Vector Template Functions

These functions apply to SVector types (and also to Vector expressions) and can return a vector expression or a scalar, like in the Dot product, or a matrix, like in the Tensor product.

Functions
template<class T >
SVector< T, 3 >	ROOT::Math::Cross (const SVector< T, 3 > &lhs, const SVector< T, 3 > &rhs)
	Vector Cross Product (only for 3-dim vectors) $\vec{c} = \vec{a}\times\vec{b}$. More...
template<class T , unsigned int D>
T	ROOT::Math::Dot (const SVector< T, D > &lhs, const SVector< T, D > &rhs)
	Vector dot product. More...
template<class T , unsigned int D>
VecExpr< UnaryOp< Fabs< T >, SVector< T, D >, T >, T, D >	ROOT::Math::fabs (const SVector< T, D > &rhs)
	abs of a vector : v2(i) = | v1(i) | returning a vector expression More...
template<class T >
T	ROOT::Math::Lmag (const SVector< T, 4 > &rhs)
	Lmag: Minkowski Lorentz-Vector norm (only for 4-dim vectors) Length of a vector Lorentz-Vector: $|\vec{v}| = \sqrt{v_0^2 - v_1^2 - v_2^2 -v_3^2}$. More...
template<class T >
T	ROOT::Math::Lmag2 (const SVector< T, 4 > &rhs)
	Lmag2: Square of Minkowski Lorentz-Vector norm (only for 4D Vectors) Template to compute $|\vec{v}|^2 = v_0^2 - v_1^2 - v_2^2 -v_3^2$. More...
template<class T , unsigned int D>
T	ROOT::Math::Mag (const SVector< T, D > &rhs)
	Vector magnitude (Euclidian norm) Compute : $|\vec{v}| = \sqrt{\sum_iv_i^2}$. More...
template<class T , unsigned int D>
T	ROOT::Math::Mag2 (const SVector< T, D > &rhs)
	Vector magnitude square Template to compute $|\vec{v}|^2 = \sum_iv_i^2$. More...
template<class T , unsigned int D>
VecExpr< BinaryOp< MulOp< T >, SVector< T, D >, SVector< T, D >, T >, T, D >	ROOT::Math::operator* (const SVector< T, D > &lhs, const SVector< T, D > &rhs)
	Element by element vector product v3(i) = v1(i)*v2(i) returning a vector expression. More...
template<class A , class T , unsigned int D>
VecExpr< BinaryOpCopyL< AddOp< T >, Constant< A >, SVector< T, D >, T >, T, D >	ROOT::Math::operator+ (const A &lhs, const SVector< T, D > &rhs)
	Addition of a scalar to each vector element v2(i) = a + v1(i) returning a vector expression. More...
template<class A , class T , unsigned int D>
VecExpr< BinaryOpCopyR< AddOp< T >, SVector< T, D >, Constant< A >, T >, T, D >	ROOT::Math::operator+ (const SVector< T, D > &lhs, const A &rhs)
	Addition of a scalar to a each vector element: v2(i) = v1(i) + a returning a vector expression. More...
template<class T , unsigned int D>
VecExpr< BinaryOp< AddOp< T >, SVector< T, D >, SVector< T, D >, T >, T, D >	ROOT::Math::operator+ (const SVector< T, D > &lhs, const SVector< T, D > &rhs)
	Addition of two vectors v3 = v1+v2 returning a vector expression. More...
template<class A , class T , unsigned int D>
