NXV4 JINRLIB - MTX class

JOINT INSTITUTE FOR NUCLEAR RESEARCH

JINRLIB Program Library

VEC / MTX - 3D geometry utility

Authors: Mihai Tiberiu Dima, Maria Dima

Highlights

The 2 classes field embodiments of 3D-vectors (vec) and 3D-matrices (mtx) in a high performance slimline templated polymorphic package - part of the NXV4 "Math_on_Paper Software" concept, allowing users to work with the computer almost as with pen on paper.

Example mtx<cpx<int>> Lz(0, i, 0,
              -i, 0, 0
             0, 0, 0)
    double u = 1.0 ;
      auto z = u+Lz ;

Evidently, z will be instantiated as mtx<cpx<double>> - transparent to the user (grace to the class' type-calculator returning the appropriate type from the "+" operator):

double + mtx<cpx<int>> = mtx<cpx<double>>

The classes are move-semantix compliant, for superior speed, and slim (all strictly non-class members being implemented as friend operators and functions - for a total of over 2836 vec and 5084 mtx instantiations of the usual algebraic/logical operators).

The classes overload the cout operator to display wave-vectors and spin operators in a pedantic manner.

Example cout << boolalpha << Lz << endl ;
     cout << z << endl ;
     cout << noboolalpha << z << endl;
     cout << boolalpha << vec<cpx<int>>(3,i,-2) << endl;

will display: | 0 i 0 |
         | -i 0 0 |.mtx<cpx.int>
      | 0 0 0 |

   | 1 i 0 |
         | -i 1 0 |.mtx<cpx.int>
      | 0 0 1 |

   | 1 i 0 |
         | -i 1 0 |
      | 0 0 1 |

   3|e1>+i|e2>-2|e3>.vec<cpx.int>

The mtx class implements exp and log functions, as well as diagonalisation and eigen-values/vec's, itself and vec together with the full complement of algebraic and logical operators for instantiations with: int, float, double, long double, cpx<int>, cpx<float>, cpx<double>, cpx<long double>.

Documentation - manual: vec and mtx, with main & application tutorials

Downloads - C++ libs^⁽¹⁾ as *.tgz, *.zip and examples: 1, 2, 3, 4, appl

^⁽¹⁾gcc-4.4.7 20120313 //... linux-2.6.32-504.12.2.el6.x86_64

This project was realised in the framework of the 05-6-1119-2014/2023 "New Investigation Tools in Computational Physics" research theme, of the Meshcheryakov Laboratory of Information Technologies JINR.