Add opnorm implementation

[farhadrclass]

Introduces a new opnorm function that efficiently computes the operator 2-norm for matrices and linear operators, dispatching to LAPACK, ARPACK, or TSVD as appropriate. Adds comprehensive tests for opnorm covering both Float64 and BigFloat types, and integrates the new test file into the test suite.

Update Project.toml

[farhadrclass]

@tmigot and @MaxenceGollier

[codecov]

Codecov Report

❌ Patch coverage is 96.87500% with 2 lines in your changes missing coverage. Please review.
✅ Project coverage is 94.93%. Comparing base (32dbc5e) to head (274e336).
⚠️ Report is 77 commits behind head on main.

Files with missing lines	Patch %	Lines
ext/LinearOperatorsOpNormExt.jl	96.87%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #375      +/-   ##
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- Coverage   95.00%   94.93%   -0.07%     
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  Files          17       22       +5     
  Lines        1100     1243     +143     
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+ Hits         1045     1180     +135     
- Misses         55       63       +8     

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[tmigot]

Thanks @farhadrclass that will be a great add. I made a first batch of comments

[Copilot]

Pull request overview

This pull request introduces a new opnorm function to efficiently compute the operator 2-norm (largest singular value) for matrices and linear operators. The implementation uses a dispatching strategy that selects LAPACK for small dense matrices, ARPACK for larger matrices with Float32/Float64/ComplexF32/ComplexF64 element types, and TSVD for other element types like BigFloat.

Changes:

• Adds opnorm function with type-based dispatch for efficient norm computation
• Adds comprehensive tests for Float64 and BigFloat matrix types
• Adds new dependencies: Arpack, GenericLinearAlgebra, and TSVD

Reviewed changes

Copilot reviewed 3 out of 4 changed files in this pull request and generated 18 comments.

File	Description
src/utilities.jl	Implements opnorm function with dispatch to opnorm_eig for square matrices and opnorm_svd for rectangular matrices, with fallback to TSVD
test/test_opnorm.jl	Adds tests for square and rectangular matrices with Float64 and BigFloat types
test/runtests.jl	Integrates new test_opnorm.jl into the test suite
Project.toml	Adds Arpack, GenericLinearAlgebra, and TSVD dependencies with version constraints

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[Copilot]

Pull request overview

Copilot reviewed 3 out of 4 changed files in this pull request and generated 15 comments.

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[farhadrclass]

.

[farhadrclass]

@tmigot and @dpo I updated the code, and also used AI to code review (to test if AI can help us automate the review)
I am now pushing the changes,

[dpo]

@farhadrclass All tests fail and the branch must be rebased.

We also need to hear from @MohamedLaghdafHABIBOULLAH and @MaxenceGollier.

[farhadrclass]

@tmigot Thanks for your feedbacks

Here is the most updated code,
Let me know so we can push this branch in so I can use it in my JSOSolvers

[farhadrclass]

hey
@tmigot ,

I was wondering if you had a chance to look at this ?

[tmigot]

I made a few comments, it looks good overall. Thanks @farhadrclass

[farhadrclass]

@tmigot
Thanks for your suggestions,
I updated them
@dpo I think it is ready for merging, I am going to re-base and send the final changes

I think I changed too much since then and I can not see your review

[farhadrclass]

@dpo I added more tests to make sure the codecov passes

[tmigot]

LGTM @farhadrclass !
Minor comments, don't add comments line if they don't bring extra information. I tried to details a little bit to illustrate.
Also, I think you didn't use the formatter.

[Copilot]

Pull request overview

Copilot reviewed 6 out of 7 changed files in this pull request and generated 2 comments.

Comments suppressed due to low confidence (2)

ext/LinearOperatorsOpNormExt.jl:134

• On failure to converge, opnorm_svd returns NaN as a Float64 literal, which makes the return type inconsistent for Float32/ComplexF32 operators. Return a NaN value of the appropriate real element type so callers (and inference) don’t see type instability when success == false.

  end

  return NaN, false
end

src/utilities.jl:320

• The PR title/description mention adding an opnorm implementation, but the public API added here is estimate_opnorm (exported) with no visible LinearAlgebra.opnorm(::AbstractLinearOperator, ...) method. If the intent is to let users call opnorm(op) directly, consider adding the appropriate LinearAlgebra.opnorm method (possibly delegating to estimate_opnorm) or updating the PR description/docs to match the actual API being introduced.

"""
    estimate_opnorm(B::AbstractLinearOperator; kwargs...)

Compute an estimate of the operator 2-norm (largest singular value) of a linear operator `B`.

This method dispatches to efficient algorithms depending on the properties and size of `B`:
- **Non-standard element types** (e.g., `BigFloat`, `Float16`): Always uses `TSVD.tsvd` as the fallback, since ARPACK only supports standard 32-bit and 64-bit floating-point types.
- **Small operators** (dimension ≤ `tiny_dense_threshold`): Attempts to convert `B` to a dense `Matrix` and uses direct LAPACK routines (`LinearAlgebra.eigen` if Hermitian, `LinearAlgebra.svd` otherwise).
- **Large, standard-type operators**:
    - If `ishermitian(B)`: Uses `Arpack.eigs` to find the eigenvalue with the largest magnitude.
    - Otherwise: Uses `Arpack.svds` to find the largest singular value.

**Note:** This function allocates memory. It requires `Arpack.jl` and `TSVD.jl` 
(and `GenericLinearAlgebra.jl` for generic types) to be loaded.

# Arguments
- `B::AbstractLinearOperator`: The linear operator to analyze.

# Keyword Arguments
- `max_attempts::Int=3`: Maximum number of retries for iterative solvers if convergence fails, doubling the Krylov subspace dimension (`ncv`) each time.
- `tiny_dense_threshold::Int=5`: If the minimum dimension of `B` is less than or equal to this threshold, it attempts to use direct dense LAPACK routines.
- `kwargs...`: Additional optional keyword arguments passed to the underlying iterative routines (`Arpack.eigs`, `Arpack.svds`, or `TSVD.tsvd`).

# Returns
- A tuple `(norm, success)` where:
    - `norm` is the estimated operator 2-norm of `B` (largest singular value or eigenvalue in absolute value).
    - `success` is a boolean indicating whether the iterative method (if used) reported successful convergence.
"""
function estimate_opnorm end

[tmigot]

@farhadrclass this is a good comment to adress

[farhadrclass]

@tmigot I updated the code and make sure the formatter run
also I fix the NaN type

Thanks for catching them