dense_subspace_unused.hpp File Reference

#include <uni20/krylov/dense_subspace.hpp>

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Classes
struct	uni20::krylov::ComplexHermitianEigensystem< Real >
	Eigenvalues and optional eigenvectors of a dense complex Hermitian matrix. More...
struct	uni20::krylov::RealBidiagonalReduction< Scalar >
	Compact Householder bidiagonal reduction of a dense real matrix. More...
struct	uni20::krylov::RealBidiagonalSvd< Scalar >
	Singular value decomposition of a real bidiagonal matrix. More...
struct	uni20::krylov::RealCompactLqFactorization< Scalar >
	Compact Householder LQ factorization of a dense real matrix. More...
struct	uni20::krylov::RealCompactQlFactorization< Scalar >
	Compact Householder QL factorization of a dense real matrix. More...
struct	uni20::krylov::RealCompactQrFactorization< Scalar >
	Compact Householder QR factorization of a dense real matrix. More...
struct	uni20::krylov::RealCompactRqFactorization< Scalar >
	Compact Householder RQ factorization of a dense real matrix. More...
struct	uni20::krylov::RealEquilibration< Scalar >
	Dense real general matrix equilibration factors. More...
struct	uni20::krylov::RealExpertLinearSolve< Scalar >
	Expert dense real linear solve result. More...
struct	uni20::krylov::RealGeneralBandExpertLinearSolve< Scalar >
	Expert real general-band linear solve result. More...
struct	uni20::krylov::RealGeneralBandFactorization< Scalar >
	LU factorization of a real square general band matrix. More...
struct	uni20::krylov::RealGeneralBandMatrix< Scalar >
	LAPACK general band storage for a real square matrix. More...
struct	uni20::krylov::RealGeneralizedHessenbergReduction< Real >
	Generalized Hessenberg reduction of a dense real matrix pencil. More...
struct	uni20::krylov::RealGeneralizedNonsymmetricBalance< Real >
	Balanced dense real nonsymmetric matrix pencil and LAPACK scaling metadata. More...
struct	uni20::krylov::RealGeneralizedNonsymmetricEigensystem< Real >
	Eigenvalues and optional right eigenvectors of a real nonsymmetric matrix pencil. More...
struct	uni20::krylov::RealGeneralizedNonsymmetricExpertEigensystem< Real >
	Expert eigensystem diagnostics for a dense real nonsymmetric matrix pencil. More...
struct	uni20::krylov::RealGeneralizedSchurConditionEstimates< Real >
	Reciprocal condition estimates for eigenpairs of a generalized real Schur form. More...
struct	uni20::krylov::RealGeneralizedSchurDecomposition< Real >
	One diagonal block of a real Schur form. More...
struct	uni20::krylov::RealGeneralizedSchurRightEigenvectors< Real >
	Right eigenvectors of a generalized real Schur form unpacked into complex columns. More...
struct	uni20::krylov::RealGeneralizedSchurSelectedSubspace< Real >
	Selected generalized real Schur subspace with LAPACK tgsen diagnostics. More...
struct	uni20::krylov::RealGeneralTridiagonalExpertLinearSolve< Scalar >
	Expert real general-tridiagonal linear solve result. More...
struct	uni20::krylov::RealGeneralTridiagonalFactorization< Scalar >
	LU factorization of a real square general tridiagonal matrix. More...
struct	uni20::krylov::RealGeneralTridiagonalMatrix< Scalar >
	LAPACK general tridiagonal storage for a real square matrix. More...
struct	uni20::krylov::RealHessenbergReduction< Scalar >
	Compact real Hessenberg reduction of a dense square matrix. More...
struct	uni20::krylov::RealLqFactorization< Scalar >
	Reduced LQ factorization of a dense real matrix. More...
struct	uni20::krylov::RealLuFactorization< Scalar >
	LU factorization of a dense real square matrix. More...
struct	uni20::krylov::RealNonsymmetricBalance< Real >
	Balanced dense real nonsymmetric matrix and LAPACK scaling metadata. More...
struct	uni20::krylov::RealNonsymmetricExpertEigensystem< Real >
	Eigenvalues and optional right eigenvectors of a real nonsymmetric matrix. More...
struct	uni20::krylov::RealPivotedCholeskyFactorization< Scalar >
	Pivoted Cholesky factorization of a dense real positive semidefinite matrix. More...
struct	uni20::krylov::RealPivotedQrFactorization< Scalar >
	Reduced QR factorization with column pivoting of a dense real matrix. More...
struct	uni20::krylov::RealQlFactorization< Scalar >
	Reduced QL factorization of a dense real matrix. More...
struct	uni20::krylov::RealQrFactorization< Scalar >
	Reduced QR factorization of a dense real matrix. More...
struct	uni20::krylov::RealRankRevealingLeastSquares< Scalar >
	Rank-revealing dense real least-squares result. More...
struct	uni20::krylov::RealRefinedLinearSolve< Scalar >
	Dense real refined linear solve result. More...
struct	uni20::krylov::RealRqFactorization< Scalar >
	Reduced RQ factorization of a dense real matrix. More...
struct	uni20::krylov::RealSchurConditionEstimates< Scalar >
	Reciprocal condition estimates for eigenpairs of a real Schur form. More...
struct	uni20::krylov::RealSchurRightEigenvectors< Scalar >
	Right eigenvectors of a real Schur form unpacked into complex columns. More...
struct	uni20::krylov::RealSchurSelectedSubspace< Scalar >
	Eigenvalues and optional right eigenvectors of a complex nonsymmetric matrix. More...
struct	uni20::krylov::RealSingularValueDecomposition< Scalar >
	Singular values and optional singular vectors of a dense real matrix. More...
struct	uni20::krylov::RealSvdLeastSquares< Scalar >
	SVD-based dense real least-squares result. More...
struct	uni20::krylov::RealSylvesterSolution< Scalar >
	Dense real Sylvester equation result. More...
struct	uni20::krylov::RealSymmetricEigensystem< Scalar >
struct	uni20::krylov::RealSymmetricIndefiniteExpertLinearSolve< Scalar >
	Expert dense real symmetric-indefinite linear solve result. More...
struct	uni20::krylov::RealSymmetricIndefiniteFactorization< Scalar >
	Bunch-Kaufman factorization of a dense real symmetric-indefinite matrix. More...
struct	uni20::krylov::RealSymmetricPositiveDefiniteBandExpertLinearSolve< Scalar >
	Expert real SPD band linear solve result. More...
struct	uni20::krylov::RealSymmetricPositiveDefiniteBandFactorization< Scalar >
	Cholesky factorization of a real SPD band matrix. More...
struct	uni20::krylov::RealSymmetricPositiveDefiniteBandMatrix< Scalar >
	LAPACK symmetric positive-definite band storage for a real square matrix. More...
