/*
 * LogicalDataType.hh
 * @brief is a complement of ParamData.hh, contain mathematics function between ParamData element
 * @see paramData.hh
 *  Created on: Dec 21, 2012
 *      Author: f.casimir
 */

#ifndef LOGICALDATATYPE_HH_
#define LOGICALDATATYPE_HH_
#define MU_0 1.25664e-06
#define RE 6.3712e+06

#include <vector>
#include <cmath>
#include <boost/lexical_cast.hpp>

#include "ParamData.hh"
#include "AMDA_constants.hh"

inline AMDA::Parameters::LogicalData castToLogicalData(int a) {
    if (isNAN(a)) {
        return AMDA::Parameters::LogicalData::NaN;
    }
    return (a >= 1) ? AMDA::Parameters::LogicalData::True : AMDA::Parameters::LogicalData::False;
}

inline AMDA::Parameters::LogicalData castToLogicalData(AMDA::Parameters::LogicalData a) {
    return a;
}

/**
 * @brief Operator And (&&) between LogicalData
 */
template<typename Type1, typename Type2>
inline AMDA::Parameters::LogicalData And(Type1 a, Type2 b) {
    AMDA::Parameters::LogicalData aa = castToLogicalData(a);
    AMDA::Parameters::LogicalData bb = castToLogicalData(b);
    AMDA::Parameters::LogicalData res = AMDA::Parameters::LogicalData::NaN;

    if (aa != AMDA::Parameters::LogicalData::NaN && bb != AMDA::Parameters::LogicalData::NaN) {
        res = ((aa == AMDA::Parameters::LogicalData::True) && (bb == AMDA::Parameters::LogicalData::True)) ? AMDA::Parameters::LogicalData::True : AMDA::Parameters::LogicalData::False;
    }

    return res;
}

/**
 * @brief Operator Or (||) between LogicalData
 */
template<typename Type1, typename Type2>
inline AMDA::Parameters::LogicalData Or(Type1 a, Type2 b) {
    AMDA::Parameters::LogicalData aa = castToLogicalData(a);
    AMDA::Parameters::LogicalData bb = castToLogicalData(b);
    AMDA::Parameters::LogicalData res = AMDA::Parameters::LogicalData::NaN;

    if (aa != AMDA::Parameters::LogicalData::NaN && bb != AMDA::Parameters::LogicalData::NaN) {
        res = ((aa == AMDA::Parameters::LogicalData::True) || (bb == AMDA::Parameters::LogicalData::True)) ? AMDA::Parameters::LogicalData::True : AMDA::Parameters::LogicalData::False;
    }

    return res;
}

/**
 * @brief Operator greater_than (>) between LogicalData
 */
template <typename Type1, typename Type2>
AMDA::Parameters::LogicalData greater_than(Type1 a, Type2 b) {
    AMDA::Parameters::LogicalData res = AMDA::Parameters::LogicalData::True;
    if (std::isfinite(a) && std::isfinite(b)) {
        res = (a > b) ? AMDA::Parameters::LogicalData::True : AMDA::Parameters::LogicalData::False;
    } else {
        res = AMDA::Parameters::LogicalData::NaN;
    }
    return res;
}

/**
 * @brief Operator greater_than (>) between table of LogicalData
 */
template<typename Type1, typename Type2>
std::vector<AMDA::Parameters::LogicalData> greater_than(std::vector<Type1> a,
        std::vector<Type2> b) {
    std::vector<AMDA::Parameters::LogicalData> r;
    if (a.size() != b.size()) {
        BOOST_THROW_EXCEPTION(
                AMDA::AMDA_exception() << AMDA::errno_code(AMDA_OPER_NOT_ALLOWED) << AMDA::ex_msg("Logical comparison between two vector of different size"));
    }

    for (unsigned int i = 0; i < a.size(); ++i) {
        r.push_back(greater_than(a[i], b[i]));
    }
    return r;
}

/**
 * @brief Operator lower_than (<) between table of LogicalData
 */
template <typename Type1, typename Type2>
AMDA::Parameters::LogicalData lower_than(Type1 a, Type2 b) {
    AMDA::Parameters::LogicalData res = AMDA::Parameters::LogicalData::True;
    if (std::isfinite(a) && std::isfinite(b)) {
        res = (a < b) ? AMDA::Parameters::LogicalData::True : AMDA::Parameters::LogicalData::False;
    } else {
        res = AMDA::Parameters::LogicalData::NaN;
    }
    return res;
}

/**
 * @brief Operator lower_than (<) between table of LogicalData
 */
template<typename Type1, typename Type2>
std::vector<AMDA::Parameters::LogicalData> lower_than(std::vector<Type1> a,
        std::vector<Type2> b) {
    std::vector<AMDA::Parameters::LogicalData> r;
    if (a.size() != b.size()) {
        BOOST_THROW_EXCEPTION(
                AMDA::AMDA_exception() << AMDA::errno_code(AMDA_OPER_NOT_ALLOWED) << AMDA::ex_msg("Logical comparison between two vector of different size"));
    }

    for (unsigned int i = 0; i < a.size(); ++i) {
        r.push_back(lower_than(a[i], b[i]));
    }
    return r;
}

/**
 * @brief Operator * between two scalars, one is LogicalData
 */
template <typename Type>
Type operator*(Type a, AMDA::Parameters::LogicalData b) {
    Type r;
    r << NotANumber();
    if (isNAN(a) || isNAN(b)) {
        return r;
    }
    r = a * (Type) b;
    return r;
}

template <typename Type>
Type operator*(AMDA::Parameters::LogicalData a, Type b) {
    return b * a;
}

/**
 * @brief Operator / between two scalars, one is LogicalData
 */
template <typename Type>
Type operator/(Type a, AMDA::Parameters::LogicalData b) {
    Type r;
    r << NotANumber();
    if (isNAN(a) || isNAN(b) || (b == AMDA::Parameters::LogicalData::False)) {
        return r;
    }
    r = a / (Type) b;
    return r;
}

template <typename Type>
Type operator/(AMDA::Parameters::LogicalData a, Type b) {
    Type r;
    r << NotANumber();
    if (isNAN(a) || isNAN(b) || (b == 0)) {
        return r;
    }
    r = (Type) a / b;
    return r;
}

/**
 * @brief Operator + between two scalars, one is LogicalData
 */
template <typename Type>
Type operator+(Type a, AMDA::Parameters::LogicalData b) {
    Type r;
    r << NotANumber();
    if (isNAN(a) || isNAN(b)) {
        return r;
    }
    r = a + (Type) b;
    return r;
}

template <typename Type>
Type operator+(AMDA::Parameters::LogicalData a, Type b) {
    return b + a;
}

/**
 * @brief Operator - between two scalars, one is LogicalData
 */
template <typename Type>
Type operator-(Type a, AMDA::Parameters::LogicalData b) {
    Type r;
    r << NotANumber();
    if (isNAN(a) || isNAN(b)) {
        return r;
    }
    r = a - (Type) b;
    return r;
}

template <typename Type>
Type operator-(AMDA::Parameters::LogicalData a, Type b) {
    Type r;
    r << NotANumber();
    if (isNAN(a) || isNAN(b)) {
        return r;
    }
    r = (Type) a - b;
    return r;
}

/**
 * @brief Operator addition between  two  vector
 * @details
 * 		r[0] = a[0] + b[0]
 * 		r[1] = a[1] + b[1]
 * 		r[2] = a[2] + b[2]
 * 	@return r
 */
template <typename Type1, typename Type2>
std::vector<Type1> operator+(std::vector<Type1> a, std::vector<Type2> b) {
    std::vector<Type1> r;
    if (a.size() != b.size()) {
        BOOST_THROW_EXCEPTION(AMDA::AMDA_exception() << AMDA::errno_code(AMDA_OPER_NOT_ALLOWED) << AMDA::ex_msg("Add two vector of different size"));
    }

    for (unsigned int i = 0; i < a.size(); ++i) {
        r.push_back((Type1) (a[i] + b[i]));
    }
    return r;
}

