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// SPDX-License-Identifier: EPL-2.0 OR GPL-2.0-or-later
// SPDX-FileCopyrightText: Bradley M. Bell <bradbell@seanet.com>
// SPDX-FileContributor: 2003-22 Bradley M. Bell
// ----------------------------------------------------------------------------
/*
{xrst_begin lu_factor.cpp}
LuFactor: Example and Test
##########################
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end lu_factor.cpp}
*/
// 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
using CppAD::NearEqual;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
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 &= NearEqual(pij, sum, eps99, eps99);
}
}
return ok;
}
// END C++
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