/*! \file pimathvector.h
 * \ingroup Math
 * \~\brief
 * \~english Math vector
 * \~russian Математический вектор
 */
/*
    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"
#include "pimathcomplex.h"


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

#define PIMATHVECTOR_ZERO_CMP (1E-100)


/// Vector templated

#define PIMV_FOR              for (uint i = 0; i < Size; ++i)

template<uint Size, typename Type = double>
class PIP_EXPORT PIMathVectorT {
	typedef PIMathVectorT<Size, Type> _CVector;
	static_assert(std::is_arithmetic<Type>::value || is_complex<Type>::value, "Type must be arithmetic or complex");
	static_assert(Size > 0, "Size must be > 0");

public:
	PIMathVectorT(const Type & v = Type()) { PIMV_FOR c[i] = v; }
	PIMathVectorT(const PIVector<Type> & val) {
		assert(Size == val.size());
		PIMV_FOR c[i] = val[i];
	}
	PIMathVectorT(std::initializer_list<Type> init_list) {
		assert(Size == init_list.size());
		PIMV_FOR c[i] = init_list.begin()[i];
	}
	static _CVector fromTwoPoints(const _CVector & st, const _CVector & fn) {
		_CVector tv;
		PIMV_FOR tv[i] = fn[i] - st[i];
		return tv;
	}

	constexpr uint size() const { return Size; }
	_CVector & fill(const Type & v) {
		PIMV_FOR c[i] = v;
		return *this;
	}
	_CVector & move(const Type & v) {
		PIMV_FOR c[i] += v;
		return *this;
	}
	_CVector & move(const _CVector & v) {
		PIMV_FOR c[i] += v[i];
		return *this;
	}
	_CVector & swapElements(uint f, uint s) {
		piSwap<Type>(c[f], c[s]);
		return *this;
	}
	Type lengthSqr() const {
		Type tv(0);
		PIMV_FOR tv += c[i] * c[i];
		return tv;
	}

	Type length() const {
		static_assert(std::is_arithmetic<Type>::value, "Unavailable for complex");
		if (std::is_arithmetic<Type>::value) return std::sqrt(lengthSqr());
		// if (is_complex<Type>::value) return 1000.; // std::sqrt(lengthSqr());
	}

	Type manhattanLength() const {
		static_assert(std::is_arithmetic<Type>::value, "Unavailable for complex");
		if (std::is_arithmetic<Type>::value) {
			Type tv(0);
			PIMV_FOR tv += piAbs<Type>(c[i]);
			return tv;
		}
	}
	Type angleCos(const _CVector & v) const {
		static_assert(std::is_arithmetic<Type>::value, "Unavailable for complex");
		if (std::is_arithmetic<Type>::value) {
			Type tv = v.length() * length();
			assert(piAbs<Type>(tv) > PIMATHVECTOR_ZERO_CMP);
			return dot(v) / tv;
		}
	}
	Type angleSin(const _CVector & v) const {
		static_assert(std::is_arithmetic<Type>::value, "Unavailable for complex");
		if (std::is_arithmetic<Type>::value) {
			Type tv = angleCos(v);
			return std::sqrt(Type(1) - tv * tv);
		}
	}
	Type angleRad(const _CVector & v) const {
		static_assert(std::is_arithmetic<Type>::value, "Unavailable for complex");
		if (std::is_arithmetic<Type>::value) {
			return std::acos(angleCos(v));
		}
	}
	Type angleDeg(const _CVector & v) const {
		static_assert(std::is_arithmetic<Type>::value, "Unavailable for complex");
		if (std::is_arithmetic<Type>::value) {
			return toDeg(angleRad(v));
		}
	}
	Type angleElevation(const _CVector & v) const {
		static_assert(std::is_arithmetic<Type>::value, "Unavailable for complex");
		if (std::is_arithmetic<Type>::value) {
			return 90.0 - angleDeg(v - *this);
		}
	}
	_CVector projection(const _CVector & v) {
		static_assert(std::is_arithmetic<Type>::value, "Unavailable for complex");
		if (std::is_arithmetic<Type>::value) {
			Type tv = v.length();
			assert(piAbs<Type>(tv) > PIMATHVECTOR_ZERO_CMP);
			return v * (dot(v) / tv);
		}
	}
	_CVector & normalize() {
		static_assert(std::is_arithmetic<Type>::value, "Unavailable for complex");
		if (std::is_arithmetic<Type>::value) {
			Type tv = length();
			assert(piAbs<Type>(tv) > PIMATHVECTOR_ZERO_CMP);
			if (tv == Type(1)) return *this;
			PIMV_FOR c[i] /= tv;
			return *this;
		}
	}
	_CVector normalized() {
		_CVector tv(*this);
		tv.normalize();
		return tv;
	}
	bool isNull() const {
		PIMV_FOR if (c[i] != Type{}) return false;
		return true;
	}
	bool isOrtho(const _CVector & v) const { return ((*this) ^ v) == Type{}; }

