casa  5.7.0-16
casacore::MatrixMath_global_functions_Linear_Algebra Struct Reference

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

`#include <MatrixMath.h>`

## Public Member Functions

template<class T >
innerProduct (const Vector< T > &x, const Vector< T > &y)
The scalar/dot/inner product of two equal length vectors. More...

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. More...

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. More...

template<class T >
crossProduct2D (const Vector< T > &x, const Vector< T > &y)
Magnitude of cross product of two 2-space vectors, x[0]*y[1] - x[1]*y[0]. More...

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. More...

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. More...

template<class T >
Vector< T > directProduct (const Vector< T > &x, const Vector< T > &y)
The direct product of two vectors. More...

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. More...

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) More...

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) More...

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. More...

template<class T >
Matrix< T > Rot3D (Int axis, T angle)
Create a 3D rotation matrix (3x3). More...

Matrix< DoubleRot3D (Int axis, Double angle)

Matrix< FloatRot3D (Int axis, Float angle)

template<class T >
Matrix< T > directProduct (const Matrix< T > &A, const Matrix< T > &B)
The direct product of two matrices. More...

Matrix< Complex > conjugate (const Matrix< Complex > &A)
The complex conjugate of the complex matrix A. More...

Matrix< DComplex > conjugate (const Matrix< DComplex > &A)
The complex conjugate of the double precision complex matrix A. More...

Matrix< Complex > adjoint (const Matrix< Complex > &A)
The conjugate/transpose or adjoint of the complex matrix A. More...

Matrix< DComplex > adjoint (const Matrix< DComplex > &A)

Matrix< Intadjoint (const Matrix< Int > &A)
define the adjoint operator as a plain old transpose when the Matrix is not complex valued. More...

Matrix< Floatadjoint (const Matrix< Float > &A)

Matrix< Doubleadjoint (const Matrix< Double > &A)

Vector< Complex > product (const Matrix< Complex > &, const Vector< Float > &)
The product of a Complex Matrix and a Real Vector. More...

Vector< Floatrproduct (const Matrix< Complex > &, const Vector< Complex > &)
The real part of a product of a Complex Matrix and a Complex Vector. More...

Matrix< Floatrproduct (const Matrix< Complex > &, const Matrix< Complex > &)
The real part of a product of a Complex Matrix and a Complex Matrix. More...

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

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

 Matrix casacore::MatrixMath_global_functions_Linear_Algebra::adjoint ( const Matrix< DComplex > & A )
 Matrix casacore::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 casacore::MatrixMath_global_functions_Linear_Algebra::adjoint ( const Matrix< Float > & A )
 Matrix casacore::MatrixMath_global_functions_Linear_Algebra::adjoint ( const Matrix< Double > & A )
 Matrix casacore::MatrixMath_global_functions_Linear_Algebra::conjugate ( const Matrix< Complex > & A )

The complex conjugate of the complex matrix A.

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

The complex conjugate of the double precision complex matrix A.

template<class T >
 Vector casacore::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 >
 T casacore::MatrixMath_global_functions_Linear_Algebra::crossProduct2D ( const Vector< T > & x, const Vector< T > & y )

Magnitude of cross product of two 2-space vectors, x[0]*y[1] - x[1]*y[0].

template<class T >
 Vector casacore::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 casacore::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 casacore::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 casacore::MatrixMath_global_functions_Linear_Algebra::innerProduct ( const Vector< Complex > & x, const Vector< Complex > & y )
 DComplex casacore::MatrixMath_global_functions_Linear_Algebra::innerProduct ( const Vector< DComplex > & x, const Vector< DComplex > & y )
 Int casacore::MatrixMath_global_functions_Linear_Algebra::norm ( const Vector< Int > & x )

The magnitude/norm of a vector.

 Float casacore::MatrixMath_global_functions_Linear_Algebra::norm ( const Vector< Float > & x )
 Double casacore::MatrixMath_global_functions_Linear_Algebra::norm ( const Vector< Double > & x )
 Float casacore::MatrixMath_global_functions_Linear_Algebra::norm ( const Vector< Complex > & x )
 Double casacore::MatrixMath_global_functions_Linear_Algebra::norm ( const Vector< DComplex > & x )
 Int casacore::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 casacore::MatrixMath_global_functions_Linear_Algebra::norm1 ( const Matrix< Float > & A )
 Double casacore::MatrixMath_global_functions_Linear_Algebra::norm1 ( const Matrix< Double > & A )
 Float casacore::MatrixMath_global_functions_Linear_Algebra::norm1 ( const Matrix< Complex > & A )
 Double casacore::MatrixMath_global_functions_Linear_Algebra::norm1 ( const Matrix< DComplex > & A )
 Int casacore::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 casacore::MatrixMath_global_functions_Linear_Algebra::normI ( const Matrix< Float > & A )
 Double casacore::MatrixMath_global_functions_Linear_Algebra::normI ( const Matrix< Double > & A )
 Float casacore::MatrixMath_global_functions_Linear_Algebra::normI ( const Matrix< Complex > & A )
 Double casacore::MatrixMath_global_functions_Linear_Algebra::normI ( const Matrix< DComplex > & A )
template<class T >
 Matrix casacore::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 casacore::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 casacore::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 casacore::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 casacore::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 casacore::MatrixMath_global_functions_Linear_Algebra::Rot3D ( Int axis, Double angle )
 Matrix casacore::MatrixMath_global_functions_Linear_Algebra::Rot3D ( Int axis, Float angle )
 Vector casacore::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 casacore::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 casacore::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: