HISTORY.md

LinearAlgebra v1.12 Release Notes

• rank can now take a QRPivoted matrix to allow rank estimation via QR factorization (#54283)
• Added keyword argument alg to eigen, eigen!, eigvals and eigvals! for self-adjoint matrix types (RealHermSymComplexHerm) to switch between different eigendecomposition algorithms (#49355)
• Added a generic version of the (unblocked) pivoted Cholesky decomposition (callable via cholesky[!](A, RowMaximum())) (#54619)
• The number of default BLAS threads now respects process affinity, instead of using the total number of logical threads available on the system (#55574)
• Added a new function zeroslike that generates zero elements for matrix-valued banded matrices. Custom array types may specialize this function (#55252)
• A * B matrix multiplication now calls matprod_dest(A, B, T::Type) to generate the destination; this function is now public (#55537)
• The function haszero(T::Type) to check if a type has a unique zero element is now public (#56223)
• Added diagview to return a view into a specific band of an AbstractMatrix (#56175)

LinearAlgebra v1.11 Release Notes

• cbrt(::AbstractMatrix{<:Real}) is now defined and returns real-valued matrix cube roots of real-valued matrices (#50661)
• eigvals/eigen(A, bunchkaufman(B)) and eigvals/eigen(A, lu(B)), which utilize the Bunchkaufman (LDL) and LU decomposition of B, now efficiently compute the generalized eigenvalues (and eigenvectors) of A and B (#50471)
• Specialized dispatch for eigvals/eigen(::Hermitian{<:Tridiagonal}) now performs a similarity transformation to create a real symmetric tridiagonal matrix and solves it using LAPACK routines (#49546)
• Structured matrices now retain either the axes of the parent (for Symmetric/Hermitian/AbstractTriangular/UpperHessenberg) or that of the principal diagonal (for banded matrices) (#52480)
• bunchkaufman and bunchkaufman! now work for any AbstractFloat, Rational, and their complex variants. bunchkaufman now also supports Integer types via internal conversion to Rational{BigInt}. Added new function inertia to compute the inertia of the diagonal factor in the Bunchkaufman factorization; for complex symmetric matrices, inertia only computes the number of zero eigenvalues of the diagonal factor (#51487)
• Packages that specialize mul! with a method signature like mul!(::AbstractMatrix, ::MyMatrix, ::AbstractMatrix, ::Number, ::Number) no longer encounter method ambiguities with LinearAlgebra’s structured matrix types (e.g., AbstractTriangular) (#52837)
• lu and issuccess(::LU) now accept an allowsingular keyword argument. When set to true, a valid factorization with rank-deficient U factor will be treated as success instead of throwing an error. Such factorizations are now shown by printing the factors together with a "rank-deficient" note rather than printing a "Failed Factorization" message (#52957)

LinearAlgebra v1.10 Release Notes

• AbstractQ no longer subtypes AbstractMatrix. Additionally, adjoint(Q::AbstractQ) now wraps Q in an AdjointQ instead of Adjoint. AdjointQ itself subtypes AbstractQ. This change clarifies that AbstractQ instances generally behave like function-based, matrix-backed linear operators, which may not allow efficient indexing. Many AbstractQ types can act on vectors/matrices of varying sizes, behaving like a matrix with context-dependent dimensions. The full API is described in the Julia documentation (#46196).
• Adjoints and transposes of Factorization objects are now wrapped in AdjointFactorization and TransposeFactorization types, respectively, instead of the generic Adjoint and Transpose wrappers. These new types subtype Factorization (#46874).
• Added new functions hermitianpart and hermitianpart! to extract the Hermitian (real symmetric) part of a matrix (#31836).
• The norm of the adjoint or transpose of an AbstractMatrix now returns the norm of the parent matrix by default, consistent with the behavior for AbstractVectors (#49020).
• eigen(A, B) and eigvals(A, B), where one of A or B is symmetric or Hermitian, are now fully supported (#49533).
• eigvals and eigen(A, cholesky(B)) now compute the generalized eigenvalues (and eigenvectors) of A and B via Cholesky decomposition for positive definite B. The second argument is the output of cholesky (#49533).

