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/**
* @file aka_math.hh
*
* @author Ramin Aghababaei <ramin.aghababaei@epfl.ch>
* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
* @author Marion Estelle Chambart <marion.chambart@epfl.ch>
* @author David Simon Kammer <david.kammer@epfl.ch>
* @author Daniel Pino Muñoz <daniel.pinomunoz@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: Tue Feb 09 2021
*
* @brief mathematical operations
*
*
* @section LICENSE
*
* Copyright (©) 2010-2021 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_common.hh"
/* -------------------------------------------------------------------------- */
#include <utility>
/* -------------------------------------------------------------------------- */
#ifndef AKANTU_AKA_MATH_H_
#define AKANTU_AKA_MATH_H_
namespace akantu {
/* -------------------------------------------------------------------------- */
namespace Math {
/// tolerance for functions that need one
extern Real tolerance; // NOLINT
/* ------------------------------------------------------------------------ */
/* Matrix algebra */
/* ------------------------------------------------------------------------ */
/// @f$ y = A*x @f$
void matrix_vector(UInt m, UInt n, const Array<Real> & A,
const Array<Real> & x, Array<Real> & y, Real alpha = 1.);
/// @f$ y = A*x @f$
inline void matrix_vector(UInt m, UInt n, Real * A, Real * x, Real * y,
Real alpha = 1.);
/// @f$ y = A^t*x @f$
inline void matrixt_vector(UInt m, UInt n, Real * A, Real * x, Real * y,
Real alpha = 1.);
/// @f$ C = A*B @f$
void matrix_matrix(UInt m, UInt n, UInt k, const Array<Real> & A,
const Array<Real> & B, Array<Real> & C, Real alpha = 1.);
/// @f$ C = A*B^t @f$
void matrix_matrixt(UInt m, UInt n, UInt k, const Array<Real> & A,
const Array<Real> & B, Array<Real> & C, Real alpha = 1.);
/// @f$ C = A*B @f$
inline void matrix_matrix(UInt m, UInt n, UInt k, Real * A, Real * B,
Real * C, Real alpha = 1.);
/// @f$ C = A^t*B @f$
inline void matrixt_matrix(UInt m, UInt n, UInt k, Real * A, Real * B,
Real * C, Real alpha = 1.);
/// @f$ C = A*B^t @f$
inline void matrix_matrixt(UInt m, UInt n, UInt k, Real * A, Real * B,
Real * C, Real alpha = 1.);
/// @f$ C = A^t*B^t @f$
inline void matrixt_matrixt(UInt m, UInt n, UInt k, Real * A, Real * B,
Real * C, Real alpha = 1.);
template <bool tr_A, bool tr_B>
inline void matMul(UInt m, UInt n, UInt k, Real alpha, Real * A, Real * B,
Real beta, Real * C);
template <bool tr_A>
inline void matVectMul(UInt m, UInt n, Real alpha, Real * A, Real * x,
Real beta, Real * y);
inline void aXplusY(UInt n, Real alpha, Real * x, Real * y);
inline void matrix33_eigenvalues(Real * A, Real * Adiag);
inline void matrix22_eigenvalues(Real * A, Real * Adiag);
template <UInt dim> inline void eigenvalues(Real * A, Real * d);
/// solve @f$ A x = \Lambda x @f$ and return d and V such as @f$ A V[i:] =
/// d[i] V[i:]@f$
template <typename T> void matrixEig(UInt n, T * A, T * d, T * V = nullptr);
/// determinent of a 2x2 matrix
Real det2(const Real * mat);
/// determinent of a 3x3 matrix
Real det3(const Real * mat);
/// determinent of a nxn matrix
template <UInt n> Real det(const Real * mat);
/// determinent of a nxn matrix
template <typename T> T det(UInt n, const T * A);
/// inverse a nxn matrix
template <UInt n> inline void inv(const Real * A, Real * inv);
/// inverse a nxn matrix
template <typename T> inline void inv(UInt n, const T * A, T * inv);
/// inverse a 3x3 matrix
inline void inv3(const Real * mat, Real * inv);
/// inverse a 2x2 matrix
inline void inv2(const Real * mat, Real * inv);
/// solve A x = b using a LU factorization
template <typename T>
inline void solve(UInt n, const T * A, T * x, const T * b);
/// return the double dot product between 2 tensors in 2d
inline Real matrixDoubleDot22(Real * A, Real * B);
/// return the double dot product between 2 tensors in 3d
inline Real matrixDoubleDot33(Real * A, Real * B);
/// extension of the double dot product to two 2nd order tensor in dimension n
inline Real matrixDoubleDot(UInt n, Real * A, Real * B);
/* ------------------------------------------------------------------------ */
/* Array algebra */
/* ------------------------------------------------------------------------ */
/// vector cross product
inline void vectorProduct3(const Real * v1, const Real * v2, Real * res);
/// normalize a vector
inline void normalize2(Real * v);
/// normalize a vector
