#include "Solver.h"

#include "Gauss.h"

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

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

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

VectAffine Solver::TriangularSystem() const {
	Matrix mat = m_Matrix;
	Gauss::GaussJordan(mat, true, true);

	Solver solver {mat.SubMatrix(0, 0, mat.GetRawCount(), mat.GetColumnCount() - 1)};

	Vect noyau = solver.Kernel();
	Matrix origin = mat.SubMatrix(0, mat.GetColumnCount() - 1, mat.GetRawCount(), 1);

	// on rajoute des 0 si il faut

	Matrix fullOrigin {mat.GetColumnCount() - 1, 1};
	for (std::size_t i = 0; i < mat.GetRawCount(); i++) {
		fullOrigin.at(i, 0) = origin.at(i, 0);
	}

	for (std::size_t i = mat.GetRawCount(); i < mat.GetColumnCount() - 1; i++) {
		fullOrigin.at(i, 0) = 0;
	}

	return {noyau, fullOrigin};
}

std::size_t Solver::Rank() const {
	return Image().GetCardinal();
}