struct	uni20::krylov::RealSymmetricPositiveDefiniteEquilibration< Scalar >
	Dense real SPD equilibration factors. More...
struct	uni20::krylov::RealSymmetricPositiveDefiniteExpertLinearSolve< Scalar >
	Expert dense real SPD linear solve result. More...
struct	uni20::krylov::RealSymmetricPositiveDefiniteFactorization< Scalar >
	Cholesky factorization of a dense real SPD matrix. More...
struct	uni20::krylov::RealSymmetricPositiveDefiniteTridiagonalExpertLinearSolve< Scalar >
	Expert real SPD tridiagonal linear solve result. More...
struct	uni20::krylov::RealSymmetricPositiveDefiniteTridiagonalFactorization< Scalar >
	Cholesky factorization of a real SPD tridiagonal matrix. More...
struct	uni20::krylov::RealSymmetricPositiveDefiniteTridiagonalMatrix< Scalar >
	Real symmetric positive-definite tridiagonal matrix storage. More...
struct	uni20::krylov::RealSymmetricTridiagonalReduction< Scalar >
	Compact real symmetric tridiagonal reduction of a dense symmetric matrix. More...

Namespaces
namespace	uni20
namespace	uni20::krylov

Enumerations
enum class	uni20::krylov::RealNonsymmetricBalanceJob { uni20::krylov::None , uni20::krylov::Permute , uni20::krylov::Scale , uni20::krylov::Both }
	LAPACK balancing operations for a dense real nonsymmetric matrix. More...

Functions
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::apply_real_bidiagonal_left_factor (RealBidiagonalReduction< Scalar > const &reduction, detail::ColumnMajorLapackMatrix< Scalar > target, MatrixSide side=MatrixSide::Left, MatrixTranspose transpose=MatrixTranspose::None)
	Apply the left orthogonal factor Q from a real bidiagonal reduction.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::apply_real_bidiagonal_right_factor (RealBidiagonalReduction< Scalar > const &reduction, detail::ColumnMajorLapackMatrix< Scalar > target, MatrixSide side=MatrixSide::Right, MatrixTranspose transpose=MatrixTranspose::None)
	Apply the right orthogonal factor P from a real bidiagonal reduction.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::apply_real_hessenberg_orthogonal_factor (RealHessenbergReduction< Scalar > const &reduction, detail::ColumnMajorLapackMatrix< Scalar > target, MatrixSide side=MatrixSide::Left, MatrixTranspose transpose=MatrixTranspose::None)
	Apply the orthogonal factor from a compact real Hessenberg reduction.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::apply_real_lq_factor (RealCompactLqFactorization< Scalar > const &factorization, detail::ColumnMajorLapackMatrix< Scalar > target, MatrixSide side=MatrixSide::Right, MatrixTranspose transpose=MatrixTranspose::None)
	Apply the orthogonal factor from a compact real LQ factorization.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::apply_real_ql_factor (RealCompactQlFactorization< Scalar > const &factorization, detail::ColumnMajorLapackMatrix< Scalar > target, MatrixSide side=MatrixSide::Left, MatrixTranspose transpose=MatrixTranspose::None)
	Apply the orthogonal factor from a compact real QL factorization.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::apply_real_qr_factor (RealCompactQrFactorization< Scalar > const &factorization, detail::ColumnMajorLapackMatrix< Scalar > target, MatrixSide side=MatrixSide::Left, MatrixTranspose transpose=MatrixTranspose::None)
	Apply the orthogonal factor from a compact real QR factorization.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::apply_real_rq_factor (RealCompactRqFactorization< Scalar > const &factorization, detail::ColumnMajorLapackMatrix< Scalar > target, MatrixSide side=MatrixSide::Right, MatrixTranspose transpose=MatrixTranspose::None)
	Apply the orthogonal factor from a compact real RQ factorization.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::apply_real_symmetric_tridiagonal_orthogonal_factor (RealSymmetricTridiagonalReduction< Scalar > const &reduction, detail::ColumnMajorLapackMatrix< Scalar > target, MatrixSide side=MatrixSide::Left, MatrixTranspose transpose=MatrixTranspose::None)
	Apply the orthogonal factor from a compact real symmetric tridiagonal reduction.
template<uni20::LapackComplexReal Real>
ComplexHermitianEigensystem< Real >	uni20::krylov::complex_generalized_hermitian_eigensystem (detail::ColumnMajorLapackMatrix< uni20::detail::standard_complex< Real > > matrix, detail::ColumnMajorLapackMatrix< uni20::detail::standard_complex< Real > > metric, bool compute_vectors, MatrixFill triangle=MatrixFill::Upper)
	Solve a dense type-1 generalized complex Hermitian eigensystem through LAPACK hegv.
template<uni20::LapackComplexReal Real>
ComplexHermitianEigensystem< Real >	uni20::krylov::complex_generalized_hermitian_eigensystem_divide_and_conquer (detail::ColumnMajorLapackMatrix< uni20::detail::standard_complex< Real > > matrix, detail::ColumnMajorLapackMatrix< uni20::detail::standard_complex< Real > > metric, bool compute_vectors, MatrixFill triangle=MatrixFill::Upper)
	Solve a dense type-1 generalized complex Hermitian eigensystem through LAPACK hegvd.
template<uni20::LapackComplexReal Real>
ComplexHermitianEigensystem< Real >	uni20::krylov::complex_generalized_hermitian_eigensystem_index_range (detail::ColumnMajorLapackMatrix< uni20::detail::standard_complex< Real > > matrix, detail::ColumnMajorLapackMatrix< uni20::detail::standard_complex< Real > > metric, std::size_t first_index, std::size_t last_index, bool compute_vectors, MatrixFill triangle=MatrixFill::Upper)
	Solve a selected dense type-1 generalized complex Hermitian eigensystem through LAPACK hegvx.
template<uni20::LapackComplexReal Real>
ComplexHermitianEigensystem< Real >	uni20::krylov::complex_hermitian_eigensystem (detail::ColumnMajorLapackMatrix< uni20::detail::standard_complex< Real > > matrix, bool compute_vectors, MatrixFill triangle=MatrixFill::Upper)
	Solve a dense complex Hermitian eigensystem through LAPACK heev.
template<uni20::LapackComplexReal Real>
ComplexHermitianEigensystem< Real >	uni20::krylov::complex_hermitian_eigensystem_divide_and_conquer (detail::ColumnMajorLapackMatrix< uni20::detail::standard_complex< Real > > matrix, bool compute_vectors, MatrixFill triangle=MatrixFill::Upper)
	Solve a dense complex Hermitian eigensystem through LAPACK heevd.