VecExpr< BinaryOpCopyL< MinOp< T >, Constant< A >, SVector< T, D >, T >, T, D >	ROOT::Math::operator- (const A &lhs, const SVector< T, D > &rhs)
	Subtraction scalar vector (for each vector element) v2(i) = a - v1(i) returning a vector expression. More...
template<class A , class T , unsigned int D>
VecExpr< BinaryOpCopyR< MinOp< T >, SVector< T, D >, Constant< A >, T >, T, D >	ROOT::Math::operator- (const SVector< T, D > &lhs, const A &rhs)
	Subtraction of a scalar from each vector element: v2(i) = v1(i) - a returning a vector expression. More...
template<class T , unsigned int D>
VecExpr< BinaryOp< MinOp< T >, SVector< T, D >, SVector< T, D >, T >, T, D >	ROOT::Math::operator- (const SVector< T, D > &lhs, const SVector< T, D > &rhs)
	Vector Subtraction: v3 = v1 - v2 returning a vector expression. More...
template<class T , unsigned int D>
VecExpr< UnaryOp< Minus< T >, SVector< T, D >, T >, T, D >	ROOT::Math::operator- (const SVector< T, D > &rhs)
	Unary - operator v2 = -v1 . More...
template<class A , class T , unsigned int D>
VecExpr< BinaryOpCopyL< DivOp< T >, Constant< A >, SVector< T, D >, T >, T, D >	ROOT::Math::operator/ (const A &lhs, const SVector< T, D > &rhs)
	Division of a scalar value by the vector element: v2(i) = a/v1(i) returning a vector expression. More...
template<class A , class T , unsigned int D>
VecExpr< BinaryOpCopyR< DivOp< T >, SVector< T, D >, Constant< A >, T >, T, D >	ROOT::Math::operator/ (const SVector< T, D > &lhs, const A &rhs)
	Division of the vector element by a scalar value: v2(i) = v1(i)/a returning a vector expression. More...
template<class T , unsigned int D>
VecExpr< BinaryOp< DivOp< T >, SVector< T, D >, SVector< T, D >, T >, T, D >	ROOT::Math::operator/ (const SVector< T, D > &lhs, const SVector< T, D > &rhs)
	Element by element division of vectors of the same dimension: v3(i) = v1(i)/v2(i) returning a vector expression. More...
template<class T , unsigned int D>
VecExpr< UnaryOp< Sqr< T >, SVector< T, D >, T >, T, D >	ROOT::Math::sqr (const SVector< T, D > &rhs)
	square of a vector v2(i) = v1(i)*v1(i) . More...
template<class T , unsigned int D>
VecExpr< UnaryOp< Sqrt< T >, SVector< T, D >, T >, T, D >	ROOT::Math::sqrt (const SVector< T, D > &rhs)
	square root of a vector (element by element) v2(i) = sqrt( v1(i) ) returning a vector expression More...
template<class T , unsigned int D1, unsigned int D2>
Expr< TensorMulOp< SVector< T, D1 >, SVector< T, D2 > >, T, D1, D2 >	ROOT::Math::TensorProd (const SVector< T, D1 > &lhs, const SVector< T, D2 > &rhs)
	Tensor Vector Product : M(i,j) = v(i) * v(j) returning a matrix expression. More...
template<class T , unsigned int D>
SVector< T, D >	ROOT::Math::Unit (const SVector< T, D > &rhs)
	Unit. More...

