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ROOT
6.06/09
Reference Guide
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ROOT
6.06/09
Reference Guide
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These function apply to matrices (and also Matrix expression) and can return a matrix expression of a particular defined type, like in the matrix multiplication or a vector, like in the matrix-vector product or a scalar like in the Similarity vector-matrix product. More...
Collaboration diagram for Matrix Template Functions:Functions | |
| template<class T , unsigned int D, unsigned int D2, class R1 , class R2 > | |
| Expr< BinaryOp< AddOp< T >, SMatrix< T, D, D2, R1 >, SMatrix< T, D, D2, R2 >, T >, T, D, D2, typename AddPolicy< T, D, D2, R1, R2 >::RepType > | ROOT::Math::operator+ (const SMatrix< T, D, D2, R1 > &lhs, const SMatrix< T, D, D2, R2 > &rhs) |
| Addition of two matrices C = A+B returning a matrix expression. More... | |
| template<class A , class T , unsigned int D, unsigned int D2, class R > | |
| Expr< BinaryOpCopyR< AddOp< T >, SMatrix< T, D, D2, R >, Constant< A >, T >, T, D, D2, R > | ROOT::Math::operator+ (const SMatrix< T, D, D2, R > &lhs, const A &rhs) |
| Addition element by element of matrix and a scalar C(i,j) = A(i,j) + s returning a matrix expression. More... | |
| template<class A , class T , unsigned int D, unsigned int D2, class R > | |
| Expr< BinaryOpCopyL< AddOp< T >, Constant< A >, SMatrix< T, D, D2, R >, T >, T, D, D2, R > | ROOT::Math::operator+ (const A &lhs, const SMatrix< T, D, D2, R > &rhs) |
| Addition element by element of matrix and a scalar C(i,j) = s + A(i,j) returning a matrix expression. More... | |
| template<class T , unsigned int D, unsigned int D2, class R1 , class R2 > | |
| Expr< BinaryOp< MinOp< T >, SMatrix< T, D, D2, R1 >, SMatrix< T, D, D2, R2 >, T >, T, D, D2, typename AddPolicy< T, D, D2, R1, R2 >::RepType > | ROOT::Math::operator- (const SMatrix< T, D, D2, R1 > &lhs, const SMatrix< T, D, D2, R2 > &rhs) |
| Subtraction of two matrices C = A-B returning a matrix expression. More... | |
| template<class A , class T , unsigned int D, unsigned int D2, class R > | |
| Expr< BinaryOpCopyR< MinOp< T >, SMatrix< T, D, D2, R >, Constant< A >, T >, T, D, D2, R > | ROOT::Math::operator- (const SMatrix< T, D, D2, R > &lhs, const A &rhs) |
| Subtraction of a scalar and a matrix (element wise) B(i,j) = A(i,j) - s returning a matrix expression. More... | |
| template<class A , class T , unsigned int D, unsigned int D2, class R > | |
| Expr< BinaryOpCopyL< MinOp< T >, Constant< A >, SMatrix< T, D, D2, R >, T >, T, D, D2, R > | ROOT::Math::operator- (const A &lhs, const SMatrix< T, D, D2, R > &rhs) |
| Subtraction of a scalar and a matrix (element wise) B(i,j) = s - A(i,j) returning a matrix expression. More... | |
| template<class T , unsigned int D, unsigned int D2, class R1 , class R2 > | |
| Expr< BinaryOp< MulOp< T >, SMatrix< T, D, D2, R1 >, SMatrix< T, D, D2, R2 >, T >, T, D, D2, typename AddPolicy< T, D, D2, R1, R2 >::RepType > | ROOT::Math::Times (const SMatrix< T, D, D2, R1 > &lhs, const SMatrix< T, D, D2, R2 > &rhs) |
