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Change default symmetriceigen algorithm back to RobustRepresentations #1363

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Jun 1, 2025
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Change default symmetriceigen algorithm back to RobustRepresentations #1363

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84d2c87
Change default symmetriceigen algorithm
jaemolihm May 28, 2025
871bf32
Update docstring
jaemolihm May 28, 2025
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16 changes: 10 additions & 6 deletions src/symmetriceigen.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -10,9 +10,9 @@ eigencopy_oftype(A::Symmetric{<:Complex}, S) = copyto!(similar(parent(A), S), A)
default_eigen_alg(A)

Return the default algorithm used to solve the eigensystem `A v = λ v` for a symmetric matrix `A`.
Defaults to `LinearAlegbra.DivideAndConquer()`, which corresponds to the LAPACK function `LAPACK.syevd!`.
Defaults to `LinearAlegbra.RobustRepresentations()`, which corresponds to the LAPACK function `LAPACK.syevr!`.
"""
default_eigen_alg(@nospecialize(A)) = DivideAndConquer()
default_eigen_alg(@nospecialize(A)) = RobustRepresentations()

# Eigensolvers for symmetric and Hermitian matrices
function eigen!(A::RealHermSymComplexHerm{<:BlasReal,<:StridedMatrix}; alg::Algorithm = default_eigen_alg(A), sortby::Union{Function,Nothing}=nothing)
Expand All @@ -37,9 +37,9 @@ matrix `F.vectors`. (The `k`th eigenvector can be obtained from the slice `F.vec
Iterating the decomposition produces the components `F.values` and `F.vectors`.

`alg` specifies which algorithm and LAPACK method to use for eigenvalue decomposition:
- `alg = DivideAndConquer()` (default): Calls `LAPACK.syevd!`.
- `alg = DivideAndConquer()`: Calls `LAPACK.syevd!`.
- `alg = QRIteration()`: Calls `LAPACK.syev!`.
- `alg = RobustRepresentations()`: Multiple relatively robust representations method, Calls `LAPACK.syevr!`.
- `alg = RobustRepresentations()` (default): Multiple relatively robust representations method, Calls `LAPACK.syevr!`.

See James W. Demmel et al, SIAM J. Sci. Comput. 30, 3, 1508 (2008) for
a comparison of the accuracy and performance of different algorithms.
Expand Down Expand Up @@ -140,14 +140,18 @@ end
Return the eigenvalues of `A`.

`alg` specifies which algorithm and LAPACK method to use for eigenvalue decomposition:
- `alg = DivideAndConquer()` (default): Calls `LAPACK.syevd!`.
- `alg = DivideAndConquer()`: Calls `LAPACK.syevd!`.
- `alg = QRIteration()`: Calls `LAPACK.syev!`.
- `alg = RobustRepresentations()`: Multiple relatively robust representations method, Calls `LAPACK.syevr!`.
- `alg = RobustRepresentations()` (default): Multiple relatively robust representations method, Calls `LAPACK.syevr!`.

See James W. Demmel et al, SIAM J. Sci. Comput. 30, 3, 1508 (2008) for
a comparison of the accuracy and performance of different methods.

The default `alg` used may change in the future.

!!! compat "Julia 1.12"
The `alg` keyword argument requires Julia 1.12 or later.

"""
function eigvals(A::RealHermSymComplexHerm; alg::Algorithm = default_eigen_alg(A), sortby::Union{Function,Nothing}=nothing)
S = eigtype(eltype(A))
Expand Down