Linear algebra functions on Vectors and Matrices. More...

#include <MatrixMath.h>

Public Member Functions
template<class T >
T	innerProduct (const Vector< T > &x, const Vector< T > &y)
	The scalar/dot/inner product of two equal length vectors.
Complex	innerProduct (const Vector< Complex > &x, const Vector< Complex > &y)
DComplex	innerProduct (const Vector< DComplex > &x, const Vector< DComplex > &y)
Int	norm (const Vector< Int > &x)
	The magnitude/norm of a vector.
Float	norm (const Vector< Float > &x)
Double	norm (const Vector< Double > &x)
Float	norm (const Vector< Complex > &x)
Double	norm (const Vector< DComplex > &x)
template<class T >
Vector< T >	crossProduct (const Vector< T > &x, const Vector< T > &y)
	The vector/cross product of two 3-space vectors.
template<class T >
Matrix< T >	product (const Vector< T > &x, const Matrix< T > &yT)
	The matrix/outer product of a vector and a transposed vector.
template<class T >
Vector< T >	product (const Matrix< T > &A, const Vector< T > &x)
	The vector/outer product of an MxN matrix and an N-length vector.
template<class T >
Vector< T >	directProduct (const Vector< T > &x, const Vector< T > &y)
	The direct product of two vectors.
template<class T >
Matrix< T >	product (const Matrix< T > &A, const Matrix< T > &B)
	The matrix multiplication or cayley product of an MxN matrix and an NxP matrix.
Int	normI (const Matrix< Int > &A)
	The infinity norm (or maximum value of the sum of the absolute values of the rows members of a matrix)
Float	normI (const Matrix< Float > &A)
Double	normI (const Matrix< Double > &A)
Float	normI (const Matrix< Complex > &A)
Double	normI (const Matrix< DComplex > &A)
Int	norm1 (const Matrix< Int > &A)
	The one norm (or maximum value of the sum of the absolute values of the column members of a matrix)
Float	norm1 (const Matrix< Float > &A)
Double	norm1 (const Matrix< Double > &A)
Float	norm1 (const Matrix< Complex > &A)
Double	norm1 (const Matrix< DComplex > &A)
template<class T >
Matrix< T >	transpose (const Matrix< T > &A)
	The NxM transpose of an MxN matrix.
template<class T >
Matrix< T >	Rot3D (Int axis, T angle)
	Create a 3D rotation matrix (3x3).
Matrix< Double >	Rot3D (Int axis, Double angle)
Matrix< Float >	Rot3D (Int axis, Float angle)
template<class T >
Matrix< T >	directProduct (const Matrix< T > &A, const Matrix< T > &B)
	The direct product of two matrices.
Matrix< Complex >	conjugate (const Matrix< Complex > &A)
	The complex conjugate of the complex matrix A.
Matrix< DComplex >	conjugate (const Matrix< DComplex > &A)
	The complex conjugate of the double precision complex matrix A.
Matrix< Complex >	adjoint (const Matrix< Complex > &A)
	The conjugate/transpose or adjoint of the complex matrix A.
Matrix< DComplex >	adjoint (const Matrix< DComplex > &A)
Matrix< Int >	adjoint (const Matrix< Int > &A)
	define the adjoint operator as a plain old transpose when the Matrix is not complex valued.
Matrix< Float >	adjoint (const Matrix< Float > &A)
Matrix< Double >	adjoint (const Matrix< Double > &A)
Vector< Complex >	product (const Matrix< Complex > &, const Vector< Float > &)
	The product of a Complex Matrix and a Real Vector.
Vector< Float >	rproduct (const Matrix< Complex > &, const Vector< Complex > &)
	The real part of a product of a Complex Matrix and a Complex Vector.
Matrix< Float >	rproduct (const Matrix< Complex > &, const Matrix< Complex > &)
	The real part of a product of a Complex Matrix and a Complex Matrix.

Detailed Description

Linear algebra functions on Vectors and Matrices.

Review Status

Reviewed By:: UNKNOWN
Date Reviewed:: before2004/08/25
Test programs:: tLinAlgebra

Definition at line 53 of file MatrixMath.h.

Member Function Documentation

Matrix<Complex> casa::MatrixMath_global_functions_Linear_Algebra::adjoint ( const Matrix< Complex > & A )

The conjugate/transpose or adjoint of the complex matrix A.

Matrix<DComplex> casa::MatrixMath_global_functions_Linear_Algebra::adjoint ( const Matrix< DComplex > & A )

Matrix<Int> casa::MatrixMath_global_functions_Linear_Algebra::adjoint ( const Matrix< Int > & A )

define the adjoint operator as a plain old transpose when the Matrix is not complex valued.

(for templating purposes)

Matrix<Float> casa::MatrixMath_global_functions_Linear_Algebra::adjoint ( const Matrix< Float > & A )

Matrix<Double> casa::MatrixMath_global_functions_Linear_Algebra::adjoint ( const Matrix< Double > & A )

Matrix<Complex> casa::MatrixMath_global_functions_Linear_Algebra::conjugate ( const Matrix< Complex > & A )

The complex conjugate of the complex matrix A.

Matrix<DComplex> casa::MatrixMath_global_functions_Linear_Algebra::conjugate ( const Matrix< DComplex > & A )

The complex conjugate of the double precision complex matrix A.

template<class T >

Vector<T> casa::MatrixMath_global_functions_Linear_Algebra::crossProduct	(	const Vector< T > &	x,
		const Vector< T > &	y
	)

The vector/cross product of two 3-space vectors.

template<class T >

Vector<T> casa::MatrixMath_global_functions_Linear_Algebra::directProduct	(	const Vector< T > &	x,
		const Vector< T > &	y
	)

The direct product of two vectors.

