Developer API

StableLinearAlgebra.mul_P! — Function

mul_P!(A, p, B)

Evaluate the matrix product $A = P \cdot B,$ where $P$ is a permutation matrix represented by the vector of integers p.

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mul_P!(A, B, p)

Evaluate the matrix product $A = B \cdot P,$ where $P$ is a permutation matrix represented by the vector of integers p.

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StableLinearAlgebra.inv_P! — Function

inv_P!(p⁻¹, p)

Calculate the inverse/transpose $P^{-1}=P^T$ of a permuation $P$ represented by the vector p, writing the result to p⁻¹.

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StableLinearAlgebra.perm_sign — Function

perm_sign(p::AbstractVector{Int})

Calculate the sign/parity of the permutation p, $\textrm{sgn}(p) = \pm 1.$

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LAPACK LinearAlgebra

StableLinearAlgebra.QRWorkspace — Type

QRWorkspace{T<:Number, E<:Real}

Allocated space for calcuating the pivoted QR factorization using the LAPACK routines geqp3! and orgqr! while avoiding dynamic memory allocations.

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StableLinearAlgebra.LUWorkspace — Type

LUWorkspace{T<:Number, E<:Real}

Allocated space for calcuating the pivoted QR factorization using the LAPACK routine getrf!. Also interfaces with the getri! and getrs! routines for inverting matrices and solving linear systems respectively.

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StableLinearAlgebra.inv_lu! — Function

inv_lu!(A::AbstractMatrix{T}, ws::LUWorkspace{T}) where {T}

Calculate the inverse of the matrix A, overwriting A in-place. Also return $\log(|\det A^{-1}|)$ and $\textrm{sign}(\det A^{-1}).$

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StableLinearAlgebra.ldiv_lu! — Function

ldiv_lu!(A::AbstractMatrix{T}, B::AbstractMatrix{T}, ws::LUWorkspace{T}) where {T}

Calculate $B:= A^{-1} B,$ modifying $B$ in-place. The matrix $A$ is over-written as well. Also return $\log(|\det A^{-1}|)$ and $\textrm{sign}(\det A^{-1}).$

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StableLinearAlgebra.det_lu! — Function

det_lu!(A::AbstractMatrix{T}, ws::LUWorkspace{T}) where {T}

Return $\log(|\det A|)$ and $\textrm{sign}(\det A).$ Note that $A$ is left modified by this function.

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