ch-05-ex-08-solution.cpp
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	/*
	* chapter-05-exercise-08.cpp
	*
	* Determinant of a matrix
	*
	* run the program as: ./ch-05-ex-06-solution M.mat
	*
	* Created on: Oct 8, 2012
	* Author: Radu Popescu <radu.popescu@epfl.ch>
	*/

	#include <cassert>
	#include <cstdlib>
	#include <cmath>
	#include <iostream>
	#include <fstream>

	#include "ArrayUtil.hpp"

	void ExtractMinor(double M, const int size, const int col, double& minor)
	{
	for (int row = 1; row < size; ++row) {
	for (int k = 0; k < col; ++k) {
	minor[row - 1][k] = M[row][k];
	}
	for (int k = col + 1; k < size; ++k) {
	minor[row - 1][k - 1] = M[row][k];
	}
	}
	}

	double Determinant(double** M, const int size)
	{
	if (size == 2) {
	return M[0][0] * M[1][1] - M[0][1] * M[1][0];
	} else {
	double det = 0;
	for (int col = 0; col < size; ++col) {
	double** minor;
	Allocate(minor, size - 1, size - 1);
	ExtractMinor(M, size, col, minor);
	det += M[0][col] * std::pow(-1.0, col)
	* Determinant(minor, size - 1);
	Delete(minor, size - 1);
	}
	return det;
	}
	}

	int main(int argc, char* argv[])
	{
	if (argc != 2) {
	std::cout << "Missing arguments. Please run program as: "
	<< " ./ch-05-ex-06-solution M.dat"
	<< std::endl;
	return -1;
	}

	const char* file_name = argv[1];

	double** M;
	int m, n;
	Read(file_name, M, m, n);

	std::cout << "The matrix is: " << std::endl;
	Print(M, m, n, std::cout);
	std::cout << "The determinant is: " << Determinant(M, m) << std::endl;

	Delete(M, m);

	return 0;
	}