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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
// ----------------------------------------------------------------------------
# include <cppad/cppad.hpp>
# include <cppad/example/atomic_two/eigen_mat_inv.hpp>
namespace { // BEGIN_EMPTY_NAMESPACE
typedef double scalar;
typedef CppAD::AD<scalar> ad_scalar;
typedef atomic_eigen_mat_inv<scalar>::ad_matrix ad_matrix;
scalar eps = 10. * std::numeric_limits<scalar>::epsilon();
using CppAD::NearEqual;
// --------------------------------------------------------------------------
/*
Test atomic_eigen_mat_inv using a non-symmetric matrix
f(x) = [ x[0] -1 ]^{-1}
[ 2 x[1] ]
= [ x[1] 1 ] / (x[0] * x[1] + 2)
[ -2 x[0] ]
y[0] = x[1] / (x[0] * x[1] + 2)
y[1] = 1.0 / (x[0] * x[1] + 2)
y[2] = -2.0 / (x[0] * x[1] + 2)
y[3] = x[0] / (x[0] * x[1] + 2)
*/
bool non_symmetric(void)
{
bool ok = true;
using Eigen::Index;
// -------------------------------------------------------------------
// object that computes inverse of a 2x2 matrix
atomic_eigen_mat_inv<scalar> mat_inv;
// -------------------------------------------------------------------
// declare independent variable vector x
size_t n = 2;
CPPAD_TESTVECTOR(ad_scalar) ad_x(n);
for(size_t j = 0; j < n; j++)
ad_x[j] = ad_scalar(j);
CppAD::Independent(ad_x);
// -------------------------------------------------------------------
// arg = [ x[0] -1 ]
// [ 2 x[1] ]
size_t nr = 2;
ad_matrix ad_arg(nr, nr);
ad_arg(0, 0) = ad_x[0];
ad_arg(0, 1) = ad_scalar(-1.0);
ad_arg(1, 0) = ad_scalar(2.0);
ad_arg(1, 1) = ad_x[1];
// -------------------------------------------------------------------
// use atomic operation to compute arg^{-1}
ad_matrix ad_result = mat_inv.op(ad_arg);
// -------------------------------------------------------------------
// declare the dependent variable vector y
size_t m = 4;
CPPAD_TESTVECTOR(ad_scalar) ad_y(4);
for(size_t i = 0; i < nr; i++)
for(size_t j = 0; j < nr; j++)
ad_y[ i * nr + j ] = ad_result( Index(i), Index(j) );
/* Used to test hand calculated derivaives
CppAD::AD<scalar> ad_dinv = 1.0 / (ad_x[0] * ad_x[1] + 2.0);
ad_y[0] = ad_x[1] * ad_dinv;
ad_y[1] = 1.0 * ad_dinv;
ad_y[2] = -2.0 * ad_dinv;
ad_y[3] = ad_x[0] * ad_dinv;
*/
CppAD::ADFun<scalar> f(ad_x, ad_y);
// -------------------------------------------------------------------
// check zero order forward mode
CPPAD_TESTVECTOR(scalar) x(n), y(m);
for(size_t i = 0; i < n; i++)
x[i] = scalar(i + 2);
scalar dinv = 1.0 / (x[0] * x[1] + 2.0);
y = f.Forward(0, x);
ok &= NearEqual(y[0], x[1] * dinv, eps, eps);
ok &= NearEqual(y[1], 1.0 * dinv, eps, eps);
ok &= NearEqual(y[2], -2.0 * dinv, eps, eps);
ok &= NearEqual(y[3], x[0] * dinv, eps, eps);
// -------------------------------------------------------------------
// check first order forward mode
