/*! \file pimathvector.h
 * \brief PIMathVector
 *
 * This file declare math vector class, which performs various vector operations
*/
/*
	PIP - Platform Independent Primitives
	PIMathVector
	Ivan Pelipenko peri4ko@yandex.ru, Andrey Bychkov work.a.b@yandex.ru

	This program 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.

	This program 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 this program.  If not, see <http://www.gnu.org/licenses/>.
*/

#ifndef PIMATHVECTOR_H
#define PIMATHVECTOR_H

#include "pimathbase.h"

template<uint Cols, uint Rows, typename Type>
class PIMathMatrixT;


/// Vector templated

#define PIMV_FOR(v, s) for (uint v = s; v < Size; ++v)

//! \brief A class that works with vector operations, the input data of which are size and the data type of the vector
//! @tparam Size number of matrix elements
//! @tparam Type is the data type of the vector. There are can be basic C++ language data and different classes where the arithmetic operators(=, +=, -=, *=, /=, ==, !=, +, -, *, /)
//!  of the C++ language are implemented
template<uint Size, typename Type = double>
class PIP_EXPORT PIMathVectorT {
	typedef PIMathVectorT<Size, Type> _CVector;
	static_assert(std::is_arithmetic<Type>::value, "Type must be arithmetic");
public:
	/**
	* @brief Constructor that calls the private resize method
	*
	*/
	PIMathVectorT() {resize();}

	/**
	* @brief Constructor that fills a vector PIMathVectorT with the values ​​of another vector "PIVector"
	*
	* @param val vector of type PIVector which is identified PIMathVectorT
	*/
	PIMathVectorT(const PIVector<Type> & val) {resize(); PIMV_FOR(i, 0) c[i] = val[i];}

	/**
	* @brief Constructor that fills a vector PIMathVectorT with the subtraction of two vectors
	*
	* @param st vector of type PIMathVectorT
	* @param fn vector of type PIMathVectorT
	*/
	PIMathVectorT(const _CVector & st, const _CVector & fn) {resize(); set(st, fn);}

	/**
    * @brief Method that returns the number of elements contained in the vector
	*
	* @return type uint shows number of elements in this vector
	*/
	uint size() const {return Size;}

	/**
    * @brief Method that set this elements to value "v"
	*
	* @param v value of which the vector is filled
    * @return reference to this
	*/
	_CVector & fill(const Type & v) {PIMV_FOR(i, 0) c[i] = v; return *this;}

	/**
    * @brief Method that set this with the subtraction of two vectors
	*
	* @param st vector of type PIMathVectorT
	* @param fn vector of type PIMathVectorT
    * @return reference to this
	*/
	_CVector & set(const _CVector & st, const _CVector & fn) {PIMV_FOR(i, 0) c[i] = fn[i] - st[i]; return *this;}

	/**
    * @brief Method that sets this using a vector, each element of which is added to the value of "v"
	*
	* @param v value of which the vector is filled
    * @return reference to this
	*/
	_CVector & move(const Type & v) {PIMV_FOR(i, 0) c[i] += v; return *this;}

	/**
    * @brief Method that sets this with a vector, each element of which is added to each element of the vector "v"
	*
	* @param v vector of type PIMathVectorT
    * @return reference to this
	*/
    _CVector & move(const _CVector & v) {PIMV_FOR(i, 0) c[i] += v[i]; return *this;}

	/**
	* @brief Method that returns sum of the squares of all elements of the vector
	*
	* @return value equal to the sum of the squares of all elements of the vector
	*/
	Type lengthSqr() const {Type tv(0); PIMV_FOR(i, 0) tv += (c[i] * c[i]); return tv;}

	/**
    * @brief Method that returns a scalar physical value equal to the absolute value of vector
	*
	* @return value equal to length of a vector
	*/
	Type length() const {return sqrt(lengthSqr());}

	/**
	* @brief Method that returns the sum of the absolute values ​​of all vector values
	*
	* @return value equal sum of the absolute values ​​of all vector values
	*/
	Type manhattanLength() const {Type tv(0); PIMV_FOR(i, 0) tv += fabs(c[i]); return tv;}

	/**
	* @brief Method that returns the cos of the current vector and vector "v"
    * If the vectors have different dimensions, it returns false
	*
	* @param v vector of type PIMathVectorT
	* @return cos value of the angle between two vectors
	*/
    Type angleCos(const _CVector & v) const {if(v.size() != Size) return false; Type tv = v.length() * length(); return (tv == Type(0) ? Type(0) : ((*this) ^ v) / tv);}

