#include "Solver.h"

Solver::Solver(const Matrix& mat) : m_Matrix(mat) {}

Vect Solver::Image() const {
	Matrix result = m_Matrix;
	result.Transpose();
	result.GaussJordan(true);
	result.Transpose();
	return {result};
}

// https://en.wikipedia.org/wiki/Kernel_(linear_algebra)#Computation_by_Gaussian_elimination
Vect Solver::Noyau() const {
	Matrix result = m_Matrix;
	result.Transpose();
	result.Augmenter(Matrix::Identity(result.GetRawCount()));
	result.GaussJordan(true);
	result.Transpose();

	// nombre de colonnes non nulles
	std::size_t origine_colonne = Vect(result.SubMatrix(0, 0, m_Matrix.GetRawCount(), m_Matrix.GetColumnCount())).GetCardinal();

	return {result.SubMatrix(m_Matrix.GetRawCount(), origine_colonne, result.GetRawCount() - m_Matrix.GetRawCount(),
		result.GetColumnCount() - origine_colonne)};
}

std::size_t Solver::Rang() const {
	Vect image = Image();
	return image.GetCardinal();
}