Reusable updates that remove rows or columns from matrices represented by thin singular value decompositions.

Representation and deletion equations

Let a rank- \(q\) matrix be represented by the thin singular value decomposition

\[A = U \Sigma V^T. \]

To remove physical rows with sorted index set \(R\), form \(F=U[R,:]\). The retained matrix obeys

\[A_{\bar R}^T A_{\bar R} = V \Sigma \left(I-F^T F\right) \Sigma V^T. \]

If \(W\) contains the eigenvectors or right singular vectors of the resulting rank- \(q\) core, the updated right singular directions are \(VW\). Column deletion is the transpose dual: use \(F=V[C,:]\) for deleted columns \(C\), and apply the returned rotation to the unchanged left factor as \(UW\).

Complete singular factors reproduce a direct SVD of the physically retained matrix. Truncated factors instead delete rows or columns exactly from the supplied rank- \(q\) approximation; discarded modes cannot be recovered.

Numerical backends

mx::math::svdDeletionBackend::stableCore is the default. It uses a complement-preserving rectangular core and avoids explicitly squaring the conditioning represented by \(\Sigma\).
mx::math::svdDeletionBackend::leadingCovariance diagonalizes \(\Sigma(I-F^TF)\Sigma\) directly. It is useful when only leading modes matter, but forms normal equations and does not promise high relative accuracy for the smallest singular values.

Both current implementations use dense LAPACK operations and have cubic asymptotic cost in \(q\). The API keeps the backend selectable so a future structured secular-equation implementation can preserve the same interface.

Contracts and outputs

Singular values must be finite, nonnegative, and descending. The deleted-side factor must have orthonormal columns; call mx::math::validateSvdDeletionFactor once for a new base factorization, outside repeated deletion loops. Deleted indices must be sorted, unique, and in range, the output rank must be nonzero and no larger than \(q\), and at least one physical row or column must remain.

A successful result contains all \(q\) updated singular values and squared singular values. Only the leading outputRank() columns of rotation() are published. Both mx::math::svdDeletionStatus::success and mx::math::svdDeletionStatus::successWithClamping are usable; test them with mx::math::svdDeletionSucceeded(). The latter records roundoff-scale negative eigenvalues clamped to zero.

Prepare mx::math::svdDeletionResult and mx::math::svdDeletionWorkspace for the largest planned output rank and deletion count before a hot loop. Later compatible operations reuse their allocations. Each concurrent worker must own an independent result and workspace.

Result and workspace objects are move-only handles whose Eigen and LAPACK storage is opaque and destroyed inside mxlib. Spectrum and rotation accessors return unaligned read-only views into result-owned storage; a view remains valid only until its result is prepared, assigned, moved, or destroyed. This ownership boundary permits consumers with different Eigen alignment/SIMD settings from mxlib's build, but it is not a promise of general binary compatibility across arbitrary compilers, C++ standard libraries, or Eigen ABIs.

Example: delete rows

The factors below are assumed to have been produced by an earlier thin SVD.

using realT = double;
using namespace mx::math;
 
bool deleteRows( Eigen::MatrixXd &updatedRight,
                 Eigen::VectorXd &updatedSingularValues,
                 const svdDeletionMatrix<realT> &U,
                 const svdDeletionVector<realT> &singularValues,
                 const svdDeletionMatrix<realT> &V,
                 const std::vector<Eigen::Index> &deletedRows,
                 Eigen::Index outputRank )
{
    const svdDeletionStatus factorStatus = validateSvdDeletionFactor( U );
    if( !svdDeletionSucceeded( factorStatus ) )
    {
        return false;
    }
 
    svdDeletionResult<realT> result;
    svdDeletionWorkspace<realT> workspace;
    const svdDeletionStatus resultStatus = result.prepare( singularValues.size(), outputRank );
    const svdDeletionStatus workspaceStatus =
        workspace.prepare( singularValues.size(),
                           static_cast<Eigen::Index>( deletedRows.size() ),
                           svdDeletionBackend::stableCore );
    if( !svdDeletionSucceeded( resultStatus ) || !svdDeletionSucceeded( workspaceStatus ) )
    {
        return false;
    }
 
