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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 "lm_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(LMID) { 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 = Communicator::getGroup("all")) {
group.allReduce(&this->res, 1, "AverageOperator reduce res", OP_SUM);
group.allReduce(&this->cpt, 1, "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 = Communicator::getGroup("all")) {
group.allReduce(&this->res, 1, "SumOperator reduce res", OP_SUM);
return this->res;
};
};
/* -------------------------------------------------------------------------- */
template <typename T> class DensityOperator : public AverageOperator<T> {
public:
virtual T result(CommGroup &group = Communicator::getGroup("all")) {
this->res = T();
group.allReduce(&this->res, 1, "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(LMID group = "group_none") {
if (group != "group_none") {
auto &comm_group = Communicator::getGroup(group);
comm_group.allReduce(&this->res, 1, "DeviationOperator reduce res",
OP_SUM);
comm_group.allReduce(&this->m2, 1, "DeviationOperator reduce m2", OP_SUM);
comm_group.allReduce(&this->cpt, 1, "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 &){/*this->res = std::max(el, this->res);*/};
T result(CommGroup &group = Communicator::getGroup("all")) {
group.allReduce(&this->res, 1, "MaxOperator reduce res", OP_MAX);
return this->res;
}
};
/* -------------------------------------------------------------------------- */
template <typename T> class MinOperator : public InterfaceOperator<T> {
public:
void account(T &){/*this->res = std::min(el, this->res);*/};
T result(CommGroup &group = Communicator::getGroup("all")) {
group.allReduce(&this->res, 1, "MinOperator reduce res", OP_MIN);
return this->res;
}
};
/* -------------------------------------------------------------------------- */
} // namespace MathTools
__END_LIBMULTISCALE__
#endif /* __LIBMULTISCALE_MATH_TOOLS_HH__ */

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