MatrixAlgebraKit.jl

module MatrixAlgebraKit

using LinearAlgebra: LinearAlgebra
using LinearAlgebra: norm # TODO: eleminate if we use VectorInterface.jl?
using LinearAlgebra: mul!, rmul!, lmul!, adjoint!, rdiv!, ldiv!
using LinearAlgebra: sylvester, lu!, diagm
using LinearAlgebra: isposdef, issymmetric
using LinearAlgebra: Diagonal, Hermitian, diag, diagind, isdiag
using LinearAlgebra: UpperTriangular, LowerTriangular, UniformScaling
using LinearAlgebra: BlasFloat, BlasReal, BlasComplex, BlasInt

export isisometric, isunitary, ishermitian, isantihermitian
export diagview, diagonal

export project_hermitian, project_antihermitian, project_isometric
export project_hermitian!, project_antihermitian!, project_isometric!
export qr_compact, qr_full, qr_null, lq_compact, lq_full, lq_null
export qr_compact!, qr_full!, qr_null!, lq_compact!, lq_full!, lq_null!
export svd_compact, svd_full, svd_vals, svd_trunc, svd_trunc_no_error
export svd_compact!, svd_full!, svd_vals!, svd_trunc!, svd_trunc_no_error!
export eigh_full, eigh_vals, eigh_trunc, eigh_trunc_no_error
export eigh_full!, eigh_vals!, eigh_trunc!, eigh_trunc_no_error!
export eig_full, eig_vals, eig_trunc, eig_trunc_no_error
export eig_full!, eig_vals!, eig_trunc!, eig_trunc_no_error!
export gen_eig_full, gen_eig_vals
export gen_eig_full!, gen_eig_vals!
export schur_full, schur_vals
export schur_full!, schur_vals!
export left_polar, right_polar
export left_polar!, right_polar!
export left_orth, right_orth, left_null, right_null
export left_orth!, right_orth!, left_null!, right_null!

export Householder, Native_HouseholderQR, Native_HouseholderLQ
export DivideAndConquer, SafeDivideAndConquer, QRIteration, Bisection, Jacobi, SVDViaPolar
export RobustRepresentations
export LAPACK_HouseholderQR, LAPACK_HouseholderLQ, LAPACK_Simple, LAPACK_Expert,
    LAPACK_QRIteration, LAPACK_Bisection, LAPACK_MultipleRelativelyRobustRepresentations,
    LAPACK_DivideAndConquer, LAPACK_Jacobi, LAPACK_SafeDivideAndConquer
export GLA_HouseholderQR, GLA_QRIteration, GS_QRIteration
export LQViaTransposedQR
export PolarViaSVD, PolarNewton
export DefaultAlgorithm
export DiagonalAlgorithm
export NativeBlocked
export CUSOLVER_Simple, CUSOLVER_HouseholderQR, CUSOLVER_QRIteration, CUSOLVER_SVDPolar,
    CUSOLVER_Jacobi, CUSOLVER_Randomized, CUSOLVER_DivideAndConquer
export ROCSOLVER_HouseholderQR, ROCSOLVER_QRIteration, ROCSOLVER_Jacobi,
    ROCSOLVER_DivideAndConquer, ROCSOLVER_Bisection

export notrunc, truncrank, trunctol, truncerror, truncfilter

@static if VERSION >= v"1.11.0-DEV.469"
    eval(
        Expr(
            :public, :default_algorithm, :findtruncated, :findtruncated_svd,
            :select_algorithm
        )
    )
    eval(
        Expr(
            :public, :TruncationByOrder, :TruncationByFilter, :TruncationByValue,
            :TruncationByError, :TruncationIntersection, :TruncationUnion, :truncate
        )
    )
    eval(
        Expr(
            :public, :left_polar_pullback!, :right_polar_pullback!,
            :qr_pullback!, :qr_null_pullback!, :lq_pullback!, :lq_null_pullback!,
            :eig_pullback!, :eig_trunc_pullback!, :eig_vals_pullback!,
            :eigh_pullback!, :eigh_trunc_pullback!, :eigh_vals_pullback!,
            :svd_pullback!, :svd_trunc_pullback!, :svd_vals_pullback!
        )
    )
    eval(
        Expr(
            :public, :remove_svd_gauge_dependence!,
            :remove_eig_gauge_dependence!, :remove_eigh_gauge_dependence!,
            :remove_qr_gauge_dependence!, :remove_qr_null_gauge_dependence!,
            :remove_lq_gauge_dependence!, :remove_lq_null_gauge_dependence!,
            :remove_left_null_gauge_dependence!, :remove_right_null_gauge_dependence!,
        )
    )
    eval(Expr(:public, :is_left_isometric, :is_right_isometric))
end

include("common/defaults.jl")
include("common/householder.jl")
include("common/initialization.jl")
include("common/pullbacks.jl")
include("common/safemethods.jl")
include("common/view.jl")
include("common/regularinv.jl")
include("common/matrixproperties.jl")

include("yalapack.jl")
include("algorithms.jl")
include("interface/projections.jl")
include("interface/decompositions.jl")
include("interface/truncation.jl")
include("interface/qr.jl")
include("interface/lq.jl")
include("interface/svd.jl")
include("interface/eig.jl")
include("interface/eigh.jl")
include("interface/gen_eig.jl")
include("interface/schur.jl")
include("interface/polar.jl")
include("interface/orthnull.jl")

include("implementations/projections.jl")
include("implementations/truncation.jl")
include("implementations/qr.jl")
include("implementations/lq.jl")
include("implementations/svd.jl")
include("implementations/eig.jl")
include("implementations/eigh.jl")
include("implementations/gen_eig.jl")
include("implementations/schur.jl")
include("implementations/polar.jl")
include("implementations/orthnull.jl")

include("common/gauge.jl") # needs to be defined after the functions are

include("pullbacks/qr.jl")
include("pullbacks/lq.jl")
include("pullbacks/eig.jl")
include("pullbacks/eigh.jl")
include("pullbacks/svd.jl")
include("pullbacks/polar.jl")

include("pushforwards/polar.jl")
include("pushforwards/eig.jl")
include("pushforwards/eigh.jl")
include("pushforwards/svd.jl")

include("precompile.jl")

end