/**
 * @brief Operator subtraction between  two  vector
 * @details
 * 		r[0] = a[0] - b[0]
 * 		r[1] = a[1] - b[1]
 * 		r[2] = a[2] - b[2]
 * 	@return r
 */
template <typename Type1, typename Type2>
std::vector<Type1> operator-(std::vector<Type1> a, std::vector<Type2> b) {
    std::vector<Type1> r;
    if (a.size() != b.size()) {
        BOOST_THROW_EXCEPTION(AMDA::AMDA_exception() << AMDA::errno_code(AMDA_OPER_NOT_ALLOWED) << AMDA::ex_msg("Subtract two vector of different size"));
    }

    for (unsigned int i = 0; i < a.size(); ++i) {
        r.push_back(a[i] - b[i]);
    }
    return r;
}

/**
 * @brief Operator dot product between  two  vector
 * @details
 * 		r = a[0]*b[0] + a[1]*b[1] + a[2]+b[2]
 * 	@return the scalar r
 */
template <typename Type1, typename Type2>
Type1 operator*(std::vector<Type1> a, std::vector<Type2> b) {
    Type1 r = 0;
    if (a.size() != b.size()) {
        BOOST_THROW_EXCEPTION(AMDA::AMDA_exception() << AMDA::errno_code(AMDA_OPER_NOT_ALLOWED) << AMDA::ex_msg("Multiply two vector of different size"));
    }

    for (unsigned int i = 0; i < a.size(); ++i) {
        r += a[i] * b[i];
    }
    return r;
}

/**
 * @brief Function dot between two vectors can be used for dot product
 */
template <typename Type1, typename Type2>
Type1 dot(std::vector<Type1> a, std::vector<Type2> b) {
    return a*b;
}

template <typename Type>
Type magnitude(std::vector<Type> a) {
    Type mag = 0;
    for (unsigned int i = 0; i < a.size(); ++i)
        mag += a[i] * a[i];
    return std::sqrt(mag);
}

template <typename Type1, typename Type2>
Type1 angle(std::vector<Type1> a, std::vector<Type2> b) {
    if (magnitude(a) == 0 || magnitude(b) == 0) {
        BOOST_THROW_EXCEPTION(AMDA::AMDA_exception() << AMDA::errno_code(AMDA_OPER_NOT_ALLOWED) << AMDA::ex_msg("One of the two vectors is NULL"));
    }
    Type1 res;
    if (dot(a, b) / magnitude(a) / magnitude(b) > 0.99999) {
        res = 0;
    } else {
        res = std::acos(dot(a, b) / magnitude(a) / magnitude(b));
    }
    return res;
}

/**
 * @brief alfvenVelocity : args magnetic field magnitude and density
 * @details
 * 
 * standard : V (m/s) = mag (T) / std::sqrt(MU_0 * density ( kg/m^3))
 *  our : V (km/s) = K * mag (nT) / sqrt(density ( 1/cm^3)) assuming mass of proton
 */
template <typename Type1, typename Type2>
Type1 alfvenVelocity(Type1 density, Type2 mag) {
    Type1 val;
    if (density <= 0) {
        val << NotANumber();
    } else {
        val = 21.83 * mag / std::sqrt(density);
    }
    return val;
}

/**
 * @brief  FAIRFIELD 1970 model of neutral sheet position 
 * @details
 * z_sm-std::sqrt(pow(11.0, 2.0) - pow(11.0, 2.0) / pow(15.0, 2.0) * pow(y_sm, 2.0)) * std::sin(x_ss);
 * where y_sm and z_sm  are the solar magnetospheric coordinates of the spacecraft and x_ss is geomagnetic latitude of the sun  (tilt angle) 

template <typename Type1, typename Type2, typename Type3>
Type1 fairfield70(Type1  y_sm, Type2 z_sm,Type3 x_ss) {
    Type1 val = z_sm-std::sqrt(pow(11.0, 2.0) - pow(11.0, 2.0) / pow(15.0, 2.0) * pow(y_sm, 2.0)) * std::sin(x_ss);
    return val;
}
 *  */

/**
 * @brief FAIRFIELD 1970 model of neutral sheet position : ..sqrt(11^2 - 11^2/15^2*y^2)... 
 * @param xyz_sm SM coordinates of the sat
 * @param x_ss tilt Angle ( deg )
 * @return delta Z 
 */
template <typename Type1, typename Type2>
Type1 fairfield70(std::vector<Type1> xyz_sm, Type2 x_ss) {
    Type1 val = xyz_sm[2] - std::sqrt(121.0 - 0.537778 * pow(xyz_sm[1], 2.0)) * std::sin(x_ss * DEG2RAD);
    return val;
}

/**
 * @brief FAIRFIELD 1980 model of neutral sheet position  
 * @param xyz_sm SM coordinates of the sat
 * @param x_ss tilt Angle
 * @return delta Z 
 */
template <typename Type1, typename Type2>
Type1 fairfield80(std::vector<Type1> xyz_sm, Type2 x_ss) {
    Type1 val = xyz_sm[2] - 10.5 * std::sqrt(1.0 - pow(xyz_sm[1], 2.0) / 289.0) * std::sin(x_ss * DEG2RAD);
    return val;
}

/**
 * @brief  Perrault and Akasofu 1978 geomagnetic storms
 * @details
 *     u(t) = E_mag(t)*B_mag(t)/4pi(7RE sin²(theta_p(t)/2))²
 * where u(t) is total energy dissipation
 *            E_mag(t) The  magnitude of  the solar-wind electric field
 *            theta_p is a measure of the angle between the geomagnetic field vector and the IMF vector at the front of the 
 *            B_mag(t) The magnitude of the IMF magnetosphere in the equatorial plane. theta_p = pi/2 -theta where theta 
 *            denotes the latitudinal angle of the IMF vector measured from the solar equatorial plane.
 */
template <typename Type1, typename Type2, typename Type3>
Type1 perreault78(Type1 E_mag, Type2 B_mag, Type3 theta_p) {
    Type1 val = E_mag * B_mag / (4 * std::atan(1)*4) * std::pow((7 * RE * std::pow(sin(theta_p / 2), 2)), 2);
    return val;
}

/**
 * @brief  NEWELL et al 2007 solar wind-magnetosphere coupling function 
 * @details d_phi/d_t = mu^4/3*Bt^2/3*sin(theta/2)^8/3
 * where mu is rate IMF field lines approach the magnetopause
 *            B_mag interplanetary field magnitude,
 *            theta IMF clock angle arctan(By/Bz)
 */
template <typename Type1, typename Type2>
Type1 newell2007(Type1 mu, std::vector<Type2> Bxyz) {
    Type2 B_mag = std::sqrt(Bxyz[0] * Bxyz[0] + Bxyz[1] * Bxyz[1] + Bxyz[2] * Bxyz[2]);
    Type2 theta = std::atan2(Bxyz[1] / Bxyz[2]);
    Type1 val = std::pow(mu, 4.0 / 3.0) * std::pow(B_mag, 2.0 / 3.0) * pow(std::sin(theta / 2), 8.0 / 3.0);
    return val;
}

