Implementations of basic algebraic routines in high-level programming languages

U današnjem tehnološkom dobu znanost i industrija vape za računalnom snagom i bore se s barijerama, raznim tehnološkim ograničenjima i ostalim ograničavajućim faktorima. U toj se borbi javlja sve veća potreba za optimizacijom postojećeg hardware-a i software-a, a sve je manji fokus na čekanju ”novog” tehnološkog otkrića i daljnjeg razvoja čvrstog dijela računala. U toj potrebi za optimizacijom konstantno su se pojavljivala nova rješenja i nova poboljšanja, a jedno od takvih novih rješenja je bio skup bazičnih algebarskih rutina - BLAS. U ovom radu, nakon kratkog uvoda u algoritme i programske jezike, dano je nekoliko primjera algoritama i njihove implementacije u odabranim programskim jezicima više razine: Fortranu i C-u. Opisan je rad s matricama i determinantama, te je dan primjer računanja determinante i njegova implementacija koristeći odabrane programske jezike. Drugi, ujedno i glavni, dio rada obuhvaća osnove BLAS-a, njegove razine i raščlambu određene rutine treće razine. Prikazana je implementacija BLAS-a pomoću softverskog rješenja LAPACK koji implementira spomenutu rutinu. Na primjeru računanja determinante matrice proizvoljne dimenzije, koristeći algoritam napisan bez korištenja bazičnih algebarskih rutina i sa njima, će se pokazati ubrzanje izvršavanja našeg primjera. Na kraju rada je navedeno nekoliko primjera korištenja programskih jezika viših razina i navedena je mogućnost korištenja BLAS-a u sklopu nastave.In today’s technological age science and industry are struggling with computer strength, barriers, various technological limitations and other limiting factors. In this struggle there is an increasing need for optimization of existing hardware and software. There is less focus on waiting for a ”new” technological breakthrough and further development of a solid part of the computer. In this need for optimization, new solutions and new improvements were constantly emerging, and one of these new solutions was a set of basic algebraic routines - BLAS. This paper contains short introduction to algorithms and programming languages and several examples of algorithms, their implementation in selected higher-level programming languages: Fortran and C.Work with matrices and determinants is described, and it is given an example of calculating determinants and their implementation using selected programming languages. The second, and also the main, part of the paper encompasses the basics of BLAS, its level and the breakdown of certain third-level routines. BLAS is shown using the LAPACK software solution that implements the mentioned routine. In the example of calculating the matrix determinant of an arbitrary dimension there will be shown the acceleration of execution of our example by using an algorithm written with or without basic algebraic routines. At the end of this paper are few examples of using higher level programming languages and BLAS that can be used as part of curriculum