#define _CRT_SECURE_NO_WARNINGS

#include <stdio.h>
#include <math.h>

#include <vector>
#include <iostream>
#include <iomanip>

typedef std::vector<double> Vector;
typedef std::vector<std::vector<double>> Matrix;

void fillZeros(Matrix& M, int n)
{
	M.clear();
	for (int i = 0; i < n; ++i)
	{
		M.push_back(std::vector<double>());
		for (int j = 0; j < n; ++j)
			M[i].push_back(0);
	}

}

void printVector(const Vector& v)
{
	int n = v.size();
	for (int i = 0; i < n; ++i)
		std::cout << std::left << std::setw(11) << v[i];
	std::cout << std::endl;
}



void fillZeros(Vector& V, int n)
{
	V.clear();
	V.resize(n, 0);
}


void read_f(double& alpha, double& beta, double& a, double& b, double& c, double& d)
{
	FILE* f;
	f = fopen("Text.txt", "r");
	fscanf_s(f, "%lf", &alpha);
	fscanf_s(f, "%lf", &beta);
	fscanf_s(f, "%lf", &a);
	fscanf_s(f, "%lf", &b);
	fscanf_s(f, "%lf", &c);
	fscanf_s(f, "%lf", &d);
	fclose(f);
}


void W_Matr(Matrix& W, Vector& x, double& alpha, double& a, double& b)
{
	fillZeros(W, 2);
	W[0][0] = (x[1] / pow(cos(x[0] * x[1] + alpha), 2)) - 2 * x[0];
	W[0][1]= (x[0] / pow(cos(x[0] * x[1] + alpha), 2));
	W[1][0] = 2 * a*x[0];
	W[1][1] = 2 * b*x[1];
}

double Det(Matrix& W)
{
	double det;
	det = W[0][0] * W[1][1] - W[0][1] * W[1][0];
	return det;
}

void W_reverese(Matrix& W, Matrix& W_rev, double& det)
{
	fillZeros(W_rev, 2);
	W_rev[0][0] = (1 / det)*W[1][1];
	W_rev[0][1] = -(1 / det)*W[0][1];
	W_rev[1][0] = -(1 / det)*W[1][0];
	W_rev[1][1] = (1 / det)*W[0][0];
}

double NormVector(const Vector& a)
{
	double sum = 0;
	for (int i = 0; i < a.size(); ++i)
		sum += a[i] * a[i];

	return sqrt(sum);
}

void SubVectors(const Vector& a, const Vector& b, Vector& r)
{
	r.clear();
	r.resize(a.size(), 0);
	int n = a.size();

	for (int i = 0; i < n; ++i)
	{
		r[i] = a[i] - b[i];
	}
}

void MulMatrixVector(const Matrix& A, const Vector& b, Vector& r)
{
	r.clear();
	r.resize(A.size(), 0);
	int n = A.size();

	for (int i = 0; i < n; ++i)
	{
		double sum = 0;
		for (int j = 0; j < n; ++j)
		{
			sum += A[i][j] * b[j];
		}
		r[i] = sum;
	}
}

void Iterations(Matrix& W_reverse, double alpha, double beta, double b, double a, double d, Vector& x)
{
	Vector F;

	fillZeros(x, 2);
	Vector r;
	fillZeros(r, 2);
	int iteration = 0;
	double err = 0, norm_D = 0;
	Vector t(2, 0);

	/*
	x[0]= ;
	x[1]= ;
	*/

	do
	{
		++iteration;

		t[0] = x[0];
		t[1] = x[1];


		x[0] = t[0]-MulMatrixVector(W_reverse, F, r);
		x[1] = t[1]-;

		Vector e(2, 0);
		e[0] = tan(x[0] * x[1] + alpha) - x[0] * x[0];
		e[1] = a * x[0] * x[0] + b * x[1] * x[1] - 1;

		err = NormVector(e);

		Vector D;
		SubVectors(x, t, D);

		norm_D = NormVector(D);

		std::cout << " * Iteration #" << iteration << ": error = " << err << ", delta = " << norm_D << std::endl;
		std::cout << "X vector: ";
		printVector(x);
		std::cout << "E vector: ";
		printVector(e);
		std::cout << "D vector: ";
		printVector(D);
	} while ((abs(err) > 0.00001) || (abs(norm_D) > 0.00001));
}