/*! \file pimathmatrix.h
 * \brief PIMathMatrix
 *
 * This file declare math matrix class, which performs various matrix operations
*/
/*
	PIP - Platform Independent Primitives
	PIMathMatrix
	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 PIMATHMATRIX_H
#define PIMATHMATRIX_H

#include "pimathvector.h"
#include "pimathcomplex.h"


template<typename T>
inline bool _PIMathMatrixNullCompare(const T v) {
	static_assert(std::is_floating_point<T>::value, "Type must be floating point");
	return (piAbs(v) < T(1E-200));
}

template<>
inline bool _PIMathMatrixNullCompare<complexf>(const complexf v) {
	return (abs(v) < float(1E-200));
}

template<>
inline bool _PIMathMatrixNullCompare<complexd>(const complexd v) {
	return (abs(v) < double(1E-200));
}


/// Matrix templated

#define PIMM_FOR(r, c) for (uint c = 0; c < Cols; ++c) { for (uint r = 0; r < Rows; ++r) {
#define PIMM_FOR_WB(r, c) for (uint c = 0; c < Cols; ++c) for (uint r = 0; r < Rows; ++r) // without brakes
#define PIMM_FOR_I(r, c) for (uint r = 0; r < Rows; ++r) { for (uint c = 0; c < Cols; ++c) {
#define PIMM_FOR_I_WB(r, c) for (uint r = 0; r < Rows; ++r) for (uint c = 0; c < Cols; ++c) // without brakes
#define PIMM_FOR_C(v) for (uint v = 0; v < Cols; ++v)
#define PIMM_FOR_R(v) for (uint v = 0; v < Rows; ++v)

#pragma pack(push, 1)

//! \brief A class that works with square matrix operations, the input data of which are columns, rows and the data type of the matrix
template<uint Rows, uint Cols = Rows, typename Type = double>
class PIP_EXPORT PIMathMatrixT {
	typedef PIMathMatrixT<Rows, Cols, Type> _CMatrix;
	typedef PIMathMatrixT<Cols, Rows, Type> _CMatrixI;
	typedef PIMathVectorT<Rows, Type> _CMCol;
	typedef PIMathVectorT<Cols, Type> _CMRow;
	static_assert(std::is_arithmetic<Type>::value, "Type must be arithmetic");
	static_assert(Rows > 0, "Row count must be > 0");
	static_assert(Cols > 0, "Column count must be > 0");
public:
	PIMathMatrixT() { resize(Rows, Cols); }

	PIMathMatrixT(const PIVector<Type> &val) {
		resize(Rows, Cols);
		int i = 0;
		PIMM_FOR_I_WB(r, c) m[r][c] = val[i++];
	}

	/**
	 * @brief Сreates a matrix whose main diagonal is filled with ones and the remaining elements are zeros
	 *
	 * @return identitied matrix of type PIMathMatrixT
	 */
	static _CMatrix identity() {
		_CMatrix tm = _CMatrix();
		PIMM_FOR_WB(r, c) tm.m[r][c] = (c == r ? Type(1) : Type(0));
		return tm;
	}

	/**
	 * @brief Creates a matrix that is filled with elements
	 *
	 * @param v is a parameter the type and value of which is selected and later filled into the matrix
	 * @return filled matrix of type PIMathMatrixT
	 */
	static _CMatrix filled(const Type &v) {
		_CMatrix tm;
		PIMM_FOR_WB(r, c) tm.m[r][c] = v;
		return tm;
	}

	/**
	 * @brief Rotation the matrix by an "angle". Works only with 2x2 matrix,
	 * else return default construction of PIMathMatrixT
*
	 * @param angle is the angle of rotation of the matrix
	 * @return rotated matrix
	 */
	static _CMatrix rotation(double angle) { return _CMatrix(); }

	/**
	 * @brief Rotation of the matrix by an "angle" along the X axis. Works only with 3x3 matrix,
	 * else return default construction of PIMathMatrixT
	 *
	 * @param angle is the angle of rotation of the matrix along the X axis
	 * @return rotated matrix
	 */
	static _CMatrix rotationX(double angle) { return _CMatrix(); }

	/**
	 * @brief Rotation of the matrix by an "angle" along the Y axis. Works only with 3x3 matrix,
	 * else return default construction of PIMathMatrixT
	 *
	 * @param angle is the angle of rotation of the matrix along the Y axis
	 * @return rotated matrix
	 */
	static _CMatrix rotationY(double angle) { return _CMatrix(); }

	/**
	 * @brief Rotation of the matrix by an "angle" along the Z axis. Works only with 3x3 matrix,
	 * else return default construction of PIMathMatrixT
	 *
	 * @param angle is the angle of rotation of the matrix along the Z axis
	 * @return rotated matrix
	 */
	static _CMatrix rotationZ(double angle) { return _CMatrix(); }

	/**
	 * @brief Scaling the matrix along the X axis by the value "factor". Works only with 3x3 and 2x2 matrix,
	 * else return default construction of PIMathMatrixT
	 *
	 * @param factor is the value of scaling by X axis
	 * @return rotated matrix
	 */
	static _CMatrix scaleX(double factor) { return _CMatrix(); }

	/**
	 * @brief Scaling the matrix along the Y axis by the value "factor". Works only with 3x3 and 2x2 matrix,
	 * else return default construction of PIMathMatrixT
	 *
	 * @param factor is the value of scaling by Y axis
	 * @return rotated matrix
	 */
	static _CMatrix scaleY(double factor) { return _CMatrix(); }