The resulting vector contains for every element of x, the product of that element and Vector y. Thus the length of the output vector is the product of the input lengths.

template<class T >

Matrix<T> casa::MatrixMath_global_functions_Linear_Algebra::directProduct	(	const Matrix< T > &	A,
		const Matrix< T > &	B
	)

The direct product of two matrices.

The resulting matrix contains for every element of A, the product of that element and Matrix B. Thus the shape of the output matrix is the (element by element) product of the input shapes.

template<class T >

T casa::MatrixMath_global_functions_Linear_Algebra::innerProduct	(	const Vector< T > &	x,
		const Vector< T > &	y
	)

The scalar/dot/inner product of two equal length vectors.

Complex casa::MatrixMath_global_functions_Linear_Algebra::innerProduct	(	const Vector< Complex > &	x,
		const Vector< Complex > &	y
	)

DComplex casa::MatrixMath_global_functions_Linear_Algebra::innerProduct	(	const Vector< DComplex > &	x,
		const Vector< DComplex > &	y
	)

Int casa::MatrixMath_global_functions_Linear_Algebra::norm ( const Vector< Int > & x )

The magnitude/norm of a vector.

Float casa::MatrixMath_global_functions_Linear_Algebra::norm ( const Vector< Float > & x )

Double casa::MatrixMath_global_functions_Linear_Algebra::norm ( const Vector< Double > & x )

Float casa::MatrixMath_global_functions_Linear_Algebra::norm ( const Vector< Complex > & x )

Double casa::MatrixMath_global_functions_Linear_Algebra::norm ( const Vector< DComplex > & x )

Int casa::MatrixMath_global_functions_Linear_Algebra::norm1 ( const Matrix< Int > & A )

The one norm (or maximum value of the sum of the absolute values of the column members of a matrix)

Float casa::MatrixMath_global_functions_Linear_Algebra::norm1 ( const Matrix< Float > & A )

Double casa::MatrixMath_global_functions_Linear_Algebra::norm1 ( const Matrix< Double > & A )

Float casa::MatrixMath_global_functions_Linear_Algebra::norm1 ( const Matrix< Complex > & A )

Double casa::MatrixMath_global_functions_Linear_Algebra::norm1 ( const Matrix< DComplex > & A )

Int casa::MatrixMath_global_functions_Linear_Algebra::normI ( const Matrix< Int > & A )

The infinity norm (or maximum value of the sum of the absolute values of the rows members of a matrix)

Float casa::MatrixMath_global_functions_Linear_Algebra::normI ( const Matrix< Float > & A )

Double casa::MatrixMath_global_functions_Linear_Algebra::normI ( const Matrix< Double > & A )

Float casa::MatrixMath_global_functions_Linear_Algebra::normI ( const Matrix< Complex > & A )

Double casa::MatrixMath_global_functions_Linear_Algebra::normI ( const Matrix< DComplex > & A )

template<class T >

Matrix<T> casa::MatrixMath_global_functions_Linear_Algebra::product	(	const Vector< T > &	x,
		const Matrix< T > &	yT
	)

The matrix/outer product of a vector and a transposed vector.

Note: The function's second argument is actually a transposed vector stored as the only row in a 1xN matrix;

template<class T >

Vector<T> casa::MatrixMath_global_functions_Linear_Algebra::product	(	const Matrix< T > &	A,
		const Vector< T > &	x
	)

The vector/outer product of an MxN matrix and an N-length vector.

template<class T >

Matrix<T> casa::MatrixMath_global_functions_Linear_Algebra::product	(	const Matrix< T > &	A,
		const Matrix< T > &	B
	)

The matrix multiplication or cayley product of an MxN matrix and an NxP matrix.

Vector<Complex> casa::MatrixMath_global_functions_Linear_Algebra::product	(	const Matrix< Complex > &	,
		const Vector< Float > &
	)

The product of a Complex Matrix and a Real Vector.

template<class T >

Matrix<T> casa::MatrixMath_global_functions_Linear_Algebra::Rot3D	(	Int	axis,
		T	angle
	)

Create a 3D rotation matrix (3x3).

Axis is 0,1,2 for x,y,z; angle is in radians.

Matrix<Double> casa::MatrixMath_global_functions_Linear_Algebra::Rot3D	(	Int	axis,
		Double	angle
	)

Matrix<Float> casa::MatrixMath_global_functions_Linear_Algebra::Rot3D	(	Int	axis,
		Float	angle
	)

Vector<Float> casa::MatrixMath_global_functions_Linear_Algebra::rproduct	(	const Matrix< Complex > &	,
		const Vector< Complex > &
	)

The real part of a product of a Complex Matrix and a Complex Vector.

Matrix<Float> casa::MatrixMath_global_functions_Linear_Algebra::rproduct	(	const Matrix< Complex > &	,
		const Matrix< Complex > &
	)

The real part of a product of a Complex Matrix and a Complex Matrix.

template<class T >

Matrix<T> casa::MatrixMath_global_functions_Linear_Algebra::transpose ( const Matrix< T > & A )

The NxM transpose of an MxN matrix.

The documentation for this struct was generated from the following file:

casacore/casa/Arrays/MatrixMath.h

Public Member Functions

Detailed Description

Review Status

Member Function Documentation