/**
 * @brief  Lopez 1990 model of magnetic latitude of the neutral sheet
 * @details
 *MLAT = -(0.14*Kp+0.69)*std::pow(phi, 1.0/3.0)*(0.065*R-0.16)*DTA;
 * where Kp is the 3-hour magnetic index, phi the magnetic local time in degrees (phi = 0° at midnight)
 * R is the radial distance in RE and DTA is the dipole tilt angle 
 */
template <typename Type1, typename Type2, typename Type3, typename Type4>
Type1 lopez90(Type1 Kp, Type2 phi, Type3 R, Type4 DTA) {
    Type1 val = -(0.14 * Kp + 0.69) * std::pow(phi, 0.3333)*(0.065 * R - 0.16) * DTA*DEG2RAD;
    return val;
}

template <typename Type1, typename Type2>
Type1 pv_ionos_te(Type1 alt, Type2 sza) {

    Type1 te;
    if (alt > 3000 || alt < 150) {
        te << NotANumber();
        return te;
    } else {

        std::vector<double> pb;
        pb.resize(4);
        // 0 was added to fdsmodt in order to keep indexes as in fortran original source 
        const std::vector< double> fdsmodt{0,
            3.567296, 1.3836078e-02, 1.5086544e-02, 6.0729804e-03, 4.0306677e-03,
            -1.3217842e-02, 7.8089219e-03, -2775.023, -123.7310, 8.828382,
            -96.94563, 15.84634, 138.9812, -139.7511, -84.03277,
            0.2649297, -1.444215, 0.6347786, -2.192531, -0.5396207,
            0.6054179, 1.0569388e-04, -8.0908003e-06, 1.3877957e-05, -1.2327257e-05,
            -1.1256760e-05, 1.3830228e-05, -1.4350858e-05};
        double s = std::sin(sza);
        double c = std::cos(sza);
        double s2 = std::sin(2 * sza);
        double c2 = std::cos(2 * sza);
        double s3 = std::sin(3 * sza);
        double c3 = std::cos(3 * sza);
        for (int j = 1; j < 5; j++) {
            int k = 7 * j;
            pb[j - 1] = fdsmodt[k - 6] + fdsmodt[k - 5] * s + fdsmodt[k - 4] * c + fdsmodt[k - 3] * s2 + fdsmodt[k - 2] * c2 +
                    fdsmodt[k - 1] * s3 + fdsmodt[k] * c3;
        }
        te = (Type1) pb[0] + pb[1] / ((alt + pb[2])*(alt + pb[2])) + pb[3] * alt;
        return te;
    }
}

template <typename Type1, typename Type2>
Type1 pv_ionos_dn(Type1 alt, Type2 sza) {

    Type1 dn;
    if (alt > 3000 || alt < 150) {
        dn << NotANumber();
        return dn;
    } else {
        std::vector<double> bp;
        bp.resize(4);
        // 0 was added to fdsmodde in order to keep indexes as in fortran original source 
        const std::vector<double> fdsmodde{0,
            5.334022, 252.5587, 120.4444, 9.1163822E-02, -6.195264,
            37.38898, 3.331818, 245.5529, 0.7587564, 0.1453792,
            -0.9461438, 127.1485, -0.3391595, 2.4936652E-02, 0.1879423,
            -5.3126566E-02, 2.9439656E-02, 1.654282, 415.7859, 2.6281483E-02,
            145.3951, 2.045347, 0.4421963, 3.036170, 9.1009791E-04,
            141.5824};
        double s2 = std::sin(sza) * std::sin(sza);
        double  szap = sza * (1. - fdsmodde[23] * s2 * std::exp(-fdsmodde[24] * s2 - fdsmodde[25]*(alt - fdsmodde[26])*(alt - fdsmodde[26])));
        double sinz = std::sin(fdsmodde[18] + szap);
        double s = fdsmodde[1] + fdsmodde[2] / (alt - fdsmodde[3])
                + sinz * fdsmodde[13]
                + fdsmodde[19] * std::exp(-fdsmodde[20]*((alt - fdsmodde[21])*(alt - fdsmodde[21])) - fdsmodde[22] * szap * szap);
        double o = fdsmodde[4] + fdsmodde[5] / (alt - fdsmodde[6]) + sinz * fdsmodde[14];
        double c = fdsmodde[7] + fdsmodde[8] / (alt - fdsmodde[9]) + sinz * fdsmodde[15];
        double m = fdsmodde[10] + fdsmodde[11] / (alt - fdsmodde[12]) + sinz * fdsmodde[16];
        double ss = s * cos(fdsmodde[17] + szap);
        double calc = (1.77245 * ss * erfc(-ss) + std::exp(-ss * ss) + o);
        if (calc <= 0)
            calc = 0.00001;
        dn = (Type1) c + m * log(calc);
        return dn;
    }
}

/**
 * @brief Operator cross product between  two  vector
 * @details
 * 		r[0] = a[1]*b[2] - a[2]*b[1]
 * 		r[1] = a[2]*b[0] - a[0]*b[2]
 * 		r[2] = a[0]*b[1] - a[1]*b[0]
 * 	@return r
 */
template <typename Type1, typename Type2>
std::vector<Type1> operator ^(std::vector<Type1> a, std::vector<Type2> b) {
    std::vector<Type1> r;
    if (a.size() != b.size() || b.size() != 3) {
        BOOST_THROW_EXCEPTION(AMDA::AMDA_exception() << AMDA::errno_code(AMDA_OPER_NOT_ALLOWED) << AMDA::ex_msg("Vector product on two vector of different size"));
    }

    r.push_back(a[1] * b[2] - a[2] * b[1]);
    r.push_back(a[2] * b[0] - a[0] * b[2]);
    r.push_back(a[0] * b[1] - a[1] * b[0]);

    return r;
}

/**
 * @brief Function cross between two vectors can be used for cross product
 */
template <typename Type1, typename Type2>
std::vector<Type1> cross(std::vector<Type1> a, std::vector<Type2> b) {
    return a^b;
}

/**
 * @brief div each coordinate one to one
 * @details
 * 		r[0] = a[0] / b[0]
 * 		r[1] = a[1] / b[1]
 * 		r[2] = a[2] /  b[2]
 */
template <typename Type1, typename Type2>
std::vector<Type1> div(std::vector<Type1> a, std::vector<Type2> b) {
    std::vector<Type1> r;
    if (a.size() != b.size()) {
        BOOST_THROW_EXCEPTION(AMDA::AMDA_exception() << AMDA::errno_code(AMDA_OPER_NOT_ALLOWED) << AMDA::ex_msg("Vector div on two vector of different size"));

    }

    for (unsigned int i = 0; i < a.size(); ++i) {
        r.push_back(a[i] / b[i]);
    }

    return r;
}

//
//Idea but more complex: template <typename Type1, typename Type2>
//auto operator ^(std::vector<Type1> a, std::vector<Type2> b)  -> std::vector<decltype(Type1()*Type2())> {
//	std::vector<decltype(Type1()*Type2())> r;


//	Idea but more complex: template <typename Type1, typename Type2>
//	double operator ^(Type1 a, Type2 b) {
//		return pow(a, b);
//	}
//	class Integer {
//		public:
//		Integer(int i) : _i(i) {};
//		int _i;
//	};
//
//	inline double operator ^(double a, Integer b) {
//		return pow(a, b._i);
//	}
//
//
//	class Double {
//		public:
//		Double(double i) : _i(i) {};
//		double _i;
//	};
//	inline double operator ^(double a, Double b) {
//		return pow(a, b._i);
//	}

// vector with scalar operation

/**
 * @brief Operator division between  a  vector and a scalar
 * @details all member of vector are divided by the scalar
 */
template <typename Type1, typename Type2>
std::vector<Type1> operator/(std::vector<Type1> a, Type2 b) {
    std::vector<Type1> r;
    for (typename std::vector<Type1>::iterator it = a.begin(); it != a.end(); ++it) {
        r.push_back((Type1) (*it / b));
    }
    return r;
}

