Ku Pe v1.1

#include "stdafx.h"
#include <iostream>
#include <fstream>

//for this task matrix D is 4x4, c 4x1, A 2x4, b 2x1, delta 4x4
//knowing that the size of simplex is defined as 6x17 (last column for matrices b and c)

static float D[4][4];
static float c[4];
static float A[2][4];
static float b[2];
static float delta[4][4];
static float simplex[6][17];

//function creating matrix D basing on entered coefficients staying near x1^2, x2^2 and x1x2
void D_initializer()
{
	std::cout << "Filling the D matrix." << std::endl;
	for (int i = 0; i < 4;i++)//initially filling with 0's
	{
		for (int j = 0;j < 4;j++)
		{
			D[i][j] = 0.0;
		}
	}
	std::cout << "Enter coefficient of x1 square: ";
	std::cin >> D[0][0];
	std::cout << "Enter coefficient of x2 square: ";
	std::cin >> D[1][1];
	std::cout << "Enter coefficient of product x1*x2: ";
	std::cin >> D[0][1];
	D[0][1] = D[0][1] / 2;//the value of x1*x2 multiplication happen twice, so it has to be divided by two
	D[1][0] = D[0][1];
	//in other positions are 0's
}

//function showing on the content of the matrix D on the console window
void D_printer()
{
	std::cout << "Matrix D" << std::endl;
	for (int i = 0;i < 4;i++)
	{
		for (int j = 0;j < 4;j++)
		{
			std::cout << D[i][j] << "\t";
		}
		std::cout << std::endl;
	}
}

//function D checks if matrix is symmetric and nonnegatively defined; if it is returns 1, otherwise returns 0;
bool D_checker()
{
	for (int i = 0;i < 4;i++)//is it symmetrical?
	{
		for (int j = i;j < 4; j++)
		{
			if(D[i][j]!=D[j][i])
			{
				std::cout << "Matrix D is not simmetrical" << std::endl;
				return 0;
			}
		}
	}
	if ((D[0][0] * D[1][1] - D[0][1] * D[1][0]) < 0)//to check if it is nonnegatively defined in this case, it is necessary to check if 2x2
	{
		std::cout << "Matrix D is negatively defined" << std::endl;
		return 0;
	}
	return 1;
}

void C_initializer()
{
	std::cout << "Enter coefficient of x1: ";
	std::cin >> c[0];
	std::cout << "Enter coefficient of x2: ";
	std::cin >> c[1];
	c[3] = 0;
	c[4] = 0;
}

//function showing on the content of the matrix c on the console window
void C_printer()
{
	std::cout << "Matrix c" << std::endl;
	for (int i = 0; i < 4;i++)
	{
		std::cout << c[i] << std::endl;
	}
}

void Ab_initializer()
{
	bool inequality;
	for (int i = 0;i < 2;i++)
	{
		std::cout << "Does the inequality sign in "<<i+1<<". constraint is =<? (1-yes, 0-no): ";
		std::cin >> inequality;
		if (inequality)
		{
			A[i][i+2] = 1;
		}
		else
		{
			A[i][i+2] = -1;
		}
		A[i][3 - i] = 0;
		std::cout << "Enter coefficient of x1 in " << i+1 << ". constraint: ";
		std::cin >> A[i][0];
		std::cout << "Enter coefficient of x2 in " << i+1 << ". constraint: ";
		std::cin >> A[i][1];
		std::cout << "Enter value of b in " << i+1 << ". constraint: ";
		std::cin >> b[i];
	}
}

//function showing on the content of the matrix A on the console window
void A_printer()
{
	std::cout << "Matrix A" << std::endl;
	for (int i = 0;i < 2;i++)
	{
		for (int j = 0;j < 4;j++)
		{
			std::cout << A[i][j] << "\t";
		}
		std::cout<<std::endl;
	}
}

//function showing on the content of the matrix b on the console window
void b_printer()
{
	std::cout << "Matrix b" << std::endl;
	std::cout << b[0] << std::endl;
	std::cout << b[1] << std::endl;
}

void delta_setter()
{
	for (int i = 0;i < 4;i++)
	{
		for (int j = i;j < 4;j++)
		{
			if (i == j)
			{
				if (c[i] < 0)
				{
					delta[i][j] = -1;
				}
				else
				{
					delta[i][j] = 1;
				}
			}
			else
			{
				delta[i][j] = delta[j][i] = 0;
			}
		}
	}
}

//function showing on the content of the delta matrix on the console window
void delta_printer()
{
	std::cout << "Delta" << std::endl;
	for (int i = 0;i < 4;i++)
	{
		for (int j = 0;j < 4;j++)
		{
			std::cout << delta[i][j] << "\t";
		}
		std::cout << std::endl;
	}
}

void simplex_setter()
{
	for (int i = 0;i < 2;i++)
	{
		for (int j = 0;j < 4;j++)
		{
			simplex[i][j] = A[i][j];
		}
	}

	for (int i = 2;i < 6;i++)
	{
		for (int j = 0;j < 4; j++)
		{
			simplex[i][j] = 2 * D[i - 2][j];
		}
	}

	for (int i = 2;i < 6;i++)
	{
		for (int j = 4; j < 6;j++)
		{
			simplex[i][j] = -A[j - 4][i - 2];
			simplex[i][j+2] = A[j - 4][i - 2];
		}
	}

	for (int i = 2;i < 6;i++)
	{
		for (int j = 8;j < 12;j++)
		{
			if (j == (i+6))
			{
				simplex[i][j] = -1;
			}
			else
			{
				simplex[i][j] = 0;
			}
		}
	}

	for (int i = 2;i < 6;i++)
	{
		for (int j = 12;j < 16;j++)
		{
			simplex[i][j] = delta[i - 2][j - 12];
		}
	}

	for (int i = 0;i < 2;i++)
	{
		simplex[i][16] = b[i];
	}

	for (int i = 2;i < 6;i++)
	{
		if (c[i - 2] != 0)
		{
			simplex[i][16] = -c[i - 2];
		}
		else
		{
			simplex[i][16] = c[i - 2];
		}
	}

	for (int j = 4;j < 16;j++)
	{
		simplex[0][j] = 0;
		simplex[1][j] = 0;
	}
}

//function showing on the content of the simplex tableaux on the console window
void simplex_printer()
{
	std::cout << "Simplex" << std::endl;
	for (int i = 0;i < 6;i++)
	{
		for (int j = 0;j < 17;j++)
		{
			std::cout << simplex[i][j] << "  ";
		}
		std::cout<<std::endl;
	}
}

//function writing on the content of the simplex tableaux into "input.txt" file
void output_creator()
{
	std::ofstream output;
	output.open("input.txt");
	for (int i = 0;i < 6;i++)
	{
		for (int j = 0;j < 17;j++)
		{
			output << simplex[i][j] << "  ";
		}
		output << std::endl;
	}
	output.close();
}

int main()
{
	std::cout << "PROBLEM OF MINIMIZATION" << std::endl;
	D_initializer();
	if (D_checker())
	{
		D_printer();
		C_initializer();
		C_printer();
		Ab_initializer();
		A_printer();
		b_printer();
		delta_setter();
		delta_printer();
		simplex_setter();
		simplex_printer();
		output_creator();
		std::cout << "Simplex succesfully created. Result is written in \"input.txt\" file." << std::endl;
	}
	else
	{
		std::cout << "Unnable to create simplex. Check wether given quadratic problem is solvable by aim of constructing matrix D or all data was entered correctly." << std::endl;
	}
	system("pause");
    return 0;
}