ProjDD {ddpca}

Projection onto the Diagonally Dominant Cone

Description

Given a matrix C, this function outputs the projection of C onto the cones of diagonally domimant matrices.

Usage

ProjDD(C)

Arguments

C

A n \times n matrix

Details

This function projects the input matrix C of size n\times n onto the cones of diagonally domimant matrices defined as

\{A = (a_{ij})_{1\le i\le n, 1\le j\le n} : a_{jj} \ge \sum_{k\not=j} |a_{jk}| \quad \textrm{for all} \quad 1\le j\le n \}

The algorithm is described in Mendoza, M., Raydan, M. and Tarazaga, P., 1998. Computing the nearest diagonally dominant matrix.

Value

A n\times n diagonally dominant matrix

Author(s)

Fan Yang <[e-mail]>

References

Mendoza, M., Raydan, M. and Tarazaga, P., 1998. Computing the nearest diagonally dominant matrix. Numerical linear algebra with applications, 5(6), pp.461-474.

Ke, Z., Xue, L. and Yang, F., 2019. Diagonally Dominant Principal Component Analysis. Journal of Computational and Graphic Statistics, under review.

See Also

ProjSDD

Examples

ProjDD(matrix(runif(100),nrow=10))