Fix SCC residuals transfer for linear problems

[ChrisRackauckas-Claude]

Summary

• Fixes issue SCC does not transfer residuals to solution object #706 where residuals were not being transferred to solution object when using SCC algorithm
• Computes residuals for linear problems as resid = A*u - b
• Ensures all residuals are properly computed and transferred to the solution object

Details

Previously, when solving SCC problems that contained LinearProblem components, the residuals were being passed as nothing in the build_linear_solution call. This resulted in a solution object with nothing values in the residuals array.

The fix computes the residuals for linear problems using the formula resid = A*u - b after solving, and passes them to build_linear_solution.

Test plan

• Added a new test case "SCC Residuals Transfer" that verifies:
  • Residuals are not nothing
  • No nothing values exist in the residuals array
  • Residuals have the correct length
  • Residuals are near zero for converged solutions
  • Residuals match manually computed values
• Verified existing tests still pass
• Tested locally with sample SCC problem containing both linear and nonlinear components

🤖 Generated with Claude Code

[ChrisRackauckas-Claude]

Updated the fix based on feedback. The LinearSolution object does have a field, but it's often by default. The updated fix now checks if is and only computes the residuals manually when needed using . This is more robust and handles both cases where the linear solver might or might not provide residuals.

[ChrisRackauckas-Claude]

Updated the fix based on feedback. The LinearSolution object does have a resid field, but it's often nothing by default. The updated fix now checks if sol.resid is nothing and only computes the residuals manually when needed using resid = A*u - b. This is more robust and handles both cases where the linear solver might or might not provide residuals.