CPPAD_TESTVECTOR(scalar) x1(n), y1(m);
scalar dinv_x0 = - x[1] * dinv * dinv;
x1[0] = 1.0;
x1[1] = 0.0;
y1 = f.Forward(1, x1);
ok &= NearEqual(y1[0], x[1] * dinv_x0, eps, eps);
ok &= NearEqual(y1[1], 1.0 * dinv_x0, eps, eps);
ok &= NearEqual(y1[2], -2.0 * dinv_x0, eps, eps);
ok &= NearEqual(y1[3], dinv + x[0] * dinv_x0, eps, eps);
//
scalar dinv_x1 = - x[0] * dinv * dinv;
x1[0] = 0.0;
x1[1] = 1.0;
y1 = f.Forward(1, x1);
ok &= NearEqual(y1[0], dinv + x[1] * dinv_x1, eps, eps);
ok &= NearEqual(y1[1], 1.0 * dinv_x1, eps, eps);
ok &= NearEqual(y1[2], -2.0 * dinv_x1, eps, eps);
ok &= NearEqual(y1[3], x[0] * dinv_x1, eps, eps);
// -------------------------------------------------------------------
// check second order forward mode
CPPAD_TESTVECTOR(scalar) x2(n), y2(m);
scalar dinv_x1_x1 = 2.0 * x[0] * x[0] * dinv * dinv * dinv;
x2[0] = 0.0;
x2[1] = 0.0;
y2 = f.Forward(2, x2);
ok &= NearEqual(2.0*y2[0], 2.0*dinv_x1 + x[1]*dinv_x1_x1, eps, eps);
ok &= NearEqual(2.0*y2[1], 1.0 * dinv_x1_x1, eps, eps);
ok &= NearEqual(2.0*y2[2], -2.0 * dinv_x1_x1, eps, eps);
ok &= NearEqual(2.0*y2[3], x[0] * dinv_x1_x1, eps, eps);
// -------------------------------------------------------------------
// check first order reverse
CPPAD_TESTVECTOR(scalar) w(m), d1w(n);
for(size_t i = 0; i < m; i++)
w[i] = 0.0;
w[0] = 1.0;
d1w = f.Reverse(1, w);
ok &= NearEqual(d1w[0], x[1] * dinv_x0, eps, eps);
ok &= NearEqual(d1w[1], dinv + x[1] * dinv_x1, eps, eps);
w[0] = 0.0;
w[1] = 1.0;
d1w = f.Reverse(1, w);
ok &= NearEqual(d1w[0], 1.0 * dinv_x0, eps, eps);
ok &= NearEqual(d1w[1], 1.0 * dinv_x1, eps, eps);
w[1] = 0.0;
w[2] = 1.0;
d1w = f.Reverse(1, w);
ok &= NearEqual(d1w[0], -2.0 * dinv_x0, eps, eps);
ok &= NearEqual(d1w[1], -2.0 * dinv_x1, eps, eps);
w[2] = 0.0;
w[3] = 1.0;
d1w = f.Reverse(1, w);
ok &= NearEqual(d1w[0], dinv + x[0] * dinv_x0, eps, eps);
ok &= NearEqual(d1w[1], x[0] * dinv_x1, eps, eps);
// -------------------------------------------------------------------
// check second order reverse
CPPAD_TESTVECTOR(scalar) d2w(2 * n);
// dinv_x1 = - x[0] * dinv * dinv;
scalar dinv_x1_x0 = 2.0 * x[0] * x[1] * dinv * dinv * dinv - dinv * dinv;
d2w = f.Reverse(2, w);
// partial f_3 w.r.t x_0
ok &= NearEqual(d2w[0 * 2 + 0], dinv + x[0] * dinv_x0, eps, eps);
// partial f_3 w.r.t x_1
ok &= NearEqual(d2w[1 * 2 + 0], x[0] * dinv_x1, eps, eps);
// partial f_3 w.r.t. x_1, x_0
ok &= NearEqual(d2w[0 * 2 + 1], dinv_x1 + x[0] * dinv_x1_x0, eps, eps);
// partial f_3 w.r.t. x_1, x_1
ok &= NearEqual(d2w[1 * 2 + 1], x[0] * dinv_x1_x1, eps, eps);
// -------------------------------------------------------------------
return ok;
}
} // END_EMPTY_NAMESPACE
bool eigen_mat_inv(void)
{ bool ok = true;
ok &= non_symmetric();
return ok;
}
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