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aka_math.cc
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/**
* @file aka_math.cc
*
* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
* @author Marion Estelle Chambart <marion.chambart@epfl.ch>
* @author David Simon Kammer <david.kammer@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
* @author Leonardo Snozzi <leonardo.snozzi@epfl.ch>
* @author Peter Spijker <peter.spijker@epfl.ch>
* @author Marco Vocialta <marco.vocialta@epfl.ch>
*
* @date creation: Wed Aug 04 2010
* @date last modification: Sun Aug 13 2017
*
* @brief Implementation of the math toolbox
*
*
* Copyright (©) 2010-2018 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* Akantu is free software: you can redistribute it and/or modify it under the
* terms of the GNU Lesser General Public License as published by the Free
* Software Foundation, either version 3 of the License, or (at your option) any
* later version.
*
* Akantu 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 Lesser General Public License for more
* details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
*
*/
/* -------------------------------------------------------------------------- */
#include "aka_math.hh"
#include "aka_array.hh"
#include "aka_iterators.hh"
/* -------------------------------------------------------------------------- */
namespace akantu {
namespace Math {
/* --------------------------------------------------------------------------
*/
void matrix_vector(UInt m, UInt n, const Array<Real> & A,
const Array<Real> & x, Array<Real> & y, Real alpha) {
AKANTU_DEBUG_IN();
AKANTU_DEBUG_ASSERT(A.size() == x.size(),
"The vector A(" << A.getID() << ") and the vector x("
<< x.getID()
<< ") must have the same size");
AKANTU_DEBUG_ASSERT(
A.getNbComponent() == m * n,
"The vector A(" << A.getID() << ") has the good number of component.");
AKANTU_DEBUG_ASSERT(x.getNbComponent() == n,
"The vector x("
<< x.getID()
<< ") do not the good number of component.");
AKANTU_DEBUG_ASSERT(y.getNbComponent() == n,
"The vector y("
<< y.getID()
<< ") do not the good number of component.");
UInt nb_element = A.size();
UInt offset_A = A.getNbComponent();
UInt offset_x = x.getNbComponent();
y.resize(nb_element);
Real * A_val = A.storage();
Real * x_val = x.storage();
Real * y_val = y.storage();
for (UInt el = 0; el < nb_element; ++el) {
matrix_vector(m, n, A_val, x_val, y_val, alpha);
A_val += offset_A;
x_val += offset_x;
y_val += offset_x;
}
AKANTU_DEBUG_OUT();
}
/* --------------------------------------------------------------------------
*/
void matrix_matrix(UInt m, UInt n, UInt k, const Array<Real> & A,
const Array<Real> & B, Array<Real> & C, Real alpha) {
AKANTU_DEBUG_IN();
AKANTU_DEBUG_ASSERT(A.size() == B.size(),
"The vector A(" << A.getID() << ") and the vector B("
<< B.getID()
<< ") must have the same size");
AKANTU_DEBUG_ASSERT(
A.getNbComponent() == m * k,
"The vector A(" << A.getID() << ") has the good number of component.");
AKANTU_DEBUG_ASSERT(B.getNbComponent() == k * n,
"The vector B("
<< B.getID()
<< ") do not the good number of component.");
AKANTU_DEBUG_ASSERT(C.getNbComponent() == m * n,
"The vector C("
<< C.getID()
<< ") do not the good number of component.");
UInt nb_element = A.size();
UInt offset_A = A.getNbComponent();
UInt offset_B = B.getNbComponent();
UInt offset_C = C.getNbComponent();
C.resize(nb_element);
Real * A_val = A.storage();
Real * B_val = B.storage();
Real * C_val = C.storage();
for (UInt el = 0; el < nb_element; ++el) {
matrix_matrix(m, n, k, A_val, B_val, C_val, alpha);
A_val += offset_A;
B_val += offset_B;
C_val += offset_C;
}
AKANTU_DEBUG_OUT();
}
/* --------------------------------------------------------------------------
*/
void matrix_matrixt(UInt m, UInt n, UInt k, const Array<Real> & A,
const Array<Real> & B, Array<Real> & C, Real alpha) {
AKANTU_DEBUG_IN();
AKANTU_DEBUG_ASSERT(A.size() == B.size(),
"The vector A(" << A.getID() << ") and the vector B("
<< B.getID()
<< ") must have the same size");
AKANTU_DEBUG_ASSERT(
A.getNbComponent() == m * k,
"The vector A(" << A.getID() << ") has the good number of component.");
AKANTU_DEBUG_ASSERT(B.getNbComponent() == k * n,
"The vector B("
<< B.getID()
<< ") do not the good number of component.");
AKANTU_DEBUG_ASSERT(C.getNbComponent() == m * n,
"The vector C("
<< C.getID()
<< ") do not the good number of component.");
UInt nb_element = A.size();
UInt offset_A = A.getNbComponent();
UInt offset_B = B.getNbComponent();
UInt offset_C = C.getNbComponent();
C.resize(nb_element);
Real * A_val = A.storage();
Real * B_val = B.storage();
Real * C_val = C.storage();
for (UInt el = 0; el < nb_element; ++el) {
matrix_matrixt(m, n, k, A_val, B_val, C_val, alpha);
A_val += offset_A;
B_val += offset_B;
C_val += offset_C;
}
AKANTU_DEBUG_OUT();
}
/* --------------------------------------------------------------------------
*/
void compute_tangents(const Array<Real> & normals, Array<Real> & tangents) {
AKANTU_DEBUG_IN();
if (normals.empty()) {
return;
}
auto spatial_dimension = normals.getNbComponent();
auto tangent_components = spatial_dimension * (spatial_dimension - 1);
if (tangent_components == 0) {
return;
}
AKANTU_DEBUG_ASSERT(
tangent_components == tangents.getNbComponent(),
"Cannot compute the tangents, the storage array for tangents"
<< " does not have the good amount of components.");
auto nb_normals = normals.size();
tangents.resize(nb_normals);
tangents.zero();
/// compute first tangent
for (auto && data : zip(make_view(normals, spatial_dimension),
make_view(tangents, tangent_components))) {
const auto & normal = std::get<0>(data);
auto & tangent = std::get<1>(data);
if (are_float_equal(norm2(normal.storage()), 0.)) {
tangent(0) = 1.;
} else {
normal2(normal.storage(), tangent.storage());
}
}
/// compute second tangent (3D case)
if (spatial_dimension == 3) {
for (auto && data : zip(make_view(normals, spatial_dimension),
make_view(tangents, tangent_components))) {
const auto & normal = std::get<0>(data);
auto & tangent = std::get<1>(data);
normal3(normal.storage(), tangent.storage(),
tangent.storage() + spatial_dimension);
}
}
AKANTU_DEBUG_OUT();
} // namespace akantu
/* --------------------------------------------------------------------------
*/
Real reduce(Array<Real> & array) {
UInt nb_values = array.size();
if (nb_values == 0) {
return 0.;
}
UInt nb_values_to_sum = nb_values >> 1;
std::sort(array.begin(), array.end());
// as long as the half is not empty
while (nb_values_to_sum != 0U) {
UInt remaining = (nb_values - 2 * nb_values_to_sum);
if (remaining != 0U) {
array(nb_values - 2) += array(nb_values - 1);
}
// sum to consecutive values and store the sum in the first half
for (UInt i = 0; i < nb_values_to_sum; ++i) {
array(i) = array(2 * i) + array(2 * i + 1);
}
nb_values = nb_values_to_sum;
nb_values_to_sum >>= 1;
}
return array(0);
}
} // namespace Math
} // namespace akantu
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