template<uni20::LapackComplexReal Real>
ComplexHermitianEigensystem< Real >	uni20::krylov::complex_hermitian_eigensystem_index_range (detail::ColumnMajorLapackMatrix< uni20::detail::standard_complex< Real > > matrix, std::size_t first_index, std::size_t last_index, bool compute_vectors, MatrixFill triangle=MatrixFill::Upper)
	Solve a selected dense complex Hermitian eigensystem through LAPACK heevr.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::real_bidiagonal_left_orthogonal_factor (RealBidiagonalReduction< Scalar > const &reduction)
	Materialize the left orthogonal factor Q from a real bidiagonal reduction.
template<uni20::LapackReal Scalar>
RealBidiagonalReduction< Scalar >	uni20::krylov::real_bidiagonal_reduction (detail::ColumnMajorLapackMatrix< Scalar > matrix)
	Reduce a dense real matrix to bidiagonal form through LAPACK gebrd.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::real_bidiagonal_right_orthogonal_factor_transpose (RealBidiagonalReduction< Scalar > const &reduction)
	Materialize the right transposed factor P^T from a real bidiagonal reduction.
template<uni20::LapackReal Scalar>
std::vector< Scalar >	uni20::krylov::real_bidiagonal_singular_values (RealBidiagonalReduction< Scalar > const &reduction)
	Compute singular values from a compact real bidiagonal reduction.
template<uni20::LapackReal Scalar>
std::vector< Scalar >	uni20::krylov::real_bidiagonal_singular_values (std::vector< Scalar > diagonal, std::vector< Scalar > offdiagonal, bool upper=true)
	Compute singular values of a real bidiagonal matrix through LAPACK bdsqr.
template<uni20::LapackReal Scalar>
RealBidiagonalSvd< Scalar >	uni20::krylov::real_bidiagonal_svd (RealBidiagonalReduction< Scalar > const &reduction, bool compute_vectors)
	Compute the SVD from a compact real bidiagonal reduction.
template<uni20::LapackReal Scalar>
RealBidiagonalSvd< Scalar >	uni20::krylov::real_bidiagonal_svd (std::vector< Scalar > diagonal, std::vector< Scalar > offdiagonal, bool compute_vectors, bool upper=true)
	Compute the SVD of a real bidiagonal matrix through LAPACK bdsdc.
template<uni20::LapackReal Scalar>
RealBidiagonalSvd< Scalar >	uni20::krylov::real_bidiagonal_svd_index_range (RealBidiagonalReduction< Scalar > const &reduction, std::size_t first_index, std::size_t last_index, bool compute_vectors)
	Compute a selected-index SVD from a compact real bidiagonal reduction.
template<uni20::LapackReal Scalar>
RealBidiagonalSvd< Scalar >	uni20::krylov::real_bidiagonal_svd_index_range (std::vector< Scalar > diagonal, std::vector< Scalar > offdiagonal, std::size_t first_index, std::size_t last_index, bool compute_vectors, bool upper=true)
	Compute a selected-index SVD of a real bidiagonal matrix through LAPACK bdsvdx.
template<uni20::LapackReal Scalar>
RealCompactLqFactorization< Scalar >	uni20::krylov::real_compact_lq_factorization (detail::ColumnMajorLapackMatrix< Scalar > matrix)
	Compute a compact dense real LQ factorization through LAPACK gelqf.
template<uni20::LapackReal Scalar>
RealCompactQlFactorization< Scalar >	uni20::krylov::real_compact_ql_factorization (detail::ColumnMajorLapackMatrix< Scalar > matrix)
	Compute a compact dense real QL factorization through LAPACK geqlf.
template<uni20::LapackReal Scalar>
RealCompactQrFactorization< Scalar >	uni20::krylov::real_compact_qr_factorization (detail::ColumnMajorLapackMatrix< Scalar > matrix)
	Compute a compact dense real QR factorization through LAPACK geqrf.
template<uni20::LapackReal Scalar>
RealCompactRqFactorization< Scalar >	uni20::krylov::real_compact_rq_factorization (detail::ColumnMajorLapackMatrix< Scalar > matrix)
	Compute a compact dense real RQ factorization through LAPACK gerqf.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::real_dense_inverse (detail::ColumnMajorLapackMatrix< Scalar > matrix)
	Invert a dense real square matrix through LAPACK getrf and getri.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::real_dense_solve_linear_system (detail::ColumnMajorLapackMatrix< Scalar > coefficients, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides)
	Solve a dense real linear system through LAPACK gesv.
template<uni20::LapackReal Scalar>
RealSvdLeastSquares< Scalar >	uni20::krylov::real_divide_and_conquer_svd_least_squares (detail::ColumnMajorLapackMatrix< Scalar > coefficients, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides, Scalar rcond=Scalar{100} *uni20::numeric_limits< Scalar >::epsilon())
	Solve a dense real divide-and-conquer SVD least-squares problem through LAPACK gelsd.
template<uni20::LapackReal Scalar>
RealEquilibration< Scalar >	uni20::krylov::real_equilibration (detail::ColumnMajorLapackMatrix< Scalar > matrix)
	Compute dense real row/column equilibration factors through LAPACK geequ.
template<uni20::LapackReal Scalar>
RealExpertLinearSolve< Scalar >	uni20::krylov::real_expert_linear_solve (detail::ColumnMajorLapackMatrix< Scalar > coefficients, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides)
	Solve a dense real linear system with LAPACK gesvx diagnostics.
template<uni20::LapackReal Scalar>
RealEquilibration< Scalar >	uni20::krylov::real_general_band_equilibration (RealGeneralBandMatrix< Scalar > band_matrix)
	Compute real general-band row/column equilibration factors through LAPACK gbequ.
template<uni20::LapackReal Scalar>
RealGeneralBandExpertLinearSolve< Scalar >	uni20::krylov::real_general_band_expert_linear_solve (RealGeneralBandMatrix< Scalar > coefficients, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides, MatrixTranspose transpose=MatrixTranspose::None)
	Solve a real general-band linear system with LAPACK gbsvx diagnostics.
template<uni20::LapackReal Scalar>
RealGeneralBandFactorization< Scalar >	uni20::krylov::real_general_band_factorization (RealGeneralBandMatrix< Scalar > matrix)
	Compute a real general-band LU factorization through LAPACK gbtrf.
template<uni20::LapackReal Scalar>
RealGeneralBandMatrix< Scalar >	uni20::krylov::real_general_band_from_dense (detail::ColumnMajorLapackMatrix< Scalar > const &matrix, std::size_t lower_bandwidth, std::size_t upper_bandwidth)
	Pack a dense real square matrix into LAPACK general-band factor storage.
template<uni20::LapackReal Scalar>
Scalar	uni20::krylov::real_general_band_matrix_norm (RealGeneralBandMatrix< Scalar > band_matrix, MatrixNorm norm)
	Compute a real general-band matrix norm through LAPACK langb.
