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// ------------------------------------------------------------------------
//
// SPDX-License-Identifier: LGPL-2.1-or-later
// Copyright (C) 2013 - 2024 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/memory_consumption.h>
#include <deal.II/base/polynomials_piecewise.h>
DEAL_II_NAMESPACE_OPEN
namespace Polynomials
{
template <typename number>
PiecewisePolynomial<number>::PiecewisePolynomial(
const Polynomial<number> &coefficients_on_interval,
const unsigned int n_intervals,
const unsigned int interval,
const bool spans_next_interval)
: polynomial(coefficients_on_interval)
, n_intervals(n_intervals)
, interval(interval)
, spans_two_intervals(spans_next_interval)
, index(numbers::invalid_unsigned_int)
{
Assert(n_intervals > 0, ExcMessage("No intervals given"));
AssertIndexRange(interval, n_intervals);
}
template <typename number>
PiecewisePolynomial<number>::PiecewisePolynomial(
const std::vector<Point<1, number>> &points,
const unsigned int index)
: n_intervals(numbers::invalid_unsigned_int)
, interval(numbers::invalid_unsigned_int)
, spans_two_intervals(false)
, index(index)
{
Assert(points.size() > 1, ExcMessage("No enough points given!"));
AssertIndexRange(index, points.size());
this->points.resize(points.size());
for (unsigned int i = 0; i < points.size(); ++i)
this->points[i] = points[i][0];
this->one_over_lengths.resize(points.size() - 1);
for (unsigned int i = 0; i < points.size() - 1; ++i)
this->one_over_lengths[i] =
number(1.0) / (points[i + 1][0] - points[i][0]);
}
template <typename number>
void
PiecewisePolynomial<number>::value(const number x,
std::vector<number> &values) const
{
Assert(values.size() > 0, ExcZero());
value(x, values.size() - 1, values.data());
}
template <typename number>
void
PiecewisePolynomial<number>::value(const number x,
const unsigned int n_derivatives,
number *values) const
{
if (points.size() > 0)
{
if (x > points[index])
values[0] = std::max<number>(0.0,
1.0 - (x - points[index]) *
one_over_lengths[index]);
else if (x < points[index])
values[0] = std::max<number>(0.0,
0.0 + (x - points[index - 1]) *
one_over_lengths[index - 1]);
else
values[0] = 1.0;
if (n_derivatives >= 1)
{
if ((x > points[index]) && (points[index + 1] >= x))
values[1] = -1.0 * one_over_lengths[index];
else if ((x < points[index]) && (points[index - 1] <= x))
values[1] = +1.0 * one_over_lengths[index - 1];
else
values[1] = 0.0;
}
// all other derivatives are zero
for (unsigned int i = 2; i <= n_derivatives; ++i)
values[i] = 0.0;
return;
}
// shift polynomial if necessary
number y = x;
double derivative_change_sign = 1.;
if (n_intervals > 0)
{
const number step = 1. / n_intervals;
// polynomial spans over two intervals
if (spans_two_intervals)
{
const double offset = step * interval;
if (x < offset || x > offset + step + step)
{
for (unsigned int k = 0; k <= n_derivatives; ++k)
values[k] = 0;
return;
}
else if (x < offset + step)
y = x - offset;
else
{
derivative_change_sign = -1.;
y = offset + step + step - x;
}
}
else
{
const double offset = step * interval;
// ROCm 5.7 throws a floating point exception in debug mode when
// trying to evaluate (x < offset || x > offset + step). Separating
// the conditions fixes the issue.
if (x < offset)
{
for (unsigned int k = 0; k <= n_derivatives; ++k)
values[k] = 0;
return;
}
else if (x > offset + step)
{
for (unsigned int k = 0; k <= n_derivatives; ++k)
values[k] = 0;
return;
}
else
y = x - offset;
}
// on subinterval boundaries, cannot evaluate derivatives properly, so
// set them to zero
if ((std::abs(y) < 1e-14 &&
(interval > 0 || derivative_change_sign == -1.)) ||
(std::abs(y - step) < 1e-14 &&
(interval < n_intervals - 1 || derivative_change_sign == -1.)))
{
values[0] = value(x);
for (unsigned int d = 1; d <= n_derivatives; ++d)
values[d] = 0;
return;
}
}
polynomial.value(y, n_derivatives, values);
// change sign if necessary
for (unsigned int j = 1; j <= n_derivatives; j += 2)
values[j] *= derivative_change_sign;
}
template <typename number>
std::size_t
PiecewisePolynomial<number>::memory_consumption() const
{
return (polynomial.memory_consumption() +
MemoryConsumption::memory_consumption(n_intervals) +
MemoryConsumption::memory_consumption(interval) +
MemoryConsumption::memory_consumption(spans_two_intervals) +
MemoryConsumption::memory_consumption(points) +
MemoryConsumption::memory_consumption(index));
}
std::vector<PiecewisePolynomial<double>>
generate_complete_Lagrange_basis_on_subdivisions(
const unsigned int n_subdivisions,
const unsigned int base_degree)
{
std::vector<Polynomial<double>> p_base =
LagrangeEquidistant::generate_complete_basis(base_degree);
for (auto &polynomial : p_base)
polynomial.scale(n_subdivisions);
std::vector<PiecewisePolynomial<double>> p;
p.reserve(n_subdivisions * base_degree + 1);
p.emplace_back(p_base[0], n_subdivisions, 0, false);
for (unsigned int s = 0; s < n_subdivisions; ++s)
for (unsigned int i = 0; i < base_degree; ++i)
p.emplace_back(p_base[i + 1],
n_subdivisions,
s,
i == (base_degree - 1) && s < n_subdivisions - 1);
return p;
}
std::vector<PiecewisePolynomial<double>>
generate_complete_linear_basis_on_subdivisions(
const std::vector<Point<1>> &points)
{
std::vector<PiecewisePolynomial<double>> p;
p.reserve(points.size());
for (unsigned int s = 0; s < points.size(); ++s)
p.emplace_back(points, s);
return p;
}
} // namespace Polynomials
// ------------------ explicit instantiations --------------- //
namespace Polynomials
{
template class PiecewisePolynomial<float>;
template class PiecewisePolynomial<double>;
template class PiecewisePolynomial<long double>;
} // namespace Polynomials
DEAL_II_NAMESPACE_CLOSE
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