/**
 * @brief Operator division between a scalar and a vector
 * @details apply the division on each vector component
 */
template <typename Type1, typename Type2>
std::vector<Type2> operator/(Type1 a, std::vector<Type2> b) {
    std::vector<Type2> r;
    for (typename std::vector<Type2>::iterator it = b.begin(); it != b.end(); ++it) {
        r.push_back((Type2) (a / *it));
    }
    return r;
}

/**
 * @brief Operator addition between  a  vector and a scalar
 * @details all member of vector are added with the scalar
 */
template <typename Type1, typename Type2>
std::vector<Type1> operator+(std::vector<Type1> a, Type2 b) {
    std::vector<Type1> r;
    for (typename std::vector<Type1>::iterator it = a.begin(); it != a.end(); ++it) {
        r.push_back((Type1) (*it + b));
    }
    return r;
}

/**
 * @brief Operator addition between a scalar and a  vector
 * @details all member of vector are added with the scalar
 */
template <typename Type1, typename Type2>
std::vector<Type2> operator+(Type1 a, std::vector<Type2> b) {
    std::vector<Type2> r;
    for (typename std::vector<Type2>::iterator it = b.begin(); it != b.end(); ++it) {
        r.push_back((Type2) (a + *it));
    }
    return r;
}

/**
 * @brief Operator subtraction  between a vector and a scalar
 * @details scalar is substracted to all vector components
 */
template <typename Type1, typename Type2>
std::vector<Type1> operator-(std::vector<Type1> a, Type2 b) {
    std::vector<Type1> r;
    for (typename std::vector<Type1>::iterator it = a.begin(); it != a.end(); ++it) {
        r.push_back((Type1) (*it - b));
    }
    return r;
}

/**
 * @brief Operator subtraction  between a scalar and a  vector
 * @details all member of vector are subtracted with the scalar
 */
template <typename Type1, typename Type2>
std::vector<Type2> operator-(Type1 a, std::vector<Type2> b) {
    std::vector<Type2> r;
    for (typename std::vector<Type2>::iterator it = b.begin(); it != b.end(); ++it) {
        r.push_back((Type2) (a - *it));
    }
    return r;
}

/**
 * @brief Operator product between a vector and a scalar
 * @details product applied in all member of vector
 */
template <typename Type1, typename Type2>
std::vector<Type1> operator*(std::vector<Type1> a, Type2 b) {
    std::vector<Type1> r;
    for (typename std::vector<Type1>::iterator it = a.begin(); it != a.end(); ++it) {
        r.push_back((Type1) ((*it) * b));
    }
    return r;
}

/**
 * @brief Operator product between a scalar and a vector
 * @details all member of vector are added by the scalar
 */
template <typename Type1, typename Type2>
std::vector<Type2> operator*(Type1 a, std::vector<Type2> b) {
    std::vector<Type2> r;
    for (typename std::vector<Type2>::iterator it = b.begin(); it != b.end(); ++it) {
        r.push_back((Type2) (a * (*it)));
    }
    return r;
}

/**
 * @return false if val is NaN or inf or -inf
 */
template <typename Type>
inline bool isFinite(Type val) {
    return std::isfinite(val);
}

inline bool isFinite(AMDA::Parameters::LogicalData val) {
    return !isNAN(val);
}

/**
 * @return false if elem of val is NaN or inf or -inf
 */
template <typename Type>
inline bool isFinite(std::vector<Type> val) {
    bool ret = false;
    auto it = val.begin();
    while (it != val.end() && !ret) {
        ret &= std::isfinite(*it);
        ++it;
    }
    return ret;
}

/**
 * @return false if elem of val is NaN or inf or -inf
 */
template <typename Type>
inline bool isFinite(const AMDA::Parameters::Tab2DData<Type>& val) {
    bool ret = false;
    for (int i = 0; i < val.getDim1Size(); ++i)
        for (int j = 0; j < val.getDim2Size(); ++j)
            ret &= std::isfinite(val[i][j]);
    return ret;
}

/**
 * @return the average of std::list
 */
template <typename Type>
inline Type average(std::list<Type> tab, int /*dim1*/, int /*dim2*/) {
    Type mean;
    if (tab.empty()) {
        mean << NotANumber();
    } else {
        mean << ElemNull();
        auto it = tab.begin();
        if (it != tab.end()) {
            unsigned int nbNan = 0;
            Type sum;
            sum << NotANumber();
            for (; it != tab.end(); ++it) {
                if (isFinite(*it) && !isNAN(*it)) {
                    if (isNAN(sum))
                        sum = *it;
                    else
                        sum = sum + *it;
                } else {
                    ++nbNan;
                }
            }
            if ((tab.size() - nbNan == 0) || isNAN(sum)) {
                mean << NotANumber();
            } else {
                mean = sum / (int) (tab.size() - nbNan);
            }
        } else {
            mean << NotANumber();
        }
    }
    return mean;
}

inline AMDA::Parameters::LogicalData average(std::list<AMDA::Parameters::LogicalData> /*tab*/, int /*dim1*/, int /*dim2*/) {
    AMDA::Parameters::LogicalData mean;
    mean << NotANumber();
    return mean;
}

template <typename Type>
inline AMDA::Parameters::Tab2DData<Type> average(std::list<AMDA::Parameters::Tab2DData<Type> > tab, int dim1, int dim2) {
    AMDA::Parameters::Tab2DData<Type> mean(dim1, dim2);
    AMDA::Parameters::Tab2DData<unsigned int > nbNan(dim1, dim2);
    AMDA::Parameters::Tab2DData<Type> sum(dim1, dim2);
    if (tab.empty()) {
        mean << NotANumber();
        return mean;
    }
    for (int index1 = 0; index1 < dim1; ++index1) {
        for (int index2 = 0; index2 < dim2; ++index2) {
            nbNan[index1][index2] = 0;
        }
    }
    sum << NotANumber();
    for (auto it = tab.begin(); it != tab.end(); ++it) {
        for (int index1 = 0; index1 < dim1; ++index1) {
            for (int index2 = 0; index2 < dim2; ++index2) {
                Type val = (*it)[index1][index2];
                if (std::isfinite(val) && !isNAN(val)) {
                    if (isNAN(sum[index1][index2]))
                        sum[index1][index2] = val;
                    else
                        sum[index1][index2] += val;
                } else {
                    ++(nbNan[index1][index2]);
                }
            }
        }
    }
    for (int index1 = 0; index1 < dim1; ++index1) {
        for (int index2 = 0; index2 < dim2; ++index2) {
            if (tab.size() - nbNan[index1][index2] == 0) {
                mean[index1][index2] << NotANumber();
            } else {
                mean[index1][index2] = sum[index1][index2] / (int) (tab.size() - nbNan[index1][index2]);
            }
        }
    }

    return mean;
}

inline AMDA::Parameters::Tab2DData<AMDA::Parameters::LogicalData> average(std::list<AMDA::Parameters::Tab2DData<AMDA::Parameters::LogicalData>> /*tab*/, int dim1, int dim2) {
    AMDA::Parameters::Tab2DData<AMDA::Parameters::LogicalData> mean(dim1, dim2);
    mean << NotANumber();
    return mean;
}

