Tiny matrix classes with optimized numerical operations which make use of vectorization features through the VVector class. More...

Classes

class Eagle::Column
A column vector. More...
class Eagle::LowerTriangular
A symmetric matrix stored in lower triangular form. More...
class Eagle::Matrix
Simple matrix class for performing fast operations on matrices of sizes known at compile-time. More...
class Eagle::Quadratic
An n x n matrix (i.e., a vector of length n*n), stored row-wise: that is, A(i,j) = A[ij], where ij = i*n + j. More...
class Eagle::Row
A row vector,. More...
class Eagle::SubMatrix
SubMatrix is a Matrix with row R and column C deleted. More...

Functions

template<class value > value Eagle::Det (const Quadratic< 1, value > &M)
Determinant of 1x1 matrix (trivial)
template<class value > value Eagle::Det (const Quadratic< 2, value > &M)
Determinant of 2x2 matrix (easy)
template<class value > value Eagle::Det (const Quadratic< 3, value > &M)
Determinant of 3x3 matrix (straightforward)
template<class value > value Eagle::Det (const Quadratic< 4, value > &M)
Determinant of 4x4 matrix (effortsome) http://www.cvl.iis.u-tokyo.ac.jp/~miyazaki/tech/teche23.html.
template<int R, int C, class value > Column< R, value > operator* (const Matrix< R, C, value > &A, const Column< C, value > &V)
Multiply r (rows) by c (columns) matrix A on the left by column vector V of dimension c on the right to produce a (column) vector C output of dimension r.
template<int N, class value > void UnsortedEigenVectors (LowerTriangular< N, value > &A, Quadratic< N, value > &RRmatrix, Row< N, value > &E, double precision=1E-10)
Eigenvalues and eigenvectors of a real symmetric matrix.

Detailed Description

Tiny matrix classes with optimized numerical operations which make use of vectorization features through the VVector class.

Function Documentation

template<int R, int C, class value >

Column< R, value > operator*	(	const Matrix< R, C, value > &	A,
		const Column< C, value > &	V
	)		`[related]`

Multiply r (rows) by c (columns) matrix A on the left by column vector V of dimension c on the right to produce a (column) vector C output of dimension r.

$\begin{pmatrix} C_{0} \\ \dots \\ C_{r-1} \end{pmatrix} = \begin{pmatrix} A_{0,0} & \dots & A_{c-1,0} \\ \hdotsfor{3} \\ A_{0,r-1} & \dots & A_{c-1,r-1} \end{pmatrix} \cdot \begin{pmatrix} V_{0} \\ \dots \\ V_{c-1} \end{pmatrix}$

template<int N, class value >

void UnsortedEigenVectors	(	LowerTriangular< N, value > &	A,
		Quadratic< N, value > &	RRmatrix,
		Row< N, value > &	E,
		double	precision = `1E-10`
	)		`[related]`

Eigenvalues and eigenvectors of a real symmetric matrix.

Parameters:

A	The input matrix, will be destroyed during computation
RR	The eigenvectors, stored column-wise in the quadratic matrics; use the column(i) function to get the i'th eigenvector
E	The eigenvalues, stored in a row
precision	Error control parameter. After diagonalization, the off-diagonal elements of A will have been reduced by this factor.

The algorithm is due to J. von Neumann. Classified by WB from C sources of the cephes library by Stephen L. Moshier.

See also:: LowerTriangular, Quadratic, Row

Example code:

   // Input data
   LowerTriangular<3, double>   InputMatrix;

   // Output data
   Quadratic<3, double>         EVectors; 
   Row<3,double>                EValues; 
   double                       precision = 1E-8;

        EigenVectors( InputMatrix, Evectors, Evalues, precision);