attr(,"coltype")
#> [1] "Industry"
svd_byname(A, which = "d")
#> c1 c2
#> r1 6.324555 0.000000
#> r2 0.000000 3.162278
#> attr(,"rowtype")
#> [1] "Product"
#> attr(,"coltype")
#> [1] "Industry"
svd_byname(A, which = "u")
#> r1 r2
#> r1 -0.4472136 -0.8944272
#> r2 -0.8944272 0.4472136
#> attr(,"rowtype")
#> [1] "Product"
#> attr(,"coltype")
#> [1] "Product"
svd_byname(A, which = "v")
#> c1 c2
#> c1 -0.7071068 -0.7071068
#> c2 0.7071068 -0.7071068
#> attr(,"rowtype")
#> [1] "Industry"
#> attr(,"coltype")
#> [1] "Industry"