	Type & operator[](uint index) { return c[index]; }
	const Type & operator[](uint index) const { return c[index]; }
	Type at(uint index) const { return c[index]; }
	inline Type & element(uint index) { return c[index]; }
	inline const Type & element(uint index) const { return c[index]; }

	_CVector & operator=(const Type & v) {
		PIMV_FOR c[i] = v;
		return *this;
	}

	bool operator==(const _CVector & v) const {
		PIMV_FOR if (c[i] != v[i]) return false;
		return true;
	}
	bool operator!=(const _CVector & v) const { return !(*this == c); }

	void operator+=(const _CVector & v) { PIMV_FOR c[i] += v[i]; }
	void operator-=(const _CVector & v) { PIMV_FOR c[i] -= v[i]; }
	void operator*=(const Type & v) { PIMV_FOR c[i] *= v; }
	void operator/=(const Type & v) {
		assert(std::abs(v) > PIMATHVECTOR_ZERO_CMP);
		PIMV_FOR c[i] /= v;
	}
	_CVector operator-() const {
		_CVector tv;
		PIMV_FOR tv[i] = -c[i];
		return tv;
	}
	_CVector operator+(const _CVector & v) const {
		_CVector tv(*this);
		PIMV_FOR tv[i] += v[i];
		return tv;
	}
	_CVector operator-(const _CVector & v) const {
		_CVector tv(*this);
		PIMV_FOR tv[i] -= v[i];
		return tv;
	}
	_CVector operator*(const Type & v) const {
		_CVector tv(*this);
		PIMV_FOR tv[i] *= v;
		return tv;
	}
	_CVector operator/(const Type & v) const {
		assert(std::abs(v) > PIMATHVECTOR_ZERO_CMP);
		_CVector tv = _CVector(*this);
		PIMV_FOR tv[i] /= v;
		return tv;
	}

	_CVector cross(const _CVector & v) const {
		static_assert(Size == 3, "cross product avalible only for 3D vectors");
		_CVector tv;
		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;
	}
	Type dot(const _CVector & v) const {
		Type tv{};
		PIMV_FOR tv += c[i] * v[i];
		return tv;
	}
	_CVector mul(const _CVector & v) const {
		_CVector tv(*this);
		PIMV_FOR tv[i] *= v[i];
		return tv;
	}
	_CVector mul(const Type & v) const { return (*this) * v; }
	_CVector div(const _CVector & v) const {
		_CVector tv(*this);
		PIMV_FOR {
			assert(std::abs(v[i]) > PIMATHVECTOR_ZERO_CMP);
			tv[i] /= v[i];
		}
		return tv;
	}
	_CVector div(const Type & v) const { return (*this) / v; }

	PIMathMatrixT<1, Size, Type> transposed() const {
		PIMathMatrixT<1, Size, Type> ret;
		PIMV_FOR ret[0][i] = c[i];
		return ret;
	}

	Type distToLine(const _CVector & lp0, const _CVector & lp1) {
		static_assert(std::is_arithmetic<Type>::value, "Unavailable for complex");
		if (std::is_arithmetic<Type>::value) {
			_CVector a(lp0, lp1);
			Type tv = a.length();
			assert(std::abs(tv) > PIMATHVECTOR_ZERO_CMP);
			_CVector b(lp0, *this);
			return piAbs<Type>(a[0] * b[1] - a[1] * b[0]) / tv;
		}
	}

