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tamaas/src/core/statistics.cpp
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statistics.cpp
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/*
* SPDX-License-Indentifier: AGPL-3.0-or-later
*
* Copyright (©) 2016-2024 EPFL (École Polytechnique Fédérale de Lausanne),
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
* Copyright (©) 2020-2024 Lucas Frérot
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU Affero General Public License as published
* by the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Affero General Public License for more details.
*
* You should have received a copy of the GNU Affero General Public License
* along with this program. If not, see <https://www.gnu.org/licenses/>.
*
*/
/* -------------------------------------------------------------------------- */
#include "statistics.hh"
#include "fft_engine.hh"
#include "loop.hh"
#include "static_types.hh"
/* -------------------------------------------------------------------------- */
namespace tamaas {
template <UInt dim>
Real Statistics<dim>::computeRMSHeights(Grid<Real, dim>& surface) {
return std::sqrt(surface.var());
}
template <UInt dim>
template <class T>
Real Statistics<dim>::rmsSlopesFromPSD(const GridHermitian<Real, dim>& psd,
const Grid<T, dim>& diff) {
return std::sqrt(Loop::reduce<operation::plus>(
[] CUDA_LAMBDA(VectorProxy<const T, dim> q, const Complex& psd_val) {
// Checking if we're in the zone that does not have hermitian symmetry
Complex qback{q.back()}, qsq{q.l2squared()};
auto factor = 2. - static_cast<double>(thrust::abs(qback) < 1e-15);
return factor * thrust::abs(qsq) * psd_val.real();
},
range<VectorProxy<const T, dim>>(diff), psd));
}
template <UInt dim>
Real Statistics<dim>::computeSpectralRMSSlope(Grid<Real, dim>& surface) {
const auto h_size =
GridHermitian<Real, dim>::hermitianDimensions(surface.sizes());
auto wavevectors =
FFTEngine::template computeFrequencies<Real, dim, true>(h_size);
// Diff operator for gradient norm is (qx^2 + qy^2), no need to change
wavevectors *= 2 * M_PI; // need q for slopes
return rmsSlopesFromPSD(computePowerSpectrum(surface), wavevectors);
}
template <UInt dim>
Real Statistics<dim>::computeFDRMSSlope(Grid<Real, dim>& surface) {
const auto h_size =
GridHermitian<Real, dim>::hermitianDimensions(surface.sizes());
auto wavevectors =
FFTEngine::template computeFrequencies<Complex, dim, true>(h_size);
// Diff operator is (exp(iqΔx) - 1)/Δx in each direction
const auto N = Partitioner<dim>::global_size(surface);
Loop::loop(
[&N](VectorProxy<Complex, dim> q) {
for (UInt i = 0; i < dim; ++i)
q(i) = (thrust::polar(1., 2 * M_PI * q(i).real() / N[i]) - 1.) *
static_cast<double>(N[i]);
},
range<VectorProxy<Complex, dim>>(wavevectors));
return rmsSlopesFromPSD(computePowerSpectrum(surface), wavevectors);
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
GridHermitian<Real, dim>
Statistics<dim>::computePowerSpectrum(Grid<Real, dim>& surface) {
const auto h_size =
GridHermitian<Real, dim>::hermitianDimensions(surface.sizes());
GridHermitian<Real, dim> psd(h_size, surface.getNbComponents());
FFTEngine::makeEngine()->forward(surface, psd);
Real factor = 1. / surface.getGlobalNbPoints();
// Squaring the fourier transform of surface and normalizing
Loop::loop(
[factor] CUDA_LAMBDA(Complex & c) {
c *= factor;
c *= conj(c);
},
psd);
return psd;
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
Grid<Real, dim>
Statistics<dim>::computeAutocorrelation(Grid<Real, dim>& surface) {
Grid<Real, dim> acf(surface.sizes(), surface.getNbComponents());
auto psd = computePowerSpectrum(surface);
FFTEngine::makeEngine()->backward(acf, psd);
acf *= acf.getGlobalNbPoints();
return acf;
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
Real Statistics<dim>::contact(const Grid<Real, dim>& tractions,
UInt perimeter) {
Real points = 0;
UInt nc = tractions.getNbComponents();
switch (nc) {
case 1:
points = Loop::reduce(
[] CUDA_LAMBDA(const Real& t) -> Real { return t > 0; }, tractions);
break;
case 2:
points = Loop::reduce(
[] CUDA_LAMBDA(VectorProxy<const Real, 2> t) -> Real {
return t.back() > 0;
},
range<VectorProxy<const Real, 2>>(tractions));
break;
case 3:
points = Loop::reduce(
[] CUDA_LAMBDA(VectorProxy<const Real, 3> t) -> Real {