template<uni20::LapackReal Scalar>
Scalar	uni20::krylov::real_general_band_one_norm_reciprocal_condition_number (RealGeneralBandFactorization< Scalar > const &factorization, Scalar original_one_norm)
	Estimate a real general-band one-norm reciprocal condition number through LAPACK gbcon.
template<uni20::LapackReal Scalar>
Scalar	uni20::krylov::real_general_band_one_norm_reciprocal_condition_number (RealGeneralBandMatrix< Scalar > matrix)
	Estimate a real general-band one-norm reciprocal condition number.
template<uni20::LapackReal Scalar>
RealEquilibration< Scalar >	uni20::krylov::real_general_band_power_of_two_equilibration (RealGeneralBandMatrix< Scalar > band_matrix)
	Compute power-of-two real general-band equilibration factors through LAPACK gbequb.
template<uni20::LapackReal Scalar>
RealRefinedLinearSolve< Scalar >	uni20::krylov::real_general_band_refined_solve (RealGeneralBandMatrix< Scalar > coefficients, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides, MatrixTranspose transpose=MatrixTranspose::None)
	Solve and refine a real general-band system through LAPACK gbrfs.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::real_general_band_solve (RealGeneralBandFactorization< Scalar > const &factorization, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides, MatrixTranspose transpose=MatrixTranspose::None)
	Solve using an existing real general-band LU factorization through LAPACK gbtrs.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::real_general_band_solve (RealGeneralBandMatrix< Scalar > coefficients, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides)
	Solve a real general-band linear system through LAPACK gbsv.
template<uni20::LapackReal Scalar>
RealGeneralTridiagonalExpertLinearSolve< Scalar >	uni20::krylov::real_general_tridiagonal_expert_linear_solve (RealGeneralTridiagonalMatrix< Scalar > coefficients, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides, MatrixTranspose transpose=MatrixTranspose::None)
	Solve a real general-tridiagonal linear system with LAPACK gtsvx diagnostics.
template<uni20::LapackReal Scalar>
RealGeneralTridiagonalFactorization< Scalar >	uni20::krylov::real_general_tridiagonal_factorization (RealGeneralTridiagonalMatrix< Scalar > matrix)
	Compute a real general tridiagonal LU factorization through LAPACK gttrf.
template<uni20::LapackReal Scalar>
RealGeneralTridiagonalMatrix< Scalar >	uni20::krylov::real_general_tridiagonal_from_dense (detail::ColumnMajorLapackMatrix< Scalar > const &matrix)
	Extract real general tridiagonal storage from a dense matrix.
template<uni20::LapackReal Scalar>
Scalar	uni20::krylov::real_general_tridiagonal_one_norm (RealGeneralTridiagonalMatrix< Scalar > const &matrix)
	Compute the one-norm of a real general tridiagonal matrix.
template<uni20::LapackReal Scalar>
Scalar	uni20::krylov::real_general_tridiagonal_one_norm_reciprocal_condition_number (RealGeneralTridiagonalFactorization< Scalar > const &factorization, Scalar original_one_norm)
	Estimate a real general-tridiagonal one-norm reciprocal condition number through LAPACK gtcon.
template<uni20::LapackReal Scalar>
Scalar	uni20::krylov::real_general_tridiagonal_one_norm_reciprocal_condition_number (RealGeneralTridiagonalMatrix< Scalar > matrix)
	Estimate a real general-tridiagonal one-norm reciprocal condition number from a matrix.
template<uni20::LapackReal Scalar>
RealRefinedLinearSolve< Scalar >	uni20::krylov::real_general_tridiagonal_refined_solve (RealGeneralTridiagonalMatrix< Scalar > coefficients, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides, MatrixTranspose transpose=MatrixTranspose::None)
	Solve and refine a real general-tridiagonal linear system through LAPACK gtrfs.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::real_general_tridiagonal_solve (RealGeneralTridiagonalFactorization< Scalar > const &factorization, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides, MatrixTranspose transpose=MatrixTranspose::None)
	Solve using an existing real general tridiagonal LU factorization through LAPACK gttrs.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::real_general_tridiagonal_solve (RealGeneralTridiagonalMatrix< Scalar > coefficients, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides)
	Solve a real general tridiagonal linear system through LAPACK gtsv.
template<uni20::LapackReal Real>
RealGeneralizedHessenbergReduction< Real >	uni20::krylov::real_generalized_hessenberg_reduction (detail::ColumnMajorLapackMatrix< Real > matrix, detail::ColumnMajorLapackMatrix< Real > upper_triangular_metric, bool compute_vectors)
	Reduce a real matrix pencil to generalized upper Hessenberg form through LAPACK gghrd.
template<uni20::LapackReal Real>
RealGeneralizedSchurDecomposition< Real >	uni20::krylov::real_generalized_hessenberg_schur (detail::ColumnMajorLapackMatrix< Real > hessenberg, detail::ColumnMajorLapackMatrix< Real > upper_triangular_metric, bool compute_vectors)
	Compute generalized real Schur form from a generalized Hessenberg pencil through LAPACK hgeqz.
template<uni20::LapackReal Real>
RealGeneralizedNonsymmetricBalance< Real >	uni20::krylov::real_generalized_nonsymmetric_balance (detail::ColumnMajorLapackMatrix< Real > matrix, detail::ColumnMajorLapackMatrix< Real > metric, RealNonsymmetricBalanceJob job=RealNonsymmetricBalanceJob::Both)
	Balance a dense real nonsymmetric matrix pencil through LAPACK ggbal.
template<uni20::LapackReal Real>
detail::ColumnMajorLapackMatrix< Real >	uni20::krylov::real_generalized_nonsymmetric_balance_backtransform_right_vectors (detail::ColumnMajorLapackMatrix< Real > vectors, RealGeneralizedNonsymmetricBalance< Real > const &balance, RealNonsymmetricBalanceJob job=RealNonsymmetricBalanceJob::Both)
	Backtransform real right eigenvectors after generalized pencil balancing.
template<uni20::LapackReal Real>
RealGeneralizedNonsymmetricEigensystem< Real >	uni20::krylov::real_generalized_nonsymmetric_eigensystem (detail::ColumnMajorLapackMatrix< Real > matrix, detail::ColumnMajorLapackMatrix< Real > metric, bool compute_right_vectors)
	Solve a dense real generalized nonsymmetric eigensystem through LAPACK ggev.
template<uni20::LapackReal Real>
RealGeneralizedNonsymmetricExpertEigensystem< Real >	uni20::krylov::real_generalized_nonsymmetric_expert_eigensystem (detail::ColumnMajorLapackMatrix< Real > matrix, detail::ColumnMajorLapackMatrix< Real > metric, bool compute_right_vectors)
	Solve a dense real generalized nonsymmetric eigensystem through LAPACK ggevx.
