Function src_error_estimate 

pub fn src_error_estimate<T>(
    r: &Matrix<T>,
) -> Result<SrcErrorEstimate, BackendLinalgError>
where
    T: MatrixTriangularSolveScalar + ComplexFloat,

Compute the Appendix C SRC error and norm estimates from an upper-triangular QR factor R.

Provenance: the formulas are Eq. (err-est) and Eq. (norm-est) in Appendix C of Camaño–Epperly–Tropp, arXiv:2504.06475, cross-checked against chriscamano/RandomMPOMPS/code/tensornetwork/incrementalqr.cpp::get_error_estimate (lines 106–119). The use of actual R plus an R† solve is an equivalent representation derived in the audit; it is not a literal port of the author’s inverse-R storage.

The helper explicitly builds R† before solving R† G = I, so complex inputs use the Hermitian adjoint rather than a plain transpose. The solve is delegated to the configured tensor4all backend and is restricted to the small sketch matrix; no general dense inverse routine is used.

Errors

Returns BackendLinalgError when r is empty, non-square, non-triangular, singular, or contains non-finite values, or when the backend triangular solve fails.

Examples

use tensor4all_tensorbackend::{src_error_estimate, Matrix};

let r = Matrix::from_col_major_vec(2, 2, vec![2.0_f64, 0.0, 1.0, 3.0]);
let estimate = src_error_estimate(&r).unwrap();
assert!(estimate.error.is_finite());
assert!(estimate.norm.is_finite());