#include "Solver.h"

#include "Gauss.h"

static int FirstNotNullElementIndexOnLine(const Matrix& mat, std::size_t line) {
	for (std::size_t i = 0; i < mat.GetColumnCount(); i++) {
		if (!IsEqualZero(mat.at(line, i))) {
			return i;
		}
	}
	return -1;
}

Vect Solver::Image(Matrix&& a_Matrix) const {
	a_Matrix.Transpose();
	Gauss::GaussJordan(a_Matrix, false, false);
	a_Matrix.Transpose();
	return {std::move(a_Matrix)};
}

// https://en.wikipedia.org/wiki/Kernel_(linear_algebra)#Computation_by_Gaussian_elimination
Vect Solver::Kernel(Matrix&& a_Matrix) const {
	std::size_t matrixRawCount = a_Matrix.GetRawCount();
	std::size_t matrixColumnCount = a_Matrix.GetColumnCount();

	a_Matrix.Transpose();
	a_Matrix.Augment(Matrix::Identity(a_Matrix.GetRawCount()));
	Gauss::GaussJordan(a_Matrix, false, true);
	a_Matrix.Transpose();

	// nombre de colonnes non nulles
	std::size_t origine_colonne = Vect(a_Matrix.SubMatrix(0, 0, matrixRawCount, matrixColumnCount)).GetCardinal();

	return {a_Matrix.SubMatrix(
		matrixRawCount, origine_colonne, a_Matrix.GetRawCount() - matrixRawCount, a_Matrix.GetColumnCount() - origine_colonne)};
}

VectAffine Solver::RectangularSystem(Matrix&& a_MatrixA, const Matrix& a_VectorB) const {
	Matrix mat = a_MatrixA;
	mat.Augment(a_VectorB);
	Gauss::GaussJordan(mat, true, true);

	Solver solver;

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

	// on calcule le vecteur qui dirige l'espace affine
	Matrix fullOrigin {mat.GetColumnCount() - 1, 1};
	for (std::size_t i = 0; i < mat.GetRawCount(); i++) {
		int pivot_index = FirstNotNullElementIndexOnLine(mat, i);
		
		if (static_cast<std::size_t>(pivot_index) == mat.GetColumnCount() - 1) {
			// on a une ligne du type 0 = n. Aucune solution !
			return {Matrix {}, Matrix::ColumnVector({0})};
		}

		// ligne entière de 0
		if (pivot_index < 0)
			continue;

		fullOrigin.at(pivot_index, 0) = origin.at(i, 0);
	}

	return {noyau, fullOrigin};
}

std::size_t Solver::Rank(Matrix&& a_Matrix) const {
	return Image(std::move(a_Matrix)).GetCardinal();
}