The magnitude at or under which a singular value counts as zero, in a rank (matrix_rank), a pseudo-inverse (pinv) or a least-squares solution (lstsq): by default NumPy's, the largest singular value times the machine epsilon times the larger dimension; relative to the largest, as NumPy's rcond and rtol; or absolute, as matrix_rank's tol. More...

#include <decomposition.hpp>

Public Member Functions
constexpr	rank_cutoff () noexcept=default
	NumPy's default: the largest singular value times the machine epsilon times the larger dimension.

double	magnitude (double largest, std::size_t rows, std::size_t cols) const noexcept
	The cutoff for a `rows × cols` matrix whose largest singular value is `largest`.

rank_cutoff	scaled (int exponent) const noexcept
	The same cutoff for the matrix divided by `2^exponent`.

Static Public Member Functions
static rank_cutoff	relative (double ratio)
	The largest singular value times `ratio`.

static rank_cutoff	absolute (double magnitude)
	`magnitude` itself, whatever the largest singular value.

Private Member Functions
constexpr	rank_cutoff (double value, bool absolute) noexcept

Static Private Member Functions
static double	checked (double value)

Private Attributes
double	value_ {-1.0}
	The ratio or the magnitude; negative for NumPy's default.

bool	absolute_ {false}
	Whether value_ is a magnitude.

Detailed Description

The magnitude at or under which a singular value counts as zero, in a rank (matrix_rank), a pseudo-inverse (pinv) or a least-squares solution (lstsq): by default NumPy's, the largest singular value times the machine epsilon times the larger dimension; relative to the largest, as NumPy's rcond and rtol; or absolute, as matrix_rank's tol.

Definition at line 2473 of file decomposition.hpp.

Constructor & Destructor Documentation

◆ rank_cutoff() [1/2]

constexpr numerical::rank_cutoff::rank_cutoff ( )

constexprdefaultnoexcept

NumPy's default: the largest singular value times the machine epsilon times the larger dimension.

◆ rank_cutoff() [2/2]

constexpr numerical::rank_cutoff::rank_cutoff	(	double	value,
		bool	absolute
	)

inlineconstexprprivatenoexcept

Definition at line 2517 of file decomposition.hpp.

Member Function Documentation

◆ absolute()

static rank_cutoff numerical::rank_cutoff::absolute ( double magnitude )

inlinestatic

magnitude itself, whatever the largest singular value.

Exceptions

std::invalid_argument If magnitude is negative or NaN.

Definition at line 2493 of file decomposition.hpp.

◆ checked()

static double numerical::rank_cutoff::checked ( double value )

inlinestaticprivate

Definition at line 2522 of file decomposition.hpp.

◆ magnitude()

double numerical::rank_cutoff::magnitude	(	double	largest,
		std::size_t	rows,
		std::size_t	cols
	)		const

inlinenoexcept

The cutoff for a rows × cols matrix whose largest singular value is largest.

Definition at line 2499 of file decomposition.hpp.

◆ relative()

static rank_cutoff numerical::rank_cutoff::relative ( double ratio )

inlinestatic

The largest singular value times ratio.

Exceptions

std::invalid_argument If ratio is negative or NaN.

Definition at line 2484 of file decomposition.hpp.

◆ scaled()

rank_cutoff numerical::rank_cutoff::scaled ( int exponent ) const

inlinenoexcept

The same cutoff for the matrix divided by 2^exponent.

Definition at line 2510 of file decomposition.hpp.

Member Data Documentation

◆ absolute_

bool numerical::rank_cutoff::absolute_ {false}

private

Whether value_ is a magnitude.

Definition at line 2531 of file decomposition.hpp.

◆ value_

double numerical::rank_cutoff::value_ {-1.0}

private

The ratio or the magnitude; negative for NumPy's default.

Definition at line 2530 of file decomposition.hpp.

The documentation for this class was generated from the following file:

include/numerical/decomposition.hpp

Public Member Functions

Static Public Member Functions

Private Member Functions

Static Private Member Functions

Private Attributes