lu_solver.hpp File Reference

A stateful partial-pivot LU solver that owns precision-adjustable temporary banks. More...

#include "bertini2/eigen_extensions.hpp"

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Classes
class	bertini::linalg::PartialPivLU< NumT >
	Stateful partial-pivot LU factor/solve with preallocated, precision-adjustable banks. More...

Namespaces
namespace	bertini
namespace	bertini::linalg

Detailed Description

A stateful partial-pivot LU solver that owns precision-adjustable temporary banks.

Eigen's generic dense LU allocates one multiprecision temporary per elementary scalar operation – O(N^3) heap allocations (mpc_init2 / mpc_clear, plus the per-alloc MPFR get_memory_functions fetch, the thread-local working-precision read, and the mimalloc ownership check) per factorization. For runtime-precision mpc that allocation churn is a large fraction of the cost and it scales with N^3.

This class factors in place, reusing a single scratch scalar across the whole elimination, so a factorization performs O(1) allocations instead of O(N^3). It owns its workspace across calls and exposes a ChangePrecision() so the owner (a Newton corrector / predictor) can move it up and down in precision the way the AMP tracker and endgames re-precision their scratch – see NewtonCorrector::ChangePrecision.