template math functions in pimathmatrix.h and pimathvector.h and pimathbase.h

add PIMathMatrixT::rotate for matrix 2x2

libs/main/math/pimathbase.h

@@ -98,9 +98,6 @@ const double rad2deg = M_180_PI;
 inline int sign(const float & x) {return (x < 0.) ? -1 : (x > 0. ? 1 : 0);}
 inline int sign(const double & x) {return (x < 0.) ? -1 : (x > 0. ? 1 : 0);}
 inline int pow2(const int p) {return 1 << p;}
-inline int sqr(const int v) {return v * v;}
-inline float sqr(const float & v) {return v * v;}
-inline double sqr(const double & v) {return v * v;}
 inline double sinc(const double & v) {if (v == 0.) return 1.; double t = M_PI * v; return sin(t) / t;}
 
 PIP_EXPORT double piJ0(const double & v);
@@ -109,22 +106,23 @@ PIP_EXPORT double piJn(int n, const double & v);
 PIP_EXPORT double piY0(const double & v);
 PIP_EXPORT double piY1(const double & v);
 PIP_EXPORT double piYn(int n, const double & v);
-inline double toDb(double val) {return 10. * log10(val);}
-inline double fromDb(double val) {return pow(10., val / 10.);}
-inline double toRad(double deg) {return deg * M_PI_180;}
-inline double toDeg(double rad) {return rad * M_180_PI;}
+
+template <typename T> inline constexpr T toDb(T val) {return T(10.) * std::log10(val);}
+template <typename T> inline constexpr T fromDb(T val) {return std::pow(T(10.), val / T(10.));}
+template <typename T> inline constexpr T toRad(T deg) {return deg * T(M_PI_180);}
+template <typename T> inline constexpr T toDeg(T rad) {return rad * T(M_180_PI);}
+template <typename T> inline constexpr T sqr(const T & v) {return v * v;}
 
 // [-1 ; 1]
 PIP_EXPORT double randomd();
 // [-1 ; 1] normal
 PIP_EXPORT double randomn(double dv = 0., double sv = 1.);
 
-
-inline PIVector<double> abs(const PIVector<double> & v) {
-	PIVector<double> result;
+template<typename T> inline PIVector<T> piAbs(const PIVector<T> & v) {
+	PIVector<T> result;
 	result.resize(v.size());
 	for (uint i = 0; i < v.size(); i++)
-        result[i] = fabs(v[i]);
+		result[i] = piAbs<T>(v[i]);
 	return result;
 }
 

libs/main/math/pimathmatrix.h

@@ -53,20 +53,15 @@ class PIP_EXPORT PIMathMatrixT {
 	static_assert(Cols > 0, "Column count must be > 0");
 public:
 	/**
-	* @brief Constructor that calls the private resize method
-	*
-	* @return identitied matrix of type PIMathMatrixT
+	* @brief Constructs PIMathMatrixT that is filled by \a new_value
 	*/
-	PIMathMatrixT() { resize(Rows, Cols); }
+	PIMathMatrixT(const Type &new_value = Type()) {PIMM_FOR m[r][c] = new_value;}
 
 	/**
-	* @brief Constructor that calls the private resize method
-	*
-	* @param val is the PIVector with which the matrix is ​​filled
-	* @return identitied matrix of type PIMathMatrixT
+	* @brief Contructs PIMathMatrixT from PIVector
 	*/
 	PIMathMatrixT(const PIVector<Type> &val) {
-		resize(Rows, Cols);
+		assert(Rows*Cols == val.size());
 		int i = 0;
 		PIMM_FOR m[r][c] = val[i++];
 	}
@@ -91,31 +86,19 @@ public:
 		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 tm.m[r][c] = v;
-		return tm;
-	}
-
 	/**
 	* @brief Method which returns number of columns in matrix
 	*
 	* @return type uint shows number of columns
 	*/
-	uint cols() const { return Cols; }
+	constexpr 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; }
+	constexpr uint rows() const {return Rows;}
 