	/**
    * @brief Method that returns the sin of the current vector and vector "v". Works only with vectors which consists of 3 elements.
    * If the vectors have different dimensions, it returns false
    *
	* @param v vector of type PIMathVectorT
	* @return sin value of the angle between two vector
	*/
    Type angleSin(const _CVector & v) const {if(v.size() != Size) return false; Type tv = angleCos(v); return sqrt(Type(1) - tv * tv);}

	/**
    * @brief Method that returns the angle between of the current vector and vector "v" in Rad.
    * If the vectors have different dimensions, it returns false
	*
	* @param v vector of type PIMathVectorT
	* @return value of the angle between two vectors in Rad
	*/
    Type angleRad(const _CVector & v) const {if(v.size() != Size) return false; return acos(angleCos(v));}

	/**
    * @brief Method that returns the angle between of the current vector and vector "v" in Deg.
    * If the vectors have different dimensions, it returns false
	*
	* @param v vector of type PIMathVectorT
	* @return value of the angle between two vectors in Deg
	*/
    Type angleDeg(const _CVector & v) const {if(v.size() != Size) return false; return toDeg(acos(angleCos(v)));}

	/**
    * @brief Method that returns the angle elevation between of the current vector and vector "v" in Deg.
    * If the vectors have different dimensions, it returns false
	*
	* @param v vector of type PIMathVectorT
	* @return value of the angle elevation between two vectors in Deg
	*/
    Type angleElevation(const _CVector & v) const {if(v.size() != Size) return false; _CVector z = v - *this; double c = z.angleCos(*this); return 90.0 - acos(c) * rad2deg;}

	/**
    * @brief Method that returns a vector equal to the projection of the current vector onto the vector "v".
    * If the vectors have different dimensions, it returns this without changing anything
	*
	* @param v vector of type PIMathVectorT
	* @return vector of type PIMathVectorT equal to the projection of the current vector onto the vector "v"
	*/
    _CVector projection(const _CVector & v) {if(v.size() != Size) return _CVector(*this); Type tv = v.length(); return (tv == Type(0) ? _CVector() : v * (((*this) ^ v) / tv));}

	/**
    * @brief Method that returns this normalized vector
	*
    * @return reference to this
	*/
	_CVector & normalize() {Type tv = length(); if (tv == Type(1)) return *this; if (piAbs<Type>(tv) <= Type(1E-100)) {fill(Type(0)); return *this;} PIMV_FOR(i, 0) c[i] /= tv; return *this;}

	/**
	* @brief Method that returns a normalized vector
	*
	* @return normalized vector of type PIMathVectorT
	*/
	_CVector normalized() {_CVector tv(*this); tv.normalize(); return tv;}

	/**
	* @brief Method that returns a vector equal to vector product of current vector and vector "v". Works only with vectors which consists of 3 elements
	*
	* @param v vector of type PIMathVectorT
	* @return vector equal to vector product of current vector and vector "v" type of PIMathVectorT
	*/
	_CVector cross(const _CVector & v) {return (*this) * v;}

	/**
	* @brief Method that returns a value equal to absolute value of dot product of current vector and vector "v"
	*
	* @param v vector of type PIMathVectorT
	* @return value equal to absolute value of dot product of current vector and vector "v"
	*/
	Type dot(const _CVector & v) const {return (*this) ^ v;}

	/**
	* @brief Method which checks if every elements of vector are zeros
	*
	* @return true if vector is zero, else false
	*/
	bool isNull() const {PIMV_FOR(i, 0) if (c[i] != Type(0)) return false; return true;}

	/**
    * @brief Method which checks if current vector is orthogonal to vector "v".
    * If the vectors have different dimensions, it returns false
	*
	* @param v vector of type PIMathVectorT
	* @return true if vectors are orthogonal, else false
	*/
    bool isOrtho(const _CVector & v) const {if(v.size() != Size) return false; return ((*this) ^ v) == Type(0);}

	/**
	* @brief Read-only access to elements reference by index of the vector element "index"
	* If you enter an index out of the border of the vector there will be "undefined behavior"
	*
	* @param index is a parameter that shows the index number of the vector of the selected element
	* @return reference to element of vector by index
	*/
	const Type & at(uint index) {return c[index];}

	/**
	* @brief Full access to the element of vector by index. If you enter an index out of the border of the vector there will be "undefined behavior"
	*
	* @param index is the index of necessary element
	* @return element of vector
	*/
	Type & operator [](uint index) {return c[index];}

	/**
	* @brief Read-only access to the element of vector by index. If you enter an index out of the border of the vector there will be "undefined behavior"
	*
	* @param index is the index of necessary element
	* @return element of vector
	*/
    const Type & operator [](uint index) const {return c[index];}

