Linear algebra vocabulary types and dense utilities for finite-element computations. More...

Collaboration diagram for Math:

Modules
	Matrix
	Fixed-size matrix type aliases.

	Vector
	Fixed-size vector type aliases.

Classes
struct	svmp::FE::math::DensePseudoInverseResult
	Result of a rank-revealing pseudo-inverse. More...

struct	svmp::FE::math::DenseMatrixDiagnostics
	SVD-based conditioning and rank diagnostics for a dense matrix. More...

struct	svmp::FE::math::DenseInverseResult
	A dense inverse together with its diagnostics. More...

struct	svmp::FE::math::DenseLUSolver
	LU factorization of a dense square matrix with a cached pivot summary. More...

Functions
double	svmp::FE::math::dense_matrix_max_abs (std::span< const double > matrix) noexcept
	Largest absolute entry of a dense matrix.

double	svmp::FE::math::dense_matrix_pivot_tolerance (std::size_t rows, std::size_t cols, double max_abs, double multiplier=double(64)) noexcept
	Scale-aware pivot tolerance for dense factorization.

double	svmp::FE::math::dense_matrix_singular_value_tolerance (std::size_t rows, std::size_t cols, double largest_singular_value, double multiplier=double(64)) noexcept
	Scale-aware singular-value tolerance for rank decisions.

double	svmp::FE::math::dense_matrix_condition_fallback_threshold () noexcept
	Condition estimate above which the inverse switches to an SVD fallback.

double	svmp::FE::math::dense_matrix_condition_error_threshold () noexcept
	Condition estimate above which validation rejects a dense inverse.

DenseMatrixDiagnostics	svmp::FE::math::dense_matrix_diagnostics (std::span< const double > matrix, std::size_t rows, std::size_t cols, std::string_view error_message_label="dense matrix")
	SVD-based rank and conditioning diagnostics for a dense matrix.

DenseLUSolver	svmp::FE::math::factor_dense_matrix (std::vector< double > matrix, std::size_t n, std::string_view error_message_label="dense matrix")
	LU-factor a dense square matrix.

std::vector< double >	svmp::FE::math::invert_dense_matrix (std::vector< double > matrix, std::size_t n, std::string_view error_message_label="dense matrix")
	Invert a dense square matrix.

DenseInverseResult	svmp::FE::math::invert_dense_matrix_with_diagnostics (std::vector< double > matrix, std::size_t n, std::string_view error_message_label="dense matrix")
	Invert a dense square matrix with diagnostics, using an SVD fallback for high-condition matrices.

void	svmp::FE::math::validate_dense_inverse_diagnostics (const DenseInverseResult &result, std::size_t expected_rank, std::string_view error_message_label="dense matrix", double max_condition=dense_matrix_condition_error_threshold())
	Validate that a dense inverse has full rank and acceptable conditioning.

std::size_t	svmp::FE::math::dense_matrix_rank (std::vector< double > matrix, std::size_t rows, std::size_t cols)
	Numerical rank of a dense matrix from its singular values.

DensePseudoInverseResult	svmp::FE::math::rank_revealing_pseudo_inverse (std::span< const double > matrix, std::size_t rows, std::size_t cols, std::string_view error_message_label="dense matrix")
	Moore-Penrose pseudo-inverse via a rank-revealing SVD.

Detailed Description

Linear algebra vocabulary types and dense utilities for finite-element computations.

The Math module defines the fixed-size vector and matrix types used in element-level kernels (as aliases of Eigen types) and dense linear algebra utilities used by basis construction and local transforms.

Function Documentation

◆ dense_matrix_condition_error_threshold()

double svmp::FE::math::dense_matrix_condition_error_threshold ( )

noexcept

Condition estimate above which validation rejects a dense inverse.

Returns: The error condition-number threshold.

◆ dense_matrix_condition_fallback_threshold()

double svmp::FE::math::dense_matrix_condition_fallback_threshold ( )

noexcept

Condition estimate above which the inverse switches to an SVD fallback.

Returns: The fallback condition-number threshold.

◆ dense_matrix_diagnostics()

DenseMatrixDiagnostics svmp::FE::math::dense_matrix_diagnostics	(	std::span< const double >	matrix,
		std::size_t	rows,
		std::size_t	cols,
		std::string_view	error_message_label = `"dense matrix"`
	)

SVD-based rank and conditioning diagnostics for a dense matrix.

Parameters

matrix	Row-major matrix of size rows * cols.
rows	Row count.
cols	Column count.
error_message_label	Prefix for the message of any exception thrown.

Returns: Rank, tolerance, singular-value, and condition diagnostics.

Exceptions

FEException If the matrix size is inconsistent or the matrix is empty.

◆ dense_matrix_max_abs()

double svmp::FE::math::dense_matrix_max_abs ( std::span< const double > matrix )

noexcept

Largest absolute entry of a dense matrix.

Parameters

matrix Row-major matrix entries.

Returns: Maximum of |entry| over all entries, or 0 for an empty matrix.

◆ dense_matrix_pivot_tolerance()

double svmp::FE::math::dense_matrix_pivot_tolerance	(	std::size_t	rows,
		std::size_t	cols,
		double	max_abs,
		double	multiplier = `double(64)`
	)

noexcept

Scale-aware pivot tolerance for dense factorization.

