Fix MatrixDepot benchmark CI failures and improve error handling

[ChrisRackauckas-Claude]

Summary

• Fixes CI stall issues in MatrixDepot benchmark that caused PR Another MatrixDepot.jmd size bump #1035 to fail
• Implements graceful error handling to prevent huge error dumps
• Adds progress tracking with heartbeats to prevent CI timeouts

Problem

PR #1035 attempted to increase the matrix size limit from 500 to 5000, but the CI system stalled because:

1. Matrix factorization failures printed huge error stacktraces, flooding the logs
2. No progress indication made CI think the job was frozen
3. The benchmark output page became unreadable due to error dumps

Solution

This PR implements comprehensive improvements:

1. Graceful Error Handling

• Wraps individual algorithm benchmarks in try-catch blocks
• Records NaN for failed algorithms without printing full stacktraces
• Only logs brief error type information instead of full dumps

2. Progress Tracking System

• Adds heartbeat messages every 30 seconds to show CI the job is still running
• Progress updates every 10 matrices showing:
  • Current matrix number and percentage complete
  • Running counts of successful/failed/skipped matrices
• Final summary with total runtime and statistics

3. Conservative Size Limit

• Increases limit from 100 to 1500 (more conservative than Another MatrixDepot.jmd size bump #1035's 5000)
• Tracks skipped matrices separately
• Allows benchmarking larger matrices while avoiding CI timeouts

4. Early Termination

• Stops benchmark if >100 matrices fail to prevent endless failures
• Prevents CI timeout from excessive failed attempts

5. Better Logging

• Uses @info, @warn, @debug for appropriate log levels
• Flushes stdout/stderr regularly for real-time CI updates
• Summarizes failed matrices at the end (up to 20 shown)

Testing

Tested locally with subset of matrices - error handling and progress tracking work correctly.

Related Issues

• Fixes the CI failure from PR Another MatrixDepot.jmd size bump #1035
• Makes benchmark output page readable by eliminating error spam

🤖 Generated with Claude Code