	/**
	 * @brief Scaling the matrix along the Z axis by the value "factor". Works only with 3x3 matrix,
	 * else return default construction of PIMathMatrixT
	 *
	 * @param factor is the value of scaling by Z axis
	 * @return rotated matrix
	 */
	static _CMatrix scaleZ(double factor) { return _CMatrix(); }

	/**
	 * @brief Method which returns number of columns in matrix
	 *
	 * @return type uint shows number of columns
	 */
	uint cols() const { return Cols; }

	/**
	* @brief Method which returns number of rows in matrix
	*
	* @return type uint shows number of rows
	*/
	uint rows() const { return Rows; }

	/**
	 * @brief Method which returns the selected column in PIMathVectorT format
	 *
	 * @param index is the number of the selected column
	 * @return column in PIMathVectorT format
	 */
	_CMCol col(uint index) {
		_CMCol tv;
		PIMM_FOR_R(i) tv[i] = m[i][index];
		return tv;
	}

	/**
	 * @brief Method which returns the selected row in PIMathVectorT format
	 *
	 * @param index is the number of the selected row
	 * @return row in PIMathVectorT format
	 */
	_CMRow row(uint index) {
		_CMRow tv;
		PIMM_FOR_C(i) tv[i] = m[index][i];
		return tv;
	}

	/**
	 * @brief Set the selected column in matrix
	 *
	 * @param index is the number of the selected column
	 * @param v is a vector of the type _CMCol that needs to fill the column
	 * @return matrix type _CMatrix
	 */
	_CMatrix &setCol(uint index, const _CMCol &v) {
		PIMM_FOR_R(i) m[i][index] = v[i];
		return *this;
	}

	/**
	 * @brief Set the selected row in matrix
	 *
	 * @param index is the number of the selected row
	 * @param v is a vector of the type _CMCol that needs to fill the row
	 * @return matrix type _CMatrix
	 */
	_CMatrix &setRow(uint index, const _CMRow &v) {
		PIMM_FOR_C(i) m[index][i] = v[i];
		return *this;
	}

	/**
	 * @brief Method which changes selected rows in a matrix
	 *
	 * @param r0 is the number of the first selected row
	 * @param r1 is the number of the second selected row
	 * @return matrix type _CMatrix
	 */
	_CMatrix &swapRows(uint r0, uint r1) {
		Type t;
		PIMM_FOR_C(i) {
			t = m[r0][i];
			m[r0][i] = m[r1][i];
			m[r1][i] = t;
		}
		return *this;
	}

	/**
	 * @brief Method which changes selected columns in a matrix
	 *
	 * @param c0 is the number of the first selected column
	 * @param c1 is the number of the second selected column
	 * @return matrix type _CMatrix
	 */
	_CMatrix &swapCols(uint c0, uint c1) {
		Type t;
		PIMM_FOR_R(i) {
			t = m[i][c0];
			m[i][c0] = m[i][c1];
			m[i][c1] = t;
		}
		return *this;
	}

	/**
	 * @brief Method which fills the matrix with selected value
	 *
	 * @param v is a parameter the type and value of which is selected and later filled into the matrix
	 * @return filled matrix type _CMatrix
	 */
	_CMatrix &fill(const Type &v) {
		PIMM_FOR_WB(r, c) m[r][c] = v;
		return *this;
	}

	/**
	 * @brief Method which checks if matrix is square
	 *
	 * @return true if matrix is square, else false
	 */
	bool isSquare() const { return cols() == rows(); }

	/**
	 * @brief Method which checks if main diagonal of matrix consists of ones and another elements are zeros
	 *
	 * @return true if matrix is identitied, else false
	 */
	bool isIdentity() const {
		PIMM_FOR_WB(r, c) if ((c == r) ? m[r][c] != Type(1) : m[r][c] != Type(0)) return false;
		return true;
	}

	/**
	 * @brief Method which checks if every elements of matrix are zeros
	 *
	 * @return true if matrix is null, else false
	 */
	bool isNull() const {
		PIMM_FOR_WB(r, c) if (m[r][c] != Type(0)) return false;
		return true;
	}

	/**
	 * @brief Full access to elements reference by row "row" and col "col"
	 *
	 * @param row is a parameter that shows the row number of the matrix of the selected element
	 * @param col is a parameter that shows the column number of the matrix of the selected element
	 * @return reference to element of matrix by row "row" and col "col"
	 */
	Type &at(uint row, uint col) { return m[row][col]; }

	/**
	 * @brief Full access to element by row "row" and col "col"
	 *
	 * @param row is a parameter that shows the row number of the matrix of the selected element
	 * @param col is a parameter that shows the column number of the matrix of the selected element
	 * @return element of matrix by row "row" and col "col"
	 */
	Type at(uint row, uint col) const { return m[row][col]; }

	/**
	 * @brief Full access to the matrix row pointer
	 *
	 * @param row is a row of necessary matrix
	 * @return matrix row pointer
	 */
	Type *operator[](uint row) { return m[row]; }

	/**
	 * @brief Read-only access to the matrix row pointer
	 *
	 * @param row is a row of necessary matrix
	 * @return matrix row pointer
	 */
	const Type *operator[](uint row) const { return m[row]; }

	/**
	 * @brief Matrix assignment to matrix "sm"
	 *
	 * @param sm matrix for the assigment
	 * @return matrix equal with sm
	 */
	_CMatrix &operator=(const _CMatrix &sm) {
		memcpy(m, sm.m, sizeof(Type) * Cols * Rows);
		return *this;
	}

	/**
	 * @brief Compare with matrix "sm"
	 *
	 * @param sm matrix for the compare
	 * @return if matrices are equal true, else false
	 */
	bool operator==(const _CMatrix &sm) const {
		PIMM_FOR_WB(r, c) if (m[r][c] != sm.m[r][c]) return false;
		return true;
	}

