pozdneev

!!---------------------------------------------------------------------------
! Gaussian elimination with partial pivoting using straightforward formulas
! and Fortran 90/95 features
!!---------------------------------------------------------------------------
! gfortran -ffree-form -Wall -Wextra -fopenmp
!!---------------------------------------------------------------------------
! [1] J. Demmel "Numerical Linear Algebra"
! [2] N. J. Nigham "Gaussian Elimination"
!
!   ELIMINATION

pozdneev

! Gaussian partitioned elimination without pivoting using straightforward
! formulas and BLAS routines
!!---------------------------------------------------------------------------
! gfortran -ffree-form -Wall -Wextra -lblas -fopenmp
!!---------------------------------------------------------------------------
!
! [1] J. Demmel "Numerical Linear Algebra"
! [2] N. J. Nigham "Gaussian Elimination"
!
!   ELIMINATION

pozdneev

! Gaussian elimination without pivoting: straightforward formulas,
! Fortran 90/95 features, BLAS routines
!!---------------------------------------------------------------------------
! gfortran -ffree-form -Wall -Wextra -lblas -fopenmp
!!---------------------------------------------------------------------------
!
! [1] J. Demmel "Numerical Linear Algebra"
! [2] N. J. Nigham "Gaussian Elimination"
!
!   ELIMINATION

pozdneev

% Border matrix
% latex filename.tex
% dvipng -T tight -D 150 filename.dvi

\documentclass{article}

\usepackage{kbordermatrix}

\begin{document}
\[

pozdneev

! Cholesky decomposition without pivoting: straightforward formulas,
! Fortran 90/95 features and BLAS routines
!!---------------------------------------------------------------------------
! gfortran -ffree-form -Wall -Wextra -lblas -fopenmp
!!---------------------------------------------------------------------------
program chol
!!---------------------------------------------------------------------------
    use omp_lib, only: omp_get_wtime

    implicit none

pozdneev

! Cholesky partitioned decomposition without pivoting: straightforward
! formulas and BLAS routines
!!---------------------------------------------------------------------------
! gfortran -ffree-form -Wall -Wextra -lblas -fopenmp
!!---------------------------------------------------------------------------
program chol
!!---------------------------------------------------------------------------
    use omp_lib, only: omp_get_wtime

    implicit none

pozdneev

/*
 * This example demonstrates the significance of understanding the moments
 * of virtual function table creation, filling, and "deallocation".
 */

#include <iostream>

class A {
    public:
        ~A() {

pozdneev

// The program demonstrates concepts of templates and multiple inheritance.
// It is allowed to inherit from template classes.
// The inherited classes are allowed to add new template parameters.
//
// g++ -Wall -Wextra templates-and-multiple-inheritance.cpp

#include <iostream>

template <class T>
struct A {

pozdneev

// Template specialization allows us to (a) provide different implementation
// based on a template parameter; (b) add extra methods to one templated
// class based on its type, but not to other templates.
//
// Inspired by
// http://www.cprogramming.com/tutorial/template_specialization.html
//
// Here, we demonstrate template specialization for a vector container.
// Vector of boolean values can be optimized for space allocation.
// Vector of boolean values can have an extra method that negates all

pozdneev

! Demonstration of various rounding/truncation methods in Fortran
!
! ## Compilation line:
! gfortran -Wall -Wextra rounding.F90
!
! ## Output:
!          a:       -1.6    -1.4     1.4     1.6
!     int(a):         -1      -1       1       1
!    nint(a):         -2      -1       1       2
! ceiling(a):         -1      -1       2       2