template<uni20::LapackReal Real>
RealGeneralizedSchurDecomposition< Real >	uni20::krylov::real_generalized_schur (detail::ColumnMajorLapackMatrix< Real > matrix, detail::ColumnMajorLapackMatrix< Real > metric, bool compute_vectors)
	Compute the generalized real Schur decomposition of a matrix pencil through LAPACK gges.
template<uni20::LapackReal Real>
RealGeneralizedSchurConditionEstimates< Real >	uni20::krylov::real_generalized_schur_condition_estimates (RealGeneralizedSchurDecomposition< Real > decomposition)
	Estimate generalized Schur eigenvalue and eigenvector conditioning through LAPACK tgsna.
template<uni20::LapackReal Real>
RealGeneralizedSchurRightEigenvectors< Real >	uni20::krylov::real_generalized_schur_right_eigenvectors (RealGeneralizedSchurDecomposition< Real > decomposition)
	Compute right eigenvectors of a generalized real Schur form through LAPACK tgevc.
template<uni20::LapackReal Real>
RealGeneralizedSchurSelectedSubspace< Real >	uni20::krylov::real_generalized_schur_selected_subspace (RealGeneralizedSchurDecomposition< Real > decomposition, std::vector< std::size_t > const &selected_blocks)
	Move selected generalized real Schur blocks to the leading deflating subspace and estimate conditioning.
template<uni20::LapackReal Scalar>
RealSymmetricEigensystem< Scalar >	uni20::krylov::real_generalized_symmetric_eigensystem (detail::ColumnMajorLapackMatrix< Scalar > matrix, detail::ColumnMajorLapackMatrix< Scalar > metric, bool compute_vectors, MatrixFill triangle=MatrixFill::Upper)
	Solve a dense type-1 generalized real symmetric eigensystem through LAPACK sygv.
template<uni20::LapackReal Scalar>
RealSymmetricEigensystem< Scalar >	uni20::krylov::real_generalized_symmetric_eigensystem_divide_and_conquer (detail::ColumnMajorLapackMatrix< Scalar > matrix, detail::ColumnMajorLapackMatrix< Scalar > metric, bool compute_vectors, MatrixFill triangle=MatrixFill::Upper)
	Solve a dense type-1 generalized real symmetric eigensystem through LAPACK sygvd.
template<uni20::LapackReal Scalar>
RealSymmetricEigensystem< Scalar >	uni20::krylov::real_generalized_symmetric_eigensystem_index_range (detail::ColumnMajorLapackMatrix< Scalar > matrix, detail::ColumnMajorLapackMatrix< Scalar > metric, std::size_t first_index, std::size_t last_index, bool compute_vectors, MatrixFill triangle=MatrixFill::Upper)
	Solve a selected dense type-1 generalized real symmetric eigensystem through LAPACK sygvx.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::real_hessenberg_orthogonal_factor (RealHessenbergReduction< Scalar > const &reduction)
	Generate the orthogonal factor from a compact real Hessenberg reduction.
template<uni20::LapackReal Scalar>
RealHessenbergReduction< Scalar >	uni20::krylov::real_hessenberg_reduction (detail::ColumnMajorLapackMatrix< Scalar > matrix)
	Reduce a dense real square matrix to upper Hessenberg form through LAPACK gehrd.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::real_least_squares (detail::ColumnMajorLapackMatrix< Scalar > coefficients, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides)
	Solve a dense real least-squares or minimum-norm problem through LAPACK gels.
template<uni20::LapackReal Scalar>
RealLqFactorization< Scalar >	uni20::krylov::real_lq_factorization (detail::ColumnMajorLapackMatrix< Scalar > matrix)
	Compute a reduced dense real LQ factorization through LAPACK gelqf and orglq.
template<uni20::LapackReal Scalar>
RealLuFactorization< Scalar >	uni20::krylov::real_lu_factorization (detail::ColumnMajorLapackMatrix< Scalar > matrix)
	Compute a dense real LU factorization through LAPACK getrf.
template<uni20::LapackReal Scalar>
Scalar	uni20::krylov::real_lu_one_norm_reciprocal_condition_number (RealLuFactorization< Scalar > const &factorization, Scalar original_one_norm)
	Estimate the one-norm reciprocal condition number from an LU factorization.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::real_lu_solve (RealLuFactorization< Scalar > const &factorization, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides, MatrixTranspose transpose=MatrixTranspose::None)
	Solve using an existing dense real LU factorization through LAPACK getrs.
template<uni20::LapackReal Scalar>
Scalar	uni20::krylov::real_matrix_norm (detail::ColumnMajorLapackMatrix< Scalar > matrix, MatrixNorm norm)
template<uni20::LapackReal Real>
RealNonsymmetricBalance< Real >	uni20::krylov::real_nonsymmetric_balance (detail::ColumnMajorLapackMatrix< Real > matrix, RealNonsymmetricBalanceJob job=RealNonsymmetricBalanceJob::Both)
	Reorder a layout-right complex Schur decomposition by moving selected entries to the front.
template<uni20::LapackReal Real>
detail::ColumnMajorLapackMatrix< Real >	uni20::krylov::real_nonsymmetric_balance_backtransform_right_vectors (detail::ColumnMajorLapackMatrix< Real > vectors, RealNonsymmetricBalance< Real > const &balance, RealNonsymmetricBalanceJob job=RealNonsymmetricBalanceJob::Both)
	Backtransform real right eigenvectors after real_nonsymmetric_balance.
template<uni20::LapackReal Real>
RealNonsymmetricExpertEigensystem< Real >	uni20::krylov::real_nonsymmetric_expert_eigensystem (detail::ColumnMajorLapackMatrix< Real > matrix, bool compute_right_vectors)
	Solve a dense real nonsymmetric eigensystem through LAPACK geev.
template<uni20::LapackReal Scalar>
Scalar	uni20::krylov::real_one_norm_reciprocal_condition_number (detail::ColumnMajorLapackMatrix< Scalar > matrix)
	Estimate the one-norm reciprocal condition number of a dense real matrix.
template<uni20::LapackReal Scalar>
RealPivotedCholeskyFactorization< Scalar >	uni20::krylov::real_pivoted_cholesky_factorization (detail::ColumnMajorLapackMatrix< Scalar > matrix, Scalar tolerance=Scalar{-1}, MatrixFill triangle=MatrixFill::Upper)
	Compute a dense real pivoted Cholesky factorization through LAPACK pstrf.
template<uni20::LapackReal Scalar>
RealPivotedQrFactorization< Scalar >	uni20::krylov::real_pivoted_qr_factorization (detail::ColumnMajorLapackMatrix< Scalar > matrix)
	Compute a reduced dense real pivoted QR factorization through LAPACK geqp3.
template<uni20::LapackReal Scalar>
RealQlFactorization< Scalar >	uni20::krylov::real_ql_factorization (detail::ColumnMajorLapackMatrix< Scalar > matrix)
	Compute a reduced dense real QL factorization through LAPACK geqlf and orgql.