	/**
    * @brief Vector assignment to vector "v" of type PIMathVectorT
	*
	* @param v vector for the assigment
	* @return vector equal to vector "v"
	*/
	_CVector & operator =(const _CVector & v) {memcpy(c, v.c, sizeof(Type) * Size); return *this;}

	/**
    * @brief Assignment operation. All vector values ​​become equal to "v"
	*
	* @param v value for the assigment
    * @return reference to this
	*/
    _CVector & operator =(const Type & v) {PIMV_FOR(i, 0) c[i] = v; return *this;}

	/**
	* @brief Compare with vector "v"
	*
	* @param v vector for the compare
	* @return if vectors are equal true, else false
	*/
	bool operator ==(const _CVector & v) const {PIMV_FOR(i, 0) if (c[i] != v[i]) return false; return true;}

	/**
	* @brief Compare with vector "v"
	*
	* @param v vector for the compare
	* @return if vectors are not equal true, else false
	*/
	bool operator !=(const _CVector & v) const {return !(*this == v);}

	/**
    * @brief Vector addition this vector with vector "v". If the vectors have different dimensions, it returns void()
	*
	* @param v vector for the addition assigment
	*/
    void operator +=(const _CVector & v) {if(v.size() != Size) return void(); PIMV_FOR(i, 0) c[i] += v[i];}

	/**
    * @brief Subtraction assignmentthis vector with vector "v". If the vectors have different dimensions, it returns void()
	*
	* @param v vector for the subtraction assigment
	*/
    void operator -=(const _CVector & v) {if(v.size() != Size) return void(); PIMV_FOR(i, 0) c[i] -= v[i];}

	/**
    * @brief Multiplication assignment this vector with value "v"
	*
	* @param v value for the multiplication assigment
	*/
	void operator *=(const Type & v) {PIMV_FOR(i, 0) c[i] *= v;}

	/**
    * @brief Multiplication assignment this vector with vector "v". If the vectors have different dimensions, it returns void()
	*
	* @param v vector for the multiplication assigment
	*/
    void operator *=(const _CVector & v) {if(v.size() != Size) return void(); PIMV_FOR(i, 0) c[i] *= v[i];}

	/**
    * @brief Division assignment with this vector value "v"
	*
	* @param v value for the division assigment
	*/
	void operator /=(const Type & v) {PIMV_FOR(i, 0) c[i] /= v;}

	/**
    * @brief Division assignment this vector with vector "v". If the vectors have different dimensions, it returns void()
	*
	* @param v vector for the division assigment
	*/
    void operator /=(const _CVector & v) {if(v.size() != Size) return void(); PIMV_FOR(i, 0) c[i] /= v[i];}

	/**
    * @brief Vector substraction this vector
	*
	* @return the result of vector substraction
	*/
	_CVector operator -() const {_CVector tv; PIMV_FOR(i, 0) tv[i] = -c[i]; return tv;}

	/**
    * @brief Vector addition this vector with vector "v". If the vectors have different dimensions, it returns this without changing anything
	*
    * @param v is vector term
    * @return the result of vector addition
	*/
    _CVector operator +(const _CVector & v) const {if(v.size() != Size) return _CVector(*this); _CVector tv = _CVector(*this); PIMV_FOR(i, 0) tv[i] += v[i]; return tv;}

	/**
    * @brief Vector substraction this vector with vector "v". If the vectors have different dimensions, it returns this without changing anything
	*
    * @param v is vector term
	* @return the result of vector substraction
	*/
    _CVector operator -(const _CVector & v) const {if(v.size() != Size) return _CVector(*this); _CVector tv = _CVector(*this); PIMV_FOR(i, 0) tv[i] -= v[i]; return tv;}

	/**
    * @brief Vector multiplication this vector with value "v"
	*
	* @param v is value factor
	* @return the result of vector multiplication
	*/
	_CVector operator *(const Type & v) const {_CVector tv = _CVector(*this); PIMV_FOR(i, 0) tv[i] *= v; return tv;}

	/**
    * @brief Vector division this vector with value "v"
	*
	* @param v is value divider
	* @return the result of vector division
	*/
	_CVector operator /(const Type & v) const {_CVector tv = _CVector(*this); PIMV_FOR(i, 0) tv[i] /= v; return tv;}

	/**
    * @brief Vector division this vector with vector "v". If the vectors have different dimensions, it returns this without changing anything
	*
	* @param v is vector divider
	* @return the result of vector division
	*/
    _CVector operator /(const _CVector & v) const {if(v.size() != Size) return _CVector(*this); _CVector tv = _CVector(*this); PIMV_FOR(i, 0) tv[i] /= v[i]; return tv;}

