Function hermitian_lanczos_lowest_eigenpair 

pub fn hermitian_lanczos_lowest_eigenpair<T, F>(
    apply_a: F,
    initial: &T,
    options: &HermitianLanczosOptions,
) -> Result<HermitianLanczosResult<T>>
where
    T: TensorVectorSpace,
    F: Fn(&T) -> Result<T>,

Compute the lowest eigenpair of a Hermitian matrix-free operator.

The operator is supplied as apply_a, which maps a vector to A * vector. The algorithm builds an orthonormal Krylov basis using modified Gram-Schmidt with a second reorthogonalization pass, forms the small projected matrix V^dagger A V, and solves that small Hermitian problem via tensorbackend. The full operator matrix is never materialized.

Arguments

• apply_a - Matrix-free Hermitian operator application.
• initial - Nonzero initial vector that defines the starting Krylov vector.
• options - Krylov dimension, convergence tolerances, and Hermitian validation settings.

Returns

The lowest Ritz eigenpair and the true residual norm.

Errors

Returns an error if the initial vector is zero, a vector-space operation fails, apply_a fails, the projected operator is not Hermitian, or the small projected eigensolver fails.

Examples

use tensor4all_core::{DynIndex, TensorDynLen, TensorVectorSpace};
use tensor4all_core::krylov::{hermitian_lanczos_lowest_eigenpair, HermitianLanczosOptions};

let i = DynIndex::new_dyn(2);
let initial = TensorDynLen::from_dense(vec![i.clone()], vec![1.0_f64, 1.0]).unwrap();
let result = hermitian_lanczos_lowest_eigenpair(
    |x: &TensorDynLen| Ok(x.clone()),
    &initial,
    &HermitianLanczosOptions::default(),
).unwrap();

assert!(result.converged);
assert!((result.eigenvalue - 1.0).abs() < 1.0e-12);