wsvd {mogsa} | R Documentation

## Weighted singular value decomposition (SVD)

### Description

The weighted version of singular value decomposition.

### Usage

        wsvd(X, D1 = diag(1, nrow(X)), D2 = diag(1, ncol(X)))

### Arguments

`X` | A numeric matrix whose wSVD decomposition is to be computed.
`D1` | A square matrix or vector. The left constraint/weight matrix (symmetric and positive in diagonal). The dimension of D1 should be the same with the number of rows in X. A vector input will be converted to a diagnal matrix.
`D2` | A square matrix or vector. The right constraint/weight matrix (symmetric, positive in diagonal). The dimension of D1 should be the same with the number of columns in X. A vector input will be converted to a diagnal matrix.

### Details

The weighted version of generalized singular value decomposition (SVD) of matrix A = UDV' with the constraints U'D1U = I and V'D2V = I D1 and D2 are two matrices express constraints imposed on the rows and the columns of matrix A.

### Value

d - singular values

u - left singular vectors

v - right singular vectors

D1 - the left weight matrix (directly from input)

D2 - the right weight matrix (directly from input)

### Author(s)

Chen Meng

### References

Herve Abdi. Singular Value Decomposition (SVD) and Generalized Singular Value Decomposition (GSVD) http://www.utdallas.edu/~herve/Abdi-SVD2007-pretty.pdf

### See Also

svd

### Examples

        set.seed(56)
        m <- matrix(rnorm(15), 5, 3)
        wl <- rnorm(5)
        wr <- runif(3)
        s <- wsvd(X=m, D1=wl, D2=wr)
        # t(s$u) %*% diag(wl) %*% s$u
        # t(s$v) %*% diag(wr) %*% s$v
        # all.equal(m, as.matrix(s$u) %*% diag(s$d) %*% t(s$v))

[Package mogsa version 1.20.0 Index]