Function Documentation

Cross()

template<class T >

SVector< T, 3 > ROOT::Math::Cross ( const SVector< T, 3 > &  lhs, const SVector< T, 3 > &  rhs  )

inline

Vector Cross Product (only for 3-dim vectors) $\vec{c} = \vec{a}\times\vec{b}$.

Author

T. Glebe

Definition at line 322 of file Functions.h.

Dot()

template<class T , unsigned int D>

T ROOT::Math::Dot ( const SVector< T, D > &  lhs, const SVector< T, D > &  rhs  )

inline

Vector dot product.

Template to compute $\vec{a}\cdot\vec{b} = \sum_i a_i\cdot b_i$.

Author

T. Glebe

Definition at line 164 of file Functions.h.

fabs()

template<class T , unsigned int D>

VecExpr< UnaryOp< Fabs< T >, SVector< T, D >, T >, T, D > ROOT::Math::fabs ( const SVector< T, D > &  rhs )

inline

abs of a vector : v2(i) = | v1(i) | returning a vector expression

Definition at line 149 of file UnaryOperators.h.

Lmag()

template<class T >

T ROOT::Math::Lmag ( const SVector< T, 4 > &  rhs )

inline

Lmag: Minkowski Lorentz-Vector norm (only for 4-dim vectors) Length of a vector Lorentz-Vector: $|\vec{v}| = \sqrt{v_0^2 - v_1^2 - v_2^2 -v_3^2}$.

Author

T. Glebe

Definition at line 299 of file Functions.h.

Lmag2()

template<class T >

T ROOT::Math::Lmag2 ( const SVector< T, 4 > &  rhs )

inline

Lmag2: Square of Minkowski Lorentz-Vector norm (only for 4D Vectors) Template to compute $|\vec{v}|^2 = v_0^2 - v_1^2 - v_2^2 -v_3^2$.

Author

T. Glebe

Definition at line 275 of file Functions.h.

Mag()

template<class T , unsigned int D>

T ROOT::Math::Mag ( const SVector< T, D > &  rhs )

inline

Vector magnitude (Euclidian norm) Compute : $|\vec{v}| = \sqrt{\sum_iv_i^2}$.

Author

T. Glebe

Definition at line 252 of file Functions.h.

Mag2()

template<class T , unsigned int D>

T ROOT::Math::Mag2 ( const SVector< T, D > &  rhs )

inline

Vector magnitude square Template to compute $|\vec{v}|^2 = \sum_iv_i^2$.

Author

T. Glebe

Definition at line 229 of file Functions.h.

operator*()

template<class T , unsigned int D>

VecExpr< BinaryOp< MulOp< T >, SVector< T, D >, SVector< T, D >, T >, T, D > ROOT::Math::operator* ( const SVector< T, D > &  lhs, const SVector< T, D > &  rhs  )

inline

Element by element vector product v3(i) = v1(i)*v2(i) returning a vector expression.

Note this is NOT the Dot, Cross or Tensor product.

Definition at line 548 of file BinaryOperators.h.

operator+() [1/3]

template<class A , class T , unsigned int D>

VecExpr< BinaryOpCopyL< AddOp< T >, Constant< A >, SVector< T, D >, T >, T, D > ROOT::Math::operator+ ( const A &  lhs, const SVector< T, D > &  rhs  )

inline

Addition of a scalar to each vector element v2(i) = a + v1(i) returning a vector expression.

Definition at line 133 of file BinaryOperators.h.

operator+() [2/3]

template<class A , class T , unsigned int D>

VecExpr< BinaryOpCopyR< AddOp< T >, SVector< T, D >, Constant< A >, T >, T, D > ROOT::Math::operator+ ( const SVector< T, D > &  lhs, const A &  rhs  )

inline

Addition of a scalar to a each vector element: v2(i) = v1(i) + a returning a vector expression.

Definition at line 116 of file BinaryOperators.h.

operator+() [3/3]

template<class T , unsigned int D>

VecExpr< BinaryOp< AddOp< T >, SVector< T, D >, SVector< T, D >, T >, T, D > ROOT::Math::operator+ ( const SVector< T, D > &  lhs, const SVector< T, D > &  rhs  )

inline

Addition of two vectors v3 = v1+v2 returning a vector expression.

Definition at line 62 of file BinaryOperators.h.

operator-() [1/4]

template<class A , class T , unsigned int D>

VecExpr< BinaryOpCopyL< MinOp< T >, Constant< A >, SVector< T, D >, T >, T, D > ROOT::Math::operator- ( const A &  lhs, const SVector< T, D > &  rhs  )

inline

Subtraction scalar vector (for each vector element) v2(i) = a - v1(i) returning a vector expression.