	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;
	}

	//! \~english
	//! \brief Returns this vector with another element type.
	//! \~russian
	//! \brief Возвращает этот вектор с другим типом элементов.
	template<typename T>
	PIMathVectorT<Size, T> toType() const {
		PIMathVectorT<Size, T> ret;
		PIMV_FOR ret[i] = element(i);
		return ret;
	}

	//! \~english
	//! \brief Returns the subvector with size SubSize. Elements takes from coordinates "offset".
	//! \details
	//! \~russian
	//! \brief Возвращает подвектор с размерами SubSize. Элементы берутся с координат "offset".
	//! \details Координаты могут быть отрицательными. Возвращаемый подвектор может быть любого размера. Если исходные элементы выходят
	//! за границы исходного подвектора, то в подвекторе будут нули.
	template<uint SubSize>
	PIMathVectorT<SubSize, Type> subvector(int offset = 0) const {
		PIMathVectorT<SubSize, Type> ret;
		for (int i = 0; i < (int)SubSize; ++i) {
			int si = i + offset;
			if (si < 0 || si >= (int)Size) continue;
			ret[i] = element(si);
		}
		return ret;
	}

	//! \~english
	//! \brief Set the subvector "v" in coordinates "index".
	//! \details
	//! \~russian
	//! \brief Устанавливает подвектор "v" в координаты "index".
	//! \details Присваивает значения из вектора "v" в область текущиего вектора, ограниченную
	//! размерами "v", самого вектор и границами, исходя из координат установки. Координаты могут быть отрицательными.
	//! Вектор "v" может быть любого размера. Возвращает ссылку на этот вектор.
	template<uint SubSize>
	PIMathVectorT<Size, Type> & setSubvector(int index, const PIMathVectorT<SubSize, Type> & v) {
		for (int i = 0; i < (int)SubSize; ++i) {
			int si = i + index;
			if (si < 0 || si >= (int)Size) continue;
			element(si) = v[i];
		}
		return *this;
	}

	static _CVector cross(const _CVector & v1, const _CVector & v2) { return v1.cross(v2); }
	static _CVector dot(const _CVector & v1, const _CVector & v2) { return v1.dot(v2); }
	static _CVector mul(const _CVector & v1, const _CVector & v2) { return v1.mul(v2); }
	static _CVector mul(const Type & v1, const _CVector & v2) { return v2 * v1; }
	static _CVector mul(const _CVector & v1, const Type & v2) { return v1 * v2; }
	static _CVector div(const _CVector & v1, const _CVector & v2) { return v1.div(v2); }
	static _CVector div(const _CVector & v1, const Type & v2) { return v1 / v2; }

private:
	Type c[Size];
};

template<uint Size, typename Type>
inline PIMathVectorT<Size, Type> operator*(const Type & x, const PIMathVectorT<Size, Type> & v) {
	return v * x;
}

template<uint Size, typename Type>
inline PICout operator<<(PICout s, const PIMathVectorT<Size, Type> & v) {
	s << "Vector{";
	PIMV_FOR {
		s << v[i];
		if (i < Size - 1) s << ", ";
	}
	s << "}";
	return s;
}


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;


#undef PIMV_FOR

/// Vector

#define PIMV_FOR for (uint i = 0; i < c.size(); ++i)

template<typename Type>
class PIP_EXPORT PIMathVector {
	typedef PIMathVector<Type> _CVector;
	template<typename P, typename Type1>
	friend PIBinaryStream<P> & operator<<(PIBinaryStream<P> & s, const PIMathVector<Type1> & v);
	template<typename P, typename Type1>
	friend PIBinaryStream<P> & operator>>(PIBinaryStream<P> & s, PIMathVector<Type1> & v);

public:
	PIMathVector(const uint size = 0, const Type & new_value = Type()) { c.resize(size, new_value); }
	PIMathVector(const PIVector<Type> & val) { c = val; }
	PIMathVector(PIVector<Type> && val): c(std::move(val)) {}
	PIMathVector(std::initializer_list<Type> init_list) { c = PIVector<Type>(init_list); }

	template<uint Size>
	PIMathVector(const PIMathVectorT<Size, Type> & val) {
		c.resize(Size);
		PIMV_FOR c[i] = val[i];
	}