/**
 * @return the average of std::list
 */
template <typename Type>
inline std::vector<Type> average(std::list<std::vector<Type> > tab, int dim1, int /*dim2*/) {
    std::vector<Type> mean;
    mean.resize(dim1);
    std::vector<unsigned int >nbNan;
    nbNan.resize(dim1);
    std::vector<Type> sum;
    sum.resize(dim1);
    if (tab.empty()) {
        mean << NotANumber();
        return mean;
    }
    for (unsigned int index = 0; index < tab.begin()->size(); ++index) {
        nbNan[index] = 0;
    }
    sum << NotANumber();
    for (auto it = tab.begin(); it != tab.end(); ++it) {
        for (unsigned int index = 0; index < it->size(); ++index) {
            Type val = it->at(index);
            if (std::isfinite(val) && !isNAN(val)) {
                if (isNAN(sum[index]))
                    sum[index] = val;
                else
                    sum[index] += val;
            } else {
                ++(nbNan[index]);
            }
        }
    }
    for (unsigned int index = 0; index < tab.begin()->size(); ++index) {
        if (tab.size() - nbNan[index] == 0) {
            mean[index] << NotANumber();
        } else {
            mean[index] = sum[index] / (int) (tab.size() - nbNan[index]);
        }
    }


    return mean;
}

inline std::vector<AMDA::Parameters::LogicalData> average(std::list<std::vector<AMDA::Parameters::LogicalData>> /*tab*/, int dim1, int /*dim2*/) {
    std::vector<AMDA::Parameters::LogicalData> mean;
    mean.resize(dim1);
    mean << NotANumber();
    return mean;
}

/**
 *
 */
template <typename Type>
inline Type interpolation(const Type& leftVal, const Type& rightVal, double coef, int /*dim1*/, int /*dim2*/) {
    Type val;
    val << NotANumber();
    if (isNAN(leftVal) || isNAN(rightVal) || coef < 0. || coef > 1.)
        return val;
    val = leftVal + (rightVal - leftVal) * coef;
    return val;
}

inline AMDA::Parameters::LogicalData interpolation(const AMDA::Parameters::LogicalData& leftVal, const AMDA::Parameters::LogicalData& rightVal, double /*coef*/, int /*dim1*/, int /*dim2*/) {
    AMDA::Parameters::LogicalData val;
    if (leftVal == rightVal) {
        val = leftVal;
    } else {
        val << NotANumber();
    }
    return val;
}

/**
 * 
 */

template <typename Type>
inline AMDA::Parameters::Tab2DData<Type> interpolation(const AMDA::Parameters::Tab2DData<Type>& leftVal, const AMDA::Parameters::Tab2DData<Type>& rightVal, double coef, int dim1, int dim2) {
    AMDA::Parameters::Tab2DData<Type> val(dim1, dim2);
    val << NotANumber();
    for (int index1 = 0; index1 < dim1; ++index1) {
        for (int index2 = 0; index2 < dim2; ++index2) {
            Type leftValComp = leftVal[index1][index2];
            Type rightValComp = rightVal[index1][index2];
            val[index1][index2] = interpolation(leftValComp, rightValComp, coef, 1, 1);
        }
    }
    return val;
}

template <typename Type>
inline std::vector<Type> interpolation(const std::vector<Type>& leftVal, const std::vector<Type>& rightVal, double coef, int dim1, int /*dim2*/) {
    std::vector<Type> val;
    val.resize(dim1);
    val << NotANumber();
    for (int index = 0; index < dim1; ++index) {
        Type leftValComp = leftVal[index];
        Type rightValComp = rightVal[index];
        val[index] = interpolation(leftValComp, rightValComp, coef, 1, 1);
    }
    return val;
}

/**
 * @brief Operator + between Tab2D and scalar
 */
template <typename Type1, typename Type2>
AMDA::Parameters::Tab2DData<Type1> operator+(const AMDA::Parameters::Tab2DData<Type1>& a, Type2 b) {
    AMDA::Parameters::Tab2DData<Type1> r(a);

    if (isNAN(b)) {
        r << NotANumber();
        return r;
    }

    for (int i = 0; i < r.getDim1Size(); ++i)
        for (int j = 0; j < r.getDim2Size(); ++j) {
            if (!isNAN(r[i][j]))
                r[i][j] += b;
        }
    return r;
}

template <typename Type1, typename Type2>
AMDA::Parameters::Tab2DData<Type2> operator+(Type1 a, const AMDA::Parameters::Tab2DData<Type2>& b) {
    return (b + a);
}

/**
 * @brief Operator - between Tab2D and scalar
 */
template <typename Type1, typename Type2>
AMDA::Parameters::Tab2DData<Type1> operator-(const AMDA::Parameters::Tab2DData<Type1>& a, Type2 b) {
    return (a + (-b));
}

template <typename Type1, typename Type2>
AMDA::Parameters::Tab2DData<Type2> operator-(Type1 a, const AMDA::Parameters::Tab2DData<Type2>& b) {
    AMDA::Parameters::Tab2DData<Type2> r(b);

    if (isNAN(a)) {
        r << NotANumber();
        return r;
    }

    for (int i = 0; i < r.getDim1Size(); ++i)
        for (int j = 0; j < r.getDim2Size(); ++j) {
            if (!isNAN(r[i][j]))
                r[i][j] = a - r[i][j];
        }
    return r;
}

/**
 * @brief Operator * between Tab2D and scalar
 */
template <typename Type1, typename Type2>
AMDA::Parameters::Tab2DData<Type1> operator*(const AMDA::Parameters::Tab2DData<Type1>& a, Type2 b) {
    AMDA::Parameters::Tab2DData<Type1> r(a);

    if (isNAN(b)) {
        r << NotANumber();
        return r;
    }

    for (int i = 0; i < r.getDim1Size(); ++i)
        for (int j = 0; j < r.getDim2Size(); ++j) {
            if (!isNAN(r[i][j]))
                r[i][j] *= b;
        }
    return r;
}

template <typename Type1, typename Type2>
AMDA::Parameters::Tab2DData<Type2> operator*(Type1 a, const AMDA::Parameters::Tab2DData<Type2>& b) {
    return (b * a);
}

/**
 * @brief Operator / between Tab2D and scalar
 */
template <typename Type1, typename Type2>
AMDA::Parameters::Tab2DData<Type1> operator/(const AMDA::Parameters::Tab2DData<Type1>& a, Type2 b) {
    if (b == 0) {
        AMDA::Parameters::Tab2DData<Type1> r(a);
        r << NotANumber();
        return r;
    }
    return (a * (1. / b));
}

template <typename Type1, typename Type2>
AMDA::Parameters::Tab2DData<Type2> operator/(Type1 a, const AMDA::Parameters::Tab2DData<Type2>& b) {
    AMDA::Parameters::Tab2DData<Type2> r(b);

    if (isNAN(a)) {
        r << NotANumber();
        return r;
    }

    for (int i = 0; i < r.getDim1Size(); ++i)
        for (int j = 0; j < r.getDim2Size(); ++j) {
            if (isNAN(r[i][j]) || (r[i][j] == 0))
                r[i][j] << NotANumber();
            else
                r[i][j] = a / r[i][j];
        }
    return r;
}