inline void normalize3(Real * v);
/// return norm of a 2-vector
inline Real norm2(const Real * v);
/// return norm of a 3-vector
inline Real norm3(const Real * v);
/// return norm of a vector
inline Real norm(UInt n, const Real * v);
/// return the dot product between 2 vectors in 2d
inline Real vectorDot2(const Real * v1, const Real * v2);
/// return the dot product between 2 vectors in 3d
inline Real vectorDot3(const Real * v1, const Real * v2);
/// return the dot product between 2 vectors
inline Real vectorDot(Real * v1, Real * v2, UInt n);
/* ------------------------------------------------------------------------ */
/* Geometry */
/* ------------------------------------------------------------------------ */
/// compute normal a normal to a vector
inline void normal2(const Real * vec, Real * normal);
/// compute normal a normal to a vector
inline void normal3(const Real * vec1, const Real * vec2, Real * normal);
/// compute the tangents to an array of normal vectors
void compute_tangents(const Array<Real> & normals, Array<Real> & tangents);
/// distance in 2D between x and y
inline Real distance_2d(const Real * x, const Real * y);
/// distance in 3D between x and y
inline Real distance_3d(const Real * x, const Real * y);
/// radius of the in-circle of a triangle in 2d space
static inline Real triangle_inradius(const Vector<Real> & coord1,
const Vector<Real> & coord2,
const Vector<Real> & coord3);
/// radius of the in-circle of a tetrahedron
inline Real tetrahedron_inradius(const Real * coord1, const Real * coord2,
const Real * coord3, const Real * coord4);
/// volume of a tetrahedron
inline Real tetrahedron_volume(const Real * coord1, const Real * coord2,
const Real * coord3, const Real * coord4);
/// compute the barycenter of n points
inline void barycenter(const Real * coord, UInt nb_points,
UInt spatial_dimension, Real * barycenter);
/// vector between x and y
inline void vector_2d(const Real * x, const Real * y, Real * res);
/// vector pointing from x to y in 3 spatial dimension
inline void vector_3d(const Real * x, const Real * y, Real * res);
/// test if two scalar are equal within a given tolerance
inline bool are_float_equal(Real x, Real y);
/// test if two vectors are equal within a given tolerance
inline bool are_vector_equal(UInt n, Real * x, Real * y);
#ifdef isnan
#error \
"You probably included <math.h> which is incompatible with aka_math please use\
<cmath> or add a \"#undef isnan\" before akantu includes"
#endif
/// test if a real is a NaN
inline bool isnan(Real x);
/// test if the line x and y intersects each other
inline bool intersects(Real x_min, Real x_max, Real y_min, Real y_max);
/// test if a is in the range [x_min, x_max]
inline bool is_in_range(Real a, Real x_min, Real x_max);
inline Real getTolerance() { return Math::tolerance; }
inline void setTolerance(Real tol) { Math::tolerance = tol; }
template <UInt p, typename T> inline T pow(T x);
template <class T1, class T2,
std::enable_if_t<std::is_integral<T1>::value and
std::is_integral<T2>::value> * = nullptr>
inline Real kronecker(T1 i, T2 j) {
return static_cast<Real>(i == j);
}
/// reduce all the values of an array, the summation is done in place and the
/// array is modified
Real reduce(Array<Real> & array);
class NewtonRaphson {
public:
NewtonRaphson(Real tolerance, Real max_iteration)
: tolerance(tolerance), max_iteration(max_iteration) {}
template <class Functor> Real solve(const Functor & funct, Real x_0);
private:
Real tolerance;
Real max_iteration;
};
struct NewtonRaphsonFunctor {
explicit NewtonRaphsonFunctor(const std::string & name) : name(name) {}
virtual ~NewtonRaphsonFunctor() = default;
NewtonRaphsonFunctor(const NewtonRaphsonFunctor & other) = default;
NewtonRaphsonFunctor(NewtonRaphsonFunctor && other) noexcept = default;
NewtonRaphsonFunctor &
operator=(const NewtonRaphsonFunctor & other) = default;
NewtonRaphsonFunctor &
operator=(NewtonRaphsonFunctor && other) noexcept = default;
virtual Real f(Real x) const = 0;
virtual Real f_prime(Real x) const = 0;
std::string name;
};
} // namespace Math
} // namespace akantu
/* -------------------------------------------------------------------------- */
/* inline functions */
/* -------------------------------------------------------------------------- */
#include "aka_math_tmpl.hh"
#endif /* AKANTU_AKA_MATH_H_ */
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