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

	/**
	 * @brief Addition assignment with matrix "sm"
	 *
	 * @param sm matrix for the addition assigment
	 */
	void operator+=(const _CMatrix &sm) { PIMM_FOR_WB(r, c) m[r][c] += sm.m[r][c]; }

	/**
	 * @brief Subtraction assignment with matrix "sm"
	 *
	 * @param sm matrix for the subtraction assigment
	 */
	void operator-=(const _CMatrix &sm) { PIMM_FOR_WB(r, c) m[r][c] -= sm.m[r][c]; }

	/**
	 * @brief Multiplication assignment with value "v"
	 *
	 * @param v value for the multiplication assigment
	 */
	void operator*=(const Type &v) { PIMM_FOR_WB(r, c) m[r][c] *= v; }

	/**
	 * @brief Division assignment with value "v"
	 *
	 * @param v value for the division assigment
	 */
	void operator/=(const Type &v) { PIMM_FOR_WB(r, c) m[r][c] /= v; }

	/**
	 * @brief Matrix substraction
	 *
	 * @return the result of matrix substraction
	 */
	_CMatrix operator-() const {
		_CMatrix tm;
		PIMM_FOR_WB(r, c) tm.m[r][c] = -m[r][c];
		return tm;
	}

	/**
	 * @brief Matrix addition
	 *
	 * @param sm is matrix term
	 * @return the result of matrix addition
	 */
	_CMatrix operator+(const _CMatrix &sm) const {
		_CMatrix tm = _CMatrix(*this);
		PIMM_FOR_WB(r, c) tm.m[r][c] += sm.m[r][c];
		return tm;
	}

	/**
	 * @brief Matrix substraction
	 *
	 * @param sm is matrix subtractor
	 * @return the result of matrix substraction
	 */
	_CMatrix operator-(const _CMatrix &sm) const {
		_CMatrix tm = _CMatrix(*this);
		PIMM_FOR_WB(r, c) tm.m[r][c] -= sm.m[r][c];
		return tm;
	}

	/**
	 * @brief Matrix multiplication
	 *
	 * @param v is value factor
	 * @return the result of matrix multiplication
	 */
	_CMatrix operator*(const Type &v) const {
		_CMatrix tm = _CMatrix(*this);
		PIMM_FOR_WB(r, c) tm.m[r][c] *= v;
		return tm;
	}

	/**
	 * @brief Matrix division
	 *
	 * @param v is value divider
	 * @return the result of matrix division
	 */
	_CMatrix operator/(const Type &v) const {
		_CMatrix tm = _CMatrix(*this);
		PIMM_FOR_WB(r, c) tm.m[r][c] /= v;
		return tm;
	}

	/**
	 * @brief Determinant of the matrix is ​​calculated
	 *
	 * @return matrix determinant
	 */
	Type determinant(bool *ok = 0) const {
		_CMatrix m(*this);
		bool k;
		Type ret = Type(0);
		m.toUpperTriangular(&k);
		if (ok) *ok = k;
		if (!k) return ret;
		ret = Type(1);
		for (uint c = 0; c < Cols; ++c)
			for (uint r = 0; r < Rows; ++r)
				if (r == c)
					ret *= m[r][c];
		return ret;
	}

	/**
	 * @brief Transforming matrix to upper triangular
	 *
	 * @return transformed upper triangular matrix
	 */
	_CMatrix &toUpperTriangular(bool *ok = 0) {
		if (Cols != Rows) {
			if (ok != 0) *ok = false;
			return *this;
		}
		_CMatrix smat(*this);
		bool ndet;
		uint crow;
		Type mul;
		for (uint i = 0; i < Cols; ++i) {
			ndet = true;
			for (uint j = 0; j < Rows; ++j) if (smat.m[i][j] != 0) ndet = false;
			if (ndet) {
				if (ok != 0) *ok = false;
				return *this;
			}
		}
		for (uint i = 0; i < Cols; ++i) {
			crow = i;
			while (smat.m[i][i] == Type(0))
				smat.swapRows(i, ++crow);
			for (uint j = i + 1; j < Rows; ++j) {
				mul = smat.m[i][j] / smat.m[i][i];
				for (uint k = i; k < Cols; ++k) smat.m[k][j] -= mul * smat.m[k][i];
			}
			if (i < Cols - 1) {
				if (fabs(smat.m[i + 1][i + 1]) < Type(1E-200)) {
					if (ok != 0) *ok = false;
					return *this;
				}
			}
		}
		if (ok != 0) *ok = true;
		memcpy(m, smat.m, sizeof(Type) * Cols * Rows);
		return *this;
	}

