selected_eigenvalues: Spectral Decomposition of a Matrix

In BGLRutils: Utilities for Bayesian Generalized Linear Regression

Description

Computes eigenvalues and eigenvectors of numeric matrices.

Usage

selected_eigenvalues(x,min_eigenvalue = 1e-10)

Arguments

x	a numeric or complex matrix whose spectral decomposition is to be computed. Logical matrices are coerced to numeric.
min_eigenvalue	smallest eigen_value to compute.

Value

The spectral decomposition of x is returned as components of a list with components

values	a vector containing the p eigenvalues of x, sorted in decreasing order, according to Mod(values) in the asymmetric case when they might be complex (even for real matrices). For real asymmetric matrices the vector will be complex only if complex conjugate pairs of eigenvalues are detected.
vectors	a p * p matrix whose columns contain the eigenvectors of x. Recall that the eigenvectors are only defined up to a constant: even when the length is specified they are still only defined up to a scalar of modulus one (the sign for real matrices).

References

Anderson. E. and ten others (1999) LAPACK Users' Guide. Third Edition. SIAM.
Available on-line at http://www.netlib.org/lapack/lug/lapack_lug.html.

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole. Springer-Verlag Lecture Notes in Computer Science 6.

Wilkinson, J. H. (1965) The Algebraic Eigenvalue Problem. Clarendon Press, Oxford.

See Also

svd, a generalization of eigen; qr, and chol for related decompositions.

To compute the determinant of a matrix, the qr decomposition is much more efficient: det.

Examples

## Not run: 

  library(BGLR)
  library(BGLRutils)
  data(wheat)
  out=selected_eigenvalues(wheat.A,min_eigenvalue=1e-5)


## End(Not run)

BGLRutils documentation built on May 2, 2019, 4:48 p.m.