return t.back() > 0;
},
range<VectorProxy<const Real, 3>>(tractions));
break;
default:
throw std::invalid_argument{
TAMAAS_MSG("Invalid number of components in traction")};
}
auto area = points / tractions.getGlobalNbPoints();
if (dim == 1)
perimeter = 0;
// Correction from Yastrebov et al. (Trib. Intl., 2017)
// 10.1016/j.triboint.2017.04.023
return area - (M_PI - 1 + std::log(2)) /
(24. * tractions.getGlobalNbPoints()) * perimeter;
}
/* -------------------------------------------------------------------------- */
namespace {
template <UInt dim>
class moment_helper {
public:
moment_helper(const std::array<UInt, dim>& exp) : exponent(exp) {}
CUDA_LAMBDA Complex operator()(VectorProxy<Real, dim> q,
const Complex& phi) const {
Real mul = 1;
for (UInt i = 0; i < dim; ++i)
mul *= std::pow(q(i), exponent[i]);
// Do not duplicate everything from hermitian symmetry
if (std::abs(q.back()) < 1e-15)
return mul * phi;
return 2 * mul * phi;
}
private:
std::array<UInt, dim> exponent;
};
} // namespace
/* -------------------------------------------------------------------------- */
template <>
std::vector<Real> Statistics<1>::computeMoments(Grid<Real, 1>& surface) {
constexpr UInt dim = 1;
std::vector<Real> moments(3);
const auto psd = computePowerSpectrum(surface);
auto wavevectors =
FFTEngine::template computeFrequencies<Real, dim, true>(psd.sizes());
// we don't multiply by 2 pi because moments are computed with k
moments[0] = Loop::reduce<operation::plus>(moment_helper<dim>{{{0}}},
range<PVector>(wavevectors), psd)
.real();
moments[1] = Loop::reduce<operation::plus>(moment_helper<dim>{{{2}}},
range<PVector>(wavevectors), psd)
.real();
moments[2] = Loop::reduce<operation::plus>(moment_helper<dim>{{{4}}},
range<PVector>(wavevectors), psd)
.real();
return moments;
}
template <>
std::vector<Real> Statistics<2>::computeMoments(Grid<Real, 2>& surface) {
constexpr UInt dim = 2;
std::vector<Real> moments(3);
const auto psd = computePowerSpectrum(surface);
auto wavevectors =
FFTEngine::template computeFrequencies<Real, dim, true>(psd.sizes());
// we don't multiply by 2 pi because moments are computed with k
moments[0] = Loop::reduce<operation::plus>(moment_helper<dim>{{{0, 0}}},
range<PVector>(wavevectors), psd)
.real();
auto m02 = Loop::reduce<operation::plus>(moment_helper<dim>{{{0, 2}}},
range<PVector>(wavevectors), psd)
.real();
auto m20 = Loop::reduce<operation::plus>(moment_helper<dim>{{{2, 0}}},
range<PVector>(wavevectors), psd)
.real();
moments[1] = (m02 + m20) / 2;
auto m22 = Loop::reduce<operation::plus>(moment_helper<dim>{{{2, 2}}},
range<PVector>(wavevectors), psd)
.real();
auto m40 = Loop::reduce<operation::plus>(moment_helper<dim>{{{4, 0}}},
range<PVector>(wavevectors), psd)
.real();
auto m04 = Loop::reduce<operation::plus>(moment_helper<dim>{{{0, 4}}},
range<PVector>(wavevectors), psd)
.real();
moments[2] = (3 * m22 + m40 + m04) / 3;
return moments;
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
Real Statistics<dim>::graphArea(const Grid<Real, dim>& zdisplacement) {
const auto h_size =
GridHermitian<Real, dim>::hermitianDimensions(zdisplacement.sizes());
GridHermitian<Real, dim> fourier_disp(h_size, 1),
fourier_gradient(h_size, dim);
Grid<Real, dim> gradient(zdisplacement.sizes(), dim);
// Compute gradient in Fourier domain
FFTEngine::makeEngine()->forward(zdisplacement, fourier_disp);
auto wavevectors =
FFTEngine::template computeFrequencies<Real, dim, true>(h_size);
wavevectors *= 2 * M_PI;
Loop::loop(
[] CUDA_LAMBDA(VectorProxy<const Real, dim> q,
VectorProxy<Complex, dim> grad, const Complex& f) {
grad = q * f;
grad *= Complex{0, 1};
},
range<VectorProxy<const Real, dim>>(wavevectors),
range<VectorProxy<Complex, dim>>(fourier_gradient), fourier_disp);
FFTEngine::makeEngine()->backward(gradient, fourier_gradient);
// Integrate area of graph formula
Real factor = Loop::reduce<operation::plus>(
[] CUDA_LAMBDA(VectorProxy<const Real, dim> grad) {
return std::sqrt(1 + grad.l2squared());
},
range<VectorProxy<const Real, dim>>(gradient));
return factor / gradient.getGlobalNbPoints();
// return 2 * M_PI * factor / gradient.getGlobalNbPoints();
}
template struct Statistics<1>;
template struct Statistics<2>;
} // namespace tamaas
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