	/**
	 * @brief Matrix inversion operation
	 *
	 * @return inverted matrix
	 */
	_CMatrix &invert(bool *ok = 0) {
		static_assert(Cols == Rows, "Only square matrix invertable");
		_CMatrix mtmp = _CMatrix::identity(), smat(*this);
		bool ndet;
		uint crow;
		Type mul, iddiv;
		for (uint i = 0; i < Cols; ++i) {
			ndet = true;
			for (uint j = 0; j < Rows; ++j) if (smat.m[i][j] != 0) ndet = false;
			if (ndet) {
				if (ok != 0) *ok = false;
				return *this;
			}
		}
		for (uint i = 0; i < Cols; ++i) {
			crow = i;
			while (smat.m[i][i] == Type(0)) {
				++crow;
				smat.swapRows(i, crow);
				mtmp.swapRows(i, crow);
			}
			for (uint j = i + 1; j < Rows; ++j) {
				mul = smat.m[i][j] / smat.m[i][i];
				for (uint k = i; k < Cols; ++k) smat.m[k][j] -= mul * smat.m[k][i];
				for (uint k = 0; k < Cols; ++k) mtmp.m[k][j] -= mul * mtmp.m[k][i];
			}
			if (i < Cols - 1) {
				if (fabs(smat.m[i + 1][i + 1]) < Type(1E-200)) {
					if (ok != 0) *ok = false;
					return *this;
				}
			}
			iddiv = smat.m[i][i];
			for (uint j = i; j < Cols; ++j) smat.m[j][i] /= iddiv;
			for (uint j = 0; j < Cols; ++j) mtmp.m[j][i] /= iddiv;
		}
		for (uint i = Cols - 1; i > 0; --i) {
			for (uint j = 0; j < i; ++j) {
				mul = smat.m[i][j];
				smat.m[i][j] -= mul;
				for (uint k = 0; k < Cols; ++k) mtmp.m[k][j] -= mtmp.m[k][i] * mul;
			}
		}
		if (ok != 0) *ok = true;
		memcpy(m, mtmp.m, sizeof(Type) * Cols * Rows);
		return *this;
	}

	/**
	 * @brief Matrix inversion operation
	 *
	 * @return inverted matrix
	 */
	_CMatrix inverted(bool *ok = 0) const {
		_CMatrix tm(*this);
		tm.invert(ok);
		return tm;
	}

	/**
	 * @brief Matrix transposition operation
	 *
	 * @return transposed matrix
	 */
	_CMatrixI transposed() const {
		_CMatrixI tm;
		PIMM_FOR_WB(r, c) tm[c][r] = m[r][c];
		return tm;
	}

private:
	void resize(uint rows_, uint cols_, const Type &new_value = Type()) {
		r_ = rows_;
		c_ = cols_;
		PIMM_FOR_WB(r, c) m[r][c] = new_value;
	}

	int c_, r_;
	Type m[Rows][Cols];

};

#pragma pack(pop)


template<>
inline PIMathMatrixT<2u, 2u> PIMathMatrixT<2u, 2u>::rotation(double angle) {
	double c = cos(angle), s = sin(angle);
	PIMathMatrixT<2u, 2u> tm;
	tm[0][0] = tm[1][1] = c;
	tm[0][1] = -s;
	tm[1][0] = s;
	return tm;
}

template<>
inline PIMathMatrixT<2u, 2u> PIMathMatrixT<2u, 2u>::scaleX(double factor) {
	PIMathMatrixT<2u, 2u> tm;
	tm[0][0] = factor;
	tm[1][1] = 1.;
	return tm;
}

template<>
inline PIMathMatrixT<2u, 2u> PIMathMatrixT<2u, 2u>::scaleY(double factor) {
	PIMathMatrixT<2u, 2u> tm;
	tm[0][0] = 1.;
	tm[1][1] = factor;
	return tm;
}

template<>
inline PIMathMatrixT<3u, 3u> PIMathMatrixT<3u, 3u>::rotationX(double angle) {
	double c = cos(angle), s = sin(angle);
	PIMathMatrixT<3u, 3u> tm;
	tm[0][0] = 1.;
	tm[1][1] = tm[2][2] = c;
	tm[2][1] = s;
	tm[1][2] = -s;
	return tm;
}

template<>
inline PIMathMatrixT<3u, 3u> PIMathMatrixT<3u, 3u>::rotationY(double angle) {
	double c = cos(angle), s = sin(angle);
	PIMathMatrixT<3u, 3u> tm;
	tm[1][1] = 1.;
	tm[0][0] = tm[2][2] = c;
	tm[2][0] = -s;
	tm[0][2] = s;
	return tm;
}

template<>
inline PIMathMatrixT<3u, 3u> PIMathMatrixT<3u, 3u>::rotationZ(double angle) {
	double c = cos(angle), s = sin(angle);
	PIMathMatrixT<3u, 3u> tm;
	tm[2][2] = 1.;
	tm[0][0] = tm[1][1] = c;
	tm[1][0] = s;
	tm[0][1] = -s;
	return tm;
}

template<>
inline PIMathMatrixT<3u, 3u> PIMathMatrixT<3u, 3u>::scaleX(double factor) {
	PIMathMatrixT<3u, 3u> tm;
	tm[1][1] = tm[2][2] = 1.;
	tm[0][0] = factor;
	return tm;
}

template<>
inline PIMathMatrixT<3u, 3u> PIMathMatrixT<3u, 3u>::scaleY(double factor) {
	PIMathMatrixT<3u, 3u> tm;
	tm[0][0] = tm[2][2] = 1.;
	tm[1][1] = factor;
	return tm;
}

template<>
inline PIMathMatrixT<3u, 3u> PIMathMatrixT<3u, 3u>::scaleZ(double factor) {
	PIMathMatrixT<3u, 3u> tm;
	tm[0][0] = tm[1][1] = 1.;
	tm[2][2] = factor;
	return tm;
}

#ifdef PIP_STD_IOSTREAM
template<uint Rows, uint Cols, typename Type>
inline std::ostream & operator <<(std::ostream & s, const PIMathMatrixT<Rows, Cols, Type> & m) {s << "{"; PIMM_FOR_I(r, c) s << m[r][c]; if (c < Cols - 1 || r < Rows - 1) s << ", ";} if (r < Rows - 1) s << std::endl << " ";} s << "}"; return s;}
#endif

template<uint Rows, uint Cols, typename Type>
inline PICout operator<<(PICout s, const PIMathMatrixT<Rows, Cols, Type> &m) {
	s << "{";
	PIMM_FOR_I(r, c) s << m[r][c];
			if (c < Cols - 1 || r < Rows - 1) s << ", "; }
		if (r < Rows - 1) s << PICoutManipulators::NewLine << " "; }
	s << "}";
	return s;
}

