Compute a dense generalized singular value decomposition

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)$values
#> [1] 0.2086137 2.6092781        NA
certificate(fit)$passed
#> [1] TRUE