Daily Test Coverage Improver - Add comprehensive tests for advanced LinearAlgebra functions

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Summary

This PR adds comprehensive unit tests for advanced LinearAlgebra functions that previously had 0% or very low test coverage, significantly improving overall project coverage.

• LinearAlgebra functions: 42 new tests covering LU decomposition, matrix solvers, inverse, determinant, pseudo-inverse, and leverage calculations
• Tests cover matrix operations, edge cases, mathematical properties, and error conditions
• All 174 tests pass (132 original + 42 new tests)

Problems Found

1. Advanced LinearAlgebra functions had 0% or minimal test coverage:

   • solveTriangularLinearSystems (matrix version) - untested
   • luDecompose - untested
   • solveLinearSystem and solveLinearSystems (LU-based) - untested
   • inverse - untested
   • determinant - untested
   • pseudoInvers - untested
   • hatMatrix, leverage, leverageBy - untested

2. Overall project coverage was low at 4.83% (99/2047 lines)

3. Many advanced matrix operations had no test coverage despite being critical for numerical linear algebra

Actions Taken

1. Created LinearAlgebraAdvancedTests.fs with 42 comprehensive tests covering:

   SolveTriangularLinearSystems (5 tests): Matrix version of triangular system solver

   • Multiple RHS columns
   • Lower and upper triangular systems
   • Identity matrix verification
   • Error handling (non-square, dimension mismatch)

   LU Decomposition (6 tests):

   • 2x2 and 3x3 matrix decomposition
   • Verification of PA = LU property
   • L diagonal verification (all ones)
   • U upper triangular verification
   • Identity matrix edge case
   • Error handling (non-square)

   Solve Linear Systems with LU (10 tests):

   • Vector version: 2x2 and 3x3 systems, identity matrix, error handling
   • Matrix version: Multiple RHS, reconstruction verification, error handling

   Matrix Inverse (5 tests):

   • 2x2 and 3x3 matrix inversion
   • A * A^-1 = I verification
   • Identity inverse
   • Involution property: (A^-1)^-1 = A
   • Error handling (non-square)

   Determinant (5 tests):

   • Identity determinant
   • 2x2 and 3x3 matrices
   • Singular matrix (det = 0)
   • Error handling (non-square)

   Pseudo-Inverse (4 tests):

   • Overdetermined systems (tall matrices)
   • Underdetermined systems (wide matrices)
   • Square invertible matrices
   • Identity matrix edge case

   Hat Matrix and Leverage (7 tests):

   • Idempotency: H*H = H
   • Symmetry: H = H^T
   • Dimension verification
   • Leverage calculation from hat matrix
   • Direct leverage computation
   • Consistency between methods
   • Non-negativity of leverages

2. Updated FsMath.Tests.fsproj to include the new test file

3. All 174 tests pass successfully

Test Coverage Results

Metric	Before	After	Change
Overall Line Coverage	4.83%	6.49%	+1.66%
Lines Covered	99/2047	133/2047	+34 lines
Branch Coverage	1.56%	2.09%	+0.53%
Branches Covered	83/5307	111/5307	+28 branches
Total Tests	132	174	+42 tests

Coverage Improvement: +34.4% relative increase in line coverage

LinearAlgebra Module Specific Coverage

The new tests significantly improved coverage for:

• luDecompose - now tested
• solveLinearSystem / solveLinearSystems - now tested
• inverse - now tested
• determinant - now tested
• pseudoInvers - now tested
• hatMatrix, leverage, leverageBy - now tested
• solveTriangularLinearSystems (matrix version) - now tested

Replicating the Test Coverage Measurements

To replicate these measurements:

# Clean previous coverage
rm -rf ./coverage ./coverage-new

# Build the project
dotnet build

# Run tests with coverage (baseline on main)
git checkout main
dotnet test tests/FsMath.Tests/FsMath.Tests.fsproj \
  --no-build \
  --collect:"XPlat Code Coverage" \
  --results-directory ./coverage \
  -- DataCollectionRunSettings.DataCollectors.DataCollector.Configuration.Format=cobertura