Definition at line 377 of file BinaryOperators.h.

operator-() [2/4]

template<class A , class T , unsigned int D>

VecExpr< BinaryOpCopyR< MinOp< T >, SVector< T, D >, Constant< A >, T >, T, D > ROOT::Math::operator- ( const SVector< T, D > &  lhs, const A &  rhs  )

inline

Subtraction of a scalar from each vector element: v2(i) = v1(i) - a returning a vector expression.

Definition at line 360 of file BinaryOperators.h.

operator-() [3/4]

template<class T , unsigned int D>

VecExpr< BinaryOp< MinOp< T >, SVector< T, D >, SVector< T, D >, T >, T, D > ROOT::Math::operator- ( const SVector< T, D > &  lhs, const SVector< T, D > &  rhs  )

inline

Vector Subtraction: v3 = v1 - v2 returning a vector expression.

Definition at line 306 of file BinaryOperators.h.

operator-() [4/4]

template<class T , unsigned int D>

VecExpr< UnaryOp< Minus< T >, SVector< T, D >, T >, T, D > ROOT::Math::operator- ( const SVector< T, D > &  rhs )

inline

Unary - operator v2 = -v1 .

returning a vector expression

Definition at line 74 of file UnaryOperators.h.

operator/() [1/3]

template<class A , class T , unsigned int D>

VecExpr< BinaryOpCopyL< DivOp< T >, Constant< A >, SVector< T, D >, T >, T, D > ROOT::Math::operator/ ( const A &  lhs, const SVector< T, D > &  rhs  )

inline

Division of a scalar value by the vector element: v2(i) = a/v1(i) returning a vector expression.

Definition at line 854 of file BinaryOperators.h.

operator/() [2/3]

template<class A , class T , unsigned int D>

VecExpr< BinaryOpCopyR< DivOp< T >, SVector< T, D >, Constant< A >, T >, T, D > ROOT::Math::operator/ ( const SVector< T, D > &  lhs, const A &  rhs  )

inline

Division of the vector element by a scalar value: v2(i) = v1(i)/a returning a vector expression.

Definition at line 837 of file BinaryOperators.h.

operator/() [3/3]

template<class T , unsigned int D>

VecExpr< BinaryOp< DivOp< T >, SVector< T, D >, SVector< T, D >, T >, T, D > ROOT::Math::operator/ ( const SVector< T, D > &  lhs, const SVector< T, D > &  rhs  )

inline

Element by element division of vectors of the same dimension: v3(i) = v1(i)/v2(i) returning a vector expression.

Definition at line 784 of file BinaryOperators.h.

sqr()

template<class T , unsigned int D>

VecExpr< UnaryOp< Sqr< T >, SVector< T, D >, T >, T, D > ROOT::Math::sqr ( const SVector< T, D > &  rhs )

inline

square of a vector v2(i) = v1(i)*v1(i) .

returning a vector expression

Definition at line 224 of file UnaryOperators.h.

sqrt()

template<class T , unsigned int D>

VecExpr< UnaryOp< Sqrt< T >, SVector< T, D >, T >, T, D > ROOT::Math::sqrt ( const SVector< T, D > &  rhs )

inline

square root of a vector (element by element) v2(i) = sqrt( v1(i) ) returning a vector expression

Definition at line 299 of file UnaryOperators.h.

TensorProd()

template<class T , unsigned int D1, unsigned int D2>

Expr< TensorMulOp< SVector< T, D1 >, SVector< T, D2 > >, T, D1, D2 > ROOT::Math::TensorProd ( const SVector< T, D1 > &  lhs, const SVector< T, D2 > &  rhs  )

inline

Tensor Vector Product : M(i,j) = v(i) * v(j) returning a matrix expression.

Definition at line 883 of file MatrixFunctions.h.

Unit()

template<class T , unsigned int D>

SVector< T, D > ROOT::Math::Unit ( const SVector< T, D > &  rhs )

inline

Unit.

Return a vector of unit length: $\vec{e}_v = \vec{v}/|\vec{v}|$.

Author

T. Glebe

Definition at line 381 of file Functions.h.