Proportional to machine epsilon scaled by the matrix size and magnitude; pivots below it are treated as rank-deficient.

Parameters

rows	Row count.
cols	Column count.
max_abs	Largest absolute matrix entry (see dense_matrix_max_abs()).
multiplier	Safety factor applied to the epsilon-scaled tolerance.

Returns: Pivot magnitude threshold.

◆ dense_matrix_rank()

std::size_t svmp::FE::math::dense_matrix_rank	(	std::vector< double >	matrix,
		std::size_t	rows,
		std::size_t	cols
	)

Numerical rank of a dense matrix from its singular values.

Parameters

matrix	Row-major matrix of size rows * cols (consumed).
rows	Row count.
cols	Column count.

Returns: Number of singular values above the scale-aware tolerance.

Exceptions

FEException If the matrix size is inconsistent.

◆ dense_matrix_singular_value_tolerance()

double svmp::FE::math::dense_matrix_singular_value_tolerance	(	std::size_t	rows,
		std::size_t	cols,
		double	largest_singular_value,
		double	multiplier = `double(64)`
	)

noexcept

Scale-aware singular-value tolerance for rank decisions.

Singular values at or below the returned tolerance are treated as zero when computing rank or a pseudo-inverse.

Parameters

rows	Row count.
cols	Column count.
largest_singular_value	Largest singular value of the matrix.
multiplier	Safety factor applied to the epsilon-scaled tolerance.

Returns: Singular-value threshold.

◆ factor_dense_matrix()

DenseLUSolver svmp::FE::math::factor_dense_matrix	(	std::vector< double >	matrix,
		std::size_t	n,
		std::string_view	error_message_label = `"dense matrix"`
	)

LU-factor a dense square matrix.

Parameters

matrix	Row-major n * n matrix (consumed).
n	Matrix dimension.
error_message_label	Prefix for the message of any exception thrown.

Returns: The factorization.

Exceptions

FEException If the size is inconsistent or the matrix is rank-deficient.

◆ invert_dense_matrix()

std::vector< double > svmp::FE::math::invert_dense_matrix	(	std::vector< double >	matrix,
		std::size_t	n,
		std::string_view	error_message_label = `"dense matrix"`
	)

Invert a dense square matrix.

Parameters

matrix	Row-major n * n matrix (consumed).
n	Matrix dimension.
error_message_label	Prefix for the message of any exception thrown.

Returns: Row-major inverse of size n * n.

Exceptions

FEException If the size is inconsistent or the matrix is singular.

◆ invert_dense_matrix_with_diagnostics()

DenseInverseResult svmp::FE::math::invert_dense_matrix_with_diagnostics	(	std::vector< double >	matrix,
		std::size_t	n,
		std::string_view	error_message_label = `"dense matrix"`
	)

Invert a dense square matrix with diagnostics, using an SVD fallback for high-condition matrices.

Parameters

matrix	Row-major n * n matrix (consumed).
n	Matrix dimension.
error_message_label	Prefix for the message of any exception thrown.

Returns: Inverse plus diagnostics and whether the SVD fallback was used.

Exceptions

FEException If the size is inconsistent or the matrix is rank-deficient.

◆ rank_revealing_pseudo_inverse()

DensePseudoInverseResult svmp::FE::math::rank_revealing_pseudo_inverse	(	std::span< const double >	matrix,
		std::size_t	rows,
		std::size_t	cols,
		std::string_view	error_message_label = `"dense matrix"`
	)

Moore-Penrose pseudo-inverse via a rank-revealing SVD.

Parameters

matrix	Row-major matrix of size rows * cols.
rows	Row count.
cols	Column count.
error_message_label	Prefix for the message of any exception thrown.

Returns: Row-major pseudo-inverse (cols * rows) plus rank/tolerance diagnostics.

Exceptions

FEException If the matrix size is inconsistent or the matrix is empty.

◆ validate_dense_inverse_diagnostics()

void svmp::FE::math::validate_dense_inverse_diagnostics	(	const DenseInverseResult &	result,
		std::size_t	expected_rank,
		std::string_view	error_message_label = `"dense matrix"`,
		double	max_condition = `dense_matrix_condition_error_threshold()`
	)

Validate that a dense inverse has full rank and acceptable conditioning.

Parameters

result	Result from invert_dense_matrix_with_diagnostics().
expected_rank	Required (full) rank.
error_message_label	Prefix for the message of any exception thrown.
max_condition	Largest acceptable condition estimate.

Exceptions

FEException If the rank is below expected_rank or the condition exceeds max_condition.

Modules

Classes

Functions

Detailed Description

Function Documentation

◆ dense_matrix_condition_error_threshold()

◆ dense_matrix_condition_fallback_threshold()

◆ dense_matrix_diagnostics()

◆ dense_matrix_max_abs()

◆ dense_matrix_pivot_tolerance()

◆ dense_matrix_rank()

◆ dense_matrix_singular_value_tolerance()

◆ factor_dense_matrix()

◆ invert_dense_matrix()

◆ invert_dense_matrix_with_diagnostics()

◆ rank_revealing_pseudo_inverse()

◆ validate_dense_inverse_diagnostics()