Add EigenvalueProblem, EigenvalueSolution, and EigenvalueTarget#1417
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| SmallestRealPart | ||
| "Eigenvalues with the largest (most positive) imaginary part (symbol `:LI`)." | ||
| LargestImaginaryPart | ||
| "Eigenvalues with the smallest (most negative) imaginary part (symbol `:SI`)." |
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get rid of the symbols, use the enums
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| - `A`: the operator whose eigenvalues are sought. | ||
| - `B`: the second operator for a generalized problem, or `nothing` for a standard one. | ||
| - `nev`: the requested number of eigenpairs. |
| - `A`: the operator whose eigenvalues are sought. | ||
| - `B`: the second operator for a generalized problem, or `nothing` for a standard one. | ||
| - `nev`: the requested number of eigenpairs. | ||
| - `which`: the [`EigenvalueTarget`](@ref) selecting the part of the spectrum. |
| - `B`: the second operator for a generalized problem, or `nothing` for a standard one. | ||
| - `nev`: the requested number of eigenpairs. | ||
| - `which`: the [`EigenvalueTarget`](@ref) selecting the part of the spectrum. | ||
| - `sigma`: the shift for shift-and-invert, or `nothing`. |
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| - `which`: which part of the spectrum to return, as an [`EigenvalueTarget`](@ref). An | ||
| ARPACK-style `Symbol` (`:LM`, `:SM`, `:LR`, `:SR`, `:LI`, `:SI`) is also accepted and | ||
| converted to the corresponding `EigenvalueTarget`. Defaults to the eigenvalues of |
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| ```math | ||
| A v = \lambda B v |
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Should define the default typing rules. If u0 is provided, then typeof(v) = typeof(u0). Otherwise it's the dense type of a row of A. Meanwhile, typeof(lambda) = eltype(A).
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Checklist
contributor guidelines, in particular the SciML Style Guide and
COLPRAC.
Additional context
EigenvalueProblem,EigenvalueSolution, and theEigenvalueTargetenum, mirroring the existingLinearProblem/LinearSolutionpattern.AbstractEigenvalueProblem/AbstractEigenvalueSolutionabstract types andbuild_eigenvalue_solution.whichnormalization (Symbol→EigenvalueTarget), and error handling.Enables SciML/LinearSolve.jl's new
EigenvalueProblemsupport (dense, Arpack, ArnoldiMethod, KrylovKit, JacobiDavidson backends) to share one canonical definition instead of duplicating it downstream.AI Usage: Usead Claude Sonnet 5
Part of SciML/LinearSolve.jl#143