| Element by element matrix multiplication C(i,j) = A(i,j)*B(i,j) returning a matrix expression. More... | |
| template<class A , class T , unsigned int D, unsigned int D2, class R > | |
| Expr< BinaryOpCopyR< MulOp< T >, SMatrix< T, D, D2, R >, Constant< A >, T >, T, D, D2, R > | ROOT::Math::operator* (const SMatrix< T, D, D2, R > &lhs, const A &rhs) |
| Multiplication (element wise) of a matrix and a scalar, B(i,j) = A(i,j) * s returning a matrix expression. More... | |
| template<class A , class T , unsigned int D, unsigned int D2, class R > | |
| Expr< BinaryOpCopyL< MulOp< T >, Constant< A >, SMatrix< T, D, D2, R >, T >, T, D, D2, R > | ROOT::Math::operator* (const A &lhs, const SMatrix< T, D, D2, R > &rhs) |
| Multiplication (element wise) of a matrix and a scalar, B(i,j) = s * A(i,j) returning a matrix expression. More... | |
| template<class T , unsigned int D, unsigned int D2, class R1 , class R2 > | |
| Expr< BinaryOp< DivOp< T >, SMatrix< T, D, D2, R1 >, SMatrix< T, D, D2, R2 >, T >, T, D, D2, typename AddPolicy< T, D, D2, R1, R2 >::RepType > | ROOT::Math::Div (const SMatrix< T, D, D2, R1 > &lhs, const SMatrix< T, D, D2, R2 > &rhs) |
| Division (element wise) of two matrices of the same dimensions: C(i,j) = A(i,j) / B(i,j) returning a matrix expression. More... | |
| template<class A , class T , unsigned int D, unsigned int D2, class R > | |
| Expr< BinaryOpCopyR< DivOp< T >, SMatrix< T, D, D2, R >, Constant< A >, T >, T, D, D2, R > | ROOT::Math::operator/ (const SMatrix< T, D, D2, R > &lhs, const A &rhs) |
| Division (element wise) of a matrix and a scalar, B(i,j) = A(i,j) / s returning a matrix expression. More... | |
| template<class A , class T , unsigned int D, unsigned int D2, class R > | |
| Expr< BinaryOpCopyL< DivOp< T >, Constant< A >, SMatrix< T, D, D2, R >, T >, T, D, D2, R > | ROOT::Math::operator/ (const A &lhs, const SMatrix< T, D, D2, R > &rhs) |
| Division (element wise) of a matrix and a scalar, B(i,j) = s / A(i,j) returning a matrix expression. More... | |
| template<class T , unsigned int D1, unsigned int D2, class R > | |
| VecExpr< VectorMatrixRowOp< SMatrix< T, D1, D2, R >, SVector< T, D2 >, D2 >, T, D1 > | ROOT::Math::operator* (const SMatrix< T, D1, D2, R > &lhs, const SVector< T, D2 > &rhs) |
| Matrix * Vector multiplication \( a(i) = \sum_{j} M(i,j) * b(j) \) returning a vector expression. More... | |
| template<class T , unsigned int D1, unsigned int D, unsigned int D2, class R1 , class R2 > | |
| Expr< MatrixMulOp< SMatrix< T, D1, D, R1 >, SMatrix< T, D, D2, R2 >, T, D >, T, D1, D2, typename MultPolicy< T, R1, R2 >::RepType > | ROOT::Math::operator* (const SMatrix< T, D1, D, R1 > &lhs, const SMatrix< T, D, D2, R2 > &rhs) |
| Matrix * Matrix multiplication , \( C(i,j) = \sum_{k} A(i,k) * B(k,j)\) returning a matrix expression. More... | |
| template<class T , unsigned int D1, unsigned int D2, class R > | |
| Expr< TransposeOp< SMatrix< T, D1, D2, R >, T, D1, D2 >, T, D2, D1, typename TranspPolicy< T, D1, D2, R >::RepType > | ROOT::Math::Transpose (const SMatrix< T, D1, D2, R > &rhs) |
| Matrix Transpose B(i,j) = A(j,i) returning a matrix expression. More... | |
| template<class T , unsigned int D, class R > | |