	/**
	* @brief Cross product of two vectors. Works only with vector containing three elements, otherwise returns current vector
	*
	* @param v is vector for cross product
	* @return the result vector equal of cross product
	*/
	_CVector operator *(const _CVector & v) const {if (Size != 3) return _CVector(); _CVector tv; tv.fill(Type(1)); tv[0] = c[1]*v[2] - v[1]*c[2]; tv[1] = v[0]*c[2] - c[0]*v[2]; tv[2] = c[0]*v[1] - v[0]*c[1]; return tv;}

	/**
    * @brief Elementwise assignment of multiplication of two vectors. If the vectors have different dimensions, it returns this without changing anything
	*
	* @param v is vector for multiplication
	* @return resulting vector
	*/
    _CVector operator &(const _CVector & v) const {if(v.size() != Size) return _CVector(*this); _CVector tv = _CVector(*this); PIMV_FOR(i, 0) tv[i] *= v[i]; return tv;}

	/**
    * @brief Absolute value of the dot product. If the vectors have different dimensions, it returns false
	*
	* @param v is vector for dot product
	* @return resulting vector
	*/
    Type operator ^(const _CVector & v) const {if(v.size() != Size) return false; Type tv(0); PIMV_FOR(i, 0) tv += c[i] * v[i]; return tv;}
	
	PIMathMatrixT<1, Size, Type> transposed() const {
		PIMathMatrixT<1, Size, Type> ret;
		PIMV_FOR(i, 0) ret[0][i] = c[i];
		return ret;
	}

	/**
	* @brief The method returns a part of the selected vector from the given vector
	*
	* @return the resulting vector that is part of this vector
	*/
	template<uint Size1, typename Type1> /// vector {Size, Type} to vector {Size1, Type1}
	PIMathVectorT<Size1, Type1> turnTo() const {PIMathVectorT<Size1, Type1> tv; uint sz = piMin<uint>(Size, Size1); for (uint i = 0; i < sz; ++i) tv[i] = c[i]; return tv;}

	/**
    * @brief Creates a vector each element of which is equal to value "v"
	*
	* @param v this value fills the cells of the vector
	* @return filled vector of type PIMathVectorT
	*/
	static _CVector filled(const Type & v) {_CVector vv; PIMV_FOR(i, 0) vv[i] = v; return vv;}

private:
	void resize(const Type & new_value = Type()) {for (uint i = 0; i < Size; ++i) c[i] = new_value;}
	
	Type c[Size];

};

/**
* @brief Inline operator which returns vector multiplication with value "x"
*
* @param x value for the multiplication
* @param v vector for the multiplication
* @return resulting vector
*/
template<uint Size, typename Type>
inline PIMathVectorT<Size, Type> operator *(const Type & x, const PIMathVectorT<Size, Type> & v) {
	return v * x;
}

/**
* @brief Inline operator for outputting the vector to the console
*
* @param s PICout type
* @param the vector type PIMathVectorT that we print to the console
* @return PIMathVectorT printed to the console
*/
template<uint Size, typename Type>
inline PICout operator <<(PICout s, const PIMathVectorT<Size, Type> & v) {s << "{"; PIMV_FOR(i, 0) {s << v[i]; if (i < Size - 1) s << ", ";} s << "}"; return s;}

/**
* @brief Inline operator checking if the cross product is zero. Works only with vector containing three elements, otherwise returns current vector
*
* @param f vector of the first operand
* @param s vector of the second operand
* @return true if the cross product is zero, else false
*/
template<uint Size, typename Type>
inline bool operator ||(const PIMathVectorT<Size, Type> & f, const PIMathVectorT<Size, Type> & s) {return (f * s).isNull();}

/**
* @brief Inline function which takes the square root of each element in the vector
*
* @param v vector of whose elements the square root is taken
* @return resulting vector
*/
template<uint Size, typename Type>
inline PIMathVectorT<Size, Type> sqrt(const PIMathVectorT<Size, Type> & v) {PIMathVectorT<Size, Type> ret; PIMV_FOR(i, 0) {ret[i] = sqrt(v[i]);} return ret;}

/**
* @brief Inline function which squares each element of the vector
*
* @param v vector whose elements are squared
* @return resulting vector
*/
template<uint Size, typename Type>
inline PIMathVectorT<Size, Type> sqr(const PIMathVectorT<Size, Type> & v) {PIMathVectorT<Size, Type> ret; PIMV_FOR(i, 0) {ret[i] = sqr(v[i]);} return ret;}

/**
* @brief Inline operator for serializing a vector into a PIByteArray
*
* @param s PIByteArray type
* @param v PIMathVectorT type
* @return PIBiteArray serialized PIMathVectorT
*/
template<uint Size, typename Type>
inline PIByteArray & operator <<(PIByteArray & s, const PIMathVectorT<Size, Type> & v) {for (uint i = 0; i < Size; ++i) s << v[i]; return s;}

