generalized_svd: Compute a dense generalized singular value decomposition

In eigencore: Certified Partial Eigenvalue and Singular Value Computation

Compute a dense generalized singular value decomposition

Description

generalized_svd() is eigencore's dense GSVD compatibility surface for matrix pairs with the same number of columns. The current native path uses LAPACK dggsvd through R's native LAPACK interface, so it requires a linked LAPACK that still provides that deprecated routine. Sparse/operator inputs are not silently densified, and complex GSVD remains explicit future scope until a complex GSVD driver is available through the eigencore native layer.

Usage

generalized_svd(A, B, tol = 1e-08, ...)

Arguments

A	Base dense real matrix with m rows and n columns.
B	Base dense real matrix with p rows and n columns.
tol	Finite non-negative reconstruction and orthogonality certification tolerance.
...	Reserved for future options.

Value

An eigencore_gsvd_result with fields alpha, beta, values, classification, U, V, Q, D1, D2, R, zero_R, A_factor, B_factor, k, l, rank, method, plan, and certificate.

Examples

A <- matrix(c(1, 2, 3, 3, 2, 1), nrow = 2, byrow = TRUE)
B <- matrix(1:9, nrow = 3)
fit <- generalized_svd(A, B)
alpha_beta(fit)$values
certificate(fit)$passed

eigencore documentation built on July 26, 2026, 1:06 a.m.