| T | ROOT::Math::Similarity (const SMatrix< T, D, D, R > &lhs, const SVector< T, D > &rhs) |
| Similarity Vector - Matrix Product: v^T * A * v returning a scalar value of type T \( s = \sum_{i,j} v(i) * A(i,j) * v(j)\). More... | |
| template<class T , unsigned int D1, unsigned int D2, class R > | |
| SMatrix< T, D1, D1, MatRepSym< T, D1 > > | ROOT::Math::Similarity (const SMatrix< T, D1, D2, R > &lhs, const SMatrix< T, D2, D2, MatRepSym< T, D2 > > &rhs) |
| Similarity Matrix Product : B = U * A * U^T for A symmetric returning a symmetric matrix expression: \( B(i,j) = \sum_{k,l} U(i,k) * A(k,l) * U(j,l) \). More... | |
| template<class T , unsigned int D1, unsigned int D2, class R > | |
| SMatrix< T, D2, D2, MatRepSym< T, D2 > > | ROOT::Math::SimilarityT (const SMatrix< T, D1, D2, R > &lhs, const SMatrix< T, D1, D1, MatRepSym< T, D1 > > &rhs) |
| Transpose Similarity Matrix Product : B = U^T * A * U for A symmetric returning a symmetric matrix expression: \( B(i,j) = \sum_{k,l} U(k,i) * A(k,l) * U(l,j) \). More... | |
| template<class T , unsigned int D, unsigned int D2, class R > | |
| Expr< UnaryOp< Minus< T >, SMatrix< T, D, D2, R >, T >, T, D, D2, R > | ROOT::Math::operator- (const SMatrix< T, D, D2, R > &rhs) |
| Unary - operator B = - A returning a matrix expression. More... | |
| template<class T , unsigned int D, unsigned int D2, class R > | |
| Expr< UnaryOp< Fabs< T >, SMatrix< T, D, D2, R >, T >, T, D, D2, R > | ROOT::Math::fabs (const SMatrix< T, D, D2, R > &rhs) |
| abs of a matrix m2(i,j) = | m1(i,j) | returning a matrix epression More... | |
| template<class T , unsigned int D, unsigned int D2, class R > | |
| Expr< UnaryOp< Sqr< T >, SMatrix< T, D, D2, R >, T >, T, D, D2, R > | ROOT::Math::sqr (const SMatrix< T, D, D2, R > &rhs) |
| square of a matrix B(i,j) = A(i,j)*A(i,j) returning a matrix expression More... | |
| template<class T , unsigned int D, unsigned int D2, class R > | |
| Expr< UnaryOp< Sqrt< T >, SMatrix< T, D, D2, R >, T >, T, D, D2, R > | ROOT::Math::sqrt (const SMatrix< T, D, D2, R > &rhs) |
| square root of a matrix (element by element) m2(i,j) = sqrt ( m1(i,j) ) returning a matrix expression More... | |
These function apply to matrices (and also Matrix expression) and can return a matrix expression of a particular defined type, like in the matrix multiplication or a vector, like in the matrix-vector product or a scalar like in the Similarity vector-matrix product.
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Division (element wise) of two matrices of the same dimensions: C(i,j) = A(i,j) / B(i,j) returning a matrix expression.
Definition at line 896 of file BinaryOperators.h.
Referenced by test21().
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abs of a matrix m2(i,j) = | m1(i,j) | returning a matrix epression
Definition at line 180 of file UnaryOperators.h.
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Matrix * Vector multiplication \( a(i) = \sum_{j} M(i,j) * b(j) \) returning a vector expression.
Definition at line 219 of file MatrixFunctions.h.
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Matrix * Matrix multiplication , \( C(i,j) = \sum_{k} A(i,k) * B(k,j)\) returning a matrix expression.
