bertini::linalg::PartialPivLU< NumT > Class Template Reference

Stateful partial-pivot LU factor/solve with preallocated, precision-adjustable banks. More...

#include <lu_solver.hpp>

Public Member Functions
void	ChangeSize (unsigned n)
	(Re)size the workspace to hold n x n systems.
void	ChangePrecision (unsigned prec)
	Re-set the precision of every mp temporary bank (a no-op for complex_dbl).
unsigned	precision () const
	Get the current working precision (digits).
MatrixSuccessCode	Factor (Mat< NumT > const &A)
	Factor a copy of A with partial pivoting; A is preserved.
MatrixSuccessCode	FactorDestructive (Mat< NumT > &A)
	Factor A destructively (no copy): on return A holds the L\U factors.
template<typename OutDerived>
void	Solve (Vec< NumT > const &b, Eigen::MatrixBase< OutDerived > const &x_out) const
	Solve A x = b using the stored factors.
Mat< NumT > const &	Factors () const
	The factored matrix (L below the diagonal, U on and above), for the caller's LUPartialPivotDecompositionSuccessful()-style health check.

Detailed Description

template<typename NumT>
class bertini::linalg::PartialPivLU< NumT >

Stateful partial-pivot LU factor/solve with preallocated, precision-adjustable banks.

Template Parameters

NumT	The (complex) scalar type – complex_dbl or complex_mp.

Numerically this is the same right-looking Gaussian elimination with partial pivoting as Eigen's PartialPivLU (unit lower-triangular L, upper-triangular U, row pivoting), so solutions agree with Eigen to backward-stable accuracy. The win is allocation behavior, not the arithmetic.

Member Function Documentation

ChangePrecision()

template<typename NumT>

void bertini::linalg::PartialPivLU< NumT >::ChangePrecision ( unsigned prec )

inline

Re-set the precision of every mp temporary bank (a no-op for complex_dbl).

Parameters

prec	The new working precision (digits).

ChangeSize()

template<typename NumT>

void bertini::linalg::PartialPivLU< NumT >::ChangeSize ( unsigned n )

inline

(Re)size the workspace to hold n x n systems.

Call on a system-size change.

Parameters

n	The matrix dimension.

Factor()

template<typename NumT>

MatrixSuccessCode bertini::linalg::PartialPivLU< NumT >::Factor ( Mat< NumT > const & A )

inline

Factor a copy of A with partial pivoting; A is preserved.

O(1) allocations.

Parameters

A	The square matrix to factor.

Returns

Success unless the factored diagonal looks near-singular / ill-conditioned.

FactorDestructive()

template<typename NumT>

MatrixSuccessCode bertini::linalg::PartialPivLU< NumT >::FactorDestructive ( Mat< NumT > & A )

inline

Factor A destructively (no copy): on return A holds the L\U factors.

Parameters

A	The square matrix; overwritten with the factorization.

Returns

Success unless the factored diagonal looks near-singular / ill-conditioned.

Factors()

template<typename NumT>

Mat< NumT > const & bertini::linalg::PartialPivLU< NumT >::Factors ( ) const

inline

The factored matrix (L below the diagonal, U on and above), for the caller's LUPartialPivotDecompositionSuccessful()-style health check.

precision()

template<typename NumT>

unsigned bertini::linalg::PartialPivLU< NumT >::precision ( ) const

inline

Get the current working precision (digits).

Solve()

template<typename NumT>

template<typename OutDerived>

void bertini::linalg::PartialPivLU< NumT >::Solve ( Vec< NumT > const & b, Eigen::MatrixBase< OutDerived > const & x_out ) const

inline

Solve A x = b using the stored factors.

Reuses scratch; O(1) allocations.

Template Parameters

OutDerived

The output type – a Vec or a writable block such as K.col(stage).

Parameters

	b	The right-hand side (must be materialized storage, distinct from x).
[out]	x_out	The solution (sized n). A temporary expression (e.g. .col()) is fine.