 	/**
 	* @brief Method which returns the selected column in PIMathVectorT format.
@@ -177,13 +160,8 @@ public:
 	* @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 {
-			t = m[r0][i];
-			m[r0][i] = m[r1][i];
-			m[r1][i] = t;
-		}
+	_CMatrix &swapRows(uint rf, uint rs) {
+		PIMM_FOR_C piSwap<Type>(m[rf][i], m[rs][i]);
 		return *this;
 	}
 
@@ -195,13 +173,8 @@ public:
 	* @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 {
-			t = m[i][c0];
-			m[i][c0] = m[i][c1];
-			m[i][c1] = t;
-		}
+	_CMatrix &swapCols(uint cf, uint cs) {
+		PIMM_FOR_R piSwap<Type>(m[i][cf], m[i][cs]);
 		return *this;
 	}
 
@@ -221,7 +194,7 @@ public:
 	*
 	* @return true if matrix is square, else false
 	*/
-	bool isSquare() const { return cols() == rows(); }
+	constexpr bool isSquare() const { return Rows == Cols; }
 
 	/**
 	* @brief Method which checks if main diagonal of matrix consists of ones and another elements are zeros
@@ -243,30 +216,41 @@ public:
 		return true;
 	}
 
-	/**
-	* @brief Full access to elements reference by row "row" and col "col".
-	* If you enter an index out of the border of the matrix there will be "undefined behavior"
-	*
-	* @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".
+	* @brief Read-only  access to element by \a row and \a col.
 	* If you enter an index out of the border of the matrix there will be "undefined behavior"
 	*
-	* @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"
+	* @param row of matrix
+	* @param col of matrix
+	* @return copy of element of matrix
 	*/
 	Type at(uint row, uint col) const { return m[row][col]; }
 
+	/**
+	* @brief Full access to element by \a row and \a col.
+	* If you enter an index out of the border of the matrix there will be "undefined behavior"
+	*
+	* @param row of matrix
+	* @param col of matrix
+	* @return element of matrix
+	*/
+	inline Type & element(uint row, uint col) {return m[row][col];}
+
+	/**
+	* @brief Read-only  access to element by \a row and \a col.
+	* If you enter an index out of the border of the matrix there will be "undefined behavior"
+	*
+	* @param row of matrix
+	* @param col of matrix
+	* @return element of matrix
+	*/
+	inline const Type & element(uint row, uint col) const {return m[row][col];}
+
 	/**
 	* @brief Full access to the matrix row pointer. If you enter an index out of the border of the matrix there will be "undefined behavior"
 	*
-	* @param row is a row of necessary matrix
+	* @param row of matrix
 	* @return matrix row pointer
 	*/
 	Type *operator[](uint row) { return m[row]; }
@@ -274,26 +258,15 @@ public:
 	/**
 	* @brief Read-only access to the matrix row pointer. If you enter an index out of the border of the matrix there will be "undefined behavior"
 	*
-	* @param row is a row of necessary matrix
+	* @param row of matrix
 	* @return matrix row pointer
 	*/
 	const Type *operator[](uint row) const {return m[row];}
 
 	/**
-	* @brief Matrix assignment to matrix "sm"
+	* @brief Matrix compare
 	*
-	* @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
+	* @param sm matrix for compare
 	* @return if matrices are equal true, else false
 	*/
 	bool operator==(const _CMatrix &sm) const {
@@ -302,9 +275,9 @@ public:
 	}
 
 	/**
-	* @brief Compare with matrix "sm"
+	* @brief Matrix negative compare
 	*
-	* @param sm matrix for the compare
+	* @param sm matrix for compare
 	* @return if matrices are not equal true, else false
 	*/
 	bool operator!=(const _CMatrix &sm) const { return !(*this == sm); }
@@ -328,14 +301,19 @@ public:
 	*
 	* @param v value for the multiplication assigment
 	*/
-	void operator*=(const Type &v) { PIMM_FOR m[r][c] *= v; }
+	void operator*=(const Type &v) {
+		PIMM_FOR m[r][c] *= v;
+	}
 