template<uni20::LapackReal Scalar>
RealQrFactorization< Scalar >	uni20::krylov::real_qr_factorization (detail::ColumnMajorLapackMatrix< Scalar > matrix)
	Compute a reduced dense real QR factorization through LAPACK geqrf and orgqr.
template<uni20::LapackReal Scalar>
RealRankRevealingLeastSquares< Scalar >	uni20::krylov::real_rank_revealing_least_squares (detail::ColumnMajorLapackMatrix< Scalar > coefficients, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides, Scalar rcond=Scalar{100} *uni20::numeric_limits< Scalar >::epsilon())
	Solve a dense real rank-revealing least-squares problem through LAPACK gelsy.
template<uni20::LapackReal Scalar>
RealRefinedLinearSolve< Scalar >	uni20::krylov::real_refined_linear_solve (detail::ColumnMajorLapackMatrix< Scalar > coefficients, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides, MatrixTranspose transpose=MatrixTranspose::None)
	Solve and refine a dense real linear system through LAPACK gerfs.
template<uni20::LapackReal Scalar>
RealRqFactorization< Scalar >	uni20::krylov::real_rq_factorization (detail::ColumnMajorLapackMatrix< Scalar > matrix)
	Compute a reduced dense real RQ factorization through LAPACK gerqf and orgrq.
template<uni20::LapackReal Scalar>
RealSchurConditionEstimates< Scalar >	uni20::krylov::real_schur_condition_estimates (RealSchurDecomposition< Scalar > decomposition)
	Estimate Schur-form eigenvalue and eigenvector conditioning through LAPACK trsna.
template<uni20::LapackReal Scalar>
RealSchurRightEigenvectors< Scalar >	uni20::krylov::real_schur_right_eigenvectors (RealSchurDecomposition< Scalar > decomposition)
	Compute right eigenvectors of a real Schur form through LAPACK trevc.
template<uni20::LapackReal Scalar>
RealSchurSelectedSubspace< Scalar >	uni20::krylov::real_schur_selected_subspace (RealSchurDecomposition< Scalar > decomposition, std::vector< std::size_t > const &selected_blocks)
	Compute the real Schur decomposition of a layout-right matrix through LAPACK gees.
template<uni20::LapackReal Scalar>
RealSingularValueDecomposition< Scalar >	uni20::krylov::real_singular_value_decomposition (detail::ColumnMajorLapackMatrix< Scalar > matrix, bool compute_vectors)
	Compute a dense real singular value decomposition through LAPACK gesvd.
template<uni20::LapackReal Scalar>
RealSingularValueDecomposition< Scalar >	uni20::krylov::real_singular_value_decomposition_divide_and_conquer (detail::ColumnMajorLapackMatrix< Scalar > matrix, bool compute_vectors)
	Compute a dense real singular value decomposition through LAPACK gesdd.
template<uni20::LapackReal Scalar>
RealSingularValueDecomposition< Scalar >	uni20::krylov::real_singular_value_decomposition_index_range (detail::ColumnMajorLapackMatrix< Scalar > matrix, std::size_t first_index, std::size_t last_index, bool compute_vectors)
	Compute a selected-index dense real SVD through LAPACK gesvdx.
template<uni20::LapackReal Scalar>
RealSvdLeastSquares< Scalar >	uni20::krylov::real_svd_least_squares (detail::ColumnMajorLapackMatrix< Scalar > coefficients, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides, Scalar rcond=Scalar{100} *uni20::numeric_limits< Scalar >::epsilon())
	Solve a dense real SVD-based least-squares problem through LAPACK gelss.
template<uni20::LapackReal Scalar>
RealSylvesterSolution< Scalar >	uni20::krylov::real_sylvester_solve (detail::ColumnMajorLapackMatrix< Scalar > left, detail::ColumnMajorLapackMatrix< Scalar > right, detail::ColumnMajorLapackMatrix< Scalar > rhs, int sign=1, MatrixTranspose transpose_left=MatrixTranspose::None, MatrixTranspose transpose_right=MatrixTranspose::None)
	Solve a dense real Sylvester equation through LAPACK trsyl.
template<uni20::LapackReal Scalar>
RealSymmetricEigensystem< Scalar >	uni20::krylov::real_symmetric_eigensystem (detail::ColumnMajorLapackMatrix< Scalar > matrix, bool compute_vectors, MatrixFill triangle=MatrixFill::Upper)
	Solve a dense real symmetric eigensystem through LAPACK syev.
template<uni20::LapackReal Scalar>
RealSymmetricEigensystem< Scalar >	uni20::krylov::real_symmetric_eigensystem_divide_and_conquer (detail::ColumnMajorLapackMatrix< Scalar > matrix, bool compute_vectors, MatrixFill triangle=MatrixFill::Upper)
	Solve a dense real symmetric eigensystem through LAPACK syevd.
template<uni20::LapackReal Scalar>
RealSymmetricEigensystem< Scalar >	uni20::krylov::real_symmetric_eigensystem_index_range (detail::ColumnMajorLapackMatrix< Scalar > matrix, std::size_t first_index, std::size_t last_index, bool compute_vectors, MatrixFill triangle=MatrixFill::Upper)
	Solve a selected dense real symmetric eigensystem through LAPACK syevr.
template<uni20::LapackReal Scalar>
RealSymmetricIndefiniteExpertLinearSolve< Scalar >	uni20::krylov::real_symmetric_indefinite_expert_solve (detail::ColumnMajorLapackMatrix< Scalar > coefficients, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides, MatrixFill triangle=MatrixFill::Upper)
	Solve a dense real symmetric-indefinite system with LAPACK sysvx diagnostics.
template<uni20::LapackReal Scalar>
RealSymmetricIndefiniteFactorization< Scalar >	uni20::krylov::real_symmetric_indefinite_factorization (detail::ColumnMajorLapackMatrix< Scalar > matrix, MatrixFill triangle=MatrixFill::Upper)
	Compute a dense real symmetric-indefinite Bunch-Kaufman factorization through LAPACK sytrf.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::real_symmetric_indefinite_inverse (detail::ColumnMajorLapackMatrix< Scalar > matrix, MatrixFill triangle=MatrixFill::Upper)
	Invert a dense real symmetric-indefinite matrix through LAPACK sytrf and sytri.
template<uni20::LapackReal Scalar>
Scalar	uni20::krylov::real_symmetric_indefinite_one_norm_reciprocal_condition_number (detail::ColumnMajorLapackMatrix< Scalar > matrix, MatrixFill triangle=MatrixFill::Upper)
	Estimate a dense real symmetric-indefinite one-norm reciprocal condition number through LAPACK sycon.
