Struct AptpNumeric 

pub struct AptpNumeric { /* private fields */ }

Complete multifrontal numeric factorization result.

Contains per-supernode factors and aggregate statistics. Created by AptpNumeric::factor and used by the triangular solve to perform forward/backward substitution.

Usage

use faer::sparse::{SparseColMat, Triplet};
use faer::sparse::linalg::cholesky::SymmetricOrdering;
use rivrs_sparse::symmetric::{AptpSymbolic, AptpOptions, AptpNumeric};

// Analyze
let symbolic = AptpSymbolic::analyze(matrix.symbolic(), SymmetricOrdering::Amd).unwrap();

// Factor
let numeric = AptpNumeric::factor(&symbolic, &matrix, &AptpOptions::default(), None).unwrap();
println!("Stats: {:?}", numeric.stats());

Implementations

impl AptpNumeric

pub fn front_factors(&self) -> &[FrontFactors]

Per-supernode factors, indexed by supernode ID.

pub fn stats(&self) -> &FactorizationStats

Aggregate factorization statistics.

pub fn per_supernode_stats(&self) -> &[PerSupernodeStats]

Per-supernode diagnostic statistics.

One entry per supernode in postorder, matching front_factors.

pub fn n(&self) -> usize

Matrix dimension.

pub fn factor( symbolic: &AptpSymbolic, matrix: &SparseColMat<usize, f64>, options: &AptpOptions, scaling: Option<&[f64]>, ) -> Result<Self, SparseError>

Factor a sparse symmetric matrix using the multifrontal method with APTP.

Traverses the assembly tree in postorder, assembling and factoring dense frontal matrices at each supernode using the dense APTP kernel.

Arguments

• symbolic: Symbolic analysis result from AptpSymbolic::analyze
• matrix: Sparse symmetric matrix (lower triangle stored). Dimensions must match symbolic.nrows()
• options: APTP configuration (threshold, fallback strategy)

Errors

• SparseError::DimensionMismatch if matrix dimensions don’t match symbolic
• SparseError::AnalysisFailure if symbolic analysis is inconsistent

Zero Pivots

If a root supernode has columns that cannot be eliminated (all pivots delayed to root but still fail the threshold), these are recorded as zero pivots in FactorizationStats::zero_pivots rather than returning an error. The factorization succeeds; the solve phase must handle the rank deficiency.

References

• Duff & Reid (1983), “The multifrontal solution of indefinite sparse symmetric linear equations”
• Liu (1992), “The Multifrontal Method for Sparse Matrix Solution”
• Hogg, Duff & Lopez (2020), “A New Sparse LDL^T Solver Using A Posteriori Threshold Pivoting”

Trait Implementations

impl Debug for AptpNumeric

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.