 	/**
 	* @brief Division assignment with value "v"
 	*
 	* @param v value for the division assigment
 	*/
-	void operator/=(const Type &v) { PIMM_FOR m[r][c] /= v; }
+	void operator/=(const Type &v) {
+		assert(piAbs<Type>(v) > PIMATHVECTOR_ZERO_CMP);
+		PIMM_FOR m[r][c] /= v;
+	}
 
 	/**
 	* @brief Matrix substraction
@@ -391,6 +369,7 @@ public:
 	* @return the result of matrix division
 	*/
 	_CMatrix operator/(const Type &v) const {
+		assert(piAbs<Type>(v) > PIMATHVECTOR_ZERO_CMP);
 		_CMatrix tm = _CMatrix(*this);
 		PIMM_FOR tm.m[r][c] /= v;
 		return tm;
@@ -446,7 +425,7 @@ public:
 				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 (piAbs<Type>(smat.m[i + 1][i + 1]) < Type(1E-200)) {
 					if (ok != 0) *ok = false;
 					return *this;
 				}
@@ -490,7 +469,7 @@ public:
 				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 (piAbs<Type>(smat.m[i + 1][i + 1]) < Type(1E-200)) {
 					if (ok != 0) *ok = false;
 					return *this;
 				}
@@ -534,23 +513,25 @@ public:
 		return tm;
 	}
 
-private:
-	void resize(uint rows_, uint cols_, const Type &new_value = Type()) {
-		r_ = rows_;
-		c_ = cols_;
-		PIMM_FOR m[r][c] = new_value;
+	_CMatrix rotate(Type angle) {
+		static_assert(Rows == 2 && Cols == 2, "Works only with 2x2 matrix");
+		Type c = std::cos(angle);
+		Type s = std::sin(angle);
+		PIMathMatrixT<2u, 2u> tm;
+		tm[0][0] = tm[1][1] = c;
+		tm[0][1] = -s;
+		tm[1][0] = s;
+		*this = *this * tm;
+		return *this;
 	}
 
-	int c_, r_;
+private:
 	Type m[Rows][Cols];
-
 };
 
 #pragma pack(pop)
 
 
-
-
 #ifdef PIP_STD_IOSTREAM
 template<uint Rows, uint Cols, typename Type>
 inline std::ostream & operator <<(std::ostream & s, const PIMathMatrixT<Rows, Cols, Type> & m) {
@@ -687,11 +668,10 @@ class PIMathMatrix;
 
 /// 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)
+#define PIMM_FOR for (uint r = 0; r < _V2D::rows_; ++r) for (uint c = 0; c < _V2D::cols_; ++c)
+#define PIMM_FOR_A for (uint i = 0; i < _V2D::mat.size(); ++i)
+#define PIMM_FOR_C for (uint i = 0; i < _V2D::cols_; ++i)
+#define PIMM_FOR_R for (uint i = 0; i < _V2D::rows_; ++i)
 
 //! \brief A class that works with matrix operations, the input data of which is the data type of the matrix
 //!  @tparam There are can be basic C++ language data and different classes where the arithmetic operators(=, +=, -=, *=, /=, ==, !=, +, -, *, /)
@@ -700,7 +680,6 @@ template<typename Type>
 class PIP_EXPORT PIMathMatrix : public PIVector2D<Type> {
 	typedef PIVector2D<Type> _V2D;
 	typedef PIMathMatrix<Type> _CMatrix;
-	typedef PIMathVector<Type> _CMCol;
 public:
 	/**
 	* @brief Constructor of class PIMathMatrix, which creates a matrix
@@ -721,7 +700,7 @@ public:
 	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++];
+		PIMM_FOR _V2D::element(r, c) = val[i++];
 	}
 
