
KhatriRao Khatri-Rao Matrix Product Description Computes Khatri-Rao products for any kind of matrices.  The Khatri-Rao product is a column-wise Kronecker product. Originally introduced by Khatri and Rao (1968), it has many different applications, see Liu and Trenkler (2008) for a survey. Notably, it is used in higher-dimensional tensor decompositions, see Bader and Kolda (2008).  Usage 
KhatriRao(X, Y = X, FUN = "*", make.dimnames = FALSE)
 Arguments  
X,Y  matrices of with the same number of columns. 
 
FUN  the (name of the) function to be used for the column-wise Kronecker products, see kronecker, defaulting to the usual multiplication. 
 
make.dimnames  logical indicating if the result should inherit dimnames from X and Y in a simple way. 
  Value a "CsparseMatrix", say R, the Khatri-Rao product of X (n x k) and Y (m x k), is of dimension (n*m) x k, where the j-th column, R[,j] is the kronecker product kronecker(X[,j], Y[,j]).  Note The current implementation is efficient for large sparse matrices.  Author(s) Original by Michael Cysouw, Univ. Marburg; minor tweaks, bug fixes etc, by Martin Maechler.  References Khatri, C. G., and Rao, C. Radhakrishna (1968) Solutions to Some Functional Equations and Their Applications to Characterization of Probability Distributions. Sankhya: Indian J. Statistics, Series A 30, 167–180.  Liu, Shuangzhe, and Gõtz Trenkler (2008) Hadamard, Khatri-Rao, Kronecker and Other Matrix Products. International J. Information and Systems Sciences 4, 160–177.  Bader, Brett W, and Tamara G Kolda (2008) Efficient MATLAB Computations with Sparse and Factored Tensors. SIAM J. Scientific Computing 30, 205–231.  See Also kronecker.  Examples 
## Example with very small matrices:
m <- matrix(1:12,3,4)
d <- diag(1:4)
KhatriRao(m,d)
KhatriRao(d,m)
dimnames(m) <- list(LETTERS[1:3], letters[1:4])
KhatriRao(m,d, make.dimnames=TRUE)
KhatriRao(d,m, make.dimnames=TRUE)
dimnames(d) <- list(NULL, paste0("D", 1:4))
KhatriRao(m,d, make.dimnames=TRUE)
KhatriRao(d,m, make.dimnames=TRUE)
dimnames(d) <- list(paste0("d", 10*1:4), paste0("D", 1:4))
(Kmd <- KhatriRao(m,d, make.dimnames=TRUE))
(Kdm <- KhatriRao(d,m, make.dimnames=TRUE))

nm <- as(m,"nMatrix")
nd <- as(d,"nMatrix")
KhatriRao(nm,nd, make.dimnames=TRUE)
KhatriRao(nd,nm, make.dimnames=TRUE)

stopifnot(dim(KhatriRao(m,d)) == c(nrow(m)*nrow(d), ncol(d)))
## border cases / checks:
zm <- nm; zm[] <- 0 # all 0 matrix
stopifnot(all(K1 <- KhatriRao(nd, zm) == 0), identical(dim(K1), c(12L, 4L)),
          all(K2 <- KhatriRao(zm, nd) == 0), identical(dim(K2), c(12L, 4L)))

d0 <- d; d0[] <- 0; m0 <- Matrix(d0[-1,])
stopifnot(all(K3 <- KhatriRao(d0, m) == 0), identical(dim(K3), dim(Kdm)),
	  all(K4 <- KhatriRao(m, d0) == 0), identical(dim(K4), dim(Kmd)),
	  all(KhatriRao(d0, d0) == 0), all(KhatriRao(m0, d0) == 0),
	  all(KhatriRao(d0, m0) == 0), all(KhatriRao(m0, m0) == 0),
	  identical(dimnames(KhatriRao(m, d0, make.dimnames=TRUE)), dimnames(Kmd)))


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