LinearAlgebra v1.9 Release Notes

• The methods a / b and b \ a, where a is a scalar and b a vector, have been removed. These were previously equivalent to a * pinv(b) but could be confusing (#44358).
• LinearAlgebra is now fully reliant on libblastrampoline (LBT) for calling BLAS and LAPACK. OpenBLAS is shipped by default. Building the system image with other BLAS/LAPACK libraries is no longer supported; instead, the LBT mechanism should be used to swap BLAS/LAPACK with vendor-provided libraries (#44360).
• lu now supports a new pivoting strategy RowNonZero() which chooses the first non-zero pivot element. This is useful for new arithmetic types and educational purposes (#44571).
• normalize(x, p=2) now supports any normed vector space x, including scalars (#44925).
• The default number of BLAS threads is now set to the number of CPU threads on ARM CPUs, and half the number of CPU threads on other architectures (#45412, #46085).

LinearAlgebra v1.8 Release Notes

• The BLAS submodule now supports the level-2 BLAS subroutine spr! (#42830).
• cholesky[!] now supports LinearAlgebra.PivotingStrategy (singleton type) values as its optional pivot argument. The default remains cholesky(A, NoPivot()) instead of cholesky(A, RowMaximum()); the previous Val{true/false}-based calls are now deprecated (#41640).
• LinearAlgebra.jl is now completely independent of SparseArrays.jl, both in source code and unit testing (#43127).
  As a result, sparse arrays are no longer silently returned by LinearAlgebra methods applied to Base or LinearAlgebra objects. Specifically, this introduces the following breaking changes:
  • Concatenations involving special "sparse" matrices (e.g., *diagonal) now return dense matrices. Consequently, the D1 and D2 fields of SVD objects constructed via getproperty are now dense matrices.
  • 3-arg similar(::SpecialSparseMatrix, ::Type, ::Dims) now returns a dense zero matrix. As a consequence, products of bi-, tri-, and symmetric tridiagonal matrices with each other produce dense output. Constructing 3-arg similar matrices for special "sparse" (nonstatic) matrices now fails due to the lack of zero(::Type{Matrix{T}}).

LinearAlgebra v1.7 Release Notes

• Use Libblastrampoline to pick a BLAS and LAPACK at runtime. By default it forwards to OpenBLAS in the Julia distribution. The forwarding mechanism can be used by packages to replace the BLAS and LAPACK with user preferences (#39455).
• On aarch64, OpenBLAS now uses an ILP64 BLAS like all other 64-bit platforms (#39436).
• OpenBLAS is updated to 0.3.13 (#39216).
• SuiteSparse is updated to 5.8.1 (#39455).
• The shape of an UpperHessenberg matrix is preserved under certain arithmetic operations, e.g. when multiplying or dividing by an UpperTriangular matrix (#40039).
• Real quasitriangular Schur factorizations S can now be efficiently converted to complex upper-triangular form with Schur{Complex}(S) (#40573).
• cis(A) now supports matrix arguments (#40194).
• dot now supports UniformScaling with AbstractMatrix (#40250).
• qr[!] and lu[!] now support LinearAlgebra.PivotingStrategy (singleton type) values as their optional pivot argument: defaults are qr(A, NoPivot()) (vs. qr(A, ColumnNorm()) for pivoting) and lu(A, RowMaximum()) (vs. lu(A, NoPivot()) without pivoting); the former Val{true/false}-based calls are deprecated (#40623).
• det(M::AbstractMatrix{BigInt}) now calls det_bareiss(M), which uses the Bareiss algorithm to calculate precise values (#40868).