/// Multiply matrices {Rows0 x CR} on {CR x Cols1}, result is {Rows0 x Cols1}
template<uint CR, uint Rows0, uint Cols1, typename Type>
inline PIMathMatrixT<Rows0, Cols1, Type> operator*(const PIMathMatrixT<Rows0, CR, Type> &fm,
												   const PIMathMatrixT<CR, Cols1, Type> &sm) {
	PIMathMatrixT<Rows0, Cols1, Type> tm;
	Type t;
	for (uint j = 0; j < Rows0; ++j) {
		for (uint i = 0; i < Cols1; ++i) {
			t = Type(0);
			for (uint k = 0; k < CR; ++k)
				t += fm[j][k] * sm[k][i];
			tm[j][i] = t;
		}
	}
	return tm;
}

/// Multiply matrix {Rows x Cols} on vector {Cols}, result is vector {Rows}
template<uint Cols, uint Rows, typename Type>
inline PIMathVectorT<Rows, Type> operator*(const PIMathMatrixT<Rows, Cols, Type> &fm,
										   const PIMathVectorT<Cols, Type> &sv) {
	PIMathVectorT<Rows, Type> tv;
	Type t;
	for (uint j = 0; j < Rows; ++j) {
		t = Type(0);
		for (uint i = 0; i < Cols; ++i)
			t += fm[j][i] * sv[i];
		tv[j] = t;
	}
	return tv;
}

/// Multiply vector {Rows} on matrix {Rows x Cols}, result is vector {Cols}
template<uint Cols, uint Rows, typename Type>
inline PIMathVectorT<Cols, Type> operator*(const PIMathVectorT<Rows, Type> &sv,
										   const PIMathMatrixT<Rows, Cols, Type> &fm) {
	PIMathVectorT<Cols, Type> tv;
	Type t;
	for (uint j = 0; j < Cols; ++j) {
		t = Type(0);
		for (uint i = 0; i < Rows; ++i)
			t += fm[i][j] * sv[i];
		tv[j] = t;
	}
	return tv;
}

/// Multiply value(T) on matrix {Rows x Cols}, result is vector {Rows}
template<uint Cols, uint Rows, typename Type>
inline PIMathMatrixT<Rows, Cols, Type> operator*(const Type &x, const PIMathMatrixT<Rows, Cols, Type> &v) {
	return v * x;
}


typedef PIMathMatrixT<2u, 2u, int> PIMathMatrixT22i;
typedef PIMathMatrixT<3u, 3u, int> PIMathMatrixT33i;
typedef PIMathMatrixT<4u, 4u, int> PIMathMatrixT44i;
typedef PIMathMatrixT<2u, 2u, double> PIMathMatrixT22d;
typedef PIMathMatrixT<3u, 3u, double> PIMathMatrixT33d;
typedef PIMathMatrixT<4u, 4u, double> PIMathMatrixT44d;


template<typename Type>
class PIMathMatrix;

#undef PIMM_FOR
#undef PIMM_FOR_WB
#undef PIMM_FOR_I
#undef PIMM_FOR_I_WB
#undef PIMM_FOR_C
#undef PIMM_FOR_R





/// Matrix

#define PIMM_FOR(c, r) for (uint c = 0; c < _V2D::cols_; ++c) for (uint r = 0; r < _V2D::rows_; ++r)
#define PIMM_FOR_I(c, r) for (uint r = 0; r < _V2D::rows_; ++r) for (uint c = 0; c < _V2D::cols_; ++c)
#define PIMM_FOR_A(v) for (uint v = 0; v < _V2D::mat.size(); ++v)
#define PIMM_FOR_C(v) for (uint v = 0; v < _V2D::cols_; ++v)
#define PIMM_FOR_R(v) for (uint v = 0; v < _V2D::rows_; ++v)

//! \brief A class that works with matrix operations, the input data of which is the data type of the matrix
template<typename Type>
class PIP_EXPORT PIMathMatrix : public PIVector2D<Type> {
	typedef PIVector2D<Type> _V2D;
	typedef PIMathMatrix<Type> _CMatrix;
	typedef PIMathVector<Type> _CMCol;
public:
	PIMathMatrix(const uint cols = 0, const uint rows = 0, const Type &f = Type()) { _V2D::resize(rows, cols, f); }

	PIMathMatrix(const uint cols, const uint rows, const PIVector<Type> &val) {
		_V2D::resize(rows, cols);
		int i = 0;
		PIMM_FOR_I(c, r) _V2D::element(r, c) = val[i++];
	}

	PIMathMatrix(const PIVector<PIVector<Type> > &val) {
		if (!val.isEmpty()) {
			_V2D::resize(val.size(), val[0].size());
			PIMM_FOR_I(c, r) _V2D::element(r, c) = val[r][c];
		}
	}

	PIMathMatrix(const PIVector2D<Type> &val) {
		if (!val.isEmpty()) {
			_V2D::resize(val.rows(), val.cols());
			PIMM_FOR_I(c, r) _V2D::element(r, c) = val.element(r, c);
		}
	}

	/**
	 * @brief Creates a matrix whose main diagonal is filled with ones and the remaining elements are zeros
	 *
	 * @param cols is number of matrix column uint type
	 * @param rows is number of matrix row uint type
	 * @return identity matrix of type PIMathMatrix
	 */
	static _CMatrix identity(const uint cols, const uint rows) {
		_CMatrix tm(cols, rows);
		for (uint r = 0; r < rows; ++r) for (uint c = 0; c < cols; ++c) tm.element(r, c) = (c == r ? Type(1) : Type(0));
		return tm;
	}

