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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: Mon Sep 11 2017
*
* @brief mathematical operations
*
* @section LICENSE
*
* 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/>.
*
*/
/* -------------------------------------------------------------------------- */
#ifndef __AKANTU_AKA_MATH_H__
#define __AKANTU_AKA_MATH_H__
/* -------------------------------------------------------------------------- */
#include <utility>
#include "aka_common.hh"
/* -------------------------------------------------------------------------- */
namespace akantu {
/* -------------------------------------------------------------------------- */
template <typename T, bool is_scal> class Array;
class Math {
/* ------------------------------------------------------------------------ */
/* Methods */
/* ------------------------------------------------------------------------ */
public:
/* ------------------------------------------------------------------------ */
/* Matrix algebra */
/* ------------------------------------------------------------------------ */
/// @f$ y = A*x @f$
static void matrix_vector(UInt m, UInt n, const Array<Real, true> & A,
const Array<Real, true> & x, Array<Real, true> & y,
Real alpha = 1.);
/// @f$ y = A*x @f$
static inline void matrix_vector(UInt m, UInt n, Real * A, Real * x, Real * y,
Real alpha = 1.);
/// @f$ y = A^t*x @f$
static inline void matrixt_vector(UInt m, UInt n, Real * A, Real * x,
Real * y, Real alpha = 1.);
/// @f$ C = A*B @f$
static void matrix_matrix(UInt m, UInt n, UInt k, const Array<Real, true> & A,
const Array<Real, true> & B, Array<Real, true> & C,
Real alpha = 1.);
/// @f$ C = A*B^t @f$
static void matrix_matrixt(UInt m, UInt n, UInt k,
const Array<Real, true> & A,
const Array<Real, true> & B, Array<Real, true> & C,
Real alpha = 1.);
/// @f$ C = A*B @f$
static 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$
static 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$
static 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$
static 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>
static inline void matMul(UInt m, UInt n, UInt k, Real alpha, Real * A,
Real * B, Real beta, Real * C);
template <bool tr_A>
static inline void matVectMul(UInt m, UInt n, Real alpha, Real * A, Real * x,
Real beta, Real * y);
static inline void aXplusY(UInt n, Real alpha, Real * x, Real * y);
static inline void matrix33_eigenvalues(Real * A, Real * Adiag);
static inline void matrix22_eigenvalues(Real * A, Real * Adiag);
template <UInt dim> static 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>
static void matrixEig(UInt n, T * A, T * d, T * V = nullptr);
/// determinent of a 2x2 matrix
static inline Real det2(const Real * mat);
/// determinent of a 3x3 matrix
static inline Real det3(const Real * mat);
/// determinent of a nxn matrix
template <UInt n> static inline Real det(const Real * mat);
/// determinent of a nxn matrix
template <typename T> static inline T det(UInt n, const T * mat);
/// inverse a nxn matrix
template <UInt n> static inline void inv(const Real * mat, Real * inv);
/// inverse a nxn matrix
template <typename T> static inline void inv(UInt n, const T * mat, T * inv);
/// inverse a 3x3 matrix
static inline void inv3(const Real * mat, Real * inv);
/// inverse a 2x2 matrix
static inline void inv2(const Real * mat, Real * inv);
/// solve A x = b using a LU factorization
template <typename T>
static inline void solve(UInt n, const T * A, T * x, const T * b);
/// return the double dot product between 2 tensors in 2d
static inline Real matrixDoubleDot22(Real * A, Real * B);
/// return the double dot product between 2 tensors in 3d
static inline Real matrixDoubleDot33(Real * A, Real * B);
/// extension of the double dot product to two 2nd order tensor in dimension n
static inline Real matrixDoubleDot(UInt n, Real * A, Real * B);
/* ------------------------------------------------------------------------ */
/* Array algebra */
/* ------------------------------------------------------------------------ */
/// vector cross product
static inline void vectorProduct3(const Real * v1, const Real * v2,
Real * res);
/// normalize a vector
static inline void normalize2(Real * v);
/// normalize a vector
static inline void normalize3(Real * v);
/// return norm of a 2-vector
static inline Real norm2(const Real * v);
/// return norm of a 3-vector
static inline Real norm3(const Real * v);
/// return norm of a vector
static inline Real norm(UInt n, const Real * v);
/// return the dot product between 2 vectors in 2d
static inline Real vectorDot2(const Real * v1, const Real * v2);
/// return the dot product between 2 vectors in 3d
static inline Real vectorDot3(const Real * v1, const Real * v2);
/// return the dot product between 2 vectors
static inline Real vectorDot(Real * v1, Real * v2, UInt n);
/* ------------------------------------------------------------------------ */
/* Geometry */
/* ------------------------------------------------------------------------ */
/// compute normal a normal to a vector
static inline void normal2(const Real * v1, Real * res);
/// compute normal a normal to a vector
static inline void normal3(const Real * v1, const Real * v2, Real * res);
/// compute the tangents to an array of normal vectors
static void compute_tangents(const Array<Real> & normals,
Array<Real> & tangents);
/// distance in 2D between x and y
static inline Real distance_2d(const Real * x, const Real * y);
/// distance in 3D between x and y
static 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_2d(const Real * coord1, const Real * coord2,
const Real * coord3);
/// radius of the in-circle of a triangle in 3d space
static inline Real triangle_inradius_3d(const Real * coord1, const Real * coord2,
const Real * coord3);
/// radius of the in-circle of a tetrahedron
static inline Real tetrahedron_inradius(const Real * coord1,
const Real * coord2,
const Real * coord3,
const Real * coord4);
/// volume of a tetrahedron
static inline Real tetrahedron_volume(const Real * coord1,
const Real * coord2,
const Real * coord3,
const Real * coord4);
/// compute the barycenter of n points
static inline void barycenter(const Real * coord, UInt nb_points,
UInt spatial_dimension, Real * barycenter);
/// vector between x and y
static inline void vector_2d(const Real * x, const Real * y, Real * vec);
/// vector pointing from x to y in 3 spatial dimension
static inline void vector_3d(const Real * x, const Real * y, Real * vec);
/// test if two scalar are equal within a given tolerance
static inline bool are_float_equal(Real x, Real y);
/// test if two vectors are equal within a given tolerance
static 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
static inline bool isnan(Real x);
/// test if the line x and y intersects each other
static 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]
static inline bool is_in_range(Real a, Real x_min, Real x_max);
static inline Real getTolerance() { return tolerance; };
static inline void setTolerance(Real tol) { tolerance = tol; };
template <UInt p, typename T> static inline T pow(T x);
/// reduce all the values of an array, the summation is done in place and the
/// array is modified
static 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(std::string name) : name(std::move(name)) {}
virtual ~NewtonRaphsonFunctor() = default;
virtual Real f(Real x) const = 0;
virtual Real f_prime(Real x) const = 0;
std::string name;
};
private:
/// tolerance for functions that need one
static Real tolerance;
};
/* -------------------------------------------------------------------------- */
/* inline functions */
/* -------------------------------------------------------------------------- */
#include "aka_math_tmpl.hh"
} // namespace akantu
#endif /* __AKANTU_AKA_MATH_H__ */
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