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math_tools.hh
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/**
* @file math_tools.hh
*
* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
* @author Peter Spijker <peter.spijker@epfl.ch>
*
* @date Thu Feb 06 09:26:56 2014
*
* @brief This provides access to a set of math functions for various usage
*
* @section LICENSE
*
* Copyright INRIA and CEA
*
* The LibMultiScale is a C++ parallel framework for the multiscale
* coupling methods dedicated to material simulations. This framework
* provides an API which makes it possible to program coupled simulations
* and integration of already existing codes.
*
* This Project was initiated in a collaboration between INRIA Futurs Bordeaux
* within ScAlApplix team and CEA/DPTA Ile de France.
* The project is now continued at the Ecole Polytechnique Fédérale de Lausanne
* within the LSMS/ENAC laboratory.
*
* This software is governed by the CeCILL-C license under French law and
* abiding by the rules of distribution of free software. You can use,
* modify and/ or redistribute the software under the terms of the CeCILL-C
* license as circulated by CEA, CNRS and INRIA at the following URL
* "http://www.cecill.info".
*
* As a counterpart to the access to the source code and rights to copy,
* modify and redistribute granted by the license, users are provided only
* with a limited warranty and the software's author, the holder of the
* economic rights, and the successive licensors have only limited
* liability.
*
* In this respect, the user's attention is drawn to the risks associated
* with loading, using, modifying and/or developing or reproducing the
* software by the user in light of its specific status of free software,
* that may mean that it is complicated to manipulate, and that also
* therefore means that it is reserved for developers and experienced
* professionals having in-depth computer knowledge. Users are therefore
* encouraged to load and test the software's suitability as regards their
* requirements in conditions enabling the security of their systems and/or
* data to be ensured and, more generally, to use and operate it in the
* same conditions as regards security.
*
* The fact that you are presently reading this means that you have had
* knowledge of the CeCILL-C license and that you accept its terms.
*
*/
#ifndef __LIBMULTISCALE_MATH_TOOLS_HH__
#define __LIBMULTISCALE_MATH_TOOLS_HH__
/* -------------------------------------------------------------------------- */
#include "communicator.hh"
/* -------------------------------------------------------------------------- */
__BEGIN_LIBMULTISCALE__
namespace MathTools {
/* series zeta(puis,ordre) = sum_{k=1}^{ordre} \frac{1}{k^{puis}} */
Real zeta(UInt puis,UInt ordre);
/* set seed for random generator */
void setSeed(long s);
/* A uniform distribution (between a and b) */
double uniformRandom(double a, double b);
/* A uniform distribution (between 0 and 1) */
Real uniform();
/* A normal (Gaussian) distribution (with mean mu and stdev sig) */
Real gaussian();
/* function to compute standard deviation of a set of values stored in an array */
Real stdev(Real *x, Real mu, UInt n);
Real stdev(std::vector<Real> & x, Real mu);
/* function to compute teh kurtosis of a set of values stored in an array */
Real kurtosis(Real *x, Real mu, Real std, UInt n);
/* function to compute teh skewness of a set of values stored in an array */
Real skewness(Real *x, Real mu, Real std, UInt n);
/* function to compute the average of a set of values stored in an array */
Real average(std::vector<Real> &x);
Real average(std::vector<Real> & x);
inline Real ipow(Real x,UInt y){
UInt i;
Real res=1.0;
for (i=y;i>0;--i){
res *= x;
}
return res;
}
/* -------------------------------------------------------------------------- */
inline Real sign(Real x){
if (x >= 0) return 1;
else return -1;
}
/* -------------------------------------------------------------------------- */
template <typename T>
class InterfaceOperator{
public:
virtual void init(){res = 0;cpt = 0;};
virtual T result(int group){return res;};
virtual void account(T & el)=0;
protected:
//! to store the result
T res;
//! often one need a counter
UInt cpt;
//! the volume of the current box
Real vol;
};
/* -------------------------------------------------------------------------- */
template <typename T>
class AverageOperator : public InterfaceOperator<T> {
public:
void account(T & el){
this->res += el; ++this->cpt;
};
virtual T result(CommGroup group = group_none){
if (group != group_none){
Communicator & comm = Communicator::getCommunicator();
comm.allReduce(&this->res,1,group,"AverageOperator reduce res",OP_SUM);
comm.allReduce(&this->cpt,1,group,"AverageOperator reduce cpt",OP_SUM);
}
DUMP("make " << this->res << " / " << this->cpt,DBG_ALL);
this->res/=this->cpt;
return this->res;
};
};
/* -------------------------------------------------------------------------- */
template <typename T>
class SumOperator : public InterfaceOperator<T> {
public:
void account(T & el){this->res += el; ++this->cpt;};
virtual T result(CommGroup group = group_none){
if (group != group_none){
Communicator & comm = Communicator::getCommunicator();
comm.allReduce(&this->res,1,group,"SumOperator reduce res",OP_SUM);
}
return this->res;
};
};
/* -------------------------------------------------------------------------- */
template <typename T>
class DensityOperator : public AverageOperator<T> {
public:
virtual T result(CommGroup group = group_none){
if (group != group_none){
Communicator & comm = Communicator::getCommunicator();
comm.allReduce(&this->res,1,group,"DensityOperator reduce res",OP_SUM);
}
this->res/=this->vol; return this->res;
};
};
/* -------------------------------------------------------------------------- */
template <typename T>
class DeviationOperator : public InterfaceOperator<T> {
public:
void init(){this->res = 0.; this->cpt = 0.; this->m2 = 0.;};
T result(CommGroup group = group_none){
if (group != group_none){
Communicator & comm = Communicator::getCommunicator();
comm.allReduce(&this->res,1,group,"DeviationOperator reduce res",OP_SUM);
comm.allReduce(&this->m2 ,1,group,"DeviationOperator reduce m2" ,OP_SUM);
comm.allReduce(&this->cpt,1,group,"DeviationOperator reduce cpt",OP_SUM);
}
m2 /= this->cpt;
this->res /= this->cpt;
T res2 = this->res;
res2 *= this->res;
T res_deviation = m2;
res_deviation -= res2;
return res_deviation;
}
void account(T & el){
T el2 = el;
el2 *= el;
this->res += el;
m2 += el2;
++this->cpt;
}
T m2;
};
/* -------------------------------------------------------------------------- */
template <typename T>
class MaxOperator : public InterfaceOperator<T> {
public:
void account(T & el){this->res = std::max(el,this->res);};
T result(CommGroup group = group_none){
if (group != group_none){
Communicator & comm = Communicator::getCommunicator();
comm.allReduce(&this->res,1,group,"MaxOperator reduce res",OP_MAX);
}
return this->res;
}
};
/* -------------------------------------------------------------------------- */
template <typename T>
class MinOperator : public InterfaceOperator<T> {
public:
void account(T & el){this->res = std::min(el,this->res);};
T result(CommGroup group = group_none){
if (group != group_none){
Communicator & comm = Communicator::getCommunicator();
comm.allReduce(&this->res,1,group,"MinOperator reduce res",OP_MIN);
}
return this->res;
}
};
/* -------------------------------------------------------------------------- */
}
__END_LIBMULTISCALE__
#endif /* __LIBMULTISCALE_MATH_TOOLS_HH__ */

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