 	/**
@@ -732,7 +711,11 @@ public:
 	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];
+			for (uint r = 0; r < _V2D::rows_; ++r) {
+				assert(val[r].size() == _V2D::cols_);
+				for (uint c = 0; c < _V2D::cols_; ++c)
+					_V2D::element(r, c) = val[r][c];
+			}
 		}
 	}
 
@@ -744,7 +727,7 @@ public:
 	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);
+			PIMM_FOR _V2D::element(r, c) = val.element(r, c);
 		}
 	}
 
@@ -761,19 +744,6 @@ public:
 		return tm;
 	}
 
-	/**
-	* @brief Creates a matrix filled by zeros
-	*
-	* @param cols is number of matrix column uint type
-	* @param rows is number of matrix row uint type
-	* @return zero matrix(cols,rows)
-	*/
-	static _CMatrix zero(const uint cols, const uint rows) {
-		_CMatrix tm(cols, rows);
-		tm.fill(Type(0));
-		return tm;
-	}
-
 	/**
 	* @brief Creates a row matrix of every element that is equal to every element of the vector
 	*
@@ -798,8 +768,9 @@ public:
 	* @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];
+	_CMatrix &setCol(uint index, const PIMathVector<Type> &v) {
+		assert(_V2D::rows == v.size());
+		PIMM_FOR_R _V2D::element(i, index) = v[i];
 		return *this;
 	}
 
@@ -810,8 +781,9 @@ public:
 	* @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];
+	_CMatrix &setRow(uint index, const PIMathVector<Type> &v) {
+		assert(_V2D::cols == v.size());
+		PIMM_FOR_C _V2D::element(index, i) = v[i];
 		return *this;
 	}
 
@@ -824,7 +796,7 @@ public:
 	* @return matrix type _CMatrix
 	*/
 	_CMatrix &swapCols(uint r0, uint r1) {
-		PIMM_FOR_C(i) { piSwap(_V2D::element(i, r0), _V2D::element(i, r1)); }
+		PIMM_FOR_C piSwap<Type>(_V2D::element(i, r0), _V2D::element(i, r1));
 		return *this;
 	}
 
@@ -837,7 +809,7 @@ public:
 	* @return matrix type _CMatrix
 	*/
 	_CMatrix &swapRows(uint c0, uint c1) {
-		PIMM_FOR_R(i) { piSwap(_V2D::element(c0, i), _V2D::element(c1, i)); }
+		PIMM_FOR_R piSwap(_V2D::element(c0, i), _V2D::element(c1, i));
 		return *this;
 	}
 
@@ -848,7 +820,7 @@ public:
 	* @return filled matrix type _CMatrix
 	*/
 	_CMatrix &fill(const Type &v) {
-		PIMM_FOR_A(i) _V2D::mat[i] = v;
+		PIMM_FOR_A _V2D::mat[i] = v;
 		return *this;
 	}
 
@@ -865,7 +837,7 @@ public:
 	* @return true if matrix is identity, 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;
+		PIMM_FOR if ((c == r) ? _V2D::element(r, c) != Type(1) : _V2D::element(r, c) != Type(0))return false;
 		return true;
 	}
 
@@ -875,7 +847,7 @@ public:
 	* @return true if matrix elements equal to zero, else false
 	*/
 	bool isNull() const {
-		PIMM_FOR_A(i) if (_V2D::mat[i] != Type(0)) return false;
+		PIMM_FOR_A if (_V2D::mat[i] != Type(0)) return false;
 		return true;
 	}
 
@@ -894,7 +866,7 @@ public:
 	void operator+=(const _CMatrix &sm) {
 		assert(_V2D::rows() == sm.rows());
 		assert(_V2D::cols() == sm.cols());
-		PIMM_FOR_A(i) _V2D::mat[i] += sm.mat[i];
+		PIMM_FOR_A _V2D::mat[i] += sm.mat[i];
 	}
 
