Verify Branch and Load Jacobians computed with Sparse::Variable

[nkoukpaizan]

Description

This adds tests for Branch and Load Jacobians.

Proposed changes

Added a Jacobian test for BranchTest and LoadTest. Using Gridkit::Sparse::Variable, we track model residual dependencies and compute the values of the Jacobian. The result is compared to the analytical Jacobian in std::map format. The Jacobians are constant matrices in these cases.

Checklist

• All tests pass.
• Code compiles cleanly with flags -Wall -Wpedantic -Wconversion -Wextra.
• The new code follows GridKit™ style guidelines.
• There are unit tests for the new code.
• The new code is documented.
• The feature branch is rebased with respect to the target branch.

[alexander-novo]

Maybe I'm misunderstanding, but wasn't the point of Sparse::Variable that we wouldn't have to write these analyticalJacobian functions manually, and would be able to call e.g. LoadTests<Sparse::Variable>::residual() to compute the same thing?

[nkoukpaizan]

Maybe I'm misunderstanding, but wasn't the point of Sparse::Variable that we wouldn't have to write these analyticalJacobian functions manually, and would be able to call e.g. LoadTests<Sparse::Variable>::residual() to compute the same thing?

This is exactly what is being done here. See for example, load.evaluateResidual(). The point of the analytical Jacobian is to verify the answer we are getting. For a unit test, we need a reference.

[shakedregev]

48%] Building CXX object examples/MatPowerTesting/CMakeFiles/test_parse_gen_row.dir/test_parse_gen_row.cpp.o
In file included from /Users/szb/GridKit_dir/GridKit/examples/MatPowerTesting/test_parse_gen_row.cpp:5:
/Users/szb/GridKit_dir/GridKit/src/Utilities/Testing.hpp:235:30: error: no template named 'map' in namespace 'std'; did you mean 'max'?
  235 |     inline bool isEqual(std::map<IdxT, RealT> a,
      |                         ~~~~~^~~
      |                              max
/opt/homebrew/Cellar/llvm/19.1.7/bin/../include/c++/v1/__algorithm/max.h:29:1: note: 'max' declared here
   29 | max(_LIBCPP_LIFETIMEBOUND const _Tp& __a, _LIBCPP_LIFETIMEBOUND const _Tp& __b, _Compare __comp) {
      | ^
In file included from /Users/szb/GridKit_dir/GridKit/examples/MatPowerTesting/test_parse_gen_row.cpp:5:
/Users/szb/GridKit_dir/GridKit/src/Utilities/Testing.hpp:235:17: error: redefinition of 'isEqual' as different kind of symbol
  235 |     inline bool isEqual(std::map<IdxT, RealT> a,
      |                 ^
/Users/szb/GridKit_dir/GridKit/src/Utilities/Testing.hpp:207:17: note: previous definition is here
  207 |     inline bool isEqual(PowerSystemData::SystemModelData<RealT, IdxT> a,
      |                 ^
/Users/szb/GridKit_dir/GridKit/src/Utilities/Testing.hpp:235:47: error: expected ')'
  235 |     inline bool isEqual(std::map<IdxT, RealT> a,
      |                                               ^
/Users/szb/GridKit_dir/GridKit/src/Utilities/Testing.hpp:235:24: note: to match this '('
  235 |     inline bool isEqual(std::map<IdxT, RealT> a,
      |                        ^
/Users/szb/GridKit_dir/GridKit/src/Utilities/Testing.hpp:237:91: error: expected ';' after top level declarator
  237 |                         const RealT           tol = std::numeric_limits<RealT>::epsilon())
      |                                                                                           ^
      |                                                                                           ;
4 errors generated.

[shakedregev]

I cannot build this code. Details above.

[pelesh]

All tests pass with Clang and GCC builds. Code clean and well commented.