template<uni20::LapackReal Scalar>
Scalar	uni20::krylov::real_symmetric_indefinite_one_norm_reciprocal_condition_number (RealSymmetricIndefiniteFactorization< Scalar > const &factorization, Scalar original_one_norm)
	Estimate a symmetric-indefinite one-norm reciprocal condition number from an existing factorization.
template<uni20::LapackReal Scalar>
RealRefinedLinearSolve< Scalar >	uni20::krylov::real_symmetric_indefinite_refined_solve (detail::ColumnMajorLapackMatrix< Scalar > coefficients, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides, MatrixFill triangle=MatrixFill::Upper)
	Solve and refine a dense real symmetric-indefinite system through LAPACK syrfs.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::real_symmetric_indefinite_solve (detail::ColumnMajorLapackMatrix< Scalar > coefficients, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides, MatrixFill triangle=MatrixFill::Upper)
	Solve a dense real symmetric indefinite system through LAPACK sytrf and sytrs.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::real_symmetric_indefinite_solve (RealSymmetricIndefiniteFactorization< Scalar > const &factorization, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides)
	Solve a dense real symmetric-indefinite system from an existing Bunch-Kaufman factorization.
template<uni20::LapackReal Scalar>
Scalar	uni20::krylov::real_symmetric_matrix_norm (detail::ColumnMajorLapackMatrix< Scalar > matrix, MatrixNorm norm, MatrixFill triangle=MatrixFill::Upper)
	Compute a dense real symmetric matrix norm through LAPACK lansy.
template<uni20::LapackReal Scalar>
RealSymmetricPositiveDefiniteBandExpertLinearSolve< Scalar >	uni20::krylov::real_symmetric_positive_definite_band_expert_linear_solve (RealSymmetricPositiveDefiniteBandMatrix< Scalar > coefficients, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides)
	Solve a real SPD band linear system with LAPACK pbsvx diagnostics.
template<uni20::LapackReal Scalar>
RealSymmetricPositiveDefiniteBandFactorization< Scalar >	uni20::krylov::real_symmetric_positive_definite_band_factorization (RealSymmetricPositiveDefiniteBandMatrix< Scalar > matrix)
	Compute a real SPD band Cholesky factorization through LAPACK pbtrf.
template<uni20::LapackReal Scalar>
RealSymmetricPositiveDefiniteBandMatrix< Scalar >	uni20::krylov::real_symmetric_positive_definite_band_from_dense (detail::ColumnMajorLapackMatrix< Scalar > const &matrix, std::size_t bandwidth, MatrixFill triangle=MatrixFill::Upper)
	Pack a dense real SPD matrix into LAPACK symmetric-band storage.
template<uni20::LapackReal Scalar>
Scalar	uni20::krylov::real_symmetric_positive_definite_band_one_norm (RealSymmetricPositiveDefiniteBandMatrix< Scalar > const &matrix)
	Compute the one-norm of a real SPD band matrix.
template<uni20::LapackReal Scalar>
Scalar	uni20::krylov::real_symmetric_positive_definite_band_one_norm_reciprocal_condition_number (RealSymmetricPositiveDefiniteBandFactorization< Scalar > const &factorization, Scalar original_one_norm)
	Estimate a real SPD band one-norm reciprocal condition number through LAPACK pbcon.
template<uni20::LapackReal Scalar>
Scalar	uni20::krylov::real_symmetric_positive_definite_band_one_norm_reciprocal_condition_number (RealSymmetricPositiveDefiniteBandMatrix< Scalar > matrix)
	Estimate a real SPD band one-norm reciprocal condition number from a matrix.
template<uni20::LapackReal Scalar>
RealRefinedLinearSolve< Scalar >	uni20::krylov::real_symmetric_positive_definite_band_refined_solve (RealSymmetricPositiveDefiniteBandMatrix< Scalar > coefficients, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides)
	Solve and refine a real SPD band linear system through LAPACK pbrfs.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::real_symmetric_positive_definite_band_solve (RealSymmetricPositiveDefiniteBandFactorization< Scalar > const &factorization, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides)
	Solve using an existing real SPD band Cholesky factorization through LAPACK pbtrs.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::real_symmetric_positive_definite_band_solve (RealSymmetricPositiveDefiniteBandMatrix< Scalar > coefficients, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides)
	Solve a real SPD band system through LAPACK pbsv.
template<uni20::LapackReal Scalar>
RealSymmetricPositiveDefiniteEquilibration< Scalar >	uni20::krylov::real_symmetric_positive_definite_equilibration (detail::ColumnMajorLapackMatrix< Scalar > matrix)
	Compute dense real SPD equilibration factors through LAPACK poequ.
template<uni20::LapackReal Scalar>
RealSymmetricPositiveDefiniteExpertLinearSolve< Scalar >	uni20::krylov::real_symmetric_positive_definite_expert_solve (detail::ColumnMajorLapackMatrix< Scalar > coefficients, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides, MatrixFill triangle=MatrixFill::Upper)
	Solve a dense real SPD linear system with LAPACK posvx diagnostics.
template<uni20::LapackReal Scalar>
RealSymmetricPositiveDefiniteFactorization< Scalar >	uni20::krylov::real_symmetric_positive_definite_factorization (detail::ColumnMajorLapackMatrix< Scalar > matrix, MatrixFill triangle=MatrixFill::Upper)
	Compute a dense real SPD Cholesky factorization through LAPACK potrf.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::real_symmetric_positive_definite_inverse (detail::ColumnMajorLapackMatrix< Scalar > matrix, MatrixFill triangle=MatrixFill::Upper)
	Invert a dense real SPD matrix through LAPACK potrf and potri.
template<uni20::LapackReal Scalar>
Scalar	uni20::krylov::real_symmetric_positive_definite_one_norm_reciprocal_condition_number (detail::ColumnMajorLapackMatrix< Scalar > matrix, MatrixFill triangle=MatrixFill::Upper)
	Estimate a dense real SPD one-norm reciprocal condition number through LAPACK pocon.
template<uni20::LapackReal Scalar>
Scalar	uni20::krylov::real_symmetric_positive_definite_one_norm_reciprocal_condition_number (RealSymmetricPositiveDefiniteFactorization< Scalar > const &factorization, Scalar original_one_norm)
	Estimate an SPD one-norm reciprocal condition number from an existing Cholesky factorization.
template<uni20::LapackReal Scalar>
RealRefinedLinearSolve< Scalar >	uni20::krylov::real_symmetric_positive_definite_refined_solve (detail::ColumnMajorLapackMatrix< Scalar > coefficients, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides, MatrixFill triangle=MatrixFill::Upper)
	Solve and refine a dense real SPD system through LAPACK porfs.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::real_symmetric_positive_definite_solve (detail::ColumnMajorLapackMatrix< Scalar > coefficients, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides, MatrixFill triangle=MatrixFill::Upper)
	Solve a dense real symmetric positive definite system through LAPACK potrf and potrs.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::real_symmetric_positive_definite_solve (RealSymmetricPositiveDefiniteFactorization< Scalar > const &factorization, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides)
	Solve a dense real SPD system from an existing Cholesky factorization.