 	/**
@@ -905,7 +877,7 @@ public:
 	void operator-=(const _CMatrix &sm) {
 		assert(_V2D::rows() == sm.rows());
 		assert(_V2D::cols() == sm.cols());
-		PIMM_FOR_A(i) _V2D::mat[i] -= sm.mat[i];
+		PIMM_FOR_A _V2D::mat[i] -= sm.mat[i];
 	}
 
 	/**
@@ -913,14 +885,19 @@ public:
 	*
 	* @param v value for the multiplication assigment
 	*/
-	void operator*=(const Type &v) { PIMM_FOR_A(i) _V2D::mat[i] *= v; }
+	void operator*=(const Type &v) {
+		PIMM_FOR_A _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; }
+	void operator/=(const Type &v) {
+		assert(piAbs<Type>(v) > PIMATHVECTOR_ZERO_CMP);
+		PIMM_FOR_A _V2D::mat[i] /= v;
+	}
 
 	/**
 	* @brief Matrix substraction
@@ -929,7 +906,7 @@ public:
 	*/
 	_CMatrix operator-() const {
 		_CMatrix tm(*this);
-		PIMM_FOR_A(i) tm.mat[i] = -_V2D::mat[i];
+		PIMM_FOR_A tm.mat[i] = -_V2D::mat[i];
 		return tm;
 	}
 
@@ -943,7 +920,7 @@ public:
 		_CMatrix tm(*this);
 		assert(tm.rows() == sm.rows());
 		assert(tm.cols() == sm.cols());
-		PIMM_FOR_A(i) tm.mat[i] += sm.mat[i];
+		PIMM_FOR_A tm.mat[i] += sm.mat[i];
 		return tm;
 	}
 
@@ -957,7 +934,7 @@ public:
 		_CMatrix tm(*this);
 		assert(tm.rows() == sm.rows());
 		assert(tm.cols() == sm.cols());
-		PIMM_FOR_A(i) tm.mat[i] -= sm.mat[i];
+		PIMM_FOR_A tm.mat[i] -= sm.mat[i];
 		return tm;
 	}
 
@@ -969,7 +946,7 @@ public:
 	*/
 	_CMatrix operator*(const Type &v) const {
 		_CMatrix tm(*this);
-		PIMM_FOR_A(i) tm.mat[i] *= v;
+		PIMM_FOR_A tm.mat[i] *= v;
 		return tm;
 	}
 
@@ -980,8 +957,9 @@ public:
 	* @return the result of matrix division
 	*/
 	_CMatrix operator/(const Type &v) const {
+		assert(piAbs<Type>(v) > PIMATHVECTOR_ZERO_CMP);
 		_CMatrix tm(*this);
-		PIMM_FOR_A(i) tm.mat[i] /= v;
+		PIMM_FOR_A tm.mat[i] /= v;
 		return tm;
 	}
 
@@ -1075,7 +1053,7 @@ public:
 	* @param sv is a vector multiplier
 	* @return copy of inverted matrix
 	*/
-	_CMatrix &invert(bool *ok = 0, _CMCol *sv = 0) {
+	_CMatrix &invert(bool *ok = 0, PIMathVector<Type> *sv = 0) {
 		if (!isSquare()) {
 			if (ok != 0) *ok = false;
 			return *this;
@@ -1149,7 +1127,7 @@ public:
 	*/
 	_CMatrix transposed() const {
 		_CMatrix tm(_V2D::rows_, _V2D::cols_);
-		PIMM_FOR(c, r) tm.element(c, r) = _V2D::element(r, c);
+		PIMM_FOR tm.element(c, r) = _V2D::element(r, c);
 		return tm;
 	}
 };
@@ -1309,7 +1287,6 @@ PIMathMatrix<complex<T> > hermitian(const PIMathMatrix<complex<T> > &m) {
 }
 