	static PIMathVector fromTwoPoints(const _CVector & st, const _CVector & fn) {
		assert(st.size() == fn.size());
		_CVector v(st.size());
		for (uint i = 0; i < v.size(); ++i)
			v.c[i] = fn[i] - st[i];
	}

	static PIMathVector zeros(const uint size) { return PIMathVector(size, Type()); }
	static PIMathVector ones(const uint size) { return PIMathVector(size, Type(1)); }
	static PIMathVector arange(const Type start, const Type stop, const Type step = Type(1)) {
		PIVector<Type> v;
		for (Type i = start; i < stop; i += step)
			v << i;
		return PIMathVector(std::move(v));
	}

	uint size() const { return c.size(); }
	_CVector & resize(uint size, const Type & new_value = Type()) {
		c.resize(size, new_value);
		return *this;
	}
	_CVector resized(uint size, const Type & new_value = Type()) {
		_CVector tv = _CVector(*this);
		tv.resize(size, new_value);
		return tv;
	}
	_CVector & fill(const Type & v) {
		c.fill(v);
		return *this;
	}
	_CVector & move(const Type & v) {
		PIMV_FOR c[i] += v;
		return *this;
	}
	_CVector & move(const _CVector & v) {
		assert(c.size() == v.size());
		PIMV_FOR c[i] += v[i];
		return *this;
	}
	_CVector & swapElements(uint f, uint s) {
		piSwap<Type>(c[f], c[s]);
		return *this;
	}
	Type lengthSqr() const {
		Type tv(0);
		PIMV_FOR tv += c[i] * c[i];
		return tv;
	}
	Type length() const { return std::sqrt(lengthSqr()); }
	Type manhattanLength() const {
		Type tv(0);
		PIMV_FOR tv += piAbs<Type>(c[i]);
		return tv;
	}
	Type angleCos(const _CVector & v) const {
		assert(c.size() == v.size());
		Type tv = v.length() * length();
		assert(std::abs(tv) > PIMATHVECTOR_ZERO_CMP);
		return dot(v) / tv;
	}
	Type angleSin(const _CVector & v) const {
		assert(c.size() == v.size());
		Type tv = angleCos(v);
		return std::sqrt(Type(1) - tv * tv);
	}
	Type angleRad(const _CVector & v) const { return std::acos(angleCos(v)); }
	Type angleDeg(const _CVector & v) const { return toDeg(angleRad(v)); }
	_CVector projection(const _CVector & v) {
		assert(c.size() == v.size());
		Type tv = v.length();
		assert(std::abs(tv) > PIMATHVECTOR_ZERO_CMP);
		return v * (dot(v) / tv);
	}
	_CVector & normalize() {
		Type tv = length();
		assert(std::abs(tv) > PIMATHVECTOR_ZERO_CMP);
		if (tv == Type(1)) return *this;
		PIMV_FOR c[i] /= tv;
		return *this;
	}
	_CVector normalized() {
		_CVector tv(*this);
		tv.normalize();
		return tv;
	}
	bool isNull() const {
		PIMV_FOR if (c[i] != Type(0)) return false;
		return true;
	}
	bool isValid() const { return !c.isEmpty(); }
	bool isOrtho(const _CVector & v) const { return dot(v) == Type(0); }

	Type & operator[](uint index) { return c[index]; }
	const Type & operator[](uint index) const { return c[index]; }
	Type at(uint index) const { return c[index]; }

	_CVector & operator=(const Type & v) {
		PIMV_FOR c[i] = v;
		return *this;
	}

	bool operator==(const _CVector & v) const { return c == v.c; }
	bool operator!=(const _CVector & v) const { return c != v.c; }

