Complex operator from its real and imaginary parts.

Builds an eigencore operator for the complex matrix re + 1i * im from two real matrices of the same dimensions, each dense or sparse (any Matrix class). This is how complex sparse matrices enter eigencore: the Matrix package has no complex sparse classes (zgCMatrix and friends are not implemented), so a complex sparse Hermitian matrix is passed as a symmetric real part and a skew-symmetric imaginary part.

Usage

complex_operator(re, im = NULL, structure = NULL)

Arguments

re

Real part: a numeric matrix or a real Matrix object.

im

Imaginary part with the dimensions of re; NULL means zero.

structure

Optional structure descriptor. By default the operator is hermitian() when re is symmetric and im skew-symmetric (to a relative tolerance of sqrt(.Machine$double.eps)), else general().

Value

An eigencore_operator of dtype = "complex" whose apply takes real or complex blocks.

Details

A Hermitian operator (re symmetric, im skew-symmetric) is solved by eig_partial() on the real symmetric 2n x 2n embedding [re -im; im re], kept sparse: native block Lanczos, CHOLMOD LDL' shift-invert and inertia counts all run on the real sparse embedding, and the eigenpairs are mapped back to complex vectors and certified on the complex operator.

Examples

re <- Matrix::sparseMatrix(i = c(1, 2, 3, 1), j = c(1, 2, 3, 2),
                           x = c(2, 3, 4, 1), dims = c(3, 3), symmetric = TRUE)
im <- Matrix::sparseMatrix(i = c(1, 2), j = c(2, 1), x = c(0.5, -0.5),
                           dims = c(3, 3))
op <- complex_operator(re, im)
fit <- eig_partial(op, k = 1, target = largest())
values(fit)
#> [1] 4