/**
* @brief Inline operator to deserialize vector from PIByteArray
*
* @param s PIByteArray type
* @param v PIMathVector type
* @return PIMathVector deserialized from PIByteArray
*/
template<uint Size, typename Type>
inline PIByteArray & operator >>(PIByteArray & s, PIMathVectorT<Size, Type> & v) {for (uint i = 0; i < Size; ++i) s >> v[i]; return s;}

/**
* @brief Inline function which returns vector size 2 and type of T
*
* @param x first element of vector
* @param y second element of vector
* @return resulting vector
*/
template<typename T>
inline PIMathVectorT<2u, T> createVectorT2(T x, T y) {return PIMathVectorT<2u, T>(PIVector<T>() << x << y);}

/**
* @brief Inline function which returns vector size 3 and type of T
*
* @param x first element of vector
* @param y second element of vector
* @param z third element of vector
* @return resulting vector
*/
template<typename T>
inline PIMathVectorT<3u, T> createVectorT3(T x, T y, T z) {return PIMathVectorT<3u, T>(PIVector<T>() << x << y << z);}

/**
* @brief Inline function which returns vector size 4 and type of T
*
* @param x first element of vector
* @param y second element of vector
* @param z third element of vector
* @param w fouth element of vector
* @return resulting vector
*/
template<typename T>
inline PIMathVectorT<4u, T> createVectorT4(T x, T y, T z, T w) {return PIMathVectorT<4u, T>(PIVector<T>() << x << y << z << w);}

typedef PIMathVectorT<2u, int> PIMathVectorT2i;
typedef PIMathVectorT<3u, int> PIMathVectorT3i;
typedef PIMathVectorT<4u, int> PIMathVectorT4i;
typedef PIMathVectorT<2u, double> PIMathVectorT2d;
typedef PIMathVectorT<3u, double> PIMathVectorT3d;
typedef PIMathVectorT<4u, double> PIMathVectorT4d;
#define createVectorT2i createVectorT2<int>
#define createVectorT3i createVectorT3<int>
#define createVectorT4i createVectorT4<int>
#define createVectorT2f createVectorT2<float>
#define createVectorT3f createVectorT3<float>
#define createVectorT4f createVectorT4<float>
#define createVectorT2d createVectorT2<double>
#define createVectorT3d createVectorT3<double>
#define createVectorT4d createVectorT4<double>

#undef PIMV_FOR

/// Vector

#define PIMV_FOR(v, s) for (uint v = s; v < c.size(); ++v)

//! \brief A class that works with vector operations, the input data of which is the data type of the vector
//! @tparam Type is the data type of the vector. There are can be basic C++ language data and different classes where the arithmetic operators(=, +=, -=, *=, /=, ==, !=, +, -, *, /)
//!  of the C++ language are implemented
template<typename Type>
class PIP_EXPORT PIMathVector {
	typedef PIMathVector<Type> _CVector;
	template<typename TypeOp> friend PIByteArray & operator <<(PIByteArray & s, const PIMathVector<TypeOp> & v);
	template<typename TypeOp> friend PIByteArray & operator >>(PIByteArray & s, PIMathVector<TypeOp> & v);
public:
	/**
	* @brief Constructor that calls the resize method
	*
	* @param size vector dimension
	*/
	PIMathVector(const uint size = 0) {c.resize(size);}

	/**
	* @brief Constructor that fills a vector PIMathVector with the values ​​of another vector "PIVector"
	*
	* @param val vector of type PIVector which is identified PIMathVector
	*/
	PIMathVector(const PIVector<Type> & val) {c.resize(val.size()); PIMV_FOR(i, 0) c[i] = val[i];}

	/**
	* @brief Constructor that fills a vector PIMathVector with the subtraction of two vectors
	*
	* @param st vector of type PIMathVector
	* @param fn vector of type PIMathVector
	*/
	PIMathVector(const _CVector & st, const _CVector & fn) {c.resize(st.size()); PIMV_FOR(i, 0) c[i] = fn[i] - st[i];}

    /**
    * @brief Method that returns the number of elements contained in the vector
    *
    * @return type uint shows number of elements in this vector
    */
	uint size() const {return c.size();}

	/**
	* @brief Returns self resized vector
	*
	* @param size new vector dimension
	* @param new_value value with which the vector is filled
    * @return reference to this
	*/
	_CVector & resize(uint size, const Type & new_value = Type()) {c.resize(size, new_value); return *this;}

	/**
	* @brief Returns copy of resized vector
	*
	* @param size new vector dimension
	* @param new_value value with which the vector is filled
	* @return resized vector
	*/
	_CVector resized(uint size, const Type & new_value = Type()) {_CVector tv = _CVector(*this); tv.resize(size, new_value); return tv;}

