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// ------------------------------------------------------------------------
//
// SPDX-License-Identifier: LGPL-2.1-or-later
// Copyright (C) 2021 - 2025 by the deal.II authors
//
// This file is part of the deal.II library.
//
// Part of the source code is dual licensed under Apache-2.0 WITH
// LLVM-exception OR LGPL-2.1-or-later. Detailed license information
// governing the source code and code contributions can be found in
// LICENSE.md and CONTRIBUTING.md at the top level directory of deal.II.
//
// ------------------------------------------------------------------------
#include <deal.II/base/function_tools.h>
#include <cmath>
DEAL_II_NAMESPACE_OPEN
namespace FunctionTools
{
template <int dim>
void
taylor_estimate_function_bounds(
const Function<dim> &function,
const BoundingBox<dim> &box,
std::pair<double, double> &value_bounds,
std::array<std::pair<double, double>, dim> &gradient_bounds,
const unsigned int component)
{
const Point<dim> center = box.center();
const double value = function.value(center, component);
const Tensor<1, dim> gradient = function.gradient(center, component);
const SymmetricTensor<2, dim> hessian = function.hessian(center, component);
// Deviation from function value at the center, based on the
// Taylor-expansion: |f'| * dx + 1/2 * |f''| * dx^2, (in 1d). dx is half
// the side-length of the box.
double taylor_bound_f = 0;
for (unsigned int i = 0; i < dim; ++i)
{
const double dx_i = .5 * box.side_length(i);
taylor_bound_f += std::abs(gradient[i]) * dx_i;
// Deviation from value of df/dx_i at the center,
// |f''| * dx, (in 1d).
double taylor_bound_dfdxi = 0;
for (unsigned int j = 0; j < dim; ++j)
{
const double dx_j = .5 * box.side_length(j);
taylor_bound_dfdxi += std::abs(hessian[i][j]) * dx_j;
taylor_bound_f += .5 * std::abs(hessian[i][j]) * dx_i * dx_j;
}
gradient_bounds[i].first = gradient[i] - taylor_bound_dfdxi;
gradient_bounds[i].second = gradient[i] + taylor_bound_dfdxi;
}
value_bounds.first = value - taylor_bound_f;
value_bounds.second = value + taylor_bound_f;
}
} // namespace FunctionTools
#include "base/function_tools.inst"
DEAL_II_NAMESPACE_CLOSE
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