	void operator+=(const _CVector & v) {
		assert(c.size() == v.size());
		PIMV_FOR c[i] += v[i];
	}
	void operator-=(const _CVector & v) {
		assert(c.size() == v.size());
		PIMV_FOR c[i] -= v[i];
	}
	void operator*=(const Type & v) { PIMV_FOR c[i] *= v; }
	void operator/=(const Type & v) {
		assert(std::abs(v) > PIMATHVECTOR_ZERO_CMP);
		PIMV_FOR c[i] /= v;
	}
	_CVector operator-() const {
		_CVector tv(c.size());
		PIMV_FOR tv[i] = -c[i];
		return tv;
	}
	_CVector operator+(const _CVector & v) const {
		assert(c.size() == v.size());
		_CVector tv(*this);
		PIMV_FOR tv[i] += v[i];
		return tv;
	}
	_CVector operator-(const _CVector & v) const {
		assert(c.size() == v.size());
		_CVector tv(*this);
		PIMV_FOR tv[i] -= v[i];
		return tv;
	}
	_CVector operator*(const Type & v) const {
		_CVector tv(*this);
		PIMV_FOR tv[i] *= v;
		return tv;
	}
	_CVector operator/(const Type & v) const {
		assert(std::abs(v) > PIMATHVECTOR_ZERO_CMP);
		_CVector tv(*this);
		PIMV_FOR tv[i] /= v;
		return tv;
	}
	_CVector cross(const _CVector & v) const {
		assert(c.size() == 3);
		assert(v.size() == 3);
		_CVector tv(3);
		tv[0] = c[1] * v[2] - v[1] * c[2];
		tv[1] = c[2] * v[0] - v[2] * c[0];
		tv[2] = c[0] * v[1] - v[0] * c[1];
		return tv;
	}
	Type dot(const _CVector & v) const {
		assert(c.size() == v.size());
		Type tv(0);
		PIMV_FOR tv += c[i] * v[i];
		return tv;
	}
	_CVector mul(const _CVector & v) const {
		assert(c.size() == v.size());
		_CVector tv(*this);
		PIMV_FOR tv[i] *= v[i];
		return tv;
	}
	_CVector mul(const Type & v) const { return (*this) * v; }
	_CVector div(const _CVector & v) const {
		assert(c.size() == v.size());
		_CVector tv(*this);
		PIMV_FOR {
			assert(std::abs(v[i]) > PIMATHVECTOR_ZERO_CMP);
			tv[i] /= v[i];
		}
		return tv;
	}
	_CVector div(const Type & v) const { return (*this) / v; }

	Type distToLine(const _CVector & lp0, const _CVector & lp1) {
		assert(c.size() == lp0.size());
		assert(c.size() == lp1.size());
		_CVector a = _CVector::fromTwoPoints(lp0, lp1);
		Type tv    = a.length();
		assert(std::abs(tv) > PIMATHVECTOR_ZERO_CMP);
		_CVector b = _CVector::fromTwoPoints(lp0, *this);
		return piAbs<Type>(a[0] * b[1] - a[1] * b[0]) / tv;
	}

	PIVector<Type> toVector() const { return c; }

	void forEach(std::function<void(const Type &)> f) const { c.forEach(f); }
	_CVector & forEach(std::function<void(Type &)> f) {
		c.forEach(f);
		return *this;
	}

	inline Type * data() { return c.data(); }
	inline const Type * data() const { return c.data(); }


	static _CVector cross(const _CVector & v1, const _CVector & v2) { return v1.cross(v2); }
	static _CVector dot(const _CVector & v1, const _CVector & v2) { return v1.dot(v2); }
	static _CVector mul(const _CVector & v1, const _CVector & v2) { return v1.mul(v2); }
	static _CVector mul(const Type & v1, const _CVector & v2) { return v2 * v1; }
	static _CVector mul(const _CVector & v1, const Type & v2) { return v1 * v2; }
	static _CVector div(const _CVector & v1, const _CVector & v2) { return v1.div(v2); }
	static _CVector div(const _CVector & v1, const Type & v2) { return v1 / v2; }

private:
	PIVector<Type> c;
};

template<typename Type>
inline PIMathVector<Type> operator*(const Type & x, const PIMathVector<Type> & v) {
	return v * x;
}

#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

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;
}

template<typename P, typename T>
inline PIBinaryStream<P> & operator<<(PIBinaryStream<P> & s, const PIMathVector<T> & v) {
	s << v.c;
	return s;
}
template<typename P, typename T>
inline PIBinaryStream<P> & operator>>(PIBinaryStream<P> & s, PIMathVector<T> & v) {
	s >> v.c;
	return s;
}


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

#endif // PIMATHVECTOR_H