/*
 * @brief Function add between a Tab2D and a vector
 */
template <typename Type1, typename Type2>
AMDA::Parameters::Tab2DData<Type1> add(const AMDA::Parameters::Tab2DData<Type1>& a, std::vector<Type2> b, int mode) {
    AMDA::Parameters::Tab2DData<Type1> r(a);

    switch (mode) {
        case 1:
            if (r.getDim1Size() != b.size()) {
                BOOST_THROW_EXCEPTION(
                        AMDA::AMDA_exception() << AMDA::errno_code(AMDA_OPER_NOT_ALLOWED) << AMDA::ex_msg("Operation not allowed due to incompatibility in data dimensions"));
            }

            for (int i = 0; i < r.getDim1Size(); ++i)
                for (int j = 0; j < r.getDim2Size(); ++j) {
                    if (isNAN(r[i][j]) || isNAN(b[i]))
                        r[i][j] << NotANumber();
                    else
                        r[i][j] += b[i];
                }
            break;
        case 2:
            if (r.getDim2Size() != b.size()) {
                BOOST_THROW_EXCEPTION(
                        AMDA::AMDA_exception() << AMDA::errno_code(AMDA_OPER_NOT_ALLOWED) << AMDA::ex_msg("Operation not allowed due to incompatibility in data dimensions"));
            }

            for (int i = 0; i < r.getDim1Size(); ++i)
                for (int j = 0; j < r.getDim2Size(); ++j) {
                    if (isNAN(r[i][j]) || isNAN(b[j]))
                        r[i][j] << NotANumber();
                    else
                        r[i][j] += b[j];
                }
            break;
        default:
            BOOST_THROW_EXCEPTION(
                    AMDA::AMDA_exception() << AMDA::errno_code(AMDA_OPER_NOT_ALLOWED) << AMDA::ex_msg("Operation not allowed due a not implemented mode"));
    }
    return r;
}

template <typename Type1, typename Type2>
AMDA::Parameters::Tab2DData<Type2> add(std::vector<Type1> a, const AMDA::Parameters::Tab2DData<Type2>& b, int mode) {
    return add(b, a, mode);
}

/**
 * @brief Operator + between Tab2D and vector
 */
template <typename Type1, typename Type2>
AMDA::Parameters::Tab2DData<Type1> operator+(const AMDA::Parameters::Tab2DData<Type1>& a, std::vector<Type2> b) {
    return add(a, b, 1);
}

template <typename Type1, typename Type2>
AMDA::Parameters::Tab2DData<Type2> operator+(std::vector<Type1> a, const AMDA::Parameters::Tab2DData<Type2>& b) {
    return add(a, b, 1);
}

/**
 * @brief Function sub between Tab2D and vector
 */
template <typename Type1, typename Type2>
AMDA::Parameters::Tab2DData<Type1> sub(const AMDA::Parameters::Tab2DData<Type1>& a, std::vector<Type2> b, int mode) {
    return add(a, (-1) * b, mode);
}

template <typename Type1, typename Type2>
AMDA::Parameters::Tab2DData<Type2> sub(std::vector<Type1> a, const AMDA::Parameters::Tab2DData<Type2>& b, int mode) {
    AMDA::Parameters::Tab2DData<Type2> r(b);

    switch (mode) {
        case 1:
            if (r.getDim1Size() != a.size()) {
                BOOST_THROW_EXCEPTION(
                        AMDA::AMDA_exception() << AMDA::errno_code(AMDA_OPER_NOT_ALLOWED) << AMDA::ex_msg("Operation not allowed due to incompatibility in data dimensions"));
            }

            for (int i = 0; i < r.getDim1Size(); ++i)
                for (int j = 0; j < r.getDim2Size(); ++j) {
                    if (isNAN(r[i][j]) || isNAN(a[i]))
                        r[i][j] << NotANumber();
                    else
                        r[i][j] = a[i] - r[i][j];
                }
            break;
        case 2:
            if (r.getDim2Size() != a.size()) {
                BOOST_THROW_EXCEPTION(
                        AMDA::AMDA_exception() << AMDA::errno_code(AMDA_OPER_NOT_ALLOWED) << AMDA::ex_msg("Operation not allowed due to incompatibility in data dimensions"));
            }

            for (int i = 0; i < r.getDim1Size(); ++i)
                for (int j = 0; j < r.getDim2Size(); ++j) {
                    if (isNAN(r[i][j]) || isNAN(a[j]))
                        r[i][j] << NotANumber();
                    else
                        r[i][j] = a[j] - r[i][j];
                }
            break;
        default:
            BOOST_THROW_EXCEPTION(
                    AMDA::AMDA_exception() << AMDA::errno_code(AMDA_OPER_NOT_ALLOWED) << AMDA::ex_msg("Operation not allowed due a not implemented mode"));
    }
    return r;
}

/**
 * @brief Operator - between Tab2D and vector
 */
template <typename Type1, typename Type2>
AMDA::Parameters::Tab2DData<Type1> operator-(const AMDA::Parameters::Tab2DData<Type1>& a, std::vector<Type2> b) {
    return sub(a, b, 1);
}

template <typename Type1, typename Type2>
AMDA::Parameters::Tab2DData<Type2> operator-(std::vector<Type1> a, const AMDA::Parameters::Tab2DData<Type2>& b) {
    return sub(a, b, 1);
}

/**
 * @brief Function mult between Tab2D and vector
 */
template <typename Type1, typename Type2>
AMDA::Parameters::Tab2DData<Type1> mult(const AMDA::Parameters::Tab2DData<Type1>& a, std::vector<Type2> b, int mode) {
    AMDA::Parameters::Tab2DData<Type1> r(a);

    switch (mode) {
        case 1:
            if (r.getDim1Size() != b.size()) {
                BOOST_THROW_EXCEPTION(
                        AMDA::AMDA_exception() << AMDA::errno_code(AMDA_OPER_NOT_ALLOWED) << AMDA::ex_msg("Operation not allowed due to incompatibility in data dimensions"));
            }

            for (int i = 0; i < r.getDim1Size(); ++i)
                for (int j = 0; j < r.getDim2Size(); ++j) {
                    if (isNAN(r[i][j]) || isNAN(b[i]))
                        r[i][j] << NotANumber();
                    else
                        r[i][j] *= b[i];
                }
            break;
        case 2:
            if (r.getDim2Size() != b.size()) {
                BOOST_THROW_EXCEPTION(
                        AMDA::AMDA_exception() << AMDA::errno_code(AMDA_OPER_NOT_ALLOWED) << AMDA::ex_msg("Operation not allowed due to incompatibility in data dimensions"));
            }

            for (int i = 0; i < r.getDim1Size(); ++i)
                for (int j = 0; j < r.getDim2Size(); ++j) {
                    if (isNAN(r[i][j]) || isNAN(b[j]))
                        r[i][j] << NotANumber();
                    else
                        r[i][j] *= b[j];
                }
            break;
        default:
            BOOST_THROW_EXCEPTION(
                    AMDA::AMDA_exception() << AMDA::errno_code(AMDA_OPER_NOT_ALLOWED) << AMDA::ex_msg("Operation not allowed due a not implemented mode"));
    }
    return r;
}

template <typename Type1, typename Type2>
AMDA::Parameters::Tab2DData<Type2> mult(std::vector<Type1> a, const AMDA::Parameters::Tab2DData<Type2>& b, int mode) {
    return mult(b, a, mode);
}

/**
 * @brief Operator * between Tab2D and vector
 */
template <typename Type1, typename Type2>
AMDA::Parameters::Tab2DData<Type1> operator*(const AMDA::Parameters::Tab2DData<Type1>& a, std::vector<Type2> b) {
    return mult(a, b, 1);
}

template <typename Type1, typename Type2>
AMDA::Parameters::Tab2DData<Type2> operator*(std::vector<Type1> a, const AMDA::Parameters::Tab2DData<Type2>& b) {
    return mult(b, a, 1);
}