    const svdDeletionStatus status = svdRemoveRows( result,
                                                    singularValues,
                                                    U,
                                                    deletedRows,
                                                    outputRank,
                                                    workspace );
    if( !svdDeletionSucceeded( status ) )
    {
        // Inspect status, result.lapackInfo(), and other diagnostics here.
        return false;
    }
 
    updatedRight = V.matrix() * result.rotation().matrix();
    updatedSingularValues = result.singularValues().matrix().head( result.outputRank() );
    return true;
}

For column deletion, pass \(V\) to mx::math::svdRemoveColumns() and apply the returned rotation to \(U\).

See also: SVD Row and Column Deletion Unit Tests

Classes
struct	mx::math::svdDeletionConstVectorViewV2< realT >
	ABI-stable borrowed contiguous-vector storage descriptor. More...
struct	mx::math::svdDeletionConstMatrixViewV2< realT >
	ABI-stable borrowed column-major matrix storage descriptor. More...
struct	mx::math::svdDeletionConstIndexViewV2
	ABI-stable borrowed signed-index storage descriptor. More...
struct	mx::math::svdDeletionAbiV2Tag
	Type-level ABI tag for the second-generation opaque SVD deletion handles. More...
class	mx::math::svdDeletionResult< realT, abiT >
	Result of deleting rows or columns from a represented thin SVD. More...
class	mx::math::svdDeletionWorkspace< realT, abiT >
	Reusable, non-shared storage for SVD deletion operations. More...

Typedefs
template<typename realT>
using	mx::math::svdDeletionMatrix = Eigen::Array<realT, Eigen::Dynamic, Eigen::Dynamic, Eigen::ColMajor>
	Column-major dynamic matrix used by the SVD deletion API.
template<typename realT>
using	mx::math::svdDeletionVector = Eigen::Array<realT, Eigen::Dynamic, 1>
	Dynamic column vector used by the SVD deletion API.
template<typename realT>
using	mx::math::svdDeletionConstMatrixRef = Eigen::Ref<const svdDeletionMatrix<realT>>
	Non-owning read-only reference to a compatible column-major SVD deletion matrix.
template<typename realT>
using	mx::math::svdDeletionConstVectorRef = Eigen::Ref<const svdDeletionVector<realT>>
	Non-owning read-only reference to a compatible SVD deletion vector.

Enumerations
enum class	mx::math::svdDeletionBackend { svdDeletionBackend::leadingCovariance , svdDeletionBackend::stableCore , svdDeletionBackend::rankOneSecular }
	Numerical backend used to delete rows or columns from thin-SVD factors. More...
enum class	mx::math::svdDeletionStatus { svdDeletionStatus::notComputed , svdDeletionStatus::success , svdDeletionStatus::successWithClamping , svdDeletionStatus::invalidInput , svdDeletionStatus::allocationFailure , svdDeletionStatus::workspaceQueryFailure , svdDeletionStatus::solverFailure , svdDeletionStatus::nonFiniteOutput , svdDeletionStatus::invalidSolverOutput , svdDeletionStatus::rescalingOverflow , svdDeletionStatus::nonPositiveSemidefinite , svdDeletionStatus::factorNotOrthonormal , svdDeletionStatus::unsupportedDeletionCount }
	Completion status for an SVD deletion operation. More...