	/**
	 * @brief Creates a matrix whose row equal to vector
	 *
	 * @param val is the vector type PIMathVector
	 * @return identity matrix by vector
	 */
	static _CMatrix matrixRow(const PIMathVector<Type> &val) { return _CMatrix(val.size(), 1, val.toVector()); }

	/**
	 * @brief Creates a matrix whose column equal to vector
	 *
	 * @param val is the vector type PIMathVector
	 * @return identity matrix by vector
	 */
	static _CMatrix matrixCol(const PIMathVector<Type> &val) { return _CMatrix(1, val.size(), val.toVector()); }

	/**
	 * @brief Set the selected column in matrix
	 *
	 * @param index is the number of the selected column
	 * @param v is a vector of the type _CMCol that needs to fill the column
	 * @return matrix type _CMatrix
	 */
	_CMatrix &setCol(uint index, const _CMCol &v) {
		PIMM_FOR_R(i) _V2D::element(i, index) = v[i];
		return *this;
	}

	/**
	 * @brief Set the selected row in matrix
	 *
	 * @param index is the number of the selected row
	 * @param v is a vector of the type _CMCol that needs to fill the row
	 * @return matrix type _CMatrix
	 */
	_CMatrix &setRow(uint index, const _CMCol &v) {
		PIMM_FOR_C(i) _V2D::element(index, i) = v[i];
		return *this;
	}

	/**
	 * @brief Method which changes selected rows in a matrix
	 *
	 * @param r0 is the number of the first selected row
	 * @param r1 is the number of the second selected row
	 * @return matrix type _CMatrix
	 */
	_CMatrix &swapCols(uint r0, uint r1) {
		PIMM_FOR_C(i) { piSwap(_V2D::element(i, r0), _V2D::element(i, r1)); }
		return *this;
	}

	/**
	 * @brief Method which changes selected columns in a matrix
	 *
	 * @param c0 is the number of the first selected column
	 * @param c1 is the number of the second selected column
	 * @return matrix type _CMatrix
	 */
	_CMatrix &swapRows(uint c0, uint c1) {
		PIMM_FOR_R(i) { piSwap(_V2D::element(c0, i), _V2D::element(c1, i)); }
		return *this;
	}

	/**
	 * @brief Method which fills the matrix with selected value
	 *
	 * @param v is a parameter the type and value of which is selected and later filled into the matrix
	 * @return filled matrix type _CMatrix
	 */
	_CMatrix &fill(const Type &v) {
		PIMM_FOR_A(i) _V2D::mat[i] = v;
		return *this;
	}

	/**
	 * @brief Method which checks if matrix is square
	 *
	 * @return true if matrix is square, else false
	 */
	bool isSquare() const { return _V2D::cols_ == _V2D::rows_; }

	/**
	 * @brief Method which checks if main diagonal of matrix consists of ones and another elements are zeros
	 *
	 * @return true if matrix is identitied, else false
	 */
	bool isIdentity() const {
		PIMM_FOR(c, r) if ((c == r) ? _V2D::element(r, c) != Type(1) : _V2D::element(r, c) != Type(0))return false;
		return true;
	}

	/**
	 * @brief Method which checks if every elements of matrix are zeros
	 *
	 * @return true if matrix is null, else false
	 */
	bool isNull() const {
		PIMM_FOR_A(i) if (_V2D::mat[i] != Type(0)) return false;
		return true;
	}

	/**
	 * @brief Method which checks if matrix is empty
	 *
	 * @return true if matrix is valid, else false
	 */
	bool isValid() const { return !PIVector2D<Type>::isEmpty(); }

	/**
	 * @brief Matrix assignment to matrix "v"
	 *
	 * @param v matrix for the assigment
	 * @return matrix equal with v
	 */
	_CMatrix &operator=(const PIVector<PIVector<Type> > &v) {
		*this = _CMatrix(v);
		return *this;
	}

	/**
	 * @brief Compare with matrix "sm"
	 *
	 * @param sm matrix for the compare
	 * @return if matrices are equal true, else false
	 */
	bool operator==(const _CMatrix &sm) const {
		PIMM_FOR_A(i) if (_V2D::mat[i] != sm.mat[i]) return false;
		return true;
	}

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

	/**
	 * @brief Addition assignment with matrix "sm"
	 *
	 * @param sm matrix for the addition assigment
	 */
	void operator+=(const _CMatrix &sm) { PIMM_FOR_A(i) _V2D::mat[i] += sm.mat[i]; }

	/**
	 * @brief Subtraction assignment with matrix "sm"
	 *
	 * @param sm matrix for the subtraction assigment
	 */
	void operator-=(const _CMatrix &sm) { PIMM_FOR_A(i) _V2D::mat[i] -= sm.mat[i]; }

	/**
	 * @brief Multiplication assignment with value "v"
	 *
	 * @param v value for the multiplication assigment
	 */
	void operator*=(const Type &v) { PIMM_FOR_A(i) _V2D::mat[i] *= v; }

	/**
	 * @brief Division assignment with value "v"
	 *
	 * @param v value for the division assigment
	 */
	void operator/=(const Type &v) { PIMM_FOR_A(i) _V2D::mat[i] /= v; }

	/**
	 * @brief Matrix substraction
	 *
	 * @return the result of matrix substraction
	 */
	_CMatrix operator-() const {
		_CMatrix tm(*this);
		PIMM_FOR_A(i) tm.mat[i] = -_V2D::mat[i];
		return tm;
	}