Definition at line 394 of file MatrixFunctions.h.
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Multiplication (element wise) of a matrix and a scalar, B(i,j) = A(i,j) * s returning a matrix expression.
Definition at line 707 of file BinaryOperators.h.
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Multiplication (element wise) of a matrix and a scalar, B(i,j) = s * A(i,j) returning a matrix expression.
Definition at line 725 of file BinaryOperators.h.
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Addition of two matrices C = A+B returning a matrix expression.
Definition at line 175 of file BinaryOperators.h.
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Addition element by element of matrix and a scalar C(i,j) = A(i,j) + s returning a matrix expression.
Definition at line 229 of file BinaryOperators.h.
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Addition element by element of matrix and a scalar C(i,j) = s + A(i,j) returning a matrix expression.
Definition at line 246 of file BinaryOperators.h.
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Unary - operator B = - A returning a matrix expression.
Definition at line 105 of file UnaryOperators.h.
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Subtraction of two matrices C = A-B returning a matrix expression.
Definition at line 419 of file BinaryOperators.h.
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Subtraction of a scalar and a matrix (element wise) B(i,j) = A(i,j) - s returning a matrix expression.
Definition at line 473 of file BinaryOperators.h.
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Subtraction of a scalar and a matrix (element wise) B(i,j) = s - A(i,j) returning a matrix expression.
Definition at line 491 of file BinaryOperators.h.
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Division (element wise) of a matrix and a scalar, B(i,j) = A(i,j) / s returning a matrix expression.
Definition at line 950 of file BinaryOperators.h.
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Division (element wise) of a matrix and a scalar, B(i,j) = s / A(i,j) returning a matrix expression.
Definition at line 968 of file BinaryOperators.h.
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Similarity Vector - Matrix Product: v^T * A * v returning a scalar value of type T \( s = \sum_{i,j} v(i) * A(i,j) * v(j)\).
Definition at line 671 of file MatrixFunctions.h.
Referenced by test4(), test_smatrix_sym_kalman(), and testInnerProd_S().
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Similarity Matrix Product : B = U * A * U^T for A symmetric returning a symmetric matrix expression: \( B(i,j) = \sum_{k,l} U(i,k) * A(k,l) * U(j,l) \).
Definition at line 744 of file MatrixFunctions.h.
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Transpose Similarity Matrix Product : B = U^T * A * U for A symmetric returning a symmetric matrix expression: \( B(i,j) = \sum_{k,l} U(k,i) * A(k,l) * U(l,j) \).
Definition at line 794 of file MatrixFunctions.h.
Referenced by test_smatrix_sym_kalman(), and testATBA_S2().
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square of a matrix B(i,j) = A(i,j)*A(i,j) returning a matrix expression
Definition at line 255 of file UnaryOperators.h.
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square root of a matrix (element by element) m2(i,j) = sqrt ( m1(i,j) ) returning a matrix expression
Definition at line 329 of file UnaryOperators.h.
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Element by element matrix multiplication C(i,j) = A(i,j)*B(i,j) returning a matrix expression.
This is not a matrix-matrix multiplication and works only for matrices of the same dimensions.
Definition at line 653 of file BinaryOperators.h.
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Matrix Transpose B(i,j) = A(j,i) returning a matrix expression.
Definition at line 546 of file MatrixFunctions.h.
Referenced by ROOT::Math::Similarity(), ROOT::Math::SimilarityT(), test10(), test12(), test14(), test16(), test24(), test_smatrix_kalman(), test_smatrix_sym_kalman(), testATBA_S(), testMT_S(), TMatrixT< Element >::TMatrixT(), TMatrixTSparse< Element >::TMatrixTSparse(), and TMatrixTSym< Element >::TMatrixTSym().
ROOT 6.06/09 - Reference Guide Generated on Sun Dec 10 2017 22:27:31 using Doxygen 1.8.9.
