refactor energy

[yunfanzhou]

• Refactor Function class. a Function can be written as f(x) where the "x" is the input variable. In our implementations, "x" will be represented as an object of the Simplex type (a tuple + the cell type). The member function get_value(x) will return the value of f(x).

• Refactor DifferentaibleFunction class. This is a child class of Function class. It will have the functions for differentiations: get_grad(x), get_hess(x).

• PSF can be written as psf(pi), where pi is the domain the function is defined on. PSF is no longer a child class of Function since the domain is different

• PSDF inherits from only PSF. The per simplex differentials take two arguments: the domain and the variable.We defineget_grad(pi, x) for example, where pi is the domain, x is the variable

• LocalFunction has a pointer to PSF as a member variable. The member function is get_value(x), where the variable x is an object of the Simplex class that holds the information of the primitive type of the variable

• LDF is a child class of LocalF and DiffF

• add get_variable function. This polymorphic function has two APIs: i) have a single domain_simplex as the argument and return three coordinates of double type. ii) have domain_simplex and variable_simplex as arguments and return three coordinate of DScalar autodiff type, where the variable that the function is differentiated wrt has the gradient bit in the DScalar type flipped to 1. This function stays in AutoDiffFunction class for now

[yunfanzhou]

1. In AutodiffFunction: change get_value_autodiff to get_function_autodiff, since this member function de facto encodes the Function defined over a specific domain wrt the variable using the autodiff convention. The function signature is
   get_function_autodiff(const Simplex& domain_simplex, const Simplex& variable_simplex)