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/**
* @file aka_math.hh
* @author Nicolas Richart <nicolas.richart@epfl.ch>
* @date Wed Jul 28 11:51:56 2010
*
* @brief mathematical operations
*
* @section LICENSE
*
* Copyright (©) 2010-2011 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 "aka_common.hh"
#include "aka_vector.hh"
/* -------------------------------------------------------------------------- */
__BEGIN_AKANTU__
class Math {
/* ------------------------------------------------------------------------ */
/* Constructors/Destructors */
/* ------------------------------------------------------------------------ */
public:
/* ------------------------------------------------------------------------ */
/* Methods */
/* ------------------------------------------------------------------------ */
public:
/* ------------------------------------------------------------------------ */
/* Matrix algebra */
/* ------------------------------------------------------------------------ */
/// @f$ y = A*x @f$
static void matrix_vector(UInt m, UInt n,
const Vector<Real> & A,
const Vector<Real> & x,
Vector<Real> & y, Real alpha = 1.);
/// @f$ y = A*x @f$
static inline void matrix_vector(UInt m, UInt n,
const Real * A,
const Real * x,
Real * y, Real alpha = 1.);
/// @f$ y = A^t*x @f$
static inline void matrixt_vector(UInt m, UInt n,
const Real * A,
const Real * x,
Real * y, Real alpha = 1.);
/// @f$ C = A*B @f$
static void matrix_matrix(UInt m, UInt n, UInt k,
const Vector<Real> & A,
const Vector<Real> & B,
Vector<Real> & C, Real alpha = 1.);
/// @f$ C = A*B^t @f$
static void matrix_matrixt(UInt m, UInt n, UInt k,
const Vector<Real> & A,
const Vector<Real> & B,
Vector<Real> & C, Real alpha = 1.);
/// @f$ C = A*B @f$
static inline void matrix_matrix(UInt m, UInt n, UInt k,
const Real * A,
const Real * B,
Real * C, Real alpha = 1.);
/// @f$ C = A^t*B @f$
static inline void matrixt_matrix(UInt m, UInt n, UInt k,
const Real * A,
const Real * B,
Real * C, Real alpha = 1.);
/// @f$ C = A*B^t @f$
static inline void matrix_matrixt(UInt m, UInt n, UInt k,
const Real * A,
const 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,
const Real * A,
const 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, const Real * A, const Real * B,
Real beta, Real * C);
template <bool tr_A>
static inline void matVectMul(UInt m, UInt n,
Real alpha, const Real * A, const Real * x,
Real beta, Real * y);
static void matrix33_eigenvalues(Real * A,
Real * Adiag);
/// determinent of a 3x3 matrix
static inline Real det3(const Real * mat);
/// determinent of a 2x2 matrix
static inline Real det2(const Real * mat);
/// 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);
/// vector cross product
static inline void vectorProduct3(const Real * v1, const Real * v2, Real * res);
/// 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);
/// 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 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);
/* ------------------------------------------------------------------------ */
/* Geometry */
/* ------------------------------------------------------------------------ */
/// 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
static inline Real triangle_inradius(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);
/// tolerance for functions that need one
static Real tolerance;
/// test if a real is a NaN
static inline bool isnan(Real x);
};
/* -------------------------------------------------------------------------- */
/* inline functions */
/* -------------------------------------------------------------------------- */
#include "aka_math_inline_impl.cc"
__END_AKANTU__
#endif /* __AKANTU_AKA_MATH_H__ */
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