Add dependency-tracking variable data type.

[pelesh]

Add a definition for a variable type that tracks its dependencies. This dependency tracking is helpful when computing e.g. Jacobian sparsity pattern.

For example, consider function template

            template <typename T>
            void residualFunction(std::vector<T>& f,
                                  const std::vector<T>& x,
                                  const std::vector<T>& p)
            {
                const T y = x[0]*x[1];
                
                f[0] = 10.0*(x[1] - x[0]); 
                f[1] = x[0]*(8.0/3.0 - x[2]) - x[1];
                f[2] = y - 28.0*x[2];
            }

Substituting template parameter GridKit::Sparse::Variable<double> would produce a function that computes vector f such that each element of f contains numerical value and the list of elements of x that are used to compute that value. For example, with values of x set as

  x[0]() = 8.0; x[1]() = 20.0; x[2]() = 2.0/3.0;

f[0] would contain double floating point value 120.0 and indices 0 and 1. See here for more details.

This PR only provides dependency tracking data type and a simple unit test.

CC @sklus

[shakedregev]

Add a definition for a variable type that tracks its dependencies. This dependency tracking is helpful when computing e.g. Jacobian sparsity pattern.

For example, consider function template

            template <typename T>
            void residualFunction(std::vector<T>& f,
                                  const std::vector<T>& x,
                                  const std::vector<T>& p)
            {
                const T y = x[0]*x[1];
                
                f[0] = 10.0*(x[1] - x[0]); 
                f[1] = x[0]*(8.0/3.0 - x[2]) - x[1];
                f[2] = y - 28.0*x[2];
            }

Substituting template parameter GridKit::Sparse::Variable<double> would produce a function that computes vector f such that each element of f contains numerical value and the list of elements of x that are used to compute that value. For example, f[0] would contain double floating point value 120. and indices 0 and 1. See here for more details.

This PR only provides dependency tracking data type and a simple unit test.

CC @sklus

Can you explain why the value is 120? I understand the indices.

[shakedregev]

No major comments and tests pass, so I'm approving. I will branch off this to make some quick fixes.

[nkoukpaizan]

The PR works as advertised. It will be helpful to expand the documentation of the functionality, so people won't have to read the paper to understand what's going on.

I am also getting many warnings I did not use to see, but I don't think these are related to this PR, but to an earlier one. e.g.,

In file included from /lustre/orion/scratch/nkouk/stf006/Codes/GridKit/tests/UnitTests/PhasorDynamics/runBranchTests.cpp:1:
In file included from /lustre/orion/scratch/nkouk/stf006/Codes/GridKit/tests/UnitTests/PhasorDynamics/BranchTests.hpp:6:
In file included from /lustre/orion/scratch/nkouk/stf006/Codes/GridKit/src/Model/PhasorDynamics/Branch/Branch.hpp:11:
/lustre/orion/scratch/nkouk/stf006/Codes/GridKit/src/Model/PhasorDynamics/Component.hpp:51:22: warning: 'nnz' overrides a member function but is not marked 'override' [-Winconsistent-missing-override]
        virtual IdxT nnz()

In file included from /lustre/orion/scratch/nkouk/stf006/Codes/GridKit/tests/UnitTests/PhasorDynamics/runBranchTests.cpp:1:
In file included from /lustre/orion/scratch/nkouk/stf006/Codes/GridKit/tests/UnitTests/PhasorDynamics/BranchTests.hpp:6:
In file included from /lustre/orion/scratch/nkouk/stf006/Codes/GridKit/src/Model/PhasorDynamics/Branch/Branch.hpp:11:
/lustre/orion/scratch/nkouk/stf006/Codes/GridKit/src/Model/PhasorDynamics/Component.hpp:56:22: warning: 'hasJacobian' overrides a member function but is not marked 'override' [-Winconsistent-missing-override]
        virtual bool hasJacobian()

[pelesh]

Can you explain why the value is 120? I understand the indices.

Updated PR description to clarify this.