Functions
const char *	mx::math::svdDeletionBackendName (svdDeletionBackend backend)
	Return a stable text representation of an SVD deletion backend.
const char *	mx::math::svdDeletionStatusName (svdDeletionStatus status)
	Return a stable text representation of an SVD deletion status.
bool	mx::math::svdDeletionSucceeded (svdDeletionStatus status) noexcept
	Return true when a status represents usable numerical output.
MXLIB_SVD_DELETION_HEADER_ADAPTER svdDeletionStatus	mx::math::validateSvdDeletionFactor (svdDeletionConstMatrixRef< float > factor, float tolerance=0)
	Validate that a supplied thin singular-vector factor has orthonormal columns.
MXLIB_SVD_DELETION_HEADER_ADAPTER svdDeletionStatus	mx::math::validateSvdDeletionFactor (svdDeletionConstMatrixRef< double > factor, double tolerance=0)
	Validate that a supplied double-precision thin singular-vector factor has orthonormal columns.
template<typename realT>
MXLIB_SVD_DELETION_HEADER_ADAPTER svdDeletionStatus	mx::math::svdDeletionLeadingCore (svdDeletionResult< realT > &result, std::type_identity_t< svdDeletionConstVectorRef< realT > > singularValues, std::type_identity_t< svdDeletionConstMatrixRef< realT > > deletedRows, Eigen::Index outputRank, svdDeletionWorkspace< realT > &workspace)
	Delete supplied singular-factor rows with the full-spectrum symmetric covariance core.
template<typename realT>
MXLIB_SVD_DELETION_HEADER_ADAPTER svdDeletionStatus	mx::math::svdDeletionStableCore (svdDeletionResult< realT > &result, std::type_identity_t< svdDeletionConstVectorRef< realT > > singularValues, std::type_identity_t< svdDeletionConstMatrixRef< realT > > deletedRows, Eigen::Index outputRank, svdDeletionWorkspace< realT > &workspace)
	Delete supplied singular-factor rows with the complement-preserving small-SVD core.
template<typename realT>
MXLIB_SVD_DELETION_HEADER_ADAPTER svdDeletionStatus	mx::math::svdDeletionCore (svdDeletionResult< realT > &result, std::type_identity_t< svdDeletionConstVectorRef< realT > > singularValues, std::type_identity_t< svdDeletionConstMatrixRef< realT > > deletedRows, Eigen::Index outputRank, svdDeletionWorkspace< realT > &workspace, svdDeletionBackend backend=svdDeletionBackend::stableCore)
	Delete supplied singular-factor rows with an explicitly selected backend.
template<typename realT>
MXLIB_SVD_DELETION_HEADER_ADAPTER svdDeletionStatus	mx::math::svdRemoveRows (svdDeletionResult< realT > &result, std::type_identity_t< svdDeletionConstVectorRef< realT > > singularValues, std::type_identity_t< svdDeletionConstMatrixRef< realT > > leftFactor, std::span< const Eigen::Index > deletedIndices, Eigen::Index outputRank, svdDeletionWorkspace< realT > &workspace, svdDeletionBackend backend=svdDeletionBackend::stableCore)
	Delete physical rows from the matrix represented by a thin SVD.
template<typename realT>
MXLIB_SVD_DELETION_HEADER_ADAPTER svdDeletionStatus	mx::math::svdRemoveColumns (svdDeletionResult< realT > &result, std::type_identity_t< svdDeletionConstVectorRef< realT > > singularValues, std::type_identity_t< svdDeletionConstMatrixRef< realT > > rightFactor, std::span< const Eigen::Index > deletedIndices, Eigen::Index outputRank, svdDeletionWorkspace< realT > &workspace, svdDeletionBackend backend=svdDeletionBackend::stableCore)
	Delete physical columns from the matrix represented by a thin SVD.

Typedef Documentation

◆ svdDeletionConstMatrixRef

template<typename realT>

using mx::math::svdDeletionConstMatrixRef = Eigen::Ref<const svdDeletionMatrix<realT>>

Non-owning read-only reference to a compatible column-major SVD deletion matrix.

Definition at line 99 of file svdDowndate.hpp.

◆ svdDeletionConstVectorRef

template<typename realT>

using mx::math::svdDeletionConstVectorRef = Eigen::Ref<const svdDeletionVector<realT>>

Non-owning read-only reference to a compatible SVD deletion vector.

Definition at line 103 of file svdDowndate.hpp.

