[ViralBShah]

cond(A, 1) and cond(A, Inf) of a singular sparse matrix throw SingularException. Dense cond returns Inf for these.

using SparseArrays, LinearAlgebra
for A in ([1.0 2; 3 6], [1.0 0; 2 0]), p in (1, Inf)
    println("cond(sparse($A), $p) = ", try cond(sparse(A), p) catch e; sprint(showerror, e) end)
end

Before

cond(sparse([1.0 2.0; 3.0 6.0]), 1) = SingularException: matrix is singular; factorization failed. Zero pivot found at index 0
cond(sparse([1.0 2.0; 3.0 6.0]), Inf) = SingularException: matrix is singular; factorization failed. Zero pivot found at index 0
cond(sparse([1.0 0.0; 2.0 0.0]), 1) = SingularException: matrix is singular; factorization failed. Zero pivot found at index 2
cond(sparse([1.0 0.0; 2.0 0.0]), Inf) = SingularException: matrix is singular; factorization failed. Zero pivot found at index 2

After

cond(sparse([1.0 2.0; 3.0 6.0]), 1) = Inf
cond(sparse([1.0 2.0; 3.0 6.0]), Inf) = Inf
cond(sparse([1.0 0.0; 2.0 0.0]), 1) = Inf
cond(sparse([1.0 0.0; 2.0 0.0]), Inf) = Inf

cond estimates the norm of the inverse with opnormestinv, which solves with factorize(A). A singular matrix makes lu throw. A triangular or diagonal matrix gets no factorization object, so its solve throws. issuccess on lu(A; check = false) would only cover the lu branch, so cond catches SingularException instead, as dense cond does. It then returns convert(float(real(eltype(A))), Inf), the same value and type as dense. A Float32 matrix gives Inf32. The inferred return types are unchanged.

A singular Hermitian matrix still throws ZeroPivotException from the LDLt in factorize. That exception is not caught, because on main a nonsingular indefinite matrix such as [0.0 1; 1 0] throws it too. #1116 makes that path fall back to lu, which throws SingularException. With both PRs a singular Hermitian matrix also gives Inf; I checked this on #1116's branch with this change applied. This PR does not depend on #1116.

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 94.70%. Comparing base (66a7b5c) to head (0b47749).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1126      +/-   ##
==========================================
- Coverage   94.70%   94.70%   -0.01%     
==========================================
  Files          16       16              
  Lines       10387    10385       -2     
==========================================
- Hits         9837     9835       -2     
  Misses        550      550              

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