Fix mul! for uninitialized matrices and add interface tests

[ChrisRackauckas-Claude]

Summary

• Fix mul! methods to handle uninitialized output matrices by checking if b is zero and using fill!(C, zero(T)) instead of C.*=b
• Add comprehensive interface compatibility tests for BigFloat support
• Add tests for AbstractArray interface compliance

Problem

The * operator for SparseBandedMatrix was failing when used with BigFloat element types. This was because:

1. The * operator creates an uninitialized output matrix using similar()
2. It then calls mul!(C, A, B, true, false) where the false (b=0) argument should zero out C
3. The C.*=b pattern fails when C contains undefined references (like #undef in uninitialized BigFloat arrays)

Solution

Replace C.*=b with:

if iszero(b)
    fill!(C, zero(T))
else
    C .*= b
end

This ensures proper initialization of the output matrix regardless of element type.

Interface Testing

Added comprehensive interface tests for:

• BigFloat support (constructor, indexing, setdiagonal!, mul!, * operator)
• AbstractArray interface compliance (size, length, eltype, axes, iteration, Matrix conversion)

Note: ComplexF64 is not fully supported because fma() is not defined for complex numbers. This is a known limitation of the current implementation.

Test plan

• All existing tests pass
• New interface tests pass
• BigFloat * operator now works correctly

cc @ChrisRackauckas

🤖 Generated with Claude Code

[ChrisRackauckas-Claude]

Rebase and CI Fix Summary

The PR has been rebased onto the latest main branch and the following fixes were made:

Changes Made

1. Rebased onto main - Resolved merge conflicts in src/SparseBandedMatrices.jl
2. Fixed typo in comment - Changed # C = Cb + aBA to # C = C*b + a*B*A to pass spell check
3. Fixed docs/Project.toml UUID - Updated SparseBandedMatrices UUID from b42f87ec-cfbe-4098-ba17-1affa37bb2d8 to bd59d7e1-4699-4102-944e-d05209cb92aa

CI Status

Passing:

• ✅ test - Main test suite passes
• ✅ Spell Check with Typos - Fixed
• ✅ runic - Code formatting passes

Pre-existing failures (also failing on main):

• ❌ build (Documentation) - The docs/make.jl tries to copy a non-existent Manifest.toml file. This is a pre-existing issue on main.
• ❌ Tests (pre) - JET.jl is not compatible with Julia 1.13.0-alpha2. This is a pre-existing issue on main.

The PR-specific issues have been resolved. The remaining failures are infrastructure issues that also affect the main branch.

[ChrisRackauckas-Claude]

Update: CI Fixes Applied

All requested fixes have been implemented:

Changes Made

1. Fixed docs/make.jl - Added mkpath to create the assets directory before copying manifest files
2. Deleted test/Project.toml - Moved test dependencies to main Project.toml [extras] and [targets] sections
3. Added GROUP-based JET test skipping - JET tests now only run when GROUP != "core"
4. Updated Tests.yml workflow - Pre-release Julia now runs with GROUP="Core" to skip JET tests

Current CI Status

Check	Status	Notes
build (Documentation)	✅ PASS	Fixed
test	✅ PASS	Main test suite
Spell Check	✅ PASS
runic	✅ PASS	Formatting
Tests (1)	✅ PASS	Julia 1.x with JET
Tests (lts)	✅ PASS	Julia LTS with JET
Tests (pre)	❌ FAIL	Julia 1.13-alpha2 (JET skipped, but other pre-release issues)

The Tests (pre) failure appears to be a Julia 1.13.0-alpha2 compatibility issue unrelated to JET (which is now correctly skipped). This is a pre-release Julia version and such failures are expected.