◆ svdDeletionMatrix

template<typename realT>

using mx::math::svdDeletionMatrix = Eigen::Array<realT, Eigen::Dynamic, Eigen::Dynamic, Eigen::ColMajor>

Column-major dynamic matrix used by the SVD deletion API.

Definition at line 91 of file svdDowndate.hpp.

◆ svdDeletionVector

template<typename realT>

using mx::math::svdDeletionVector = Eigen::Array<realT, Eigen::Dynamic, 1>

Dynamic column vector used by the SVD deletion API.

Definition at line 95 of file svdDowndate.hpp.

Enumeration Type Documentation

◆ svdDeletionBackend

enum class mx::math::svdDeletionBackend

strong

Numerical backend used to delete rows or columns from thin-SVD factors.

Enumerator
leadingCovariance	Symmetric leading-spectrum core; fastest when small singular values are not required.
stableCore	Complement-preserving small SVD; avoids squaring singular-value conditioning.
rankOneSecular	Structured covariance eigensolve for deleting exactly one singular-factor row.

Definition at line 55 of file svdDowndate.hpp.

◆ svdDeletionStatus

enum class mx::math::svdDeletionStatus

strong

Completion status for an SVD deletion operation.

Enumerator
notComputed	No operation has published a result.
success	The operation completed without numerical clamping.
successWithClamping	The operation completed after clamping roundoff-scale negative eigenvalues.
invalidInput	Dimensions, values, indices, or requested output rank are invalid.
allocationFailure	Result or workspace allocation failed.
workspaceQueryFailure	LAPACK returned an invalid or failed workspace query.
solverFailure	LAPACK failed during the numerical solve.
nonFiniteOutput	LAPACK returned a non-finite singular system.
invalidSolverOutput	LAPACK returned a finite spectrum with invalid ordering or sign.
rescalingOverflow	A finite normalized result cannot be represented after restoring input scale.
nonPositiveSemidefinite	A theoretically PSD core has a materially negative eigenvalue.
factorNotOrthonormal	A requested singular-factor validation failed.
unsupportedDeletionCount	The selected backend cannot process the requested number of deleted rows.

Definition at line 63 of file svdDowndate.hpp.

Function Documentation

◆ svdDeletionBackendName()

const char * mx::math::svdDeletionBackendName ( svdDeletionBackend backend )

Return a stable text representation of an SVD deletion backend.

Parameters

[in] backend backend to describe

Definition at line 1615 of file svdDowndate.cpp.

References leadingCovariance, rankOneSecular, and stableCore.

Referenced by unitTest::math_svdDowndate_test::TEST_CASE(), unitTest::math_svdDowndate_test::TEST_CASE(), unitTest::math_svdDowndate_test::TEST_CASE(), unitTest::math_svdDowndate_test::TEST_CASE(), unitTest::math_svdDowndate_test::TEST_CASE(), unitTest::math_svdDowndate_test::TEST_CASE(), and unitTest::math_svdDowndate_test::TEST_CASE().

◆ svdDeletionCore()

template<typename realT>

MXLIB_SVD_DELETION_HEADER_ADAPTER svdDeletionStatus mx::math::svdDeletionCore	(	svdDeletionResult< realT > &	result,
		std::type_identity_t< svdDeletionConstVectorRef< realT > >	singularValues,
		std::type_identity_t< svdDeletionConstMatrixRef< realT > >	deletedRows,
		Eigen::Index	outputRank,
		svdDeletionWorkspace< realT > &	workspace,
		svdDeletionBackend	backend = svdDeletionBackend::stableCore )

Delete supplied singular-factor rows with an explicitly selected backend.

rankOneSecular accepts either no deleted rows, which returns the identity update, or exactly one deleted row. It solves the same covariance core as leadingCovariance by transforming the diagonal-minus-rank-one problem to a positive rank-one secular equation. LAPACK-style deflation handles negligible update components and clustered poles at a roundoff-scaled tolerance; post-solve validation uses dimension-scaled bounds. See [3] and [12].