	/**
	 * @brief Matrix addition
	 *
	 * @param sm is matrix term
	 * @return the result of matrix addition
	 */
	_CMatrix operator+(const _CMatrix &sm) const {
		_CMatrix tm(*this);
		PIMM_FOR_A(i) tm.mat[i] += sm.mat[i];
		return tm;
	}

	/**
	 * @brief Matrix subtraction
	 *
	 * @param sm is matrix subtractor
	 * @return the result of matrix subtraction
	 */
	_CMatrix operator-(const _CMatrix &sm) const {
		_CMatrix tm(*this);
		PIMM_FOR_A(i) tm.mat[i] -= sm.mat[i];
		return tm;
	}

	/**
	 * @brief Matrix multiplication
	 *
	 * @param v is value factor
	 * @return the result of matrix multiplication
	 */
	_CMatrix operator*(const Type &v) const {
		_CMatrix tm(*this);
		PIMM_FOR_A(i) tm.mat[i] *= v;
		return tm;
	}

	/**
	 * @brief Matrix division
	 *
	 * @param v is value divider
	 * @return the result of matrix division
	 */
	_CMatrix operator/(const Type &v) const {
		_CMatrix tm(*this);
		PIMM_FOR_A(i) tm.mat[i] /= v;
		return tm;
	}

	/**
	 * @brief Determinant of the matrix is ​​calculated
	 *
	 * @return matrix determinant
	 */
	Type determinant(bool *ok = 0) const {
		_CMatrix m(*this);
		bool k;
		Type ret = Type(0);
		m.toUpperTriangular(&k);
		if (ok) *ok = k;
		if (!k) return ret;
		ret = Type(1);
		for (uint c = 0; c < _V2D::cols_; ++c)
			for (uint r = 0; r < _V2D::rows_; ++r)
				if (r == c)
					ret *= m.element(r, c);
		return ret;
	}

	/**
	 * @brief Trace of the matrix is calculated
	 *
	 * @return matrix trace
	 */
	Type trace(bool *ok = 0) const {
		Type ret = Type(0);
		if (!isSquare()) {
			if (ok != 0) *ok = false;
			return ret;
		}
		for (uint i = 0; i < _V2D::cols_; ++i) {
			ret += _V2D::element(i, i);
		}
		if (ok != 0) *ok = true;
		return ret;
	}

	/**
	 * @brief Transforming matrix to upper triangular
	 *
	 * @return transformed upper triangular matrix
	 */
	_CMatrix &toUpperTriangular(bool *ok = 0) {
		if (!isSquare()) {
			if (ok != 0) *ok = false;
			return *this;
		}
		_CMatrix smat(*this);
		bool ndet;
		uint crow;
		Type mul;
		for (uint i = 0; i < _V2D::cols_; ++i) {
			ndet = true;
			for (uint j = 0; j < _V2D::rows_; ++j) if (smat.element(i, j) != 0) ndet = false;
			if (ndet) {
				if (ok != 0) *ok = false;
				return *this;
			}
		}
		for (uint i = 0; i < _V2D::cols_; ++i) {
			crow = i;
			while (smat.element(i, i) == Type(0))
				smat.swapRows(i, ++crow);
			for (uint j = i + 1; j < _V2D::rows_; ++j) {
				mul = smat.element(i, j) / smat.element(i, i);
				for (uint k = i; k < _V2D::cols_; ++k) smat.element(k, j) -= mul * smat.element(k, i);
			}
			if (i < _V2D::cols_ - 1) {
				if (_PIMathMatrixNullCompare(smat.element(i + 1, i + 1))) {
					if (ok != 0) *ok = false;
					return *this;
				}
			}
		}
		if (ok != 0) *ok = true;
		_V2D::mat.swap(smat.mat);
		return *this;
	}

	/**
	 * @brief Matrix inversion operation
	 *
	 * @return inverted matrix
	 */
	_CMatrix &invert(bool *ok = 0, _CMCol *sv = 0) {
		if (!isSquare()) {
			if (ok != 0) *ok = false;
			return *this;
		}
		_CMatrix mtmp = _CMatrix::identity(_V2D::cols_, _V2D::rows_), smat(*this);
		bool ndet;
		uint crow;
		Type mul, iddiv;
		for (uint i = 0; i < _V2D::cols_; ++i) {
			ndet = true;
			for (uint j = 0; j < _V2D::rows_; ++j) if (smat.element(i, j) != Type(0)) ndet = false;
			if (ndet) {
				if (ok != 0) *ok = false;
				return *this;
			}
		}
		for (uint i = 0; i < _V2D::cols_; ++i) {
			crow = i;
			while (smat.element(i, i) == Type(0)) {
				++crow;
				smat.swapRows(i, crow);
				mtmp.swapRows(i, crow);
				if (sv != 0) sv->swap(i, crow);
			}
			for (uint j = i + 1; j < _V2D::rows_; ++j) {
				mul = smat.element(i, j) / smat.element(i, i);
				for (uint k = i; k < _V2D::cols_; ++k) smat.element(k, j) -= mul * smat.element(k, i);
				for (uint k = 0; k < _V2D::cols_; ++k) mtmp.element(k, j) -= mul * mtmp.element(k, i);
				if (sv != 0) (*sv)[j] -= mul * (*sv)[i];
			}
			if (i < _V2D::cols_ - 1) {
				if (_PIMathMatrixNullCompare(smat.element(i + 1, i + 1))) {
					if (ok != 0) *ok = false;
					return *this;
				}
			}
			iddiv = smat.element(i, i);
			for (uint j = i; j < _V2D::cols_; ++j) smat.element(j, i) /= iddiv;
			for (uint j = 0; j < _V2D::cols_; ++j) mtmp.element(j, i) /= iddiv;
			if (sv != 0) (*sv)[i] /= iddiv;
		}
		for (uint i = _V2D::cols_ - 1; i > 0; --i) {
			for (uint j = 0; j < i; ++j) {
				mul = smat.element(i, j);
				smat.element(i, j) -= mul;
				for (uint k = 0; k < _V2D::cols_; ++k) mtmp.element(k, j) -= mul * mtmp.element(k, i);
				if (sv != 0) (*sv)[j] -= mul * (*sv)[i];
			}
		}
		if (ok != 0) *ok = true;
		PIVector2D<Type>::swap(mtmp);
		return *this;
	}

