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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_ratio.cpp app}
LuRatio: Example and Test
#########################
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end lu_ratio.cpp}
*/
// BEGIN C++
# include <cstdlib> // for rand function
# include <cassert>
# include <cppad/cppad.hpp>
namespace { // Begin empty namespace
CppAD::ADFun<double> *NewFactor(
size_t n ,
const CPPAD_TESTVECTOR(double) &x ,
bool &ok ,
CPPAD_TESTVECTOR(size_t) &ip ,
CPPAD_TESTVECTOR(size_t) &jp )
{ using CppAD::AD;
using CppAD::ADFun;
size_t i, j, k;
// values for independent and dependent variables
CPPAD_TESTVECTOR(AD<double>) Y(n*n+1), X(n*n);
// values for the LU factor
CPPAD_TESTVECTOR(AD<double>) LU(n*n);
// record the LU factorization corresponding to this value of x
AD<double> Ratio;
for(k = 0; k < n*n; k++)
X[k] = x[k];
Independent(X);
for(k = 0; k < n*n; k++)
LU[k] = X[k];
CppAD::LuRatio(ip, jp, LU, Ratio);
for(k = 0; k < n*n; k++)
Y[k] = LU[k];
Y[n*n] = Ratio;
// use a function pointer so can return ADFun object
ADFun<double> *FunPtr = new ADFun<double>(X, Y);
// check value of ratio during recording
ok &= (Ratio == 1.);
// 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]);
}
}
}
return FunPtr;
}
bool CheckLuFactor(
size_t n ,
const CPPAD_TESTVECTOR(double) &x ,
const CPPAD_TESTVECTOR(double) &y ,
const CPPAD_TESTVECTOR(size_t) &ip ,
const CPPAD_TESTVECTOR(size_t) &jp )
{ bool ok = true;
using CppAD::NearEqual;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
double sum; // element of L * U
double pij; // element of permuted x
size_t i, j, k; // temporary indices
// L and U factors
CPPAD_TESTVECTOR(double) L(n*n), U(n*n);
// Extract L from LU factorization
for(i = 0; i < n; i++)
{ // elements along and below the diagonal
for(j = 0; j <= i; j++)
L[i * n + j] = y[ 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 factorization
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] = y[ 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 = x[ ip[i] * n + jp[j] ];
// compare
ok &= NearEqual(pij, sum, eps99, eps99);
}
}
return ok;
}
} // end Empty namespace
bool LuRatio(void)
{ bool ok = true;
size_t n = 2; // number rows in A
double ratio;
// values for independent and dependent variables
CPPAD_TESTVECTOR(double) x(n*n), y(n*n+1);
// pivot vectors
CPPAD_TESTVECTOR(size_t) ip(n), jp(n);
// set x equal to the identity matrix
x[0] = 1.; x[1] = 0;
x[2] = 0.; x[3] = 1.;
// create a fnction object corresponding to this value of x
CppAD::ADFun<double> *FunPtr = NewFactor(n, x, ok, ip, jp);
// use function object to factor matrix
y = FunPtr->Forward(0, x);
ratio = y[n*n];
ok &= (ratio == 1.);
ok &= CheckLuFactor(n, x, y, ip, jp);
// set x so that the pivot ratio will be infinite
x[0] = 0. ; x[1] = 1.;
x[2] = 1. ; x[3] = 0.;
// try to use old function pointer to factor matrix
y = FunPtr->Forward(0, x);
ratio = y[n*n];
// check to see if we need to refactor matrix
ok &= (ratio > 10.);
if( ratio > 10. )
{ delete FunPtr; // to avoid a memory leak
FunPtr = NewFactor(n, x, ok, ip, jp);
}
// now we can use the function object to factor matrix
y = FunPtr->Forward(0, x);
ratio = y[n*n];
ok &= (ratio == 1.);
ok &= CheckLuFactor(n, x, y, ip, jp);
delete FunPtr; // avoid memory leak
return ok;
}
// END C++
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