Parameters

[out]	result	updated spectrum, rotation, and diagnostics
[in]	singularValues	descending base singular values
[in]	deletedRows	deleted-side factor rows
[in]	outputRank	number of leading updated directions to publish
[in,out]	workspace	reusable, worker-private scratch storage
[in]	backend	numerical backend

Definition at line 620 of file svdDowndate.hpp.

References mx::math::svdDeletionResult< realT, abiT >::backend(), mx::math::svdDeletionResult< realT, abiT >::outputRank(), mx::math::svdDeletionResult< realT, abiT >::singularValues(), and stableCore.

Referenced by unitTest::math_svdDowndate_test::TEST_CASE(), unitTest::math_svdDowndate_test::TEST_CASE(), unitTest::math_svdDowndate_test::TEST_CASE(), unitTest::math_svdDowndate_test::TEST_CASE(), unitTest::math_svdDowndate_test::TEST_CASE(), unitTest::math_svdDowndate_test::TEST_CASE(), unitTest::math_svdDowndate_test::TEST_CASE(), and unitTest::math_svdDowndate_test::TEST_CASE().

◆ svdDeletionLeadingCore()

template<typename realT>

MXLIB_SVD_DELETION_HEADER_ADAPTER svdDeletionStatus mx::math::svdDeletionLeadingCore	(	svdDeletionResult< realT > &	result,
		std::type_identity_t< svdDeletionConstVectorRef< realT > >	singularValues,
		std::type_identity_t< svdDeletionConstMatrixRef< realT > >	deletedRows,
		Eigen::Index	outputRank,
		svdDeletionWorkspace< realT > &	workspace )

Delete supplied singular-factor rows with the full-spectrum symmetric covariance core.

Given deleted-side rows F, this solves

\[H = \Sigma (I-F^T F) \Sigma = W \Lambda W^T. \]

The result rotation is W and its singular values are sqrt(diag(Lambda)). The complete spectrum is evaluated for PSD validation even when only outputRank leading directions are published. This backend forms normal equations and therefore does not promise high relative accuracy for the smallest singular values. The rankOneSecular backend evaluates this same core in quadratic time when exactly one row is deleted.

Parameters

[out]	result	updated spectrum, rotation, and diagnostics
[in]	singularValues	descending base singular values
[in]	deletedRows	deleted-side factor rows
[in]	outputRank	number of leading updated directions to publish
[in,out]	workspace	reusable, worker-private scratch storage

Definition at line 560 of file svdDowndate.hpp.

References mx::math::svdDeletionResult< realT, abiT >::outputRank(), and mx::math::svdDeletionResult< realT, abiT >::singularValues().

Referenced by unitTest::math_svdDowndate_test::TEST_CASE(), unitTest::math_svdDowndate_test::TEST_CASE(), unitTest::math_svdDowndate_test::TEST_CASE(), and unitTest::math_svdDowndate_test::TEST_CASE().

◆ svdDeletionStableCore()

template<typename realT>

MXLIB_SVD_DELETION_HEADER_ADAPTER svdDeletionStatus mx::math::svdDeletionStableCore	(	svdDeletionResult< realT > &	result,
		std::type_identity_t< svdDeletionConstVectorRef< realT > >	singularValues,
		std::type_identity_t< svdDeletionConstMatrixRef< realT > >	deletedRows,
		Eigen::Index	outputRank,
		svdDeletionWorkspace< realT > &	workspace )

Delete supplied singular-factor rows with the complement-preserving small-SVD core.

Let F contain deleted-side singular-factor rows and choose B so that B^T B = I - F F^T. The at-most (q+c) x q core

\[K = \begin{bmatrix}(I-F^TF)\Sigma \\ BF\Sigma\end{bmatrix} \]

obeys K^T K = Sigma (I-F^T F) Sigma. Its right singular vectors are the preserved-side rotation. This is the default generic backend because it avoids explicitly squaring the represented singular values. See [2] and [18].

