GSVD | R Documentation |
Given the matrix A
of order nxm
, the generalized singular value decomposition (GSVD) involves the use of two sets of positive square matrices of order nxn
and mxm
respectively. These two matrices express constraints imposed, respectively, on the lines and columns of A
.
GSVD(data, plin = NULL, pcol = NULL)
data |
Matrix used for decomposition. |
plin |
Weight for rows. |
pcol |
Weight for columns |
If plin or pcol is not used, it will be calculated as the usual singular value decomposition.
d |
Eigenvalues, that is, line vector with singular values of the decomposition. |
u |
Eigenvectors referring rows. |
v |
Eigenvectors referring columns. |
Paulo Cesar Ossani
Marcelo Angelo Cirillo
Abdi, H. Singular Value Decomposition (SVD) and Generalized Singular Value Decomposition (GSVD). In: SALKIND, N. J. (Ed.). Encyclopedia of measurement and statistics. Thousand Oaks: Sage, 2007. p. 907-912.
data <- matrix(c(1,2,3,4,5,6,7,8,9,10,11,12), nrow = 4, ncol = 3)
svd(data) # Usual Singular Value Decomposition
GSVD(data) # GSVD with the same previous results
# GSVD with weights for rows and columns
GSVD(data, plin = c(0.1,0.5,2,1.5), pcol = c(1.3,2,0.8))
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