 #undef PIMM_FOR
-#undef PIMM_FOR_I
 #undef PIMM_FOR_A
 #undef PIMM_FOR_C
 #undef PIMM_FOR_R

libs/main/math/pimathvector.h

@@ -56,16 +56,20 @@ public:
 		return tv;
 	}
 
-	uint size() const {return Size;}
+	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 {return sqrt(lengthSqr());}
+	Type length() const {return std::sqrt(lengthSqr());}
 	Type manhattanLength() const {
 		Type tv(0);
 		PIMV_FOR tv += piAbs<Type>(c[i]);
@@ -78,10 +82,10 @@ public:
 	}
 	Type angleSin(const _CVector & v) const {
 		Type tv = angleCos(v);
-		return sqrt(Type(1) - tv * tv);
+		return std::sqrt(Type(1) - tv * tv);
 	}
-	Type angleRad(const _CVector & v) const {return acos(angleCos(v));}
-	Type angleDeg(const _CVector & v) const {return toDeg(angleRad(v));}
+	Type angleRad(const _CVector & v) const {return std::acos(angleCos(v));}
+	Type angleDeg(const _CVector & v) const {return toDeg<Type>(angleRad(v));}
 	Type angleElevation(const _CVector & v) const {return 90.0 - angleDeg(v - *this);}
 	_CVector projection(const _CVector & v) {
 		Type tv = v.length();
@@ -99,13 +103,15 @@ public:
 	bool isNull() const {PIMV_FOR if (c[i] != Type(0)) return false; return true;}
 	bool isOrtho(const _CVector & v) const {return ((*this) ^ v) == Type(0);}
 
-	Type & at(uint index) {return c[index];}
-	Type at(uint index) const {return c[index];}
 	Type & operator [](uint index) {return c[index];}
-	Type operator [](uint index) const {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 {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;}
@@ -287,8 +293,8 @@ public:
 		PIMV_FOR c[i] += v[i];
 		return *this;
 	}
-	_CVector & swapElements(uint fe, uint se) {
-		piSwap<Type>(c[fe], c[se]);
+	_CVector & swapElements(uint f, uint s) {
+		piSwap<Type>(c[f], c[s]);
 		return *this;
 	}
 	Type lengthSqr() const {
@@ -296,7 +302,7 @@ public:
 		PIMV_FOR tv += c[i] * c[i];
 		return tv;
 	}
-	Type length() const {return sqrt(lengthSqr());}
+	Type length() const {return std::sqrt(lengthSqr());}
 	Type manhattanLength() const {
 		Type tv(0);
 		PIMV_FOR tv += piAbs<Type>(c[i]);
@@ -311,9 +317,9 @@ public:
 	Type angleSin(const _CVector & v) const {
 		assert(c.size() == v.size());
 		Type tv = angleCos(v);
-		return sqrt(Type(1) - tv * tv);
+		return std::sqrt(Type(1) - tv * tv);
 	}
-	Type angleRad(const _CVector & v) const {return acos(angleCos(v));}
+	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());
@@ -340,12 +346,15 @@ public:
 	bool isValid() const {return !c.isEmpty();}
 	bool isOrtho(const _CVector & v) const {return dot(v) == Type(0);}
 
-	Type & at(uint index) {return c[index];}
-	Type at(uint index) const {return c[index];}
 	Type & operator [](uint index) {return c[index];}
-	Type operator [](uint index) const {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];

main.cpp

@@ -45,5 +45,9 @@ int main() {
 	PIMathVectord v2({3,2,1});
 	piCout << v;
 	piCout << v2;
+	PIMathMatrixT22d m = PIMathMatrixT22d::identity();
+	piCout << m;
+	m.rotate(toRad(90.));
+	piCout << m;
 	return 0;
 }