    /**
    * @brief Method that set this elements to value "v"
    *
    * @param v value of which the vector is filled
    * @return reference to this
    */
	_CVector & fill(const Type & v) {PIMV_FOR(i, 0) c[i] = v; return *this;}

    /**
    * @brief Method that sets this using a vector, each element of which is added to the value of "v"
    *
    * @param v value of which the vector is filled
    * @return reference to this
    */
	_CVector & move(const Type & v) {PIMV_FOR(i, 0) c[i] += v; return *this;}

    /**
    * @brief Method that sets this with a vector, each element of which is added to each element of the vector "v".
    * If the vectors have different dimensions, it returns this without changing anything
    *
    * @param v vector of type PIMathVectorT
    * @return reference to this
    */
    _CVector & move(const _CVector & v) {if(v.size() != c.size()) return *this; PIMV_FOR(i, 0) c[i] += v[i]; return *this;}

	/**
    * @brief Method that replaces two elements in this vector by indices. You cannot use an index larger than the number vector dimension,
	*  otherwise there will be "undefined behavior"
	*
	* @param fe index of the first element
	* @param se index of the second element
    * @return reference to this
	*/
	_CVector & swap(uint fe, uint se) {piSwap<Type>(c[fe], c[se]); return *this;}

	/**
	* @brief Method that returns sum of the squares of all elements of the vector
	*
	* @return value equal to the sum of the squares of all elements of the vector
	*/
	Type lengthSqr() const {Type tv(0); PIMV_FOR(i, 0) tv += (c[i] * c[i]); return tv;}

    /**
    * @brief Method that returns a scalar physical value equal to the absolute value of vector
    *
    * @return value equal to length of a vector
    */
	Type length() const {return sqrt(lengthSqr());}

	/**
	* @brief Method that returns the sum of the absolute values ​​of all vector values
	*
	* @return value equal sum of the absolute values ​​of all vector values
	*/
	Type manhattanLength() const {Type tv(0); PIMV_FOR(i, 0) tv += fabs(c[i]); return tv;}

	/**
    * @brief Method that returns the cos of the current vector and vector "v". If the vectors have different dimensions, it returns false
	*
	* @param v vector of type PIMathVector
	* @return cos value of the angle between two vectors
	*/
    Type angleCos(const _CVector & v) const {if(v.size() != c.size()) return false; Type tv = v.length() * length(); return (tv == Type(0) ? Type(0) : ((*this) ^ v) / tv);}

	/**
    * @brief Method that returns the sin of the current vector and vector "v". Works only with vectors which consists of 3 elements.
    * If the vectors have different dimensions, it returns false
	*
	* @param v vector of type PIMathVector
	* @return sin value of the angle between two vector
	*/
    Type angleSin(const _CVector & v) const {if(v.size() != c.size()) return false; Type tv = angleCos(v); return sqrt(Type(1) - tv * tv);}

	/**
    * @brief Method that returns the angle between of the current vector and vector "v" in Rad.
    * If the vectors have different dimensions, it returns false
	*
	* @param v vector of type PIMathVector
	* @return value of the angle between two vectors in Rad
	*/
    Type angleRad(const _CVector & v) const {if(v.size() != c.size()) return false; return acos(angleCos(v));}

	/**
    * @brief Method that returns the angle between of the current vector and vector "v" in Deg.
    * If the vectors have different dimensions, it returns false
	*
	* @param v vector of type PIMathVectorT
	* @return value of the angle between two vectors in Deg
	*/
    Type angleDeg(const _CVector & v) const {if(v.size() != c.size()) return false; return toDeg(acos(angleCos(v)));}

	/**
    * @brief Method that returns a vector equal to the projection of the current vector onto the vector "v".
    * If the vectors have different dimensions, it returns this without changing anything
	*
	* @param v vector of type PIMathVector
	* @return vector of type PIMathVector equal to the projection of the current vector onto the vector "v"
	*/
    _CVector projection(const _CVector & v) {if(v.size() != c.size()) return *this; Type tv = v.length(); return (tv == Type(0) ? _CVector() : v * (((*this) ^ v) / tv));}

	/**
	* @brief Method that returns a normalized vector
	*
	* @return copy of normalized vector of type PIMathVector
	*/
	_CVector & normalize() {Type tv = length(); if (tv == Type(1)) return *this; if (piAbs<Type>(tv) <= Type(1E-100)) {fill(Type(0)); return *this;} PIMV_FOR(i, 0) c[i] /= tv; return *this;}

	/**
	* @brief Method that returns a normalized vector
	*
	* @return normalized vector of type PIMathVector
	*/
	_CVector normalized() {_CVector tv(*this); tv.normalize(); return tv;}

