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If you use LinearOperators.jl in your work, please cite using the format given inCITATION.cff.

Operators behave like matrices (with some exceptions - see below) but are defined by their effect when applied to a vector. They can be transposed, conjugated, or combined with other operators cheaply. The costly operation is deferred until multiplied with a vector.

Julia 1.6 and up.

pkg> add LinearOperatorspkg> test LinearOperators

Check thetutorial.

Operators can be transposed (transpose(A)), conjugated (conj(A)) and conjugate-transposed (A').Operators can be sliced (A[:,3],A[2:4,1:5],A[1,1]), but unlike matrices, slices always returnoperators (see differences below).

Unlike matrices, an operator never reduces to a vector or a number.

A=rand(5,5)opA=LinearOperator(A)A[:,1]*3# VectoropA[:,1]*3# LinearOperatorA[:,1]* [3]# ERRORopA[:,1]* [3]# Vector

This is also true forA[i,J], which returns vectors on 0.5, and for the scalarA[i,j].Similarly,opA[1,1] is an operator of size (1,1):"

opA[1,1]# LinearOperatorA[1,1]# Number

In the same spirit, the operatorfull always returns a matrix.

full(opA[:,1])# nx1 matrix

• LimitedLDLFactorizations features a limited-memoryLDL^T factorization operator that may be used as preconditionerin iterative methods
• MUMPS.jl features a fulldistributed-memory factorization operator that may be used to represent thepreconditioner in, e.g., constraint-preconditioned Krylov methods.

If you think you found a bug, feel free to open anissue.Focused suggestions and requests can also be opened as issues. Before opening a pull request, start an issue or a discussion on the topic, please.

If you want to ask a question not suited for a bug report, feel free to start a discussionhere. This forum is for general discussion about this repository and theJuliaSmoothOptimizers organization, so questions about any of our packages are welcome.