Arithmetic Types

Arithmetic types that can be used in funcy have to fulfil the following requirements:

Requirements

1. Copyable:
   T must be CopyConstructible and CopyAssignable.
2. Multiplication with arithmetic types:
   Given:
   • An object t of type T.
   • An object a of an arithmetic type, such as double or int.
   At least one of the following expressions must be valid:
   • T s = a*t;
   • t *= a;
3. Summation:
   Objects t and s of type T must be summable, i.e. at least one of the following expressions must be valid:
   • T r = s + t;
   • t += s;
4. Multiplication (for matrix types only):
   Compatible matrices t and s must be multipliable, i.e. at least one of the following expressions must be valid:
   • auto r = t*s;
   • t*=s; (for square matrices)
   • auto r = t.rightmultiplany(s); (for DUNE matrices)
5. Access to data:
   Access to the entries of a matrix or vector t via at least one of the following expressions:
   • auto a = t[1][2]; (for matrices) or auto a = t[1]; (for vectors).
   • auto a = t(1,2); (for matrices) or auto a = t(1); (for vectors).
6. Access to number of rows and columns (matrices and vectors):
   
   • Fixed size:
     A specialization of the template classes
     template <class Matrix, class> struct NumberOfRows;
     and
     template <class Matrix, class> struct NumberOfColumns;
     must be provided. For the cases that, for some scalar type S and n,m of type unsigned or int, the employed matrix class is of the form
     • Matrix<n,m>
     • Matrix<S,n,m>
     suitable specializations are available and access to the number of rows and columns is supported without need to do anything. Similar specializations exist for vectors.
   • Dynamic size:
     Access to the number of rows and columns of an object t must be supported via at least one of the following expressions:
     • t.rows() resp. t.cols()
     • t.n_rows resp. t.n_cols

Optional

1. Default-constructible:
   If T is DefaultConstructible then functions that take arguments of type T also a default constructor, else the default constructor is deleted.
2. Construction of the zero matrix:
   If you want to use the functions zero<Matrix>() and unitMatrix<Matrix>(), a specialization of
   template <class Matrix,class> struct Zero;
   must be provided. Suitable implementations exist for the cases that a zero matrix can be created by one of the following expressions:
   • auto zeroMatrix = Matrix(0.);
   • auto zeroMatrix;
zeroMatrix.zeroes();
     

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