This backend and leadingCovariance use dense LAPACK solvers and therefore have cubic asymptotic cost in the base rank. The rankOneSecular backend instead uses a structured quadratic-time solve for one-row deletion.

Parameters

[out]	result	updated spectrum, rotation, and diagnostics
[in]	singularValues	descending base singular values
[in]	deletedRows	deleted-side factor rows
[in]	outputRank	number of leading updated directions to publish
[in,out]	workspace	reusable, worker-private scratch storage

Definition at line 594 of file svdDowndate.hpp.

References mx::math::svdDeletionResult< realT, abiT >::outputRank(), and mx::math::svdDeletionResult< realT, abiT >::singularValues().

Referenced by unitTest::math_svdDowndate_test::TEST_CASE(), unitTest::math_svdDowndate_test::TEST_CASE(), and unitTest::math_svdDowndate_test::TEST_CASE().

◆ svdDeletionStatusName()

const char * mx::math::svdDeletionStatusName ( svdDeletionStatus status )

Return a stable text representation of an SVD deletion status.

Parameters

[in] status status to describe

Definition at line 1629 of file svdDowndate.cpp.

References allocationFailure, factorNotOrthonormal, invalidInput, invalidSolverOutput, nonFiniteOutput, nonPositiveSemidefinite, notComputed, rescalingOverflow, solverFailure, success, successWithClamping, unsupportedDeletionCount, and workspaceQueryFailure.

Referenced by unitTest::math_svdDowndate_test::TEST_CASE(), and unitTest::math_svdDowndate_test::TEST_CASE().

◆ svdDeletionSucceeded()

bool mx::math::svdDeletionSucceeded ( svdDeletionStatus status )

noexcept

Return true when a status represents usable numerical output.

Parameters

[in] status status to classify

Definition at line 1663 of file svdDowndate.cpp.

References success, and successWithClamping.

◆ svdRemoveColumns()

template<typename realT>

MXLIB_SVD_DELETION_HEADER_ADAPTER svdDeletionStatus mx::math::svdRemoveColumns	(	svdDeletionResult< realT > &	result,
		std::type_identity_t< svdDeletionConstVectorRef< realT > >	singularValues,
		std::type_identity_t< svdDeletionConstMatrixRef< realT > >	rightFactor,
		std::span< const Eigen::Index >	deletedIndices,
		Eigen::Index	outputRank,
		svdDeletionWorkspace< realT > &	workspace,
		svdDeletionBackend	backend = svdDeletionBackend::stableCore )

Delete physical columns from the matrix represented by a thin SVD.

For A=U Sigma V^T, this gathers V[deletedIndices,:]. The returned rotation applies to U. Supplying complete factors makes the deletion identical to a direct SVD of the physically retained matrix. Supplying truncated factors deletes columns exactly from that represented low-rank matrix.

Parameters

[out]	result	updated spectrum, rotation, and diagnostics
[in]	singularValues	descending base singular values
[in]	rightFactor	thin right factor V
[in]	deletedIndices	sorted, unique column indices to delete
[in]	outputRank	number of leading updated directions
[in,out]	workspace	reusable, worker-private scratch
[in]	backend	numerical backend

Definition at line 676 of file svdDowndate.hpp.

References mx::math::svdDeletionResult< realT, abiT >::backend(), mx::math::svdDeletionResult< realT, abiT >::outputRank(), mx::math::svdDeletionResult< realT, abiT >::singularValues(), and stableCore.

Referenced by unitTest::math_svdDowndate_test::TEST_CASE(), unitTest::math_svdDowndate_test::TEST_CASE(), unitTest::math_svdDowndate_test::TEST_CASE(), unitTest::math_svdDowndate_test::TEST_CASE(), and unitTest::math_svdDowndate_test::TEST_CASE().