LinearAlgebra v1.6 Release Notes

• New method LinearAlgebra.issuccess(::CholeskyPivoted) for checking whether pivoted Cholesky factorization was successful (#36002)
• UniformScaling can now be indexed using ranges to return dense matrices and vectors (#24359)
• New function LinearAlgebra.BLAS.get_num_threads() for getting the number of BLAS threads (#36360)
• (+)(::UniformScaling) is now defined, making +I a valid unary operation (#36784)
• Instances of UniformScaling are no longer isequal to matrices; previous behavior violated the rule that isequal(x, y) implies hash(x) == hash(y)
• Transposing *Triangular matrices now returns matrices of the opposite triangular type, consistent with adjoint!(::*Triangular) and transpose!(::*Triangular). Packages containing methods with, e.g., Adjoint{<:Any,<:LowerTriangular{<:Any,<:OwnMatrixType}} should replace that by UpperTriangular{<:Any,<:Adjoint{<:Any,<:OwnMatrixType}} in the method signature (#38168)

LinearAlgebra v1.5 Release Notes

• The BLAS submodule now supports the level-2 BLAS subroutine hpmv! (#34211).
• normalize now supports multidimensional arrays (#34239).
• lq factorizations can now be used to compute the minimum-norm solution to under-determined systems (#34350).
• sqrt(::Hermitian) now treats slightly negative eigenvalues as zero for nearly semidefinite matrices, and accepts a new rtol keyword argument for this tolerance (#35057).
• The BLAS submodule now supports the level-2 BLAS subroutine spmv! (#34320).
• The BLAS submodule now supports the level-1 BLAS subroutine rot! (#35124).
• New generic rotate!(x, y, c, s) and reflect!(x, y, c, s) functions (#35124).

LinearAlgebra v1.4 Release Notes

• qr and qr! functions support blocksize keyword argument (#33053).
• dot now admits a 3-argument method dot(x, A, y) to compute generalized dot products dot(x, A*y) without computing and storing an intermediate result A*y (#32739).
• ldlt and non-pivoted lu now throw a new ZeroPivotException type (#33372).
• cond(A, p) with p=1 or p=Inf now computes the exact condition number instead of an estimate (#33547).
• UniformScaling objects may now be exponentiated such that (a*I)^x = a^x * I.

LinearAlgebra v1.3 Release Notes

• The BLAS submodule no longer exports dot, which conflicted with that in LinearAlgebra (#31838).
• diagm and spdiagm now accept optional m,n initial arguments to specify a size (#31654).
• Hessenberg factorizations H now support efficient shifted solves (H+µI) \ b and determinants, and use a specialized tridiagonal factorization for Hermitian matrices. There is also a new UpperHessenberg matrix type (#31853).
• Added keyword argument alg to svd and svd! to switch between different SVD algorithms (#31057).
• Five-argument mul!(C, A, B, α, β) now implements in-place multiplication fused with addition C = A B α + C β (#23919).

LinearAlgebra v1.2 Release Notes

• Added keyword arguments rtol and atol to pinv and nullspace (#29998).
• UniformScaling instances are now callable such that e.g. I(3) will produce a Diagonal matrix (#30298).
• Eigenvalues λ of general matrices are now sorted lexicographically by (Re λ, Im λ) (#21598).
• one for structured matrices (Diagonal, Bidiagonal, Tridiagonal, Symtridiagonal) now preserves structure and type (#29777).
• diagm(v) is now shorthand for diagm(0 => v) (#31125).

LinearAlgebra v1.1 Release Notes

• isdiag and isposdef now support Diagonal and UniformScaling (#29638).
• Added mul!, rmul!, and lmul! methods for UniformScaling (#29506).
• Symmetric and Hermitian matrices now preserve the wrapper when scaled with a number (#29469).
• Exponentiation operator ^ now supports raising an Irrational to an AbstractMatrix power (#29782).
• Added keyword arguments rtol and atol to rank (#29926).