# Extract baseline metrics
BASELINE_FILE=$(find ./coverage -name "coverage.cobertura.xml" | head -n 1)
grep -oP 'line-rate="\K[^"]*' "$BASELINE_FILE" | head -n 1  # Should show 0.0483
grep -oP 'lines-covered="\K[^"]*' "$BASELINE_FILE" | head -n 1  # Should show 99

# Run tests with coverage (on this branch)
git checkout test-coverage/linear-algebra-advanced-20251012
dotnet build
dotnet test tests/FsMath.Tests/FsMath.Tests.fsproj \
  --no-build \
  --collect:"XPlat Code Coverage" \
  --results-directory ./coverage-new \
  -- DataCollectionRunSettings.DataCollectors.DataCollector.Configuration.Format=cobertura

# Extract new metrics
NEW_FILE=$(find ./coverage-new -name "coverage.cobertura.xml" | head -n 1)
grep -oP 'line-rate="\K[^"]*' "$NEW_FILE" | head -n 1  # Should show 0.0649
grep -oP 'lines-covered="\K[^"]*' "$NEW_FILE" | head -n 1  # Should show 133

# Verify test count increased
dotnet test tests/FsMath.Tests/FsMath.Tests.fsproj --no-build | grep "Passed"  # Should show 174 tests (+42)

Possible Other Areas for Future Improvement

Based on the coverage report and code analysis, the following areas have 0% or very low coverage and could benefit from additional tests:

High Priority (Foundation - 0% coverage, not inline):

1. Algebra/SVD.fs (0% coverage) - Singular Value Decomposition
2. Algebra/EVD.fs (0% coverage) - Eigenvalue Decomposition
3. Algebra/MatrixExt.fs (0% coverage) - Matrix extension methods
4. AlgTypesTopLevelOps.fs (0% coverage) - Top-level utility functions
5. Vector.fs (partial coverage) - Core vector type operations beyond basics

Medium Priority (Inline but valuable to test):

6. SpanPrimitives.fs (0% coverage, inline) - Low-level SIMD operations (PRs Daily Test Coverage Improver - Add tests for VectorOps operators #15, Daily Test Coverage Improver - Add tests for SpanMath operations #17 tested related modules)
7. SIMDUtils.fs (0% coverage, partial inline) - SIMD detection and utilities

Also Possible:

8. More functions in Algebra/LinearAlgebra.fs - There are still untested functions like symmetricEigenspectrum
9. Matrix.fs - Additional matrix operations beyond what's currently tested

Recommendation: The next logical areas would be Algebra/SVD.fs and Algebra/EVD.fs as they provide advanced matrix factorizations that build upon the LU/QR decompositions now better covered.

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Execution Details (bash commands, web searches, web pages fetched)

Bash Commands Run:

• git checkout -b test-coverage/linear-algebra-advanced-20251012
• find tests/FsMath.Tests -name "*LinearAlgebra*" (to check existing tests)
• dotnet build tests/FsMath.Tests/FsMath.Tests.fsproj (multiple times during development)
• dotnet test tests/FsMath.Tests/FsMath.Tests.fsproj --no-build (multiple times to verify tests pass)
• dotnet test tests/FsMath.Tests/FsMath.Tests.fsproj --no-build --collect:"XPlat Code Coverage" --results-directory ./coverage-new
• Coverage extraction and comparison commands
• git add tests/FsMath.Tests/LinearAlgebraAdvancedTests.fs tests/FsMath.Tests/FsMath.Tests.fsproj
• git commit -m "Add comprehensive tests for advanced LinearAlgebra functions"

Web Searches:

None performed

Web Pages Fetched:

None fetched

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AI generated by Daily Test Coverage Improver

AI generated by Daily Test Coverage Improver