Go to the source code of this file.
Defines | |
| #define | AIPS_ARRAY_INDEX_CHECK |
Functions | |
| template<class T > | |
| T | innerProduct (const Vector< T > &x, const Vector< T > &y) |
| template<class T > | |
| T | norm (const Vector< T > &x) |
| The magnitude/norm of a vector. | |
| template<class T > | |
| Matrix< T > | Rot3D (Int axis, T angle) |
| Create a 3D rotation matrix (3x3). | |
| 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 > | |
| Matrix< T > | outerProduct (const Vector< T > &x, const Matrix< T > &yT) |
| 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 > | outerProduct (const Matrix< T > &A, const Vector< T > &x) |
| 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. | |
| template<class T > | |
| Matrix< T > | cayleyProduct (const Matrix< T > &A, const Matrix< T > &B) |
| template<class T > | |
| Matrix< T > | transpose (const Matrix< T > &A) |
| The NxM transpose of an MxN matrix. | |
| Matrix< Complex > | conjugate (const Matrix< Complex > &A) |
complex space function specifications | |
| 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) |
| The conjugate/transpose or adjoint of the double precision complex matrix A. | |
| template<class T > | |
| Matrix< T > | inverse (const Matrix< T > &A) |
| template<class T > | |
| Matrix< T > | inverse (const LUdecomp< T > &LU) |
| The inverse of an LUdecomp which is the Lower/upper decomposition of a matrix A. | |
| template<class T > | |
| T | determinant (const Matrix< T > &A) |
| The determinant of a matrix; Note: The LU decomposition of the matrix is a hidden calculation; . | |
| template<class T > | |
| T | determinant (const LUdecomp< T > &LU) |
| the determinant (A) of an LUdecomp which is the lower/upper decomposition of a matrix A. | |
| template<class T > | |
| Vector< T > | solve (const Matrix< T > &A, const Vector< T > &y, double &ferr, double &berr) |
| Given a matrix "A", and given some vector "y" which is the right hand side of the equation "Ax=y", then "solve(A, y, error1, error2)" returns the computed vector "x". | |
| template<class T > | |
| Vector< T > | solve (const LUdecomp< T > &myLU, const Vector< T > &y, double &ferr, double &berr) |
| Given an LUdecomp "myLU" which is the LU decomposition of some matrix "A", and given some vector "y" which is the right hand side of the equation "Ax=y", then "solve(myLU, y, error1, error2)" returns the computed vector "x". | |
| template<class T > | |
| Matrix< T > | solve (const Matrix< T > &A, const Matrix< T > &B, Vector< double > &Ferr, Vector< double > &Berr) |
| Given a matrix "A", and given a matrix "B" whose columns are the stored set of vectors "y1", "y2", . | |
| template<class T > | |
| Matrix< T > | solve (const LUdecomp< T > &myLU, const Matrix< T > &B, Vector< double > &Ferr, Vector< double > &Berr) |
| Given an LUdecomp "myLU" which is the LU decomposition of some matrix "A", and given a matrix "B" whose columns are the stored set of vectors "y1", "y2", . | |
| #define AIPS_ARRAY_INDEX_CHECK |
Definition at line 33 of file MatrixMath.h.
| Matrix<DComplex> adjoint | ( | const Matrix< DComplex > & | A | ) |
The conjugate/transpose or adjoint of the double precision complex matrix A.
/div> Requires linking of the LAPACK libraries. The LAPACK libraries can be attained by FTPing to the netlib directory at Research.ATT.com or by contacting the Numerical Algorithms Group.