	/**
	* @brief Method which checks if every elements of vector are zeros
	*
	* @return true if vector is zero, else false
	*/
	bool isNull() const {PIMV_FOR(i, 0) if (c[i] != Type(0)) return false; return true;}

	/**
	* @brief Method which checks if vector is valid
	*
	* @return true if vector is valid, else false
	*/
	bool isValid() const {return !c.isEmpty();}

	/**
    * @brief Method which checks if current vector is orthogonal to vector "v".
    * If the vectors have different dimensions, it returns false
	*
	* @param v vector of type PIMathVector
	* @return true if vectors are orthogonal, else false
	*/
    bool isOrtho(const _CVector & v) const {if(v.size() != c.size()) return false; return ((*this) ^ v) == Type(0);}

	/**
	* @brief Read-only access to elements reference by index of the vector element "index"
	* If you enter an index out of the border of the vector there will be "undefined behavior"
	*
	* @param index is a parameter that shows the index number of the vector of the selected element
	* @return reference to element of vector by index
	*/
	const Type & at(uint index) {return c[index];}

	/**
	* @brief Full access to the element of vector by index. If you enter an index out of the border of the vector there will be "undefined behavior"
	*
	* @param index is the index of necessary element
	* @return element of vector
	*/
	Type & operator [](uint index) {return c[index];}

	/**
	* @brief Read-only access to the element of vector by index. If you enter an index out of the border of the vector there will be "undefined behavior"
	*
	* @param index is the index of necessary element
	* @return element of vector
	*/
    const Type & operator [](uint index) const {return c[index];}

	/**
	* @brief Vector assignment to vector "v" of type PIMathVector
    * If the vectors have different dimensions, it returns this without changing anything
	*
	* @param v vector for the assigment
    * @return reference to this
	*/
    _CVector & operator =(const _CVector & v) {if(v.size() != c.size()) return *this; c = v.c; return *this;}

	/**
	* @brief Vector assignment to value "v"
	*
	* @param v value for the assigment
    * @return reference to this
	*/
	_CVector & operator =(const Type & v) {PIMV_FOR(i, 0) c[i] = v; return *this;}

	/**
	* @brief Compare with vector "v"
	*
	* @param v vector for the compare
	* @return if vectors are equal true, else false
	*/
    bool operator ==(const _CVector & v) const {PIMV_FOR(i, 0) if ((c[i] != v[i]) || (v.size() != c.size())) return false; return true;}

	/**
	* @brief Compare with vector "v"
	*
	* @param v vector for the compare
	* @return if vectors are not equal true, else false
	*/
	bool operator !=(const _CVector & v) const {return !(*this == v);}

	/**
    * @brief Addition assignment this vector with vector "v". If the vectors have different dimensions, it returns void()
	*
	* @param v vector for the addition assigment
	*/
    void operator +=(const _CVector & v) {if(v.size() != c.size()) return void(); PIMV_FOR(i, 0) c[i] += v[i];}

	/**
    * @brief Subtraction assignment this vector with vector "v". If the vectors have different dimensions, it returns void()
	*
	* @param v vector for the subtraction assigment
	*/
    void operator -=(const _CVector & v) {if(v.size() != c.size()) return void(); PIMV_FOR(i, 0) c[i] -= v[i];}

	/**
    * @brief Multiplication assignment this vector with value "v"
	*
	* @param v value for the multiplication assigment
	*/
	void operator *=(const Type & v) {PIMV_FOR(i, 0) c[i] *= v;}

	/**
    * @brief Multiplication assignment this vector with vector "v". If the vectors have different dimensions, it returns void()
	*
	* @param v vector for the multiplication assigment
	*/
    void operator *=(const _CVector & v) {if(v.size() != c.size()) return void(); PIMV_FOR(i, 0) c[i] *= v[i];}

	/**
    * @brief Division assignment this vector with value "v"
	*
	* @param v value for the division assigment
	*/
	void operator /=(const Type & v) {PIMV_FOR(i, 0) c[i] /= v;}

	/**
    * @brief Division assignment this vector with vector "v". If the vectors have different dimensions, it returns void()
	*
	* @param v vector for the division assigment
	*/
    void operator /=(const _CVector & v) {if(v.size() != c.size()) return void(); PIMV_FOR(i, 0) c[i] /= v[i];}

	/**
    * @brief Vector substraction this vector
	*
	* @return the result of vector substraction
	*/
	_CVector operator -() const {_CVector tv; PIMV_FOR(i, 0) tv[i] = -c[i]; return tv;}