/**
 * @brief Function div between Tab2D and vector
 */
template <typename Type1, typename Type2>
AMDA::Parameters::Tab2DData<Type1> div(const AMDA::Parameters::Tab2DData<Type1>& a, std::vector<Type2> b, int mode) {
    AMDA::Parameters::Tab2DData<Type1> r(a);

    switch (mode) {
        case 1:
            if (r.getDim1Size() != b.size()) {
                BOOST_THROW_EXCEPTION(
                        AMDA::AMDA_exception() << AMDA::errno_code(AMDA_OPER_NOT_ALLOWED) << AMDA::ex_msg("Operation not allowed due to incompatibility in data dimensions"));
            }

            for (int i = 0; i < r.getDim1Size(); ++i)
                for (int j = 0; j < r.getDim2Size(); ++j) {
                    if (isNAN(r[i][j]) || isNAN(b[i]) || (b[i] == 0))
                        r[i][j] << NotANumber();
                    else
                        r[i][j] = r[i][j] / b[i];
                }
            break;
        case 2:
            if (r.getDim2Size() != b.size()) {
                BOOST_THROW_EXCEPTION(
                        AMDA::AMDA_exception() << AMDA::errno_code(AMDA_OPER_NOT_ALLOWED) << AMDA::ex_msg("Operation not allowed due to incompatibility in data dimensions"));
            }

            for (int i = 0; i < r.getDim1Size(); ++i)
                for (int j = 0; j < r.getDim2Size(); ++j) {
                    if (isNAN(r[i][j]) || isNAN(b[j]) || (b[j] == 0))
                        r[i][j] << NotANumber();
                    else
                        r[i][j] = r[i][j] / b[j];
                }
            break;
        default:
            BOOST_THROW_EXCEPTION(
                    AMDA::AMDA_exception() << AMDA::errno_code(AMDA_OPER_NOT_ALLOWED) << AMDA::ex_msg("Operation not allowed due a not implemented mode"));
    }
    return r;
}

template <typename Type1, typename Type2>
AMDA::Parameters::Tab2DData<Type2> div(std::vector<Type1> a, const AMDA::Parameters::Tab2DData<Type2>& b, int mode) {
    AMDA::Parameters::Tab2DData<Type2> r(b);

    switch (mode) {
        case 1:
            if (r.getDim1Size() != a.size()) {
                BOOST_THROW_EXCEPTION(
                        AMDA::AMDA_exception() << AMDA::errno_code(AMDA_OPER_NOT_ALLOWED) << AMDA::ex_msg("Operation not allowed due to incompatibility in data dimensions"));
            }

            for (int i = 0; i < r.getDim1Size(); ++i)
                for (int j = 0; j < r.getDim2Size(); ++j) {
                    if (isNAN(r[i][j]) || isNAN(a[i]) || (r[i][j] == 0))
                        r[i][j] << NotANumber();
                    else
                        r[i][j] = a[i] / r[i][j];
                }
            break;
        case 2:
            if (r.getDim2Size() != a.size()) {
                BOOST_THROW_EXCEPTION(
                        AMDA::AMDA_exception() << AMDA::errno_code(AMDA_OPER_NOT_ALLOWED) << AMDA::ex_msg("Operation not allowed due to incompatibility in data dimensions"));
            }

            for (int i = 0; i < r.getDim1Size(); ++i)
                for (int j = 0; j < r.getDim2Size(); ++j) {
                    if (isNAN(r[i][j]) || isNAN(a[j]) || (r[i][j] == 0))
                        r[i][j] << NotANumber();
                    else
                        r[i][j] = a[j] / r[i][j];
                }
            break;
        default:
            BOOST_THROW_EXCEPTION(
                    AMDA::AMDA_exception() << AMDA::errno_code(AMDA_OPER_NOT_ALLOWED) << AMDA::ex_msg("Operation not allowed due a not implemented mode"));
    }
    return r;
}

/**
 * @brief Operator / between Tab2D and vector
 */
template <typename Type1, typename Type2>
AMDA::Parameters::Tab2DData<Type1> operator/(const AMDA::Parameters::Tab2DData<Type1>& a, std::vector<Type2> b) {
    return div(a, b, 1);
}

template <typename Type1, typename Type2>
AMDA::Parameters::Tab2DData<Type2> operator/(std::vector<Type1> a, const AMDA::Parameters::Tab2DData<Type2>& b) {
    return div(b, a, 1);
}

/**
 * @brief Operator + between two Tab2D
 */
template <typename Type1, typename Type2>
AMDA::Parameters::Tab2DData<Type1> operator+(const AMDA::Parameters::Tab2DData<Type1>& a, const AMDA::Parameters::Tab2DData<Type2>& b) {
    if ((a.getDim1Size() != b.getDim1Size()) || (a.getDim2Size() != b.getDim2Size())) {
        BOOST_THROW_EXCEPTION(
                AMDA::AMDA_exception() << AMDA::errno_code(AMDA_OPER_NOT_ALLOWED) << AMDA::ex_msg("Operation not allowed due to incompatibility in data dimensions"));
    }

    AMDA::Parameters::Tab2DData<Type1> r(a);

    for (int i = 0; i < r.getDim1Size(); ++i)
        for (int j = 0; j < r.getDim2Size(); ++j) {
            if (isNAN(a[i][j]) || isNAN(b[i][j]))
                r[i][j] << NotANumber();
            else
                r[i][j] = a[i][j] + b[i][j];
        }

    return r;
}

/**
 * @brief Operator - between two Tab2D
 */
template <typename Type1, typename Type2>
AMDA::Parameters::Tab2DData<Type1> operator-(const AMDA::Parameters::Tab2DData<Type1>& a, const AMDA::Parameters::Tab2DData<Type2>& b) {
    if ((a.getDim1Size() != b.getDim1Size()) || (a.getDim2Size() != b.getDim2Size())) {
        BOOST_THROW_EXCEPTION(
                AMDA::AMDA_exception() << AMDA::errno_code(AMDA_OPER_NOT_ALLOWED) << AMDA::ex_msg("Operation not allowed due to incompatibility in data dimensions"));
    }

    AMDA::Parameters::Tab2DData<Type1> r(a);

    for (int i = 0; i < r.getDim1Size(); ++i)
        for (int j = 0; j < r.getDim2Size(); ++j) {
            if (isNAN(a[i][j]) || isNAN(b[i][j]))
                r[i][j] << NotANumber();
            else
                r[i][j] = a[i][j] - b[i][j];
        }
    return r;
}

/**
 * @brief Operator * between two Tab2D
 */
template <typename Type1, typename Type2>
AMDA::Parameters::Tab2DData<Type1> operator*(const AMDA::Parameters::Tab2DData<Type1>& a, const AMDA::Parameters::Tab2DData<Type2>& b) {
    if ((a.getDim1Size() != b.getDim1Size()) || (a.getDim2Size() != b.getDim2Size())) {
        BOOST_THROW_EXCEPTION(
                AMDA::AMDA_exception() << AMDA::errno_code(AMDA_OPER_NOT_ALLOWED) << AMDA::ex_msg("Operation not allowed due to incompatibility in data dimensions"));
    }

    AMDA::Parameters::Tab2DData<Type1> r(a);

    for (int i = 0; i < r.getDim1Size(); ++i)
        for (int j = 0; j < r.getDim2Size(); ++j) {
            if (isNAN(a[i][j]) || isNAN(b[i][j]))
                r[i][j] << NotANumber();
            else
                r[i][j] = a[i][j] * b[i][j];
        }
    return r;
}

/**
 * @brief Operator + between two Tab2D
 */
template <typename Type1, typename Type2>
AMDA::Parameters::Tab2DData<Type1> operator/(const AMDA::Parameters::Tab2DData<Type1>& a, const AMDA::Parameters::Tab2DData<Type2>& b) {
    if ((a.getDim1Size() != b.getDim1Size()) || (a.getDim2Size() != b.getDim2Size())) {
        BOOST_THROW_EXCEPTION(
                AMDA::AMDA_exception() << AMDA::errno_code(AMDA_OPER_NOT_ALLOWED) << AMDA::ex_msg("Operation not allowed due to incompatibility in data dimensions"));
    }

