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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 jac_lu_det.cpp}
Gradient of Determinant Using Lu Factorization: Example and Test
################################################################
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end jac_lu_det.cpp}
*/
// BEGIN C++
// Complex examples should suppress conversion warnings
# include <cppad/wno_conversion.hpp>
# include <cppad/cppad.hpp>
# include <cppad/speed/det_by_lu.hpp>
// The AD complex case is used by this example so must
// define a specializatgion of LeqZero,AbsGeq for the AD<Complex> case
namespace CppAD {
CPPAD_BOOL_BINARY( std::complex<double> , AbsGeq )
CPPAD_BOOL_UNARY( std::complex<double> , LeqZero )
}
bool JacLuDet(void)
{ bool ok = true;
using namespace CppAD;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
typedef std::complex<double> Complex;
typedef AD<Complex> ADComplex;
size_t n = 2;
// object for computing determinants
det_by_lu<ADComplex> Det(n);
// independent and dependent variable vectors
CPPAD_TESTVECTOR(ADComplex) X(n * n);
CPPAD_TESTVECTOR(ADComplex) D(1);
// value of the independent variable
size_t i;
for(i = 0; i < n * n; i++)
X[i] = Complex( double(i), -double(i) );
// set the independent variables
Independent(X);
// compute the determinant
D[0] = Det(X);
// create the function object
ADFun<Complex> f(X, D);
// argument value
CPPAD_TESTVECTOR(Complex) x( n * n );
for(i = 0; i < n * n; i++)
x[i] = Complex( double(2 * i) , double(i) );
// first derivative of the determinant
CPPAD_TESTVECTOR(Complex) J( n * n );
J = f.Jacobian(x);
/*
f(x) = x[0] * x[3] - x[1] * x[2]
*/
Complex Jtrue[] = { x[3], -x[2], -x[1], x[0] };
for( i = 0; i < n*n; i++)
ok &= NearEqual( Jtrue[i], J[i], eps99 , eps99 );
return ok;
}
// END C++
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