The inverse of a matrix;
Note: The LU decomposition of the matrix is a hidden calculation;
| Matrix<Complex> adjoint | ( | const Matrix< Complex > & | A | ) |
The conjugate/transpose or adjoint of the complex matrix A.
| Matrix<T> cayleyProduct | ( | const Matrix< T > & | A, | |
| const Matrix< T > & | B | |||
| ) | [inline] |
| Matrix<DComplex> conjugate | ( | const Matrix< DComplex > & | A | ) |
The complex conjugate of the double precision complex matrix A.
| Matrix<Complex> conjugate | ( | const Matrix< Complex > & | A | ) |
The complex conjugate of the complex matrix A.
| Vector<T> crossProduct | ( | const Vector< T > & | x, | |
| const Vector< T > & | y | |||
| ) | [inline] |
The vector/cross product of two 3-space vectors.
| T determinant | ( | const LUdecomp< T > & | LU | ) | [inline] |
the determinant (A) of an LUdecomp which is the lower/upper decomposition of a matrix A.
| T determinant | ( | const Matrix< T > & | A | ) | [inline] |
The determinant of a matrix;
Note: The LU decomposition of the matrix is a hidden calculation;
.
| T innerProduct | ( | const Vector< T > & | x, | |
| const Vector< T > & | y | |||
| ) | [inline] |
ArrayError BlasError
Referenced by casa::StokesUtil_global_functions_StokesVector_ancillary_Functions::abs().
| Matrix<T> inverse | ( | const LUdecomp< T > & | LU | ) | [inline] |
The inverse of an LUdecomp which is the Lower/upper decomposition of a matrix A.
| Matrix<T> inverse | ( | const Matrix< T > & | A | ) | [inline] |
| T norm | ( | const Vector< T > & | x | ) | [inline] |
The magnitude/norm of a vector.
| Vector<T> outerProduct | ( | const Matrix< T > & | A, | |
| const Vector< T > & | x | |||
| ) | [inline] |
| Matrix<T> outerProduct | ( | const Vector< T > & | x, | |
| const Matrix< T > & | yT | |||
| ) | [inline] |
| Matrix<T> product | ( | const Matrix< T > & | A, | |
| const Matrix< T > & | B | |||
| ) | [inline] |
The matrix multiplication or cayley product of an MxN matrix and an NxP matrix.
| Vector<T> product | ( | const Matrix< T > & | A, | |
| const Vector< T > & | x | |||
| ) | [inline] |
The vector/outer product of an MxN matrix and an N-length vector.
| Matrix<T> product | ( | const Vector< T > & | x, | |
| const Matrix< T > & | yT | |||
| ) | [inline] |
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;
| Matrix<T> Rot3D | ( | Int | axis, | |
| T | angle | |||
| ) | [inline] |
Create a 3D rotation matrix (3x3).
Axis is 0,1,2 for x,y,z; angle is in radians.
| Matrix<T> solve | ( | const LUdecomp< T > & | myLU, | |
| const Matrix< T > & | B, | |||
| Vector< double > & | Ferr, | |||
| Vector< double > & | Berr | |||
| ) | [inline] |
Given an LUdecomp "myLU" which is the LU decomposition of some matrix "A", and given a matrix "B" whose columns are the stored set of vectors "y1", "y2", .
.."yN" which are independent right hand sides to the equation "Ax", e.g. "Ax=y", then "solve(myLU, B, Error1, Error2)" returns the computed matrix "X", whose columns are the stored set of vectors "x1", "x2", ..."xN" which satisfy the equation "Ax=y" for each respective "y". (for further details, see the LAPACK man page for "sgesvx".)
solve(LUdecomp<T>, Matrix<T>,...) arguments are (in order): 1) LUdecomp<T> - (input) the LU decomposition of the matrix "A" that is being modeled by the equation "Ax=y". 2) Matrix<T> - (input) MxN matrix "B" of N possible M-length vectors "y1", "y2",..."yN" stored as columns in a single matrix "B" where "A*x1=y1, A*x2=y2,..."A*xN=yN" => "AX=B". 3) Vector<double> - (output) an N-length vector "Ferr with error bounds for returned matrix X, i.e. max(X.column(i)-Xtrue.column(i)) Ferr(i) > -------------------------------- max(X.column(i))
4) Vector<double> - (output) an N-length vector "Berr" with error bounds for input matrix "B", i.e Berr(i) > |max(A*X.column(i)-B.column(i))|
| Matrix<T> solve | ( | const Matrix< T > & | A, | |
| const Matrix< T > & | B, | |||
| Vector< double > & | Ferr, | |||
| Vector< double > & | Berr | |||
| ) | [inline] |
Given a matrix "A", and given a matrix "B" whose columns are the stored set of vectors "y1", "y2", .