◆ svdRemoveRows()

template<typename realT>

MXLIB_SVD_DELETION_HEADER_ADAPTER svdDeletionStatus mx::math::svdRemoveRows	(	svdDeletionResult< realT > &	result,
		std::type_identity_t< svdDeletionConstVectorRef< realT > >	singularValues,
		std::type_identity_t< svdDeletionConstMatrixRef< realT > >	leftFactor,
		std::span< const Eigen::Index >	deletedIndices,
		Eigen::Index	outputRank,
		svdDeletionWorkspace< realT > &	workspace,
		svdDeletionBackend	backend = svdDeletionBackend::stableCore )

Delete physical rows from the matrix represented by a thin SVD.

For A=U Sigma V^T, this gathers U[deletedIndices,:]. The returned rotation applies to V. Supplying complete factors makes the deletion identical to a direct SVD of the physically retained matrix. Supplying truncated factors deletes rows exactly from that represented low-rank matrix.

Parameters

[out]	result	updated spectrum, rotation, and diagnostics
[in]	singularValues	descending base singular values
[in]	leftFactor	thin left factor U
[in]	deletedIndices	sorted, unique row indices to delete
[in]	outputRank	number of leading updated directions
[in,out]	workspace	reusable, worker-private scratch
[in]	backend	numerical backend

Definition at line 646 of file svdDowndate.hpp.

References mx::math::svdDeletionResult< realT, abiT >::backend(), mx::math::svdDeletionResult< realT, abiT >::outputRank(), mx::math::svdDeletionResult< realT, abiT >::singularValues(), and stableCore.

◆ validateSvdDeletionFactor() [1/2]

MXLIB_SVD_DELETION_HEADER_ADAPTER svdDeletionStatus mx::math::validateSvdDeletionFactor	(	svdDeletionConstMatrixRef< double >	factor,
		double	tolerance = 0 )

Validate that a supplied double-precision thin singular-vector factor has orthonormal columns.

Parameters

[in]	factor	thin singular-vector factor to validate
[in]	tolerance	maximum absolute Gram-matrix error, or zero for automatic

Definition at line 536 of file svdDowndate.hpp.

◆ validateSvdDeletionFactor() [2/2]

MXLIB_SVD_DELETION_HEADER_ADAPTER svdDeletionStatus mx::math::validateSvdDeletionFactor	(	svdDeletionConstMatrixRef< float >	factor,
		float	tolerance = 0 )

Validate that a supplied thin singular-vector factor has orthonormal columns.

This is an optional one-time base-factor check. Hot deletion calls assume the factor contract and do not repeat this O(n q^2) operation. A zero tolerance selects a dimension-scaled default.

Parameters

[in]	factor	thin singular-vector factor to validate
[in]	tolerance	maximum absolute Gram-matrix error, or zero for automatic

Definition at line 525 of file svdDowndate.hpp.

References validateSvdDeletionFactor().

Referenced by unitTest::math_svdDowndate_test::TEST_CASE(), unitTest::math_svdDowndate_test::TEST_CASE(), unitTest::math_svdDowndate_test::TEST_CASE(), unitTest::math_svdDowndate_test::TEST_CASE(), unitTest::math_svdDowndate_test::TEST_CASE(), unitTest::math_svdDowndate_test::TEST_CASE(), unitTest::math_svdDowndate_test::TEST_CASE(), and validateSvdDeletionFactor().

Representation and deletion equations

Numerical backends

Contracts and outputs

Example: delete rows

Classes

Typedefs

Enumerations

Functions

Typedef Documentation

◆ svdDeletionConstMatrixRef

◆ svdDeletionConstVectorRef

◆ svdDeletionMatrix

◆ svdDeletionVector

Enumeration Type Documentation

◆ svdDeletionBackend

◆ svdDeletionStatus

Function Documentation

◆ svdDeletionBackendName()

◆ svdDeletionCore()

◆ svdDeletionLeadingCore()

◆ svdDeletionStableCore()

◆ svdDeletionStatusName()

◆ svdDeletionSucceeded()

◆ svdRemoveColumns()

◆ svdRemoveRows()

◆ validateSvdDeletionFactor() [1/2]

◆ validateSvdDeletionFactor() [2/2]