    AMDA::Parameters::Tab2DData<Type1> r(a);

    for (int i = 0; i < r.getDim1Size(); ++i)
        for (int j = 0; j < r.getDim2Size(); ++j) {
            if (isNAN(a[i][j]) || isNAN(b[i][j]) || (b[i][j] == 0))
                r[i][j] << NotANumber();
            else
                r[i][j] = a[i][j] / b[i][j];
        }
    return r;
}

/**
 * @brief Function total on all components of a vector => result is a scalar
 */
template <typename Type>
Type total(const std::vector<Type>& a) {
    Type sum;
    sum << NotANumber();

    for (int j = 0; j < a.size(); ++j) {
        if (isFinite(a[j])) {
            if (isNAN(sum))
                sum = a[j];
            else
                sum += a[j];
        }
    }
    return sum;
}

/**
 * @brief Function total on all components of a Tab2D => result is a scalar
 */
template <typename Type>
Type total(const AMDA::Parameters::Tab2DData<Type>& a) {
    Type sum;
    sum << NotANumber();

    for (int i = 0; i < a.getDim1Size(); ++i)
        for (int j = 0; j < a.getDim2Size(); ++j) {
            if (isFinite(a[i][j])) {
                if (isNAN(sum))
                    sum = a[i][j];
                else
                    sum += a[i][j];
            }
        }
    return sum;
}

/**
 * @brief Function total on lines or columns of a Tab2D => result is a vector
 * mode = 1 => sum on lines
 * mode = 2 => sum on columns
 */
template <typename Type>
std::vector<Type> total(const AMDA::Parameters::Tab2DData<Type>& a, int mode) {
    std::vector<Type> sum;

    switch (mode) {
        case 1:
            for (int j = 0; j < a.getDim2Size(); ++j) {
                Type elem;
                elem << NotANumber();
                for (int i = 0; i < a.getDim1Size(); ++i) {
                    if (isFinite(a[i][j])) {
                        if (isNAN(elem))
                            elem = a[i][j];
                        else
                            elem += a[i][j];
                    }
                }
                sum.push_back(elem);
            }
            break;
        case 2:
            for (int i = 0; i < a.getDim1Size(); ++i) {
                Type elem;
                elem << NotANumber();
                for (int j = 0; j < a.getDim2Size(); ++j) {
                    if (isFinite(a[i][j])) {
                        if (isNAN(elem))
                            elem = a[i][j];
                        else
                            elem += a[i][j];
                    }
                }
                sum.push_back(elem);
            }
            break;
        default:
            BOOST_THROW_EXCEPTION(
                    AMDA::AMDA_exception() << AMDA::errno_code(AMDA_OPER_NOT_ALLOWED) << AMDA::ex_msg("Operation not allowed due a not implemented mode"));
    }

    return sum;
}

// Reshape a Tab2D to a vector

template <typename Type>
std::vector<Type> reshapeToVector(const AMDA::Parameters::Tab2DData<Type>& a) {
    std::vector<Type> v;
    v.resize(a.getDim1Size() * a.getDim2Size());
    for (int r = 0; r < a.getDim1Size(); ++r) {
        for (int c = 0; c < a.getDim2Size(); ++c) {
            v[r * a.getDim2Size() + c] = a[r][c];
        }
    }

    return v;
}

/*
 * Evaluation of SuperMAG auroral electrojet indices as indicators
 * of substorms and auroral power
 *  JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116, A12211, doi:10.1029/2011JA016779, 2011
 */
template <typename Type>
Type newell2011(Type a) {
    return 0.048 * a + 0.241 * std::sqrt(a);
}

template <typename Type1, typename Type2>
std::vector<Type1> operator+(AMDA::Parameters::TabRow<Type1> a, AMDA::Parameters::TabRow<Type2> b) {
    std::vector<Type1> av(a);
    std::vector<Type1> bv(b);
    return av + bv;
}

template <typename Type1, typename Type2>
std::vector<Type1> operator+(std::vector<Type1> a, AMDA::Parameters::TabRow<Type2> b) {
    std::vector<Type2> bv(b);
    return a + bv;
}

template <typename Type1, typename Type2>
std::vector<Type1> operator+(AMDA::Parameters::TabRow<Type1> a, std::vector<Type2> b) {
    std::vector<Type1> av(a);
    return av + b;
}

template <typename Type1, typename Type2>
std::vector<Type1> operator*(AMDA::Parameters::TabRow<Type1> a, AMDA::Parameters::TabRow<Type2> b) {
    std::vector<Type1> av(a);
    std::vector<Type1> bv(b);
    return av*bv;
}

template <typename Type1, typename Type2>
std::vector<Type1> operator*(std::vector<Type1> a, AMDA::Parameters::TabRow<Type2> b) {
    std::vector<Type2> bv(b);
    return a*bv;
}

template <typename Type1, typename Type2>
std::vector<Type1> operator*(AMDA::Parameters::TabRow<Type1> a, std::vector<Type2> b) {
    std::vector<Type1> av(a);
    return av*b;
}

template <typename Type1, typename Type2>
std::vector<Type1> operator-(AMDA::Parameters::TabRow<Type1> a, AMDA::Parameters::TabRow<Type2> b) {
    std::vector<Type1> av(a);
    std::vector<Type1> bv(b);
    return av - bv;
}

template <typename Type1, typename Type2>
std::vector<Type1> operator-(std::vector<Type1> a, AMDA::Parameters::TabRow<Type2> b) {
    std::vector<Type2> bv(b);
    return a - bv;
}

template <typename Type1, typename Type2>
std::vector<Type1> operator-(AMDA::Parameters::TabRow<Type1> a, std::vector<Type2> b) {
    std::vector<Type1> av(a);
    return av - b;
}

template <typename Type1, typename Type2>
std::vector<Type1> operator/(AMDA::Parameters::TabRow<Type1> a, AMDA::Parameters::TabRow<Type2> b) {
    std::vector<Type1> av(a);
    std::vector<Type1> bv(b);
    return av / bv;
}

template <typename Type1, typename Type2>
std::vector<Type1> operator/(std::vector<Type1> a, AMDA::Parameters::TabRow<Type2> b) {
    std::vector<Type2> bv(b);
    return a / bv;
}

template <typename Type1, typename Type2>
std::vector<Type1> operator/(AMDA::Parameters::TabRow<Type1> a, std::vector<Type2> b) {
    std::vector<Type1> av(a);
    return av / b;
}

template<typename Type>
bool isValid(const std::string& num) {
    bool flag = true;
    try {
        boost::lexical_cast<Type>(num);
    } catch (boost::bad_lexical_cast &e) {
        flag = false;
    }
    return flag;
}

template <typename Type>
std::pair<Type, Type> operator-(std::pair<Type, Type> a, std::pair<Type, Type> b) {
    std::pair<Type, Type> c;
    c.first = a.first - b.firest;
    c.second = a.second - b.second;
    return c;
}

template <typename Type>
std::pair<Type, Type> operator+(std::pair<Type, Type> a, std::pair<Type, Type> b) {
    std::pair<Type, Type> c;
    c.first = a.first + b.firest;
    c.second = a.second + b.second;
    return c;
}

template <typename Type>
std::pair<Type, Type> operator*(std::pair<Type, Type> a, std::pair<Type, Type> b) {
    std::pair<Type, Type> c;
    c.first = a.first * b.firest;
    c.second = a.second * b.second;
    return c;
}

template <typename Type, typename Type2>
std::pair<Type, Type> operator/(std::pair<Type, Type> a, Type2 b) {
    std::pair<Type, Type> c;
    c.first = a.first / b;
    c.second = a.second / b;
    return c;
}

#endif /* LOGICALDATATYPE_HH_ */