Add error reduction function for selective component error calculation

[ChrisRackauckas-Claude]

Summary

This implements the feature requested in issue #5, allowing users to specify a custom reduction function to compute errors only on specific components of a solution rather than all components.

This addresses the use case where users want to measure error only on specific indices (e.g., the third component of a system like the Quorum Sensing problem mentioned in the issue).

Changes

• Add default_reduction function (identity) as the default behavior
• Add reduction keyword argument to appxtrue functions (both TestSolution and AbstractODESolution variants)
• Pass reduction through to WorkPrecision, WorkPrecisionSet, Shootout, ShootoutSet, and analyticless_test_convergence functions
• Add comprehensive tests for the reduction functionality
• Export default_reduction for user extensibility

Example Usage

# Compute error only on the third component of a system
errsol = appxtrue(sol, ref_sol; reduction = x -> x[3])

# Compute error only on first two components
wp = WorkPrecision(prob, alg, abstols, reltols;
    appxsol = test_sol, reduction = x -> x[1:2])

# Compute error on a function of the solution
shoot = Shootout(prob, setups; 
    appxsol = test_sol, reduction = x -> sum(x))

Test Results

Testing error reduction feature...
✓ default_reduction export test passed
✓ appxtrue default test passed
✓ appxtrue custom reduction test passed
✓ appxtrue TestSolution test passed
✓ WorkPrecision reduction test passed
✓ WorkPrecisionSet reduction test passed
✓ Shootout reduction test passed

Error values with different reductions:
  Default (all components): final = 3.195463769811724e-6
  First component only:     final = 5.23092241744294e-6
  Second component only:    final = 1.1600051221805074e-6

✓ All error reduction tests passed!

Test plan

• Verify default_reduction is identity function
• Test appxtrue with TestSolution and AbstractODESolution
• Test WorkPrecision with custom reduction
• Test WorkPrecisionSet with custom reduction
• Test Shootout with custom reduction
• Verify different reductions produce different error values

Closes #5

@ChrisRackauckas - Please review this implementation.

🤖 Generated with Claude Code

[ChrisRackauckas-Claude]

I have fixed the issue where the keyword was being passed to in for . This was because was not explicitly captured in the function signature for (unlike other methods). I have also applied the reduction function to the error calculation in that method for consistency.