	/**
	 * @brief Matrix inversion operation
	 *
	 * @return inverted matrix
	 */
	_CMatrix inverted(bool *ok = 0) const {
		_CMatrix tm(*this);
		tm.invert(ok);
		return tm;
	}

	/**
	 * @brief Matrix transposition operation
	 *
	 * @return transposed matrix
	 */
	_CMatrix transposed() const {
		_CMatrix tm(_V2D::rows_, _V2D::cols_);
		PIMM_FOR(c, r) tm.element(c, r) = _V2D::element(r, c);
		return tm;
	}
};


#ifdef PIP_STD_IOSTREAM
template<typename Type>
inline std::ostream & operator <<(std::ostream & s, const PIMathMatrix<Type> & m) {s << "{"; for (uint r = 0; r < m.rows(); ++r) { for (uint c = 0; c < m.cols(); ++c) { s << m.element(r, c); if (c < m.cols() - 1 || r < m.rows() - 1) s << ", ";} if (r < m.rows() - 1) s << std::endl << " ";} s << "}"; return s;}
#endif

template<typename Type>
inline PICout operator<<(PICout s, const PIMathMatrix<Type> &m) {
	s << "Matrix{";
	for (uint r = 0; r < m.rows(); ++r) {
		for (uint c = 0; c < m.cols(); ++c) {
			s << m.element(r, c);
			if (c < m.cols() - 1 || r < m.rows() - 1) s << ", ";
		}
		if (r < m.rows() - 1) s << PICoutManipulators::NewLine << " ";
	}
	s << "}";
	return s;
}

template<typename Type>
inline PIByteArray &operator<<(PIByteArray &s, const PIMathMatrix<Type> &v) {
	s << (const PIVector2D<Type> &) v;
	return s;
}

template<typename Type>
inline PIByteArray &operator>>(PIByteArray &s, PIMathMatrix<Type> &v) {
	s >> (PIVector2D<Type> &) v;
	return s;
}


/// Multiply matrices {CR x Rows0} on {Cols1 x CR}, result is {Cols1 x Rows0}
template<typename Type>
inline PIMathMatrix<Type> operator*(const PIMathMatrix<Type> &fm,
									const PIMathMatrix<Type> &sm) {
	uint cr = fm.cols(), rows0 = fm.rows(), cols1 = sm.cols();
	PIMathMatrix<Type> tm(cols1, rows0);
	if (fm.cols() != sm.rows()) return tm;
	Type t;
	for (uint j = 0; j < rows0; ++j) {
		for (uint i = 0; i < cols1; ++i) {
			t = Type(0);
			for (uint k = 0; k < cr; ++k)
				t += fm.element(j, k) * sm.element(k, i);
			tm.element(j, i) = t;
		}
	}
	return tm;
}

/// Multiply matrix {Cols x Rows} on vector {Cols}, result is vector {Rows}
template<typename Type>
inline PIMathVector<Type> operator*(const PIMathMatrix<Type> &fm,
									const PIMathVector<Type> &sv) {
	uint c = fm.cols(), r = fm.rows();
	PIMathVector<Type> tv(r);
	if (c != sv.size()) return tv;
	Type t;
	for (uint j = 0; j < r; ++j) {
		t = Type(0);
		for (uint i = 0; i < c; ++i)
			t += fm.element(j, i) * sv[i];
		tv[j] = t;
	}
	return tv;
}


/// Multiply vector {Rows} on matrix {Rows x Cols}, result is vector {Cols}
template<typename Type>
inline PIMathVector<Type> operator*(const PIMathVector<Type> &sv,
									const PIMathMatrix<Type> &fm) {
	uint c = fm.cols(), r = fm.rows();
	PIMathVector<Type> tv(c);
	Type t;
	for (uint j = 0; j < c; ++j) {
		t = Type(0);
		for (uint i = 0; i < r; ++i)
			t += fm.element(i, j) * sv[i];
		tv[j] = t;
	}
	return tv;
}

/// Multiply value(T) on matrix {Rows x Cols}, result is vector {Rows}
template<typename Type>
inline PIMathMatrix<Type> operator*(const Type &x, const PIMathMatrix<Type> &v) {
	return v * x;
}

typedef PIMathMatrix<int> PIMathMatrixi;
typedef PIMathMatrix<double> PIMathMatrixd;

template<typename T>
PIMathMatrix<complex<T> > hermitian(const PIMathMatrix<complex<T> > &m) {
	PIMathMatrix<complex<T> > ret(m);
	for (uint r = 0; r < ret.rows(); ++r)
		for (uint c = 0; c < ret.cols(); ++c)
			ret.element(r, c).imag(-(ret.element(r, c).imag()));
	return ret.transposed();
}

#undef PIMM_FOR
#undef PIMM_FOR_I
#undef PIMM_FOR_A
#undef PIMM_FOR_C
#undef PIMM_FOR_R

#endif // PIMATHMATRIX_H