// $Id: lu_factor.cpp 3757 2015-11-30 12:03:07Z bradbell $
/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell

CppAD is distributed under multiple licenses. This distribution is under
the terms of the
                    GNU General Public License Version 3.

A copy of this license is included in the COPYING file of this distribution.
Please visit http://www.coin-or.org/CppAD/ for information on other licenses.
-------------------------------------------------------------------------- */

/*
$begin lu_factor.cpp$$
$spell
	Geq
	Cpp
	Lu
$$

$section LuFactor: Example and Test$$
$mindex LuFactor$$


$code
$verbatim%example/lu_factor.cpp%0%// BEGIN C++%// END C++%1%$$
$$

$end
*/

// BEGIN C++
# include <cstdlib>               // for rand function
# include <cppad/utility/lu_factor.hpp>      // for CppAD::LuFactor
# include <cppad/utility/near_equal.hpp>     // for CppAD::NearEqual
# include <cppad/utility/vector.hpp>  // for CppAD::vector

bool LuFactor(void)
{	bool  ok = true;

# ifndef _MSC_VER
	using std::rand;
	using std::srand;
# endif

	size_t  n = 5;                        // number rows in A
	double  rand_max = double(RAND_MAX);  // maximum rand value
	double  sum;                          // element of L * U
	double  pij;                          // element of permuted A
	size_t  i, j, k;                      // temporary indices

	// A is an n by n matrix
	CppAD::vector<double> A(n*n), LU(n*n), L(n*n), U(n*n);

	// set A equal to an n by n random matrix
	for(i = 0; i < n; i++)
		for(j = 0; j < n; j++)
			A[i * n + j] = rand() / rand_max;

	// pivot vectors
	CppAD::vector<size_t> ip(n);
	CppAD::vector<size_t> jp(n);

	// factor the matrix A
	LU       = A;
	CppAD::LuFactor(ip, jp, LU);

	// check that ip and jp are permutations of the indices 0, ... , n-1
	for(i = 0; i < n; i++)
	{	ok &= (ip[i] < n);
		ok &= (jp[i] < n);
		for(j = 0; j < n; j++)
		{	if( i != j )
			{	ok &= (ip[i] != ip[j]);
				ok &= (jp[i] != jp[j]);
			}
		}
	}

	// Extract L from LU
	for(i = 0; i < n; i++)
	{	// elements along and below the diagonal
		for(j = 0; j <= i; j++)
			L[i * n + j] = LU[ ip[i] * n + jp[j] ];
		// elements above the diagonal
		for(j = i+1; j < n; j++)
			L[i * n + j] = 0.;
	}

	// Extract U from LU
	for(i = 0; i < n; i++)
	{	// elements below the diagonal
		for(j = 0; j < i; j++)
			U[i * n + j] = 0.;
		// elements along the diagonal
		U[i * n + i] = 1.;
		// elements above the diagonal
		for(j = i+1; j < n; j++)
			U[i * n + j] = LU[ ip[i] * n + jp[j] ];
	}

	// Compute L * U
	for(i = 0; i < n; i++)
	{	for(j = 0; j < n; j++)
		{	// compute element (i,j) entry in L * U
			sum = 0.;
			for(k = 0; k < n; k++)
				sum += L[i * n + k] * U[k * n + j];
			// element (i,j) in permuted version of A
			pij  = A[ ip[i] * n + jp[j] ];
			// compare
			ok  &= CppAD::NearEqual(pij, sum, 1e-10, 1e-10);
		}
	}

	return ok;
}

// END C++