.."yN" which are independent right hand sides to the equation "Ax", e.g. "Ax=y", then "solve(A, B, Error1, Error2)" returns the computed matrix "X", whose columns are the stored set of vectors "x1", "x2", ..."xN" which satisfy the equation "Ax=y" for each respective "y". (for further details, see the LAPACK man page for "sgesvx".)
solve(LUdecomp<T>, Matrix<T>,...) arguments are (in order): 1) Matrix<T> - (input) the matrix "A" that is being modeled by the equation "Ax=y". 2) Matrix<T> - (input) MxN matrix "B" of N possible M-length vectors "y1", "y2",..."yN" stored as columns in a single matrix "B" where "A*x1=y1, A*x2=y2,..."A*xN=yN" => "AX=B". 3) Vector<double> - (output) an N-length vector "Ferr with error bounds for returned matrix X, i.e. max(X.column(i)-Xtrue.column(i)) Ferr(i) > -------------------------------- max(X.column(i))
4) Vector<double> - (output) an N-length vector "Berr" with error bounds for input matrix "B", i.e Berr(i) > |max(A*X.column(i)-B.column(i))|
Note: The LU decomposition of the matrix is a hidden calculation;
| Vector<T> solve | ( | const LUdecomp< T > & | myLU, | |
| const Vector< T > & | y, | |||
| double & | ferr, | |||
| double & | berr | |||
| ) | [inline] |
Given an LUdecomp "myLU" which is the LU decomposition of some matrix "A", and given some vector "y" which is the right hand side of the equation "Ax=y", then "solve(myLU, y, error1, error2)" returns the computed vector "x".
(for further details, see the LAPACK man page for "sgesvx".)
solve(LUdecomp<T>, Vector<T>, ...) arguments are (in order): 1) LUdecomp<T> - (input) the LU decomposition of the matrix "A" that is being modeled by the equation "Ax=y". 2) Vector<T> - (input) the vector "y" that is being modeled by the equation "Ax=y". 3) double - (output) the error bound "forwardError" on the returned vector x, i.e |max(x - xtrue)| forwardError > ---------------- |max(x)|
4) double - (output) the error bound "backwardError" on the input vector "y". i.e. backwardError > |Ax-y|
| Vector<T> solve | ( | const Matrix< T > & | A, | |
| const Vector< T > & | y, | |||
| double & | ferr, | |||
| double & | berr | |||
| ) | [inline] |
Given a matrix "A", and given some vector "y" which is the right hand side of the equation "Ax=y", then "solve(A, y, error1, error2)" returns the computed vector "x".
(for further details, see the LAPACK man page for "sgesvx".)
solve(LUdecomp<T>, Vector<T>, ...) arguments are (in order): 1) Matrix<T> - (input) the matrix "A" that is being modeled by the equation "Ax=y". 2) Vector<T> - (input) the vector "y" that is being modeled by the equation "Ax=y". 3) double - (output) the error bound "forwardError" on the returned vector x, i.e |max(x - xtrue)| forwardError > ---------------- |max(x)|
4) double - (output) the error bound "backwardError" on the input vector "y". i.e. backwardError > |Ax-y|
Note: The LU decomposition of the matrix is a hidden calculation;
| Matrix<T> transpose | ( | const Matrix< T > & | A | ) | [inline] |
The NxM transpose of an MxN matrix.
1.6.1