template<uni20::LapackReal Scalar>
RealSymmetricPositiveDefiniteTridiagonalExpertLinearSolve< Scalar >	uni20::krylov::real_symmetric_positive_definite_tridiagonal_expert_linear_solve (RealSymmetricPositiveDefiniteTridiagonalMatrix< Scalar > coefficients, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides)
	Solve a real SPD tridiagonal linear system with LAPACK ptsvx diagnostics.
template<uni20::LapackReal Scalar>
RealSymmetricPositiveDefiniteTridiagonalFactorization< Scalar >	uni20::krylov::real_symmetric_positive_definite_tridiagonal_factorization (RealSymmetricPositiveDefiniteTridiagonalMatrix< Scalar > matrix)
	Compute a real SPD tridiagonal factorization through LAPACK pttrf.
template<uni20::LapackReal Scalar>
RealSymmetricPositiveDefiniteTridiagonalMatrix< Scalar >	uni20::krylov::real_symmetric_positive_definite_tridiagonal_from_dense (detail::ColumnMajorLapackMatrix< Scalar > const &matrix)
	Extract real SPD tridiagonal storage from a dense matrix.
template<uni20::LapackReal Scalar>
Scalar	uni20::krylov::real_symmetric_positive_definite_tridiagonal_one_norm (RealSymmetricPositiveDefiniteTridiagonalMatrix< Scalar > const &matrix)
	Compute the one-norm of a real SPD tridiagonal matrix.
template<uni20::LapackReal Scalar>
Scalar	uni20::krylov::real_symmetric_positive_definite_tridiagonal_one_norm_reciprocal_condition_number (RealSymmetricPositiveDefiniteTridiagonalFactorization< Scalar > const &factorization, Scalar original_one_norm)
	Estimate a real SPD tridiagonal one-norm reciprocal condition number through LAPACK ptcon.
template<uni20::LapackReal Scalar>
Scalar	uni20::krylov::real_symmetric_positive_definite_tridiagonal_one_norm_reciprocal_condition_number (RealSymmetricPositiveDefiniteTridiagonalMatrix< Scalar > matrix)
	Estimate a real SPD tridiagonal one-norm reciprocal condition number from a matrix.
template<uni20::LapackReal Scalar>
RealRefinedLinearSolve< Scalar >	uni20::krylov::real_symmetric_positive_definite_tridiagonal_refined_solve (RealSymmetricPositiveDefiniteTridiagonalMatrix< Scalar > coefficients, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides)
	Solve and refine a real SPD tridiagonal linear system through LAPACK ptrfs.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::real_symmetric_positive_definite_tridiagonal_solve (RealSymmetricPositiveDefiniteTridiagonalFactorization< Scalar > const &factorization, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides)
	Solve using an existing real SPD tridiagonal factorization through LAPACK pttrs.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::real_symmetric_positive_definite_tridiagonal_solve (RealSymmetricPositiveDefiniteTridiagonalMatrix< Scalar > coefficients, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides)
	Solve a real SPD tridiagonal system through LAPACK ptsv.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::real_symmetric_tridiagonal_orthogonal_factor (RealSymmetricTridiagonalReduction< Scalar > const &reduction)
	Generate the orthogonal factor from a compact real symmetric tridiagonal reduction.
template<uni20::LapackReal Scalar>
RealSymmetricTridiagonalReduction< Scalar >	uni20::krylov::real_symmetric_tridiagonal_reduction (detail::ColumnMajorLapackMatrix< Scalar > matrix, MatrixFill triangle=MatrixFill::Upper)
	Reduce a dense real symmetric matrix to tridiagonal form through LAPACK sytrd.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::real_triangular_inverse (detail::ColumnMajorLapackMatrix< Scalar > matrix, MatrixFill triangle=MatrixFill::Upper, bool unit_diagonal=false)
	Invert a dense real triangular matrix through LAPACK trtri.
template<uni20::LapackReal Scalar>
Scalar	uni20::krylov::real_triangular_matrix_norm (detail::ColumnMajorLapackMatrix< Scalar > matrix, MatrixNorm norm, MatrixFill triangle=MatrixFill::Upper, bool unit_diagonal=false)
	Compute a dense real triangular or trapezoidal matrix norm through LAPACK lantr.
template<uni20::LapackReal Scalar>
Scalar	uni20::krylov::real_triangular_one_norm_reciprocal_condition_number (detail::ColumnMajorLapackMatrix< Scalar > matrix, MatrixFill triangle=MatrixFill::Upper, bool unit_diagonal=false)
	Estimate a dense real triangular one-norm reciprocal condition number through LAPACK trcon.
template<uni20::LapackReal Scalar>
RealRefinedLinearSolve< Scalar >	uni20::krylov::real_triangular_refined_solve (detail::ColumnMajorLapackMatrix< Scalar > coefficients, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides, MatrixFill triangle=MatrixFill::Upper, MatrixTranspose transpose=MatrixTranspose::None, bool unit_diagonal=false)
	Solve and refine a dense real triangular system through LAPACK trrfs.
template<uni20::LapackReal Scalar>
detail::ColumnMajorLapackMatrix< Scalar >	uni20::krylov::real_triangular_solve (detail::ColumnMajorLapackMatrix< Scalar > coefficients, detail::ColumnMajorLapackMatrix< Scalar > right_hand_sides, MatrixFill triangle=MatrixFill::Upper, MatrixTranspose transpose=MatrixTranspose::None, bool unit_diagonal=false)
	Solve a dense real triangular system through LAPACK trtrs.
template<uni20::LapackReal Real>
RealGeneralizedSchurDecomposition< Real >	uni20::krylov::reorder_real_generalized_schur (RealGeneralizedSchurDecomposition< Real > decomposition, std::vector< std::size_t > const &leading_block_order)
	Reorder a generalized real Schur decomposition by moving selected blocks to the front.
template<uni20::LapackReal Scalar>
TridiagonalEigensystem< Scalar >	uni20::krylov::symmetric_tridiagonal_eigensystem_divide_and_conquer (std::vector< Scalar > diagonal, std::vector< Scalar > subdiagonal, bool compute_vectors)
	Solve a real symmetric tridiagonal eigenvalue problem through LAPACK sterf.
template<uni20::LapackReal Scalar>
TridiagonalEigensystem< Scalar >	uni20::krylov::symmetric_tridiagonal_eigensystem_index_range (std::vector< Scalar > diagonal, std::vector< Scalar > subdiagonal, std::size_t first_index, std::size_t last_index, bool compute_vectors)
	Solve a selected real symmetric tridiagonal eigensystem through LAPACK stevr.