	/**
    * @brief Vector addition this vector with vector "v". If the vectors have different dimensions, it returns this without changing anything
	*
    * @param v is vector term
	* @return the result of matrix addition
	*/
    _CVector operator +(const _CVector & v) const {if(v.size() != c.size()) return _CVector(*this); _CVector tv = _CVector(*this); PIMV_FOR(i, 0) tv[i] += v[i]; return tv;}

	/**
    * @brief Vector substraction this vector with vector "v". If the vectors have different dimensions, it returns this without changing anything
	*
    * @param v is vector term
	* @return the result of vector substraction
	*/
    _CVector operator -(const _CVector & v) const {if(v.size() != c.size()) return _CVector(*this); _CVector tv = _CVector(*this); PIMV_FOR(i, 0) tv[i] -= v[i]; return tv;}

	/**
    * @brief Vector multiplicationthis vector with value "v"
	*
	* @param v is value factor
	* @return the result of vector multiplication
	*/
	_CVector operator *(const Type & v) const {_CVector tv = _CVector(*this); PIMV_FOR(i, 0) tv[i] *= v; return tv;}

	/**
    * @brief Vector division this vector with value "v"
	*
	* @param v is value divider
	* @return the result of vector division
	*/
	_CVector operator /(const Type & v) const {_CVector tv = _CVector(*this); PIMV_FOR(i, 0) tv[i] /= v; return tv;}

	/**
	* @brief Cross product of two vectors. Works only with vector containing three elements, otherwise returns current vector
	*
	* @param v is vector for cross product
	* @return the result vector equal of cross product
	*/
    _CVector operator *(const _CVector & v) const {if ((c.size() != 3) || (v.size() != 3)) return _CVector(); _CVector tv(3); tv.fill(Type(1)); tv[0] = c[1]*v[2] - v[1]*c[2]; tv[1] = v[0]*c[2] - c[0]*v[2]; tv[2] = c[0]*v[1] - v[0]*c[1]; return tv;}

	/**
    * @brief Elementwise assignment of multiplication of two vectors. If the vectors have different dimensions, it returns this without changing anything
	*
	* @param v is vector for multiplication
	* @return resulting vector
	*/
    _CVector operator &(const _CVector & v) const {if(v.size() != c.size()) return _CVector(*this); _CVector tv = _CVector(*this); PIMV_FOR(i, 0) tv[i] *= v[i]; return tv;}

	/**
    * @brief Value of the dot product. If the vectors have different dimensions, it returns false
	*
	* @param v is vector for dot product
    * @return resulting value
	*/
    Type operator ^(const _CVector & v) const {if(v.size() != c.size()) return false; Type tv(0); PIMV_FOR(i, 0) tv += c[i] * v[i]; return tv;}

	/**
	* @brief Converts PIMathVector to PIVector type
	*
	* @return vector equal PIMathVector but in PIVector type
	*/
	PIVector<Type> toVector() const {return c;}

	/**
	* @brief Returns full access data of vector
	*
	* @return data of vector
	*/
	inline Type * data() {return c.data();}

	/**
	* @brief Returns read-only data of vector
	*
	* @return data of vector
	*/
	inline const Type * data() const {return c.data();}

private:
	PIVector<Type> c;

};

#undef PIMV_FOR

#ifdef PIP_STD_IOSTREAM
template<typename Type>
inline std::ostream & operator <<(std::ostream & s, const PIMathVector<Type> & v) {s << "{"; for (uint i = 0; i < v.size(); ++i) {s << v[i]; if (i < v.size() - 1) s << ", ";} s << "}"; return s;}
#endif

/**
* @brief Inline operator for outputting the vector to the console
*
* @param s PICout type
* @param the vector type PIMathVector that we print to the console
* @return PIMathVector printed to the console
*/
template<typename Type>
inline PICout operator <<(PICout s, const PIMathVector<Type> & v) {s << "Vector{"; for (uint i = 0; i < v.size(); ++i) {s << v[i]; if (i < v.size() - 1) s << ", ";} s << "}"; return s;}

/**
* @brief Inline operator for serializing a vector into a PIByteArray
*
* @param s PIByteArray type
* @param v PIMathVector type
* @return PIBiteArray serialized PIMathVector
*/
template<typename Type>
inline PIByteArray & operator <<(PIByteArray & s, const PIMathVector<Type> & v) {s << v.c; return s;}

/**
* @brief Inline operator to deserialize vector from PIByteArray
*
* @param s PIByteArray type
* @param v PIMathVector type
* @return PIMathVector deserialized from PIByteArray
*/
template<typename Type>
inline PIByteArray & operator >>(PIByteArray & s, PIMathVector<Type> & v) {s >> v.c; return s;}


typedef PIMathVector<int> PIMathVectori;
typedef PIMathVector<double> PIMathVectord;

#endif // PIMATHVECTOR_H